%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU782^1 : 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.tIh6hvfftO true
% Computer : n031.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 04:56:20 PM UTC 2025
% Result : Theorem 128.61s 16.89s
% Output : Refutation 130.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.14 % Problem : SEU782^1 : TPTP v9.2.0. Released v3.7.0.
% 0.06/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.tIh6hvfftO true
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 1 16:12:08 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in HO mode
% 0.49/0.63 % Total configuration time : 828
% 0.49/0.63 % Estimated wc time : 1656
% 0.49/0.63 % Estimated cpu time (8 cpus) : 207.0
% 0.50/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.50/0.71 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.50/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.50/0.73 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.50/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.50/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.50/0.74 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.50/0.74 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 128.61/16.89 % Solved by lams/40_b.comb.sh.
% 128.61/16.89 % done 0 iterations in 15.685s
% 128.61/16.89 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 128.61/16.89 % SZS output start Refutation
% 128.61/16.89 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 128.61/16.89 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 128.61/16.89 thf(notdexE_type, type, notdexE: $o).
% 128.61/16.89 thf(setunionAx_type, type, setunionAx: $o).
% 128.61/16.89 thf(setminusELneg_type, type, setminusELneg: $o).
% 128.61/16.89 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 128.61/16.89 thf(beta1_type, type, beta1: $o).
% 128.61/16.89 thf(powersetE_type, type, powersetE: $o).
% 128.61/16.89 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 128.61/16.89 thf(omegaSAx_type, type, omegaSAx: $o).
% 128.61/16.89 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 128.61/16.89 thf(exuI1_type, type, exuI1: $o).
% 128.61/16.89 thf(binunionTEcontra_type, type, binunionTEcontra: $o).
% 128.61/16.89 thf(exuI2_type, type, exuI2: $o).
% 128.61/16.89 thf(notequalI2_type, type, notequalI2: $o).
% 128.61/16.89 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 128.61/16.89 thf(demorgan1b_type, type, demorgan1b: $o).
% 128.61/16.89 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 128.61/16.89 thf(demorgan2a_type, type, demorgan2a: $o).
% 128.61/16.89 thf(subsetTI_type, type, subsetTI: $o).
% 128.61/16.89 thf(upairsubunion_type, type, upairsubunion: $o).
% 128.61/16.89 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 128.61/16.89 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 128.61/16.89 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 128.61/16.89 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 128.61/16.89 $o).
% 128.61/16.89 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 128.61/16.89 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 128.61/16.89 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 128.61/16.89 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 128.61/16.89 thf(setminusILneg_type, type, setminusILneg: $o).
% 128.61/16.89 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 128.61/16.89 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 128.61/16.89 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 128.61/16.89 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 128.61/16.89 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 128.61/16.89 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 128.61/16.89 thf(brelnall1_type, type, brelnall1: $o).
% 128.61/16.89 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 128.61/16.89 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 128.61/16.89 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 128.61/16.89 thf('#sk44_type', type, '#sk44': $i).
% 128.61/16.89 thf(complementT_lem_type, type, complementT_lem: $o).
% 128.61/16.89 thf(funcextLem_type, type, funcextLem: $o).
% 128.61/16.89 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 128.61/16.89 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 128.61/16.89 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 128.61/16.89 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 128.61/16.89 thf(demorgan2b2_type, type, demorgan2b2: $o).
% 128.61/16.89 thf(breln1compE_type, type, breln1compE: $o).
% 128.61/16.89 thf(demorgan2b_type, type, demorgan2b: $o).
% 128.61/16.89 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 128.61/16.89 thf(ex1E1_type, type, ex1E1: $o).
% 128.61/16.89 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 128.61/16.89 thf(setukpairIR_type, type, setukpairIR: $o).
% 128.61/16.89 thf(breln1invprop_type, type, breln1invprop: $o).
% 128.61/16.89 thf(binunionE_type, type, binunionE: $o).
% 128.61/16.89 thf(setext_type, type, setext: $o).
% 128.61/16.89 thf(lam2p_type, type, lam2p: $o).
% 128.61/16.89 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 128.61/16.89 thf(breln1_type, type, breln1: $i > $i > $o).
% 128.61/16.89 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 128.61/16.89 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 128.61/16.89 thf(theeq_type, type, theeq: $o).
% 128.61/16.89 thf(descr__Cong_type, type, descr__Cong: $o).
% 128.61/16.89 thf(theprop_type, type, theprop: $o).
% 128.61/16.89 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 128.61/16.89 $o).
% 128.61/16.89 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 128.61/16.89 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 128.61/16.89 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 128.61/16.89 thf(in_type, type, in: $i > $i > $o).
% 128.61/16.89 thf(lamProp_type, type, lamProp: $o).
% 128.61/16.89 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 128.61/16.89 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 128.61/16.89 thf(setextT_type, type, setextT: $o).
% 128.61/16.89 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 128.61/16.89 thf(binunion_type, type, binunion: $i > $i > $i).
% 128.61/16.89 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 128.61/16.89 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 128.61/16.89 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 128.61/16.89 thf(ap2p_type, type, ap2p: $o).
% 128.61/16.89 thf(eqbreln_type, type, eqbreln: $o).
% 128.61/16.89 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 128.61/16.89 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 128.61/16.89 thf(ex1I2_type, type, ex1I2: $o).
% 128.61/16.89 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 128.61/16.89 thf(woz1_1_type, type, woz1_1: $o).
% 128.61/16.89 thf(demorgan1_type, type, demorgan1: $o).
% 128.61/16.89 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 128.61/16.89 thf(symdiffI2_type, type, symdiffI2: $o).
% 128.61/16.89 thf(upairset2IR_type, type, upairset2IR: $o).
% 128.61/16.89 thf('#sk43_type', type, '#sk43': $i).
% 128.61/16.89 thf(breln1compI_type, type, breln1compI: $o).
% 128.61/16.89 thf(subsetE_type, type, subsetE: $o).
% 128.61/16.89 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 128.61/16.89 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 128.61/16.89 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 128.61/16.89 thf(setbeta_type, type, setbeta: $o).
% 128.61/16.89 thf(binunionTE_type, type, binunionTE: $o).
% 128.61/16.89 thf(eqinunit_type, type, eqinunit: $o).
% 128.61/16.89 thf(upairsetIL_type, type, upairsetIL: $o).
% 128.61/16.89 thf(powersetI1_type, type, powersetI1: $o).
% 128.61/16.89 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 128.61/16.89 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 128.61/16.89 thf(powersetTE1_type, type, powersetTE1: $o).
% 128.61/16.89 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 128.61/16.89 thf(app_type, type, app: $o).
% 128.61/16.89 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 128.61/16.89 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 128.61/16.89 thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1:
% 128.61/16.89 $o).
% 128.61/16.89 thf(powersetAx_type, type, powersetAx: $o).
% 128.61/16.89 thf(lamp_type, type, lamp: $o).
% 128.61/16.89 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 128.61/16.89 thf(ifSingleton_type, type, ifSingleton: $o).
% 128.61/16.89 thf(iffalse_type, type, iffalse: $o).
% 128.61/16.89 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 128.61/16.89 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 128.61/16.89 thf(powersetI_type, type, powersetI: $o).
% 128.61/16.89 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 128.61/16.89 thf(upairsetIR_type, type, upairsetIR: $o).
% 128.61/16.89 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 128.61/16.89 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 128.61/16.89 thf(funcext2_type, type, funcext2: $o).
% 128.61/16.89 thf(inCongP_type, type, inCongP: $o).
% 128.61/16.89 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 128.61/16.89 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 128.61/16.89 thf(exuE3e_type, type, exuE3e: $o).
% 128.61/16.89 thf(emptysetE_type, type, emptysetE: $o).
% 128.61/16.89 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 128.61/16.89 thf(setunionI_type, type, setunionI: $o).
% 128.61/16.89 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 128.61/16.89 thf(prop2setI_type, type, prop2setI: $o).
% 128.61/16.89 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 128.61/16.89 thf(setminusER_type, type, setminusER: $o).
% 128.61/16.89 thf(exuE2_type, type, exuE2: $o).
% 128.61/16.89 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 128.61/16.89 thf(emptyset_type, type, emptyset: $i).
% 128.61/16.89 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 128.61/16.89 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 128.61/16.89 thf(complementTI1_type, type, complementTI1: $o).
% 128.61/16.89 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o).
% 128.61/16.89 thf(breln_type, type, breln: $i > $i > $i > $o).
% 128.61/16.89 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 128.61/16.89 thf(subbreln1_type, type, subbreln1: $o).
% 128.61/16.89 thf(powersetsubset_type, type, powersetsubset: $o).
% 128.61/16.89 thf(upairequniteq_type, type, upairequniteq: $o).
% 128.61/16.89 thf(woz1_4_type, type, woz1_4: $o).
% 128.61/16.89 thf(subPowSU_type, type, subPowSU: $o).
% 128.61/16.89 thf(notequalI1_type, type, notequalI1: $o).
% 128.61/16.89 thf(notinemptyset_type, type, notinemptyset: $o).
% 128.61/16.89 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 128.61/16.89 thf(subsetTrans_type, type, subsetTrans: $o).
% 128.61/16.89 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 128.61/16.89 thf(kpairp_type, type, kpairp: $o).
% 128.61/16.89 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 128.61/16.89 thf(setminusI_type, type, setminusI: $o).
% 128.61/16.89 thf(eta1_type, type, eta1: $o).
% 128.61/16.89 thf(binunionIL_type, type, binunionIL: $o).
% 128.61/16.89 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 128.61/16.89 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 128.61/16.89 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 128.61/16.89 thf(subsetE2_type, type, subsetE2: $o).
% 128.61/16.89 thf('#sk45_type', type, '#sk45': $i).
% 128.61/16.89 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 128.61/16.89 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 128.61/16.89 thf(eta2_type, type, eta2: $o).
% 128.61/16.89 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 128.61/16.89 thf(setextsub_type, type, setextsub: $o).
% 128.61/16.89 thf(binunionLsub_type, type, binunionLsub: $o).
% 128.61/16.89 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 128.61/16.89 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 128.61/16.89 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 128.61/16.89 thf(setunionE_type, type, setunionE: $o).
% 128.61/16.89 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 128.61/16.89 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 128.61/16.89 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 128.61/16.89 thf(binunionIR_type, type, binunionIR: $o).
% 128.61/16.89 thf(iftrue_type, type, iftrue: $o).
% 128.61/16.89 thf(setadjoinE_type, type, setadjoinE: $o).
% 128.61/16.89 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 128.61/16.89 thf(woz1_5_type, type, woz1_5: $o).
% 128.61/16.89 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 128.61/16.89 thf(beta2_type, type, beta2: $o).
% 128.61/16.89 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 128.61/16.89 $o).
% 128.61/16.89 thf(brelnall2_type, type, brelnall2: $o).
% 128.61/16.89 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 128.61/16.89 thf(exuE1_type, type, exuE1: $o).
% 128.61/16.89 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 128.61/16.89 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 128.61/16.89 thf(ifp_type, type, ifp: $o).
% 128.61/16.89 thf(setminusLsub_type, type, setminusLsub: $o).
% 128.61/16.89 thf(woz1_3_type, type, woz1_3: $o).
% 128.61/16.89 thf(notinsingleton_type, type, notinsingleton: $o).
% 128.61/16.89 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 128.61/16.89 thf(exuEu_type, type, exuEu: $o).
% 128.61/16.89 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 128.61/16.89 thf(upairsetE_type, type, upairsetE: $o).
% 128.61/16.89 thf(omega0Ax_type, type, omega0Ax: $o).
% 128.61/16.89 thf(breln1invI_type, type, breln1invI: $o).
% 128.61/16.89 thf(complementTE1_type, type, complementTE1: $o).
% 128.61/16.89 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 128.61/16.89 thf(notsubsetI_type, type, notsubsetI: $o).
% 128.61/16.89 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions:
% 128.61/16.89 $o).
% 128.61/16.89 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 128.61/16.89 thf(setextAx_type, type, setextAx: $o).
% 128.61/16.89 thf(setOfPairsIsBReln1_type, type, setOfPairsIsBReln1: $o).
% 128.61/16.89 thf(breln1SetBreln1_type, type, breln1SetBreln1: $o).
% 128.61/16.89 thf(powersetE1_type, type, powersetE1: $o).
% 128.61/16.89 thf(bs114d_type, type, bs114d: $o).
% 128.61/16.89 thf(breln1all2_type, type, breln1all2: $o).
% 128.61/16.89 thf(woz13rule0_type, type, woz13rule0: $o).
% 128.61/16.89 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 128.61/16.89 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 128.61/16.89 thf(woz1_2_type, type, woz1_2: $o).
% 128.61/16.89 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 128.61/16.89 thf(subsetI1_type, type, subsetI1: $o).
% 128.61/16.89 thf(symdiffE_type, type, symdiffE: $o).
% 128.61/16.89 thf(descrp_type, type, descrp: $o).
% 128.61/16.89 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 128.61/16.89 thf(foundationAx_type, type, foundationAx: $o).
% 128.61/16.89 thf(emptysetAx_type, type, emptysetAx: $o).
% 128.61/16.89 thf(emptyI_type, type, emptyI: $o).
% 128.61/16.89 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 128.61/16.89 thf(binintersectEL_type, type, binintersectEL: $o).
% 128.61/16.89 thf(emptyE1_type, type, emptyE1: $o).
% 128.61/16.89 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 128.61/16.89 thf(demorgan2_type, type, demorgan2: $o).
% 128.61/16.89 thf(vacuousDall_type, type, vacuousDall: $o).
% 128.61/16.89 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 128.61/16.89 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 128.61/16.89 thf(ex1E2_type, type, ex1E2: $o).
% 128.61/16.89 thf(binintersectI_type, type, binintersectI: $o).
% 128.61/16.89 thf(woz13rule3_type, type, woz13rule3: $o).
% 128.61/16.89 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 128.61/16.89 thf(woz13rule2_type, type, woz13rule2: $o).
% 128.61/16.89 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 128.61/16.89 thf(breln1invE_type, type, breln1invE: $o).
% 128.61/16.89 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 128.61/16.89 thf(choice2fnsingleton_type, type, choice2fnsingleton: $o).
% 128.61/16.89 thf(apProp_type, type, apProp: $o).
% 128.61/16.89 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 128.61/16.89 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 128.61/16.89 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 128.61/16.89 thf(demorgan2a2_type, type, demorgan2a2: $o).
% 128.61/16.89 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 128.61/16.89 thf(symdiffI1_type, type, symdiffI1: $o).
% 128.61/16.89 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 128.61/16.89 thf(subsetI2_type, type, subsetI2: $o).
% 128.61/16.89 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 128.61/16.89 thf(setminusERneg_type, type, setminusERneg: $o).
% 128.61/16.89 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 128.61/16.89 thf(omega__Cong_type, type, omega__Cong: $o).
% 128.61/16.89 thf(subsetRefl_type, type, subsetRefl: $o).
% 128.61/16.89 thf(uniqinunit_type, type, uniqinunit: $o).
% 128.61/16.89 thf(breln1compprop_type, type, breln1compprop: $o).
% 128.61/16.89 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 128.61/16.89 thf(prop2setE_type, type, prop2setE: $o).
% 128.61/16.89 thf(binunionEcases_type, type, binunionEcases: $o).
% 128.61/16.89 thf(omega_type, type, omega: $i).
% 128.61/16.89 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions:
% 128.61/16.89 $o).
% 128.61/16.89 thf(nonemptyI_type, type, nonemptyI: $o).
% 128.61/16.89 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 128.61/16.89 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 128.61/16.89 thf(exuE3u_type, type, exuE3u: $o).
% 128.61/16.89 thf(setminusEL_type, type, setminusEL: $o).
% 128.61/16.89 thf(woz13rule4_type, type, woz13rule4: $o).
% 128.61/16.89 thf(breln1all1_type, type, breln1all1: $o).
% 128.61/16.89 thf(breln1compEex_type, type, breln1compEex: $o).
% 128.61/16.89 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 128.61/16.89 thf(sepSubset_type, type, sepSubset: $o).
% 128.61/16.89 thf(upairset2E_type, type, upairset2E: $o).
% 128.61/16.89 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 128.61/16.89 thf(eqbreln1_type, type, eqbreln1: $o).
% 128.61/16.89 thf(woz13rule1_type, type, woz13rule1: $o).
% 128.61/16.89 thf(exuI3_type, type, exuI3: $o).
% 128.61/16.89 thf(notdallE_type, type, notdallE: $o).
% 128.61/16.89 thf(demorgan1a_type, type, demorgan1a: $o).
% 128.61/16.89 thf(binintersectER_type, type, binintersectER: $o).
% 128.61/16.89 thf(powerset_type, type, powerset: $i > $i).
% 128.61/16.89 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 128.61/16.89 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 128.61/16.89 thf(subbreln_type, type, subbreln: $o).
% 128.61/16.89 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 128.61/16.89 thf(exu__Cong_type, type, exu__Cong: $o).
% 128.61/16.89 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 128.61/16.89 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 128.61/16.89 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 128.61/16.89 thf(powersetTI1_type, type, powersetTI1: $o).
% 128.61/16.89 thf(funcext_type, type, funcext: $o).
% 128.61/16.89 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 128.61/16.89 thf(ex1I_type, type, ex1I: $o).
% 128.61/16.89 thf(secondinupair_type, type, secondinupair: $o).
% 128.61/16.89 thf(singletonprop_type, type, singletonprop: $o).
% 128.61/16.89 thf(singletonsubset_type, type, singletonsubset: $o).
% 128.61/16.89 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 128.61/16.89 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 128.61/16.89 thf(replAx_type, type, replAx: $o).
% 128.61/16.89 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 128.61/16.89 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 128.61/16.89 thf(setukpairIL_type, type, setukpairIL: $o).
% 128.61/16.89 thf(setunionE2_type, type, setunionE2: $o).
% 128.61/16.89 thf(inPowerset_type, type, inPowerset: $o).
% 128.61/16.89 thf(demorgan2a1_type, type, demorgan2a1: $o).
% 128.61/16.89 thf(cartprod_type, type, cartprod: $i > $i > $i).
% 128.61/16.89 thf(subset_type, type, subset: $i > $i > $o).
% 128.61/16.89 thf(complementUnionInPowersetComplement_type, type, complementUnionInPowersetComplement:
% 128.61/16.89 $o).
% 128.61/16.89 thf(in__Cong_type, type, in__Cong: $o).
% 128.61/16.89 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 128.61/16.89 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 128.61/16.89 thf(binunionRsub_type, type, binunionRsub: $o).
% 128.61/16.89 thf(subset2powerset_type, type, subset2powerset: $o).
% 128.61/16.89 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 128.61/16.89 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 128.61/16.89 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 128.61/16.89 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 128.61/16.89 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 128.61/16.89 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 128.61/16.89 thf(breln1unionprop, conjecture,
% 128.61/16.89 (( setextAx ) =>
% 128.61/16.89 ( ( emptysetAx ) =>
% 128.61/16.89 ( ( setadjoinAx ) =>
% 128.61/16.89 ( ( powersetAx ) =>
% 128.61/16.89 ( ( setunionAx ) =>
% 128.61/16.89 ( ( omega0Ax ) =>
% 128.61/16.89 ( ( omegaSAx ) =>
% 128.61/16.89 ( ( omegaIndAx ) =>
% 128.61/16.89 ( ( replAx ) =>
% 128.61/16.89 ( ( foundationAx ) =>
% 128.61/16.89 ( ( wellorderingAx ) =>
% 128.61/16.89 ( ( descrp ) =>
% 128.61/16.89 ( ( dsetconstrI ) =>
% 128.61/16.89 ( ( dsetconstrEL ) =>
% 128.61/16.89 ( ( dsetconstrER ) =>
% 128.61/16.89 ( ( exuE1 ) =>
% 128.61/16.89 ( ( prop2setE ) =>
% 128.61/16.89 ( ( emptysetE ) =>
% 128.61/16.89 ( ( emptysetimpfalse ) =>
% 128.61/16.89 ( ( notinemptyset ) =>
% 128.61/16.89 ( ( exuE3e ) =>
% 128.61/16.89 ( ( setext ) =>
% 128.61/16.89 ( ( emptyI ) =>
% 128.61/16.89 ( ( noeltsimpempty ) =>
% 128.61/16.89 ( ( setbeta ) =>
% 128.61/16.89 ( ( nonemptyE1 ) =>
% 128.61/16.89 ( ( nonemptyI ) =>
% 128.61/16.89 ( ( nonemptyI1 ) =>
% 128.61/16.89 ( ( setadjoinIL ) =>
% 128.61/16.89 ( ( emptyinunitempty ) =>
% 128.61/16.89 ( ( setadjoinIR ) =>
% 128.61/16.89 ( ( setadjoinE ) =>
% 128.61/16.89 ( (
% 128.61/16.89 setadjoinOr ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setoftrueEq ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 powersetI ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 emptyinPowerset ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 emptyInPowerset ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 powersetE ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setunionI ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setunionE ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 subPowSU ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 exuE2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 nonemptyImpWitness ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 uniqinunit ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 notinsingleton ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 eqinunit ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 singletonsswitch ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 upairsetE ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 upairsetIL ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 upairsetIR ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 emptyE1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 vacuousDall ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 quantDeMorgan1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 quantDeMorgan2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 quantDeMorgan3 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 quantDeMorgan4 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 prop2setI ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 prop2set2propI ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 notdexE ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 notdallE ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 exuI1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 exuI3 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 exuI2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 inCongP ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 in__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 exuE3u ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 exu__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 emptyset__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setadjoin__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 powerset__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setunion__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 omega__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 exuEu ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 descr__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 dsetconstr__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 subsetI1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 eqimpsubset2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 eqimpsubset1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 subsetI2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 emptysetsubset ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 subsetE ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 subsetE2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 notsubsetI ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 notequalI1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 notequalI2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 subsetRefl ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 subsetTrans ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setadjoinSub ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setadjoinSub2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 subset2powerset ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setextsub ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 subsetemptysetimpeq ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 powersetI1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 powersetE1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 inPowerset ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 powersetsubset ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 sepInPowerset ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 sepSubset ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binunionIL ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 upairset2IR ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binunionIR ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binunionEcases ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binunionE ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binunionLsub ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binunionRsub ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binintersectI ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binintersectSubset5 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binintersectEL ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binintersectLsub ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binintersectSubset2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binintersectSubset3 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binintersectER ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 disjointsetsI1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binintersectRsub ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binintersectSubset4 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binintersectSubset1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 bs114d ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setminusI ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setminusEL ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setminusER ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setminusSubset2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setminusERneg ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setminusELneg ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setminusILneg ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setminusIRneg ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setminusLsub ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setminusSubset1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 symdiffE ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 symdiffI1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 symdiffI2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 symdiffIneg1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 symdiffIneg2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 secondinupair ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setukpairIL ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setukpairIR ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 kpairiskpair ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 kpairp ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 singletonsubset ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 singletoninpowerset ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 singletoninpowunion ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 upairset2E ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 upairsubunion ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 upairinpowunion ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 ubforcartprodlem1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 ubforcartprodlem2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 ubforcartprodlem3 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 cartprodpairin ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 cartprodmempair1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 cartprodmempair ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setunionE2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setunionsingleton1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setunionsingleton2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setunionsingleton ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 singletonprop ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 ex1E1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 ex1I ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 ex1I2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 singletonsuniq ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setukpairinjL1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 kfstsingleton ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 theprop ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 kfstpairEq ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 cartprodfstin ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setukpairinjL2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setukpairinjL ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setukpairinjR11 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setukpairinjR12 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setukpairinjR1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 upairequniteq ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setukpairinjR2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setukpairinjR ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 ksndsingleton ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 ksndpairEq ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 kpairsurjEq ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 cartprodsndin ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 cartprodpairmemEL ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 cartprodpairmemER ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 cartprodmempaircEq ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 cartprodfstpairEq ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 cartprodsndpairEq ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 cartprodpairsurjEq ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 dpsetconstrI ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 dpsetconstrSub ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setOfPairsIsBReln ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 dpsetconstrERa ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 dpsetconstrEL1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 dpsetconstrEL2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 dpsetconstrER ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 funcImageSingleton ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 apProp ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 app ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 infuncsetfunc ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 ap2p ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 funcinfuncset ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 lamProp ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 lamp ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 lam2p ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 brelnall1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 brelnall2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 ex1E2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 funcGraphProp1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 funcGraphProp3 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 funcGraphProp2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 funcextLem ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 funcGraphProp4 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 subbreln ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 eqbreln ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 funcext ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 funcext2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 ap2apEq1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 ap2apEq2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 beta1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 eta1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 lam2lamEq ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 beta2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 eta2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 iffalseProp1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 iffalseProp2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 iftrueProp1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 iftrueProp2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 ifSingleton ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 ifp ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 theeq ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 iftrue ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 iffalse ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 iftrueorfalse ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binintersectT_lem ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binunionT_lem ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 powersetT_lem ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setminusT_lem ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 complementT_lem ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setextT ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 subsetTI ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 powersetTI1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 powersetTE1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 complementTI1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 complementTE1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binintersectTELcontra ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binintersectTERcontra ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 contrasubsetT ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 contrasubsetT1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 contrasubsetT2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 contrasubsetT3 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 doubleComplementI1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 doubleComplementE1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 doubleComplementSub1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 doubleComplementSub2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 doubleComplementEq ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 complementTnotintersectT ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 complementImpComplementIntersect ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 complementSubsetComplementIntersect ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 complementInPowersetComplementIntersect ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 contraSubsetComplement ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 complementTcontraSubset ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binunionTILcontra ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binunionTIRcontra ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 inIntersectImpInUnion ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 inIntersectImpInUnion2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 inIntersectImpInIntersectUnions ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 intersectInPowersetIntersectUnions ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 inComplementUnionImpNotIn1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 inComplementUnionImpInComplement1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binunionTE ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 binunionTEcontra ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 demorgan2a1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 complementUnionInPowersetComplement ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 demorgan2a2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 demorgan1a ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 demorgan1b ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 demorgan1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 demorgan2a ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 demorgan2b2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 demorgan2b ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 demorgan2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 woz13rule0 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 woz13rule1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 woz13rule2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 woz13rule3 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 woz13rule4 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 woz1_1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 woz1_2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 woz1_3 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 woz1_4 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 woz1_5 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 breln1all2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 breln1SetBreln1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 choice2fnsingleton ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setOfPairsIsBReln1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 breln1all1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 subbreln1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 eqbreln1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 breln1invprop ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 breln1invI ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 breln1invE ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 breln1compprop ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 breln1compI ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 breln1compE ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 breln1compEex ) =>
% 128.61/16.89 (
% 128.61/16.89 ![
% 128.61/16.89 A:$i,R:$i]:
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 breln1 @
% 128.61/16.89 A @ R ) =>
% 128.61/16.89 (
% 128.61/16.89 ![
% 128.61/16.89 S:$i]:
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 breln1 @
% 128.61/16.89 A @ S ) =>
% 128.61/16.89 (
% 128.61/16.89 breln1 @
% 128.61/16.89 A @
% 128.61/16.89 (
% 128.61/16.89 binunion @
% 128.61/16.89 R @ S ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 128.61/16.89 thf(zf_stmt_0, negated_conjecture,
% 128.61/16.89 (~( ( setextAx ) =>
% 128.61/16.89 ( ( emptysetAx ) =>
% 128.61/16.89 ( ( setadjoinAx ) =>
% 128.61/16.89 ( ( powersetAx ) =>
% 128.61/16.89 ( ( setunionAx ) =>
% 128.61/16.89 ( ( omega0Ax ) =>
% 128.61/16.89 ( ( omegaSAx ) =>
% 128.61/16.89 ( ( omegaIndAx ) =>
% 128.61/16.89 ( ( replAx ) =>
% 128.61/16.89 ( ( foundationAx ) =>
% 128.61/16.89 ( ( wellorderingAx ) =>
% 128.61/16.89 ( ( descrp ) =>
% 128.61/16.89 ( ( dsetconstrI ) =>
% 128.61/16.89 ( ( dsetconstrEL ) =>
% 128.61/16.89 ( ( dsetconstrER ) =>
% 128.61/16.89 ( ( exuE1 ) =>
% 128.61/16.89 ( ( prop2setE ) =>
% 128.61/16.89 ( ( emptysetE ) =>
% 128.61/16.89 ( ( emptysetimpfalse ) =>
% 128.61/16.89 ( ( notinemptyset ) =>
% 128.61/16.89 ( ( exuE3e ) =>
% 128.61/16.89 ( ( setext ) =>
% 128.61/16.89 ( ( emptyI ) =>
% 128.61/16.89 ( ( noeltsimpempty ) =>
% 128.61/16.89 ( ( setbeta ) =>
% 128.61/16.89 ( ( nonemptyE1 ) =>
% 128.61/16.89 ( ( nonemptyI ) =>
% 128.61/16.89 ( ( nonemptyI1 ) =>
% 128.61/16.89 ( ( setadjoinIL ) =>
% 128.61/16.89 ( ( emptyinunitempty ) =>
% 128.61/16.89 ( ( setadjoinIR ) =>
% 128.61/16.89 ( (
% 128.61/16.89 setadjoinE ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setadjoinOr ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setoftrueEq ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 powersetI ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 emptyinPowerset ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 emptyInPowerset ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 powersetE ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setunionI ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setunionE ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 subPowSU ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 exuE2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 nonemptyImpWitness ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 uniqinunit ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 notinsingleton ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 eqinunit ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 singletonsswitch ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 upairsetE ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 upairsetIL ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 upairsetIR ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 emptyE1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 vacuousDall ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 quantDeMorgan1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 quantDeMorgan2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 quantDeMorgan3 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 quantDeMorgan4 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 prop2setI ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 prop2set2propI ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 notdexE ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 notdallE ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 exuI1 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 exuI3 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 exuI2 ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 inCongP ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 in__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 exuE3u ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 exu__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 emptyset__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setadjoin__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 powerset__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 setunion__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 omega__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 exuEu ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 descr__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 dsetconstr__Cong ) =>
% 128.61/16.89 (
% 128.61/16.89 (
% 128.61/16.89 subsetI1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 eqimpsubset2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 eqimpsubset1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 subsetI2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 emptysetsubset ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 subsetE ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 subsetE2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 notsubsetI ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 notequalI1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 notequalI2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 subsetRefl ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 subsetTrans ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setadjoinSub ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setadjoinSub2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 subset2powerset ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setextsub ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 subsetemptysetimpeq ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 powersetI1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 powersetE1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 inPowerset ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 powersetsubset ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 sepInPowerset ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 sepSubset ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binunionIL ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 upairset2IR ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binunionIR ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binunionEcases ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binunionE ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binunionLsub ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binunionRsub ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binintersectI ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binintersectSubset5 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binintersectEL ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binintersectLsub ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binintersectSubset2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binintersectSubset3 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binintersectER ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 disjointsetsI1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binintersectRsub ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binintersectSubset4 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binintersectSubset1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 bs114d ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setminusI ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setminusEL ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setminusER ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setminusSubset2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setminusERneg ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setminusELneg ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setminusILneg ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setminusIRneg ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setminusLsub ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setminusSubset1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 symdiffE ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 symdiffI1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 symdiffI2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 symdiffIneg1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 symdiffIneg2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 secondinupair ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setukpairIL ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setukpairIR ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 kpairiskpair ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 kpairp ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 singletonsubset ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 singletoninpowerset ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 singletoninpowunion ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 upairset2E ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 upairsubunion ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 upairinpowunion ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ubforcartprodlem1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ubforcartprodlem2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ubforcartprodlem3 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 cartprodpairin ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 cartprodmempair1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 cartprodmempair ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setunionE2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setunionsingleton1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setunionsingleton2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setunionsingleton ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 singletonprop ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ex1E1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ex1I ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ex1I2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 singletonsuniq ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setukpairinjL1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 kfstsingleton ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 theprop ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 kfstpairEq ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 cartprodfstin ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setukpairinjL2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setukpairinjL ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setukpairinjR11 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setukpairinjR12 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setukpairinjR1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 upairequniteq ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setukpairinjR2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setukpairinjR ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ksndsingleton ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ksndpairEq ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 kpairsurjEq ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 cartprodsndin ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 cartprodpairmemEL ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 cartprodpairmemER ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 cartprodmempaircEq ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 cartprodfstpairEq ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 cartprodsndpairEq ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 cartprodpairsurjEq ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 dpsetconstrI ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 dpsetconstrSub ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setOfPairsIsBReln ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 dpsetconstrERa ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 dpsetconstrEL1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 dpsetconstrEL2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 dpsetconstrER ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 funcImageSingleton ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 apProp ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 app ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 infuncsetfunc ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ap2p ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 funcinfuncset ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 lamProp ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 lamp ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 lam2p ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 brelnall1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 brelnall2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ex1E2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 funcGraphProp1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 funcGraphProp3 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 funcGraphProp2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 funcextLem ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 funcGraphProp4 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 subbreln ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 eqbreln ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 funcext ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 funcext2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ap2apEq1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ap2apEq2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 beta1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 eta1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 lam2lamEq ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 beta2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 eta2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 iffalseProp1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 iffalseProp2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 iftrueProp1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 iftrueProp2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ifSingleton ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ifp ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 theeq ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 iftrue ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 iffalse ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 iftrueorfalse ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binintersectT_lem ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binunionT_lem ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 powersetT_lem ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setminusT_lem ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 complementT_lem ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setextT ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 subsetTI ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 powersetTI1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 powersetTE1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 complementTI1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 complementTE1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binintersectTELcontra ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binintersectTERcontra ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 contrasubsetT ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 contrasubsetT1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 contrasubsetT2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 contrasubsetT3 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 doubleComplementI1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 doubleComplementE1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 doubleComplementSub1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 doubleComplementSub2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 doubleComplementEq ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 complementTnotintersectT ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 complementImpComplementIntersect ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 complementSubsetComplementIntersect ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 complementInPowersetComplementIntersect ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 contraSubsetComplement ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 complementTcontraSubset ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binunionTILcontra ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binunionTIRcontra ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 inIntersectImpInUnion ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 inIntersectImpInUnion2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 inIntersectImpInIntersectUnions ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 intersectInPowersetIntersectUnions ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 inComplementUnionImpNotIn1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 inComplementUnionImpInComplement1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binunionTE ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 binunionTEcontra ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 demorgan2a1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 complementUnionInPowersetComplement ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 demorgan2a2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 demorgan1a ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 demorgan1b ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 demorgan1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 demorgan2a ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 demorgan2b2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 demorgan2b ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 demorgan2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 woz13rule0 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 woz13rule1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 woz13rule2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 woz13rule3 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 woz13rule4 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 woz1_1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 woz1_2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 woz1_3 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 woz1_4 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 woz1_5 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 breln1all2 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 breln1SetBreln1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 choice2fnsingleton ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 setOfPairsIsBReln1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 breln1all1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 subbreln1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 eqbreln1 ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 breln1invprop ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 breln1invI ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 breln1invE ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 breln1compprop ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 breln1compI ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 breln1compE ) =>
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 breln1compEex ) =>
% 128.61/16.90 (
% 128.61/16.90 ![
% 128.61/16.90 A:$i,R:$i]:
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 breln1 @
% 128.61/16.90 A @ R ) =>
% 128.61/16.90 (
% 128.61/16.90 ![
% 128.61/16.90 S:$i]:
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 breln1 @
% 128.61/16.90 A @ S ) =>
% 128.61/16.90 (
% 128.61/16.90 breln1 @
% 128.61/16.90 A @
% 128.61/16.90 (
% 128.61/16.90 binunion
% 128.61/16.90 @
% 128.61/16.90 R @ S ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 128.61/16.90 inference('cnf.neg', [status(esa)], [breln1unionprop])).
% 128.61/16.90 thf(zip_derived_cl0, plain,
% 128.61/16.90 (~ (((setextAx) =>
% 128.61/16.90 (((emptysetAx) =>
% 128.61/16.90 (((setadjoinAx) =>
% 128.61/16.90 (((powersetAx) =>
% 128.61/16.90 (((setunionAx) =>
% 128.61/16.90 (((omega0Ax) =>
% 128.61/16.90 (((omegaSAx) =>
% 128.61/16.90 (((omegaIndAx) =>
% 128.61/16.90 (((replAx) =>
% 128.61/16.90 (((foundationAx) =>
% 128.61/16.90 (((wellorderingAx) =>
% 128.61/16.90 (((descrp) =>
% 128.61/16.90 (((dsetconstrI) =>
% 128.61/16.90 (((dsetconstrEL) =>
% 128.61/16.90 (((dsetconstrER) =>
% 128.61/16.90 (((exuE1) =>
% 128.61/16.90 (((prop2setE) =>
% 128.61/16.90 (((emptysetE) =>
% 128.61/16.90 (((emptysetimpfalse) =>
% 128.61/16.90 (((notinemptyset) =>
% 128.61/16.90 (((exuE3e) =>
% 128.61/16.90 (((setext) =>
% 128.61/16.90 (((emptyI) =>
% 128.61/16.90 (((noeltsimpempty) =>
% 128.61/16.90 (((setbeta) =>
% 128.61/16.90 (((nonemptyE1) =>
% 128.61/16.90 (((nonemptyI) =>
% 128.61/16.90 (((nonemptyI1) =>
% 128.61/16.90 (((setadjoinIL) =>
% 128.61/16.90 (((emptyinunitempty) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoinIR) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoinE) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoinOr) =>
% 128.61/16.90 ((
% 128.61/16.90 (setoftrueEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetI) =>
% 128.61/16.90 ((
% 128.61/16.90 (emptyinPowerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (emptyInPowerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetE) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionI) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionE) =>
% 128.61/16.90 ((
% 128.61/16.90 (subPowSU) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuE2) =>
% 128.61/16.90 ((
% 128.61/16.90 (nonemptyImpWitness) =>
% 128.61/16.90 ((
% 128.61/16.90 (uniqinunit) =>
% 128.61/16.90 ((
% 128.61/16.90 (notinsingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (eqinunit) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletonsswitch) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairsetE) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairsetIL) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairsetIR) =>
% 128.61/16.90 ((
% 128.61/16.90 (emptyE1) =>
% 128.61/16.90 ((
% 128.61/16.90 (vacuousDall) =>
% 128.61/16.90 ((
% 128.61/16.90 (quantDeMorgan1) =>
% 128.61/16.90 ((
% 128.61/16.90 (quantDeMorgan2) =>
% 128.61/16.90 ((
% 128.61/16.90 (quantDeMorgan3) =>
% 128.61/16.90 ((
% 128.61/16.90 (quantDeMorgan4) =>
% 128.61/16.90 ((
% 128.61/16.90 (prop2setI) =>
% 128.61/16.90 ((
% 128.61/16.90 (prop2set2propI) =>
% 128.61/16.90 ((
% 128.61/16.90 (notdexE) =>
% 128.61/16.90 ((
% 128.61/16.90 (notdallE) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuI3) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuI2) =>
% 128.61/16.90 ((
% 128.61/16.90 (inCongP) =>
% 128.61/16.90 ((
% 128.61/16.90 (in__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuE3u) =>
% 128.61/16.90 ((
% 128.61/16.90 (exu__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (emptyset__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoin__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (powerset__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunion__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (omega__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuEu) =>
% 128.61/16.90 ((
% 128.61/16.90 (descr__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (dsetconstr__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (eqimpsubset2) =>
% 128.61/16.90 ((
% 128.61/16.90 (eqimpsubset1) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetI2) =>
% 128.61/16.90 ((
% 128.61/16.90 (emptysetsubset) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetE) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetE2) =>
% 128.61/16.90 ((
% 128.61/16.90 (notsubsetI) =>
% 128.61/16.90 ((
% 128.61/16.90 (notequalI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (notequalI2) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetRefl) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetTrans) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoinSub) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoinSub2) =>
% 128.61/16.90 ((
% 128.61/16.90 (subset2powerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (setextsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetemptysetimpeq) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetE1) =>
% 128.61/16.90 ((
% 128.61/16.90 (inPowerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetsubset) =>
% 128.61/16.90 ((
% 128.61/16.90 (sepInPowerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (sepSubset) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionIL) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairset2IR) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionIR) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionEcases) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionE) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionLsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionRsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectI) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset5) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectEL) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectLsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset2) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset3) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectER) =>
% 128.61/16.90 ((
% 128.61/16.90 (disjointsetsI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectRsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset4) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset1) =>
% 128.61/16.90 ((
% 128.61/16.90 (bs114d) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusI) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusEL) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusER) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusSubset2) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusERneg) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusELneg) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusILneg) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusIRneg) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusLsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusSubset1) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffE) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffI2) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffIneg1) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffIneg2) =>
% 128.61/16.90 ((
% 128.61/16.90 (secondinupair) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairIL) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairIR) =>
% 128.61/16.90 ((
% 128.61/16.90 (kpairiskpair) =>
% 128.61/16.90 ((
% 128.61/16.90 (kpairp) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletonsubset) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletoninpowerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletoninpowunion) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairset2E) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairsubunion) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairinpowunion) =>
% 128.61/16.90 ((
% 128.61/16.90 (ubforcartprodlem1) =>
% 128.61/16.90 ((
% 128.61/16.90 (ubforcartprodlem2) =>
% 128.61/16.90 ((
% 128.61/16.90 (ubforcartprodlem3) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodpairin) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodmempair1) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodmempair) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionE2) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionsingleton1) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionsingleton2) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionsingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletonprop) =>
% 128.61/16.90 ((
% 128.61/16.90 (ex1E1) =>
% 128.61/16.90 ((
% 128.61/16.90 (ex1I) =>
% 128.61/16.90 ((
% 128.61/16.90 (ex1I2) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletonsuniq) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjL1) =>
% 128.61/16.90 ((
% 128.61/16.90 (kfstsingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (theprop) =>
% 128.61/16.90 ((
% 128.61/16.90 (kfstpairEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodfstin) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjL2) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjL) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjR11) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjR12) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjR1) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairequniteq) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjR2) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjR) =>
% 128.61/16.90 ((
% 128.61/16.90 (ksndsingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (ksndpairEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (kpairsurjEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodsndin) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodpairmemEL) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodpairmemER) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodmempaircEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodfstpairEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodsndpairEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodpairsurjEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrI) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrSub) =>
% 128.61/16.90 ((
% 128.61/16.90 (setOfPairsIsBReln) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrERa) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrEL1) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrEL2) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrER) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcImageSingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (apProp) =>
% 128.61/16.90 ((
% 128.61/16.90 (app) =>
% 128.61/16.90 ((
% 128.61/16.90 (infuncsetfunc) =>
% 128.61/16.90 ((
% 128.61/16.90 (ap2p) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcinfuncset) =>
% 128.61/16.90 ((
% 128.61/16.90 (lamProp) =>
% 128.61/16.90 ((
% 128.61/16.90 (lamp) =>
% 128.61/16.90 ((
% 128.61/16.90 (lam2p) =>
% 128.61/16.90 ((
% 128.61/16.90 (brelnall1) =>
% 128.61/16.90 ((
% 128.61/16.90 (brelnall2) =>
% 128.61/16.90 ((
% 128.61/16.90 (ex1E2) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcGraphProp1) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcGraphProp3) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcGraphProp2) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcextLem) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcGraphProp4) =>
% 128.61/16.90 ((
% 128.61/16.90 (subbreln) =>
% 128.61/16.90 ((
% 128.61/16.90 (eqbreln) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcext) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcext2) =>
% 128.61/16.90 ((
% 128.61/16.90 (ap2apEq1) =>
% 128.61/16.90 ((
% 128.61/16.90 (ap2apEq2) =>
% 128.61/16.90 ((
% 128.61/16.90 (beta1) =>
% 128.61/16.90 ((
% 128.61/16.90 (eta1) =>
% 128.61/16.90 ((
% 128.61/16.90 (lam2lamEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (beta2) =>
% 128.61/16.90 ((
% 128.61/16.90 (eta2) =>
% 128.61/16.90 ((
% 128.61/16.90 (iffalseProp1) =>
% 128.61/16.90 ((
% 128.61/16.90 (iffalseProp2) =>
% 128.61/16.90 ((
% 128.61/16.90 (iftrueProp1) =>
% 128.61/16.90 ((
% 128.61/16.90 (iftrueProp2) =>
% 128.61/16.90 ((
% 128.61/16.90 (ifSingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (ifp) =>
% 128.61/16.90 ((
% 128.61/16.90 (theeq) =>
% 128.61/16.90 ((
% 128.61/16.90 (iftrue) =>
% 128.61/16.90 ((
% 128.61/16.90 (iffalse) =>
% 128.61/16.90 ((
% 128.61/16.90 (iftrueorfalse) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectT_lem) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionT_lem) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetT_lem) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusT_lem) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementT_lem) =>
% 128.61/16.90 ((
% 128.61/16.90 (setextT) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetTI) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetTI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetTE1) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementTI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementTE1) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectTELcontra) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectTERcontra) =>
% 128.61/16.90 ((
% 128.61/16.90 (contrasubsetT) =>
% 128.61/16.90 ((
% 128.61/16.90 (contrasubsetT1) =>
% 128.61/16.90 ((
% 128.61/16.90 (contrasubsetT2) =>
% 128.61/16.90 ((
% 128.61/16.90 (contrasubsetT3) =>
% 128.61/16.90 ((
% 128.61/16.90 (doubleComplementI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (doubleComplementE1) =>
% 128.61/16.90 ((
% 128.61/16.90 (doubleComplementSub1) =>
% 128.61/16.90 ((
% 128.61/16.90 (doubleComplementSub2) =>
% 128.61/16.90 ((
% 128.61/16.90 (doubleComplementEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementTnotintersectT) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementImpComplementIntersect) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementSubsetComplementIntersect) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementInPowersetComplementIntersect) =>
% 128.61/16.90 ((
% 128.61/16.90 (contraSubsetComplement) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementTcontraSubset) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionTILcontra) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionTIRcontra) =>
% 128.61/16.90 ((
% 128.61/16.90 (inIntersectImpInUnion) =>
% 128.61/16.90 ((
% 128.61/16.90 (inIntersectImpInUnion2) =>
% 128.61/16.90 ((
% 128.61/16.90 (inIntersectImpInIntersectUnions) =>
% 128.61/16.90 ((
% 128.61/16.90 (intersectInPowersetIntersectUnions) =>
% 128.61/16.90 ((
% 128.61/16.90 (inComplementUnionImpNotIn1) =>
% 128.61/16.90 ((
% 128.61/16.90 (inComplementUnionImpInComplement1) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionTE) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionTEcontra) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2a1) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementUnionInPowersetComplement) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2a2) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan1a) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan1b) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan1) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2a) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2b2) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2b) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz13rule0) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz13rule1) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz13rule2) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz13rule3) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz13rule4) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz1_1) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz1_2) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz1_3) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz1_4) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz1_5) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1all2) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1SetBreln1) =>
% 128.61/16.90 ((
% 128.61/16.90 (choice2fnsingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (setOfPairsIsBReln1) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1all1) =>
% 128.61/16.90 ((
% 128.61/16.90 (subbreln1) =>
% 128.61/16.90 ((
% 128.61/16.90 (eqbreln1) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1invprop) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1invI) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1invE) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1compprop) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1compI) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1compE) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1compEex) =>
% 128.61/16.90 ((
% 128.61/16.90 (!!) @ (
% 128.61/16.90 ^[Y0 : $i]:
% 128.61/16.90 ((
% 128.61/16.90 (!!) @ (
% 128.61/16.90 ^[Y1 : $i]:
% 128.61/16.90 ((
% 128.61/16.90 (breln1 @
% 128.61/16.90 Y0 @
% 128.61/16.90 Y1) =>
% 128.61/16.90 ((
% 128.61/16.90 (!!) @ (
% 128.61/16.90 ^[Y2 : $i]:
% 128.61/16.90 ((
% 128.61/16.90 (breln1 @
% 128.61/16.90 Y0 @
% 128.61/16.90 Y2) =>
% 128.61/16.90 (breln1 @
% 128.61/16.90 Y0 @
% 128.61/16.90 (
% 128.61/16.90 binunion @
% 128.61/16.90 Y1 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.61/16.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 128.61/16.90 thf(zip_derived_cl1, plain,
% 128.61/16.90 (~ (((setextAx) =>
% 128.61/16.90 (((emptysetAx) =>
% 128.61/16.90 (((setadjoinAx) =>
% 128.61/16.90 (((powersetAx) =>
% 128.61/16.90 (((setunionAx) =>
% 128.61/16.90 (((omega0Ax) =>
% 128.61/16.90 (((omegaSAx) =>
% 128.61/16.90 (((omegaIndAx) =>
% 128.61/16.90 (((replAx) =>
% 128.61/16.90 (((foundationAx) =>
% 128.61/16.90 (((wellorderingAx) =>
% 128.61/16.90 (((descrp) =>
% 128.61/16.90 (((dsetconstrI) =>
% 128.61/16.90 (((dsetconstrEL) =>
% 128.61/16.90 (((dsetconstrER) =>
% 128.61/16.90 (((exuE1) =>
% 128.61/16.90 (((prop2setE) =>
% 128.61/16.90 (((emptysetE) =>
% 128.61/16.90 (((emptysetimpfalse) =>
% 128.61/16.90 (((notinemptyset) =>
% 128.61/16.90 (((exuE3e) =>
% 128.61/16.90 (((setext) =>
% 128.61/16.90 (((emptyI) =>
% 128.61/16.90 (((noeltsimpempty) =>
% 128.61/16.90 (((setbeta) =>
% 128.61/16.90 (((nonemptyE1) =>
% 128.61/16.90 (((nonemptyI) =>
% 128.61/16.90 (((nonemptyI1) =>
% 128.61/16.90 (((setadjoinIL) =>
% 128.61/16.90 (((emptyinunitempty) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoinIR) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoinE) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoinOr) =>
% 128.61/16.90 ((
% 128.61/16.90 (setoftrueEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetI) =>
% 128.61/16.90 ((
% 128.61/16.90 (emptyinPowerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (emptyInPowerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetE) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionI) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionE) =>
% 128.61/16.90 ((
% 128.61/16.90 (subPowSU) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuE2) =>
% 128.61/16.90 ((
% 128.61/16.90 (nonemptyImpWitness) =>
% 128.61/16.90 ((
% 128.61/16.90 (uniqinunit) =>
% 128.61/16.90 ((
% 128.61/16.90 (notinsingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (eqinunit) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletonsswitch) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairsetE) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairsetIL) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairsetIR) =>
% 128.61/16.90 ((
% 128.61/16.90 (emptyE1) =>
% 128.61/16.90 ((
% 128.61/16.90 (vacuousDall) =>
% 128.61/16.90 ((
% 128.61/16.90 (quantDeMorgan1) =>
% 128.61/16.90 ((
% 128.61/16.90 (quantDeMorgan2) =>
% 128.61/16.90 ((
% 128.61/16.90 (quantDeMorgan3) =>
% 128.61/16.90 ((
% 128.61/16.90 (quantDeMorgan4) =>
% 128.61/16.90 ((
% 128.61/16.90 (prop2setI) =>
% 128.61/16.90 ((
% 128.61/16.90 (prop2set2propI) =>
% 128.61/16.90 ((
% 128.61/16.90 (notdexE) =>
% 128.61/16.90 ((
% 128.61/16.90 (notdallE) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuI3) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuI2) =>
% 128.61/16.90 ((
% 128.61/16.90 (inCongP) =>
% 128.61/16.90 ((
% 128.61/16.90 (in__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuE3u) =>
% 128.61/16.90 ((
% 128.61/16.90 (exu__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (emptyset__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoin__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (powerset__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunion__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (omega__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuEu) =>
% 128.61/16.90 ((
% 128.61/16.90 (descr__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (dsetconstr__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (eqimpsubset2) =>
% 128.61/16.90 ((
% 128.61/16.90 (eqimpsubset1) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetI2) =>
% 128.61/16.90 ((
% 128.61/16.90 (emptysetsubset) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetE) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetE2) =>
% 128.61/16.90 ((
% 128.61/16.90 (notsubsetI) =>
% 128.61/16.90 ((
% 128.61/16.90 (notequalI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (notequalI2) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetRefl) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetTrans) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoinSub) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoinSub2) =>
% 128.61/16.90 ((
% 128.61/16.90 (subset2powerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (setextsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetemptysetimpeq) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetE1) =>
% 128.61/16.90 ((
% 128.61/16.90 (inPowerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetsubset) =>
% 128.61/16.90 ((
% 128.61/16.90 (sepInPowerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (sepSubset) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionIL) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairset2IR) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionIR) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionEcases) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionE) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionLsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionRsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectI) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset5) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectEL) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectLsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset2) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset3) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectER) =>
% 128.61/16.90 ((
% 128.61/16.90 (disjointsetsI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectRsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset4) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset1) =>
% 128.61/16.90 ((
% 128.61/16.90 (bs114d) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusI) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusEL) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusER) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusSubset2) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusERneg) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusELneg) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusILneg) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusIRneg) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusLsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusSubset1) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffE) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffI2) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffIneg1) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffIneg2) =>
% 128.61/16.90 ((
% 128.61/16.90 (secondinupair) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairIL) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairIR) =>
% 128.61/16.90 ((
% 128.61/16.90 (kpairiskpair) =>
% 128.61/16.90 ((
% 128.61/16.90 (kpairp) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletonsubset) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletoninpowerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletoninpowunion) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairset2E) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairsubunion) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairinpowunion) =>
% 128.61/16.90 ((
% 128.61/16.90 (ubforcartprodlem1) =>
% 128.61/16.90 ((
% 128.61/16.90 (ubforcartprodlem2) =>
% 128.61/16.90 ((
% 128.61/16.90 (ubforcartprodlem3) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodpairin) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodmempair1) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodmempair) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionE2) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionsingleton1) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionsingleton2) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionsingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletonprop) =>
% 128.61/16.90 ((
% 128.61/16.90 (ex1E1) =>
% 128.61/16.90 ((
% 128.61/16.90 (ex1I) =>
% 128.61/16.90 ((
% 128.61/16.90 (ex1I2) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletonsuniq) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjL1) =>
% 128.61/16.90 ((
% 128.61/16.90 (kfstsingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (theprop) =>
% 128.61/16.90 ((
% 128.61/16.90 (kfstpairEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodfstin) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjL2) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjL) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjR11) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjR12) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjR1) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairequniteq) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjR2) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjR) =>
% 128.61/16.90 ((
% 128.61/16.90 (ksndsingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (ksndpairEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (kpairsurjEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodsndin) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodpairmemEL) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodpairmemER) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodmempaircEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodfstpairEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodsndpairEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodpairsurjEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrI) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrSub) =>
% 128.61/16.90 ((
% 128.61/16.90 (setOfPairsIsBReln) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrERa) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrEL1) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrEL2) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrER) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcImageSingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (apProp) =>
% 128.61/16.90 ((
% 128.61/16.90 (app) =>
% 128.61/16.90 ((
% 128.61/16.90 (infuncsetfunc) =>
% 128.61/16.90 ((
% 128.61/16.90 (ap2p) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcinfuncset) =>
% 128.61/16.90 ((
% 128.61/16.90 (lamProp) =>
% 128.61/16.90 ((
% 128.61/16.90 (lamp) =>
% 128.61/16.90 ((
% 128.61/16.90 (lam2p) =>
% 128.61/16.90 ((
% 128.61/16.90 (brelnall1) =>
% 128.61/16.90 ((
% 128.61/16.90 (brelnall2) =>
% 128.61/16.90 ((
% 128.61/16.90 (ex1E2) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcGraphProp1) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcGraphProp3) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcGraphProp2) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcextLem) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcGraphProp4) =>
% 128.61/16.90 ((
% 128.61/16.90 (subbreln) =>
% 128.61/16.90 ((
% 128.61/16.90 (eqbreln) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcext) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcext2) =>
% 128.61/16.90 ((
% 128.61/16.90 (ap2apEq1) =>
% 128.61/16.90 ((
% 128.61/16.90 (ap2apEq2) =>
% 128.61/16.90 ((
% 128.61/16.90 (beta1) =>
% 128.61/16.90 ((
% 128.61/16.90 (eta1) =>
% 128.61/16.90 ((
% 128.61/16.90 (lam2lamEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (beta2) =>
% 128.61/16.90 ((
% 128.61/16.90 (eta2) =>
% 128.61/16.90 ((
% 128.61/16.90 (iffalseProp1) =>
% 128.61/16.90 ((
% 128.61/16.90 (iffalseProp2) =>
% 128.61/16.90 ((
% 128.61/16.90 (iftrueProp1) =>
% 128.61/16.90 ((
% 128.61/16.90 (iftrueProp2) =>
% 128.61/16.90 ((
% 128.61/16.90 (ifSingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (ifp) =>
% 128.61/16.90 ((
% 128.61/16.90 (theeq) =>
% 128.61/16.90 ((
% 128.61/16.90 (iftrue) =>
% 128.61/16.90 ((
% 128.61/16.90 (iffalse) =>
% 128.61/16.90 ((
% 128.61/16.90 (iftrueorfalse) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectT_lem) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionT_lem) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetT_lem) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusT_lem) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementT_lem) =>
% 128.61/16.90 ((
% 128.61/16.90 (setextT) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetTI) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetTI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetTE1) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementTI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementTE1) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectTELcontra) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectTERcontra) =>
% 128.61/16.90 ((
% 128.61/16.90 (contrasubsetT) =>
% 128.61/16.90 ((
% 128.61/16.90 (contrasubsetT1) =>
% 128.61/16.90 ((
% 128.61/16.90 (contrasubsetT2) =>
% 128.61/16.90 ((
% 128.61/16.90 (contrasubsetT3) =>
% 128.61/16.90 ((
% 128.61/16.90 (doubleComplementI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (doubleComplementE1) =>
% 128.61/16.90 ((
% 128.61/16.90 (doubleComplementSub1) =>
% 128.61/16.90 ((
% 128.61/16.90 (doubleComplementSub2) =>
% 128.61/16.90 ((
% 128.61/16.90 (doubleComplementEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementTnotintersectT) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementImpComplementIntersect) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementSubsetComplementIntersect) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementInPowersetComplementIntersect) =>
% 128.61/16.90 ((
% 128.61/16.90 (contraSubsetComplement) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementTcontraSubset) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionTILcontra) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionTIRcontra) =>
% 128.61/16.90 ((
% 128.61/16.90 (inIntersectImpInUnion) =>
% 128.61/16.90 ((
% 128.61/16.90 (inIntersectImpInUnion2) =>
% 128.61/16.90 ((
% 128.61/16.90 (inIntersectImpInIntersectUnions) =>
% 128.61/16.90 ((
% 128.61/16.90 (intersectInPowersetIntersectUnions) =>
% 128.61/16.90 ((
% 128.61/16.90 (inComplementUnionImpNotIn1) =>
% 128.61/16.90 ((
% 128.61/16.90 (inComplementUnionImpInComplement1) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionTE) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionTEcontra) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2a1) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementUnionInPowersetComplement) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2a2) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan1a) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan1b) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan1) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2a) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2b2) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2b) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz13rule0) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz13rule1) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz13rule2) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz13rule3) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz13rule4) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz1_1) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz1_2) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz1_3) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz1_4) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz1_5) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1all2) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1SetBreln1) =>
% 128.61/16.90 ((
% 128.61/16.90 (choice2fnsingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (setOfPairsIsBReln1) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1all1) =>
% 128.61/16.90 ((
% 128.61/16.90 (subbreln1) =>
% 128.61/16.90 ((
% 128.61/16.90 (eqbreln1) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1invprop) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1invI) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1invE) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1compprop) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1compI) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1compE) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1compEex) =>
% 128.61/16.90 ((
% 128.61/16.90 (!!) @ (
% 128.61/16.90 (('#B') @ (
% 128.61/16.90 !!) @
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ('#S') @ (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 '#S') @
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 =>))) @
% 128.61/16.90 breln1)))) @
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 !!))) @
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ('#S') @ (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 '#B') @
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 '#S') @
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 =>))) @
% 128.61/16.90 breln1)))))) @
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ('#C') @ (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 '#B') @
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 '#B') @
% 128.61/16.90 breln1)))) @
% 128.61/16.90 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.61/16.90 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 128.61/16.90 thf(omega0Ax, axiom,(( omega0Ax ) = ((in @ emptyset @ omega)))).
% 128.61/16.90 thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 128.61/16.90 define([status(thm)])).
% 128.61/16.90 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 128.61/16.90 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))).
% 128.61/16.90 thf('1', plain,
% 128.61/16.90 (( emptyinunitempty ) =
% 128.61/16.90 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 128.61/16.90 define([status(thm)])).
% 128.61/16.90 thf(emptyset__Cong, axiom,(( emptyset__Cong ) =
% 128.61/16.90 ((((emptyset) = (emptyset)))))).
% 128.61/16.90 thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 128.61/16.90 define([status(thm)])).
% 128.61/16.90 thf(omega__Cong, axiom,(( omega__Cong ) = ((((omega) = (omega)))))).
% 128.61/16.90 thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 128.61/16.90 define([status(thm)])).
% 128.61/16.90 thf(zip_derived_cl2, plain,
% 128.61/16.90 (~ (((setextAx) =>
% 128.61/16.90 (((emptysetAx) =>
% 128.61/16.90 (((setadjoinAx) =>
% 128.61/16.90 (((powersetAx) =>
% 128.61/16.90 (((setunionAx) =>
% 128.61/16.90 (((in @ emptyset @ omega) =>
% 128.61/16.90 (((omegaSAx) =>
% 128.61/16.90 (((omegaIndAx) =>
% 128.61/16.90 (((replAx) =>
% 128.61/16.90 (((foundationAx) =>
% 128.61/16.90 (((wellorderingAx) =>
% 128.61/16.90 (((descrp) =>
% 128.61/16.90 (((dsetconstrI) =>
% 128.61/16.90 (((dsetconstrEL) =>
% 128.61/16.90 (((dsetconstrER) =>
% 128.61/16.90 (((exuE1) =>
% 128.61/16.90 (((prop2setE) =>
% 128.61/16.90 (((emptysetE) =>
% 128.61/16.90 (((emptysetimpfalse) =>
% 128.61/16.90 (((notinemptyset) =>
% 128.61/16.90 (((exuE3e) =>
% 128.61/16.90 (((setext) =>
% 128.61/16.90 (((emptyI) =>
% 128.61/16.90 (((noeltsimpempty) =>
% 128.61/16.90 (((setbeta) =>
% 128.61/16.90 (((nonemptyE1) =>
% 128.61/16.90 (((nonemptyI) =>
% 128.61/16.90 (((nonemptyI1) =>
% 128.61/16.90 (((setadjoinIL) =>
% 128.61/16.90 (((in @
% 128.61/16.90 emptyset @
% 128.61/16.90 (setadjoin @
% 128.61/16.90 emptyset @
% 128.61/16.90 emptyset)) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoinIR) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoinE) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoinOr) =>
% 128.61/16.90 ((
% 128.61/16.90 (setoftrueEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetI) =>
% 128.61/16.90 ((
% 128.61/16.90 (emptyinPowerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (emptyInPowerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetE) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionI) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionE) =>
% 128.61/16.90 ((
% 128.61/16.90 (subPowSU) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuE2) =>
% 128.61/16.90 ((
% 128.61/16.90 (nonemptyImpWitness) =>
% 128.61/16.90 ((
% 128.61/16.90 (uniqinunit) =>
% 128.61/16.90 ((
% 128.61/16.90 (notinsingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (eqinunit) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletonsswitch) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairsetE) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairsetIL) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairsetIR) =>
% 128.61/16.90 ((
% 128.61/16.90 (emptyE1) =>
% 128.61/16.90 ((
% 128.61/16.90 (vacuousDall) =>
% 128.61/16.90 ((
% 128.61/16.90 (quantDeMorgan1) =>
% 128.61/16.90 ((
% 128.61/16.90 (quantDeMorgan2) =>
% 128.61/16.90 ((
% 128.61/16.90 (quantDeMorgan3) =>
% 128.61/16.90 ((
% 128.61/16.90 (quantDeMorgan4) =>
% 128.61/16.90 ((
% 128.61/16.90 (prop2setI) =>
% 128.61/16.90 ((
% 128.61/16.90 (prop2set2propI) =>
% 128.61/16.90 ((
% 128.61/16.90 (notdexE) =>
% 128.61/16.90 ((
% 128.61/16.90 (notdallE) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuI3) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuI2) =>
% 128.61/16.90 ((
% 128.61/16.90 (inCongP) =>
% 128.61/16.90 ((
% 128.61/16.90 (in__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuE3u) =>
% 128.61/16.90 ((
% 128.61/16.90 (exu__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 ((
% 128.61/16.90 (emptyset) =
% 128.61/16.90 (emptyset))) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoin__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (powerset__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunion__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 ((
% 128.61/16.90 (omega) =
% 128.61/16.90 (omega))) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuEu) =>
% 128.61/16.90 ((
% 128.61/16.90 (descr__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (dsetconstr__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (eqimpsubset2) =>
% 128.61/16.90 ((
% 128.61/16.90 (eqimpsubset1) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetI2) =>
% 128.61/16.90 ((
% 128.61/16.90 (emptysetsubset) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetE) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetE2) =>
% 128.61/16.90 ((
% 128.61/16.90 (notsubsetI) =>
% 128.61/16.90 ((
% 128.61/16.90 (notequalI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (notequalI2) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetRefl) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetTrans) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoinSub) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoinSub2) =>
% 128.61/16.90 ((
% 128.61/16.90 (subset2powerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (setextsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetemptysetimpeq) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetE1) =>
% 128.61/16.90 ((
% 128.61/16.90 (inPowerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (powersetsubset) =>
% 128.61/16.90 ((
% 128.61/16.90 (sepInPowerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (sepSubset) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionIL) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairset2IR) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionIR) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionEcases) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionE) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionLsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionRsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectI) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset5) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectEL) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectLsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset2) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset3) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectER) =>
% 128.61/16.90 ((
% 128.61/16.90 (disjointsetsI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectRsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset4) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset1) =>
% 128.61/16.90 ((
% 128.61/16.90 (bs114d) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusI) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusEL) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusER) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusSubset2) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusERneg) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusELneg) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusILneg) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusIRneg) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusLsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusSubset1) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffE) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffI2) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffIneg1) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffIneg2) =>
% 128.61/16.90 ((
% 128.61/16.90 (secondinupair) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairIL) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairIR) =>
% 128.61/16.90 ((
% 128.61/16.90 (kpairiskpair) =>
% 128.61/16.90 ((
% 128.61/16.90 (kpairp) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletonsubset) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletoninpowerset) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletoninpowunion) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairset2E) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairsubunion) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairinpowunion) =>
% 128.61/16.90 ((
% 128.61/16.90 (ubforcartprodlem1) =>
% 128.61/16.90 ((
% 128.61/16.90 (ubforcartprodlem2) =>
% 128.61/16.90 ((
% 128.61/16.90 (ubforcartprodlem3) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodpairin) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodmempair1) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodmempair) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionE2) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionsingleton1) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionsingleton2) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunionsingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletonprop) =>
% 128.61/16.90 ((
% 128.61/16.90 (ex1E1) =>
% 128.61/16.90 ((
% 128.61/16.90 (ex1I) =>
% 128.61/16.90 ((
% 128.61/16.90 (ex1I2) =>
% 128.61/16.90 ((
% 128.61/16.90 (singletonsuniq) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjL1) =>
% 128.61/16.90 ((
% 128.61/16.90 (kfstsingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (theprop) =>
% 128.61/16.90 ((
% 128.61/16.90 (kfstpairEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodfstin) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjL2) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjL) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjR11) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjR12) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjR1) =>
% 128.61/16.90 ((
% 128.61/16.90 (upairequniteq) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjR2) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairinjR) =>
% 128.61/16.90 ((
% 128.61/16.90 (ksndsingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (ksndpairEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (kpairsurjEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodsndin) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodpairmemEL) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodpairmemER) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodmempaircEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodfstpairEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodsndpairEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (cartprodpairsurjEq) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrI) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrSub) =>
% 128.61/16.90 ((
% 128.61/16.90 (setOfPairsIsBReln) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrERa) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrEL1) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrEL2) =>
% 128.61/16.90 ((
% 128.61/16.90 (dpsetconstrER) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcImageSingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (apProp) =>
% 128.61/16.90 ((
% 128.61/16.90 (app) =>
% 128.61/16.90 ((
% 128.61/16.90 (infuncsetfunc) =>
% 128.61/16.90 ((
% 128.61/16.90 (ap2p) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcinfuncset) =>
% 128.61/16.90 ((
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% 128.61/16.90 ((
% 128.61/16.90 (lamp) =>
% 128.61/16.90 ((
% 128.61/16.90 (lam2p) =>
% 128.61/16.90 ((
% 128.61/16.90 (brelnall1) =>
% 128.61/16.90 ((
% 128.61/16.90 (brelnall2) =>
% 128.61/16.90 ((
% 128.61/16.90 (ex1E2) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcGraphProp1) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcGraphProp3) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcGraphProp2) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcextLem) =>
% 128.61/16.90 ((
% 128.61/16.90 (funcGraphProp4) =>
% 128.61/16.90 ((
% 128.61/16.90 (subbreln) =>
% 128.61/16.90 ((
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% 128.61/16.90 ((
% 128.61/16.90 (funcext2) =>
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% 128.61/16.90 ((
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% 128.61/16.90 ((
% 128.61/16.90 (eta1) =>
% 128.61/16.90 ((
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% 128.61/16.90 ((
% 128.61/16.90 (beta2) =>
% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
% 128.61/16.90 (iftrueProp1) =>
% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 (iftrueorfalse) =>
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
% 128.61/16.90 (powersetTE1) =>
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% 128.61/16.90 (complementTE1) =>
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% 128.61/16.90 ((
% 128.61/16.90 (binintersectTERcontra) =>
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% 128.61/16.90 ((
% 128.61/16.90 (contrasubsetT1) =>
% 128.61/16.90 ((
% 128.61/16.90 (contrasubsetT2) =>
% 128.61/16.90 ((
% 128.61/16.90 (contrasubsetT3) =>
% 128.61/16.90 ((
% 128.61/16.90 (doubleComplementI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (doubleComplementE1) =>
% 128.61/16.90 ((
% 128.61/16.90 (doubleComplementSub1) =>
% 128.61/16.90 ((
% 128.61/16.90 (doubleComplementSub2) =>
% 128.61/16.90 ((
% 128.61/16.90 (doubleComplementEq) =>
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% 128.61/16.90 (complementTnotintersectT) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementImpComplementIntersect) =>
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% 128.61/16.90 (complementSubsetComplementIntersect) =>
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% 128.61/16.90 (complementInPowersetComplementIntersect) =>
% 128.61/16.90 ((
% 128.61/16.90 (contraSubsetComplement) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementTcontraSubset) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionTILcontra) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionTIRcontra) =>
% 128.61/16.90 ((
% 128.61/16.90 (inIntersectImpInUnion) =>
% 128.61/16.90 ((
% 128.61/16.90 (inIntersectImpInUnion2) =>
% 128.61/16.90 ((
% 128.61/16.90 (inIntersectImpInIntersectUnions) =>
% 128.61/16.90 ((
% 128.61/16.90 (intersectInPowersetIntersectUnions) =>
% 128.61/16.90 ((
% 128.61/16.90 (inComplementUnionImpNotIn1) =>
% 128.61/16.90 ((
% 128.61/16.90 (inComplementUnionImpInComplement1) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionTE) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionTEcontra) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2a1) =>
% 128.61/16.90 ((
% 128.61/16.90 (complementUnionInPowersetComplement) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2a2) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan1a) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan1b) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan1) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2a) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2b2) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2b) =>
% 128.61/16.90 ((
% 128.61/16.90 (demorgan2) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz13rule0) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz13rule1) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz13rule2) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz13rule3) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz13rule4) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz1_1) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz1_2) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz1_3) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz1_4) =>
% 128.61/16.90 ((
% 128.61/16.90 (woz1_5) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1all2) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1SetBreln1) =>
% 128.61/16.90 ((
% 128.61/16.90 (choice2fnsingleton) =>
% 128.61/16.90 ((
% 128.61/16.90 (setOfPairsIsBReln1) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1all1) =>
% 128.61/16.90 ((
% 128.61/16.90 (subbreln1) =>
% 128.61/16.90 ((
% 128.61/16.90 (eqbreln1) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1invprop) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1invI) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1invE) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1compprop) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1compI) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1compE) =>
% 128.61/16.90 ((
% 128.61/16.90 (breln1compEex) =>
% 128.61/16.90 ((
% 128.61/16.90 (!!) @ (
% 128.61/16.90 (('#B') @ (
% 128.61/16.90 !!) @
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ('#S') @ (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 '#S') @
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 =>))) @
% 128.61/16.90 breln1)))) @
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 !!))) @
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ('#S') @ (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 '#B') @
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 '#S') @
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 =>))) @
% 128.61/16.90 breln1)))))) @
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ('#C') @ (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 '#B') @
% 128.61/16.90 (
% 128.61/16.90 (
% 128.61/16.90 ('#B') @ (
% 128.61/16.90 '#B') @
% 128.61/16.90 breln1)))) @
% 128.61/16.90 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.61/16.90 inference('rw', [status(thm)], [zip_derived_cl1, '0', '1', '2', '3'])).
% 128.61/16.90 thf(zip_derived_cl3, plain,
% 128.61/16.90 (~ (((setextAx) =>
% 128.61/16.90 (((emptysetAx) =>
% 128.61/16.90 (((setadjoinAx) =>
% 128.61/16.90 (((powersetAx) =>
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% 128.61/16.90 (((in @ emptyset @ omega) =>
% 128.61/16.90 (((omegaSAx) =>
% 128.61/16.90 (((omegaIndAx) =>
% 128.61/16.90 (((replAx) =>
% 128.61/16.90 (((foundationAx) =>
% 128.61/16.90 (((wellorderingAx) =>
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% 128.61/16.90 (((dsetconstrI) =>
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% 128.61/16.90 (((dsetconstrER) =>
% 128.61/16.90 (((exuE1) =>
% 128.61/16.90 (((prop2setE) =>
% 128.61/16.90 (((emptysetE) =>
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% 128.61/16.90 (((notinemptyset) =>
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% 128.61/16.90 (((noeltsimpempty) =>
% 128.61/16.90 (((setbeta) =>
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% 128.61/16.90 (setadjoin @
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% 128.61/16.90 ((
% 128.61/16.90 (setadjoinE) =>
% 128.61/16.90 ((
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% 128.61/16.90 ((
% 128.61/16.90 (setoftrueEq) =>
% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
% 128.61/16.90 (emptyInPowerset) =>
% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
% 128.61/16.90 (setunionE) =>
% 128.61/16.90 ((
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% 128.61/16.90 ((
% 128.61/16.90 (exuE2) =>
% 128.61/16.90 ((
% 128.61/16.90 (nonemptyImpWitness) =>
% 128.61/16.90 ((
% 128.61/16.90 (uniqinunit) =>
% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
% 128.61/16.90 (quantDeMorgan3) =>
% 128.61/16.90 ((
% 128.61/16.90 (quantDeMorgan4) =>
% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
% 128.61/16.90 (in__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuE3u) =>
% 128.61/16.90 ((
% 128.61/16.90 (exu__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (setadjoin__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (powerset__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (setunion__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (exuEu) =>
% 128.61/16.90 ((
% 128.61/16.90 (descr__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (dsetconstr__Cong) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (eqimpsubset2) =>
% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
% 128.61/16.90 (subsetRefl) =>
% 128.61/16.90 ((
% 128.61/16.90 (subsetTrans) =>
% 128.61/16.90 ((
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% 128.61/16.90 ((
% 128.61/16.90 (setadjoinSub2) =>
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
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% 128.61/16.90 ((
% 128.61/16.90 (upairset2IR) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionIR) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionEcases) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionE) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionLsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (binunionRsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectI) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset5) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectEL) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectLsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset2) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset3) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectER) =>
% 128.61/16.90 ((
% 128.61/16.90 (disjointsetsI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectRsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset4) =>
% 128.61/16.90 ((
% 128.61/16.90 (binintersectSubset1) =>
% 128.61/16.90 ((
% 128.61/16.90 (bs114d) =>
% 128.61/16.90 ((
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% 128.61/16.90 ((
% 128.61/16.90 (setminusEL) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusER) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusSubset2) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusERneg) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusELneg) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusILneg) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusIRneg) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusLsub) =>
% 128.61/16.90 ((
% 128.61/16.90 (setminusSubset1) =>
% 128.61/16.90 ((
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% 128.61/16.90 ((
% 128.61/16.90 (symdiffI1) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffI2) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffIneg1) =>
% 128.61/16.90 ((
% 128.61/16.90 (symdiffIneg2) =>
% 128.61/16.90 ((
% 128.61/16.90 (secondinupair) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairIL) =>
% 128.61/16.90 ((
% 128.61/16.90 (setukpairIR) =>
% 128.61/16.90 ((
% 128.61/16.90 (kpairiskpair) =>
% 128.61/16.90 ((
% 128.61/16.90 (kpairp) =>
% 128.61/16.90 ((
% 128.77/16.90 (singletonsubset) =>
% 128.77/16.90 ((
% 128.77/16.90 (singletoninpowerset) =>
% 128.77/16.90 ((
% 128.77/16.90 (singletoninpowunion) =>
% 128.77/16.90 ((
% 128.77/16.90 (upairset2E) =>
% 128.77/16.90 ((
% 128.77/16.90 (upairsubunion) =>
% 128.77/16.90 ((
% 128.77/16.90 (upairinpowunion) =>
% 128.77/16.90 ((
% 128.77/16.90 (ubforcartprodlem1) =>
% 128.77/16.90 ((
% 128.77/16.90 (ubforcartprodlem2) =>
% 128.77/16.90 ((
% 128.77/16.90 (ubforcartprodlem3) =>
% 128.77/16.90 ((
% 128.77/16.90 (cartprodpairin) =>
% 128.77/16.90 ((
% 128.77/16.90 (cartprodmempair1) =>
% 128.77/16.90 ((
% 128.77/16.90 (cartprodmempair) =>
% 128.77/16.90 ((
% 128.77/16.90 (setunionE2) =>
% 128.77/16.90 ((
% 128.77/16.90 (setunionsingleton1) =>
% 128.77/16.90 ((
% 128.77/16.90 (setunionsingleton2) =>
% 128.77/16.90 ((
% 128.77/16.90 (setunionsingleton) =>
% 128.77/16.90 ((
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% 128.77/16.90 (ex1E1) =>
% 128.77/16.90 ((
% 128.77/16.90 (ex1I) =>
% 128.77/16.90 ((
% 128.77/16.90 (ex1I2) =>
% 128.77/16.90 ((
% 128.77/16.90 (singletonsuniq) =>
% 128.77/16.90 ((
% 128.77/16.90 (setukpairinjL1) =>
% 128.77/16.90 ((
% 128.77/16.90 (kfstsingleton) =>
% 128.77/16.90 ((
% 128.77/16.90 (theprop) =>
% 128.77/16.90 ((
% 128.77/16.90 (kfstpairEq) =>
% 128.77/16.90 ((
% 128.77/16.90 (cartprodfstin) =>
% 128.77/16.90 ((
% 128.77/16.90 (setukpairinjL2) =>
% 128.77/16.90 ((
% 128.77/16.90 (setukpairinjL) =>
% 128.77/16.90 ((
% 128.77/16.90 (setukpairinjR11) =>
% 128.77/16.90 ((
% 128.77/16.90 (setukpairinjR12) =>
% 128.77/16.90 ((
% 128.77/16.90 (setukpairinjR1) =>
% 128.77/16.90 ((
% 128.77/16.90 (upairequniteq) =>
% 128.77/16.90 ((
% 128.77/16.90 (setukpairinjR2) =>
% 128.77/16.90 ((
% 128.77/16.90 (setukpairinjR) =>
% 128.77/16.90 ((
% 128.77/16.90 (ksndsingleton) =>
% 128.77/16.90 ((
% 128.77/16.90 (ksndpairEq) =>
% 128.77/16.90 ((
% 128.77/16.90 (kpairsurjEq) =>
% 128.77/16.90 ((
% 128.77/16.90 (cartprodsndin) =>
% 128.77/16.90 ((
% 128.77/16.90 (cartprodpairmemEL) =>
% 128.77/16.90 ((
% 128.77/16.90 (cartprodpairmemER) =>
% 128.77/16.90 ((
% 128.77/16.90 (cartprodmempaircEq) =>
% 128.77/16.90 ((
% 128.77/16.90 (cartprodfstpairEq) =>
% 128.77/16.90 ((
% 128.77/16.90 (cartprodsndpairEq) =>
% 128.77/16.90 ((
% 128.77/16.90 (cartprodpairsurjEq) =>
% 128.77/16.90 ((
% 128.77/16.90 (dpsetconstrI) =>
% 128.77/16.90 ((
% 128.77/16.90 (dpsetconstrSub) =>
% 128.77/16.90 ((
% 128.77/16.90 (setOfPairsIsBReln) =>
% 128.77/16.90 ((
% 128.77/16.90 (dpsetconstrERa) =>
% 128.77/16.90 ((
% 128.77/16.90 (dpsetconstrEL1) =>
% 128.77/16.90 ((
% 128.77/16.90 (dpsetconstrEL2) =>
% 128.77/16.90 ((
% 128.77/16.90 (dpsetconstrER) =>
% 128.77/16.90 ((
% 128.77/16.90 (funcImageSingleton) =>
% 128.77/16.90 ((
% 128.77/16.90 (apProp) =>
% 128.77/16.90 ((
% 128.77/16.90 (app) =>
% 128.77/16.90 ((
% 128.77/16.90 (infuncsetfunc) =>
% 128.77/16.90 ((
% 128.77/16.90 (ap2p) =>
% 128.77/16.90 ((
% 128.77/16.90 (funcinfuncset) =>
% 128.77/16.90 ((
% 128.77/16.90 (lamProp) =>
% 128.77/16.90 ((
% 128.77/16.90 (lamp) =>
% 128.77/16.90 ((
% 128.77/16.90 (lam2p) =>
% 128.77/16.90 ((
% 128.77/16.90 (brelnall1) =>
% 128.77/16.90 ((
% 128.77/16.90 (brelnall2) =>
% 128.77/16.90 ((
% 128.77/16.90 (ex1E2) =>
% 128.77/16.90 ((
% 128.77/16.90 (funcGraphProp1) =>
% 128.77/16.90 ((
% 128.77/16.90 (funcGraphProp3) =>
% 128.77/16.90 ((
% 128.77/16.90 (funcGraphProp2) =>
% 128.77/16.90 ((
% 128.77/16.90 (funcextLem) =>
% 128.77/16.90 ((
% 128.77/16.90 (funcGraphProp4) =>
% 128.77/16.90 ((
% 128.77/16.90 (subbreln) =>
% 128.77/16.90 ((
% 128.77/16.90 (eqbreln) =>
% 128.77/16.90 ((
% 128.77/16.90 (funcext) =>
% 128.77/16.90 ((
% 128.77/16.90 (funcext2) =>
% 128.77/16.90 ((
% 128.77/16.90 (ap2apEq1) =>
% 128.77/16.90 ((
% 128.77/16.90 (ap2apEq2) =>
% 128.77/16.90 ((
% 128.77/16.90 (beta1) =>
% 128.77/16.90 ((
% 128.77/16.90 (eta1) =>
% 128.77/16.90 ((
% 128.77/16.90 (lam2lamEq) =>
% 128.77/16.90 ((
% 128.77/16.90 (beta2) =>
% 128.77/16.90 ((
% 128.77/16.90 (eta2) =>
% 128.77/16.90 ((
% 128.77/16.90 (iffalseProp1) =>
% 128.77/16.90 ((
% 128.77/16.90 (iffalseProp2) =>
% 128.77/16.90 ((
% 128.77/16.90 (iftrueProp1) =>
% 128.77/16.90 ((
% 128.77/16.90 (iftrueProp2) =>
% 128.77/16.90 ((
% 128.77/16.90 (ifSingleton) =>
% 128.77/16.90 ((
% 128.77/16.90 (ifp) =>
% 128.77/16.90 ((
% 128.77/16.90 (theeq) =>
% 128.77/16.90 ((
% 128.77/16.90 (iftrue) =>
% 128.77/16.90 ((
% 128.77/16.90 (iffalse) =>
% 128.77/16.90 ((
% 128.77/16.90 (iftrueorfalse) =>
% 128.77/16.90 ((
% 128.77/16.90 (binintersectT_lem) =>
% 128.77/16.90 ((
% 128.77/16.90 (binunionT_lem) =>
% 128.77/16.90 ((
% 128.77/16.90 (powersetT_lem) =>
% 128.77/16.90 ((
% 128.77/16.90 (setminusT_lem) =>
% 128.77/16.90 ((
% 128.77/16.90 (complementT_lem) =>
% 128.77/16.90 ((
% 128.77/16.90 (setextT) =>
% 128.77/16.90 ((
% 128.77/16.90 (subsetTI) =>
% 128.77/16.90 ((
% 128.77/16.90 (powersetTI1) =>
% 128.77/16.90 ((
% 128.77/16.90 (powersetTE1) =>
% 128.77/16.90 ((
% 128.77/16.90 (complementTI1) =>
% 128.77/16.90 ((
% 128.77/16.90 (complementTE1) =>
% 128.77/16.90 ((
% 128.77/16.90 (binintersectTELcontra) =>
% 128.77/16.90 ((
% 128.77/16.90 (binintersectTERcontra) =>
% 128.77/16.90 ((
% 128.77/16.90 (contrasubsetT) =>
% 128.77/16.90 ((
% 128.77/16.90 (contrasubsetT1) =>
% 128.77/16.90 ((
% 128.77/16.90 (contrasubsetT2) =>
% 128.77/16.90 ((
% 128.77/16.90 (contrasubsetT3) =>
% 128.77/16.90 ((
% 128.77/16.90 (doubleComplementI1) =>
% 128.77/16.90 ((
% 128.77/16.90 (doubleComplementE1) =>
% 128.77/16.90 ((
% 128.77/16.90 (doubleComplementSub1) =>
% 128.77/16.90 ((
% 128.77/16.90 (doubleComplementSub2) =>
% 128.77/16.90 ((
% 128.77/16.90 (doubleComplementEq) =>
% 128.77/16.90 ((
% 128.77/16.90 (complementTnotintersectT) =>
% 128.77/16.90 ((
% 128.77/16.90 (complementImpComplementIntersect) =>
% 128.77/16.90 ((
% 128.77/16.90 (complementSubsetComplementIntersect) =>
% 128.77/16.90 ((
% 128.77/16.90 (complementInPowersetComplementIntersect) =>
% 128.77/16.90 ((
% 128.77/16.90 (contraSubsetComplement) =>
% 128.77/16.90 ((
% 128.77/16.90 (complementTcontraSubset) =>
% 128.77/16.90 ((
% 128.77/16.90 (binunionTILcontra) =>
% 128.77/16.90 ((
% 128.77/16.90 (binunionTIRcontra) =>
% 128.77/16.90 ((
% 128.77/16.90 (inIntersectImpInUnion) =>
% 128.77/16.90 ((
% 128.77/16.90 (inIntersectImpInUnion2) =>
% 128.77/16.90 ((
% 128.77/16.90 (inIntersectImpInIntersectUnions) =>
% 128.77/16.90 ((
% 128.77/16.90 (intersectInPowersetIntersectUnions) =>
% 128.77/16.90 ((
% 128.77/16.90 (inComplementUnionImpNotIn1) =>
% 128.77/16.90 ((
% 128.77/16.90 (inComplementUnionImpInComplement1) =>
% 128.77/16.90 ((
% 128.77/16.90 (binunionTE) =>
% 128.77/16.90 ((
% 128.77/16.90 (binunionTEcontra) =>
% 128.77/16.90 ((
% 128.77/16.90 (demorgan2a1) =>
% 128.77/16.90 ((
% 128.77/16.90 (complementUnionInPowersetComplement) =>
% 128.77/16.90 ((
% 128.77/16.90 (demorgan2a2) =>
% 128.77/16.90 ((
% 128.77/16.90 (demorgan1a) =>
% 128.77/16.90 ((
% 128.77/16.90 (demorgan1b) =>
% 128.77/16.90 ((
% 128.77/16.90 (demorgan1) =>
% 128.77/16.90 ((
% 128.77/16.90 (demorgan2a) =>
% 128.77/16.90 ((
% 128.77/16.90 (demorgan2b2) =>
% 128.77/16.90 ((
% 128.77/16.90 (demorgan2b) =>
% 128.77/16.90 ((
% 128.77/16.90 (demorgan2) =>
% 128.77/16.90 ((
% 128.77/16.90 (woz13rule0) =>
% 128.77/16.90 ((
% 128.77/16.90 (woz13rule1) =>
% 128.77/16.90 ((
% 128.77/16.90 (woz13rule2) =>
% 128.77/16.90 ((
% 128.77/16.90 (woz13rule3) =>
% 128.77/16.90 ((
% 128.77/16.90 (woz13rule4) =>
% 128.77/16.90 ((
% 128.77/16.90 (woz1_1) =>
% 128.77/16.90 ((
% 128.77/16.90 (woz1_2) =>
% 128.77/16.90 ((
% 128.77/16.90 (woz1_3) =>
% 128.77/16.90 ((
% 128.77/16.90 (woz1_4) =>
% 128.77/16.90 ((
% 128.77/16.90 (woz1_5) =>
% 128.77/16.90 ((
% 128.77/16.90 (breln1all2) =>
% 128.77/16.90 ((
% 128.77/16.90 (breln1SetBreln1) =>
% 128.77/16.90 ((
% 128.77/16.90 (choice2fnsingleton) =>
% 128.77/16.90 ((
% 128.77/16.90 (setOfPairsIsBReln1) =>
% 128.77/16.90 ((
% 128.77/16.90 (breln1all1) =>
% 128.77/16.90 ((
% 128.77/16.90 (subbreln1) =>
% 128.77/16.90 ((
% 128.77/16.90 (eqbreln1) =>
% 128.77/16.90 ((
% 128.77/16.90 (breln1invprop) =>
% 128.77/16.90 ((
% 128.77/16.90 (breln1invI) =>
% 128.77/16.90 ((
% 128.77/16.90 (breln1invE) =>
% 128.77/16.90 ((
% 128.77/16.90 (breln1compprop) =>
% 128.77/16.90 ((
% 128.77/16.90 (breln1compI) =>
% 128.77/16.90 ((
% 128.77/16.90 (breln1compE) =>
% 128.77/16.90 ((
% 128.77/16.90 (breln1compEex) =>
% 128.77/16.90 ((
% 128.77/16.90 (!!) @ (
% 128.77/16.90 (('#B') @ (
% 128.77/16.90 !!) @
% 128.77/16.90 (
% 128.77/16.90 (
% 128.77/16.90 ('#S') @ (
% 128.77/16.90 (
% 128.77/16.90 ('#B') @ (
% 128.77/16.90 '#S') @
% 128.77/16.90 (
% 128.77/16.90 (
% 128.77/16.90 ('#B') @ (
% 128.77/16.90 (
% 128.77/16.90 ('#B') @ (
% 128.77/16.90 =>))) @
% 128.77/16.90 breln1)))) @
% 128.77/16.90 (
% 128.77/16.90 (
% 128.77/16.90 ('#B') @ (
% 128.77/16.90 (
% 128.77/16.90 ('#B') @ (
% 128.77/16.90 !!))) @
% 128.77/16.90 (
% 128.77/16.90 (
% 128.77/16.90 ('#S') @ (
% 128.77/16.90 (
% 128.77/16.90 ('#B') @ (
% 128.77/16.90 '#B') @
% 128.77/16.90 (
% 128.77/16.90 (
% 128.77/16.90 ('#B') @ (
% 128.77/16.90 '#S') @
% 128.77/16.90 (
% 128.77/16.90 (
% 128.77/16.90 ('#B') @ (
% 128.77/16.90 (
% 128.77/16.90 ('#B') @ (
% 128.77/16.90 =>))) @
% 128.77/16.90 breln1)))))) @
% 128.77/16.90 (
% 128.77/16.90 (
% 128.77/16.90 ('#C') @ (
% 128.77/16.90 (
% 128.77/16.90 ('#B') @ (
% 128.77/16.90 '#B') @
% 128.77/16.90 (
% 128.77/16.90 (
% 128.77/16.90 ('#B') @ (
% 128.77/16.90 '#B') @
% 128.77/16.90 breln1)))) @
% 128.77/16.90 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.77/16.90 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl2])).
% 128.77/16.90 thf(zip_derived_cl5, plain,
% 128.77/16.90 (~ (((emptysetAx) =>
% 128.77/16.90 (((setadjoinAx) =>
% 128.77/16.90 (((powersetAx) =>
% 128.77/16.90 (((setunionAx) =>
% 128.77/16.90 (((in @ emptyset @ omega) =>
% 128.77/16.90 (((omegaSAx) =>
% 128.77/16.90 (((omegaIndAx) =>
% 128.77/16.90 (((replAx) =>
% 128.77/16.90 (((foundationAx) =>
% 128.77/16.90 (((wellorderingAx) =>
% 128.77/16.90 (((descrp) =>
% 128.77/16.90 (((dsetconstrI) =>
% 128.77/16.90 (((dsetconstrEL) =>
% 128.77/16.90 (((dsetconstrER) =>
% 128.77/16.90 (((exuE1) =>
% 128.77/16.90 (((prop2setE) =>
% 128.77/16.90 (((emptysetE) =>
% 128.77/16.90 (((emptysetimpfalse) =>
% 128.77/16.90 (((notinemptyset) =>
% 128.77/16.90 (((exuE3e) =>
% 128.77/16.90 (((setext) =>
% 128.77/16.90 (((emptyI) =>
% 128.77/16.90 (((noeltsimpempty) =>
% 128.77/16.90 (((setbeta) =>
% 128.77/16.90 (((nonemptyE1) =>
% 128.77/16.90 (((nonemptyI) =>
% 128.77/16.90 (((nonemptyI1) =>
% 128.77/16.90 (((setadjoinIL) =>
% 128.77/16.90 (((in @
% 128.77/16.90 emptyset @
% 128.77/16.90 (setadjoin @
% 128.77/16.90 emptyset @
% 128.77/16.90 emptyset)) =>
% 128.77/16.90 (((setadjoinIR) =>
% 128.77/16.90 ((
% 128.77/16.90 (setadjoinE) =>
% 128.77/16.90 ((
% 128.77/16.90 (setadjoinOr) =>
% 128.77/16.90 ((
% 128.77/16.90 (setoftrueEq) =>
% 128.77/16.90 ((
% 128.77/16.90 (powersetI) =>
% 128.77/16.90 ((
% 128.77/16.90 (emptyinPowerset) =>
% 128.77/16.90 ((
% 128.77/16.90 (emptyInPowerset) =>
% 128.77/16.90 ((
% 128.77/16.90 (powersetE) =>
% 128.77/16.90 ((
% 128.77/16.90 (setunionI) =>
% 128.77/16.90 ((
% 128.77/16.90 (setunionE) =>
% 128.77/16.90 ((
% 128.77/16.90 (subPowSU) =>
% 128.77/16.90 ((
% 128.77/16.90 (exuE2) =>
% 128.77/16.90 ((
% 128.77/16.90 (nonemptyImpWitness) =>
% 128.77/16.90 ((
% 128.77/16.90 (uniqinunit) =>
% 128.77/16.90 ((
% 128.77/16.90 (notinsingleton) =>
% 128.77/16.90 ((
% 128.77/16.90 (eqinunit) =>
% 128.77/16.90 ((
% 128.77/16.90 (singletonsswitch) =>
% 128.77/16.90 ((
% 128.77/16.90 (upairsetE) =>
% 128.77/16.90 ((
% 128.77/16.90 (upairsetIL) =>
% 128.77/16.90 ((
% 128.77/16.90 (upairsetIR) =>
% 128.77/16.90 ((
% 128.77/16.90 (emptyE1) =>
% 128.77/16.90 ((
% 128.77/16.90 (vacuousDall) =>
% 128.77/16.90 ((
% 128.77/16.90 (quantDeMorgan1) =>
% 128.77/16.90 ((
% 128.77/16.90 (quantDeMorgan2) =>
% 128.77/16.90 ((
% 128.77/16.90 (quantDeMorgan3) =>
% 128.77/16.90 ((
% 128.77/16.90 (quantDeMorgan4) =>
% 128.77/16.90 ((
% 128.77/16.90 (prop2setI) =>
% 128.77/16.90 ((
% 128.77/16.90 (prop2set2propI) =>
% 128.77/16.90 ((
% 128.77/16.90 (notdexE) =>
% 128.77/16.90 ((
% 128.77/16.90 (notdallE) =>
% 128.77/16.90 ((
% 128.77/16.90 (exuI1) =>
% 128.77/16.90 ((
% 128.77/16.90 (exuI3) =>
% 128.77/16.90 ((
% 128.77/16.90 (exuI2) =>
% 128.77/16.90 ((
% 128.77/16.90 (inCongP) =>
% 128.77/16.90 ((
% 128.77/16.90 (in__Cong) =>
% 128.77/16.90 ((
% 128.77/16.90 (exuE3u) =>
% 128.77/16.90 ((
% 128.77/16.90 (exu__Cong) =>
% 128.77/16.90 ((
% 128.77/16.90 (setadjoin__Cong) =>
% 128.77/16.90 ((
% 128.77/16.90 (powerset__Cong) =>
% 128.77/16.90 ((
% 128.77/16.90 (setunion__Cong) =>
% 128.77/16.90 ((
% 128.77/16.90 (exuEu) =>
% 128.77/16.90 ((
% 128.77/16.90 (descr__Cong) =>
% 128.77/16.90 ((
% 128.77/16.90 (dsetconstr__Cong) =>
% 128.77/16.90 ((
% 128.77/16.90 (subsetI1) =>
% 128.77/16.90 ((
% 128.77/16.90 (eqimpsubset2) =>
% 128.77/16.90 ((
% 128.77/16.90 (eqimpsubset1) =>
% 128.77/16.90 ((
% 128.77/16.90 (subsetI2) =>
% 128.77/16.90 ((
% 128.77/16.90 (emptysetsubset) =>
% 128.77/16.90 ((
% 128.77/16.90 (subsetE) =>
% 128.77/16.90 ((
% 128.77/16.90 (subsetE2) =>
% 128.77/16.90 ((
% 128.77/16.90 (notsubsetI) =>
% 128.77/16.90 ((
% 128.77/16.90 (notequalI1) =>
% 128.77/16.90 ((
% 128.77/16.90 (notequalI2) =>
% 128.77/16.90 ((
% 128.77/16.90 (subsetRefl) =>
% 128.77/16.90 ((
% 128.77/16.90 (subsetTrans) =>
% 128.77/16.90 ((
% 128.77/16.90 (setadjoinSub) =>
% 128.77/16.90 ((
% 128.77/16.90 (setadjoinSub2) =>
% 128.77/16.90 ((
% 128.77/16.90 (subset2powerset) =>
% 128.77/16.90 ((
% 128.77/16.90 (setextsub) =>
% 128.77/16.90 ((
% 128.77/16.90 (subsetemptysetimpeq) =>
% 128.77/16.90 ((
% 128.77/16.90 (powersetI1) =>
% 128.77/16.90 ((
% 128.77/16.90 (powersetE1) =>
% 128.77/16.90 ((
% 128.77/16.90 (inPowerset) =>
% 128.77/16.90 ((
% 128.77/16.90 (powersetsubset) =>
% 128.77/16.90 ((
% 128.77/16.90 (sepInPowerset) =>
% 128.77/16.90 ((
% 128.77/16.90 (sepSubset) =>
% 128.77/16.90 ((
% 128.77/16.90 (binunionIL) =>
% 128.77/16.90 ((
% 128.77/16.90 (upairset2IR) =>
% 128.77/16.90 ((
% 128.77/16.90 (binunionIR) =>
% 128.77/16.90 ((
% 128.77/16.90 (binunionEcases) =>
% 128.77/16.90 ((
% 128.77/16.90 (binunionE) =>
% 128.77/16.90 ((
% 128.77/16.90 (binunionLsub) =>
% 128.77/16.90 ((
% 128.77/16.90 (binunionRsub) =>
% 128.77/16.90 ((
% 128.77/16.90 (binintersectI) =>
% 128.77/16.90 ((
% 128.77/16.90 (binintersectSubset5) =>
% 128.77/16.90 ((
% 128.77/16.90 (binintersectEL) =>
% 128.77/16.90 ((
% 128.77/16.90 (binintersectLsub) =>
% 128.77/16.90 ((
% 128.77/16.90 (binintersectSubset2) =>
% 128.77/16.90 ((
% 128.77/16.90 (binintersectSubset3) =>
% 128.77/16.90 ((
% 128.77/16.90 (binintersectER) =>
% 128.77/16.90 ((
% 128.77/16.90 (disjointsetsI1) =>
% 128.77/16.90 ((
% 128.77/16.90 (binintersectRsub) =>
% 128.77/16.90 ((
% 128.77/16.90 (binintersectSubset4) =>
% 128.77/16.90 ((
% 128.77/16.90 (binintersectSubset1) =>
% 128.77/16.90 ((
% 128.77/16.90 (bs114d) =>
% 128.77/16.90 ((
% 128.77/16.90 (setminusI) =>
% 128.77/16.90 ((
% 128.77/16.90 (setminusEL) =>
% 128.77/16.90 ((
% 128.77/16.90 (setminusER) =>
% 128.77/16.90 ((
% 128.77/16.90 (setminusSubset2) =>
% 128.77/16.90 ((
% 128.77/16.90 (setminusERneg) =>
% 128.77/16.90 ((
% 128.77/16.90 (setminusELneg) =>
% 128.77/16.90 ((
% 128.77/16.90 (setminusILneg) =>
% 128.77/16.90 ((
% 128.77/16.90 (setminusIRneg) =>
% 128.77/16.90 ((
% 128.77/16.90 (setminusLsub) =>
% 128.77/16.90 ((
% 128.77/16.90 (setminusSubset1) =>
% 128.77/16.90 ((
% 128.77/16.90 (symdiffE) =>
% 128.77/16.90 ((
% 128.77/16.90 (symdiffI1) =>
% 128.77/16.90 ((
% 128.77/16.90 (symdiffI2) =>
% 128.77/16.90 ((
% 128.77/16.90 (symdiffIneg1) =>
% 128.77/16.90 ((
% 128.77/16.90 (symdiffIneg2) =>
% 128.77/16.90 ((
% 128.77/16.90 (secondinupair) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairIL) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairIR) =>
% 128.77/16.91 ((
% 128.77/16.91 (kpairiskpair) =>
% 128.77/16.91 ((
% 128.77/16.91 (kpairp) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonsubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletoninpowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletoninpowunion) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairset2E) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsubunion) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairinpowunion) =>
% 128.77/16.91 ((
% 128.77/16.91 (ubforcartprodlem1) =>
% 128.77/16.91 ((
% 128.77/16.91 (ubforcartprodlem2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ubforcartprodlem3) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairin) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodmempair1) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodmempair) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionE2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionsingleton1) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionsingleton2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1E1) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1I) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1I2) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonsuniq) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjL1) =>
% 128.77/16.91 ((
% 128.77/16.91 (kfstsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (theprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (kfstpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodfstin) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjL2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjL) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR11) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR12) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR1) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairequniteq) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR) =>
% 128.77/16.91 ((
% 128.77/16.91 (ksndsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (ksndpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (kpairsurjEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodsndin) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairmemEL) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairmemER) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodmempaircEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodfstpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodsndpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairsurjEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrI) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrSub) =>
% 128.77/16.91 ((
% 128.77/16.91 (setOfPairsIsBReln) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrERa) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrEL1) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrEL2) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrER) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcImageSingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (apProp) =>
% 128.77/16.91 ((
% 128.77/16.91 (app) =>
% 128.77/16.91 ((
% 128.77/16.91 (infuncsetfunc) =>
% 128.77/16.91 ((
% 128.77/16.91 (ap2p) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcinfuncset) =>
% 128.77/16.91 ((
% 128.77/16.91 (lamProp) =>
% 128.77/16.91 ((
% 128.77/16.91 (lamp) =>
% 128.77/16.91 ((
% 128.77/16.91 (lam2p) =>
% 128.77/16.91 ((
% 128.77/16.91 (brelnall1) =>
% 128.77/16.91 ((
% 128.77/16.91 (brelnall2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1E2) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp1) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp3) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp2) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcextLem) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp4) =>
% 128.77/16.91 ((
% 128.77/16.91 (subbreln) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqbreln) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcext) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcext2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ap2apEq1) =>
% 128.77/16.91 ((
% 128.77/16.91 (ap2apEq2) =>
% 128.77/16.91 ((
% 128.77/16.91 (beta1) =>
% 128.77/16.91 ((
% 128.77/16.91 (eta1) =>
% 128.77/16.91 ((
% 128.77/16.91 (lam2lamEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (beta2) =>
% 128.77/16.91 ((
% 128.77/16.91 (eta2) =>
% 128.77/16.91 ((
% 128.77/16.91 (iffalseProp1) =>
% 128.77/16.91 ((
% 128.77/16.91 (iffalseProp2) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrueProp1) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrueProp2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ifSingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (ifp) =>
% 128.77/16.91 ((
% 128.77/16.91 (theeq) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrue) =>
% 128.77/16.91 ((
% 128.77/16.91 (iffalse) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrueorfalse) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (setextT) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetTI) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetTI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetTE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectTELcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectTERcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT1) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT2) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT3) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementSub1) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementSub2) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTnotintersectT) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementImpComplementIntersect) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementSubsetComplementIntersect) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementInPowersetComplementIntersect) =>
% 128.77/16.91 ((
% 128.77/16.91 (contraSubsetComplement) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTcontraSubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTILcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTIRcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (inIntersectImpInUnion) =>
% 128.77/16.91 ((
% 128.77/16.91 (inIntersectImpInUnion2) =>
% 128.77/16.91 ((
% 128.77/16.91 (inIntersectImpInIntersectUnions) =>
% 128.77/16.91 ((
% 128.77/16.91 (intersectInPowersetIntersectUnions) =>
% 128.77/16.91 ((
% 128.77/16.91 (inComplementUnionImpNotIn1) =>
% 128.77/16.91 ((
% 128.77/16.91 (inComplementUnionImpInComplement1) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTE) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTEcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2a1) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementUnionInPowersetComplement) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2a2) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan1a) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan1b) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan1) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2a) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2b2) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2b) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule0) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule1) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule2) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule3) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule4) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_1) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_2) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_3) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_4) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_5) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1all2) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1SetBreln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (choice2fnsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (setOfPairsIsBReln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1all1) =>
% 128.77/16.91 ((
% 128.77/16.91 (subbreln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqbreln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1invprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1invI) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1invE) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compI) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compE) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compEex) =>
% 128.77/16.91 ((
% 128.77/16.91 (!!) @ (
% 128.77/16.91 (('#B') @ (
% 128.77/16.91 !!) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#S') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#S') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 =>))) @
% 128.77/16.91 breln1)))) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 !!))) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#S') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#B') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#S') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 =>))) @
% 128.77/16.91 breln1)))))) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#C') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#B') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#B') @
% 128.77/16.91 breln1)))) @
% 128.77/16.91 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.77/16.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])).
% 128.77/16.91 thf(zip_derived_cl8, plain,
% 128.77/16.91 (~ (((setadjoinAx) =>
% 128.77/16.91 (((powersetAx) =>
% 128.77/16.91 (((setunionAx) =>
% 128.77/16.91 (((in @ emptyset @ omega) =>
% 128.77/16.91 (((omegaSAx) =>
% 128.77/16.91 (((omegaIndAx) =>
% 128.77/16.91 (((replAx) =>
% 128.77/16.91 (((foundationAx) =>
% 128.77/16.91 (((wellorderingAx) =>
% 128.77/16.91 (((descrp) =>
% 128.77/16.91 (((dsetconstrI) =>
% 128.77/16.91 (((dsetconstrEL) =>
% 128.77/16.91 (((dsetconstrER) =>
% 128.77/16.91 (((exuE1) =>
% 128.77/16.91 (((prop2setE) =>
% 128.77/16.91 (((emptysetE) =>
% 128.77/16.91 (((emptysetimpfalse) =>
% 128.77/16.91 (((notinemptyset) =>
% 128.77/16.91 (((exuE3e) =>
% 128.77/16.91 (((setext) =>
% 128.77/16.91 (((emptyI) =>
% 128.77/16.91 (((noeltsimpempty) =>
% 128.77/16.91 (((setbeta) =>
% 128.77/16.91 (((nonemptyE1) =>
% 128.77/16.91 (((nonemptyI) =>
% 128.77/16.91 (((nonemptyI1) =>
% 128.77/16.91 (((setadjoinIL) =>
% 128.77/16.91 (((in @
% 128.77/16.91 emptyset @
% 128.77/16.91 (setadjoin @
% 128.77/16.91 emptyset @
% 128.77/16.91 emptyset)) =>
% 128.77/16.91 (((setadjoinIR) =>
% 128.77/16.91 (((setadjoinE) =>
% 128.77/16.91 ((
% 128.77/16.91 (setadjoinOr) =>
% 128.77/16.91 ((
% 128.77/16.91 (setoftrueEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetI) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptyinPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptyInPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetE) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionI) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionE) =>
% 128.77/16.91 ((
% 128.77/16.91 (subPowSU) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuE2) =>
% 128.77/16.91 ((
% 128.77/16.91 (nonemptyImpWitness) =>
% 128.77/16.91 ((
% 128.77/16.91 (uniqinunit) =>
% 128.77/16.91 ((
% 128.77/16.91 (notinsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqinunit) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonsswitch) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsetE) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsetIL) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsetIR) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptyE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (vacuousDall) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan1) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan2) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan3) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan4) =>
% 128.77/16.91 ((
% 128.77/16.91 (prop2setI) =>
% 128.77/16.91 ((
% 128.77/16.91 (prop2set2propI) =>
% 128.77/16.91 ((
% 128.77/16.91 (notdexE) =>
% 128.77/16.91 ((
% 128.77/16.91 (notdallE) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuI3) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuI2) =>
% 128.77/16.91 ((
% 128.77/16.91 (inCongP) =>
% 128.77/16.91 ((
% 128.77/16.91 (in__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuE3u) =>
% 128.77/16.91 ((
% 128.77/16.91 (exu__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (setadjoin__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (powerset__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunion__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuEu) =>
% 128.77/16.91 ((
% 128.77/16.91 (descr__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (dsetconstr__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqimpsubset2) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqimpsubset1) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetI2) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptysetsubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetE) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetE2) =>
% 128.77/16.91 ((
% 128.77/16.91 (notsubsetI) =>
% 128.77/16.91 ((
% 128.77/16.91 (notequalI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (notequalI2) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetRefl) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetTrans) =>
% 128.77/16.91 ((
% 128.77/16.91 (setadjoinSub) =>
% 128.77/16.91 ((
% 128.77/16.91 (setadjoinSub2) =>
% 128.77/16.91 ((
% 128.77/16.91 (subset2powerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (setextsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetemptysetimpeq) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (inPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetsubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (sepInPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (sepSubset) =>
% 128.77/16.91 ((
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% 128.77/16.91 ((
% 128.77/16.91 (upairset2IR) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionIR) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionEcases) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionE) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionLsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionRsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectI) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset5) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectEL) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectLsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset2) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset3) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectER) =>
% 128.77/16.91 ((
% 128.77/16.91 (disjointsetsI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectRsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset4) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset1) =>
% 128.77/16.91 ((
% 128.77/16.91 (bs114d) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusI) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusEL) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusER) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusSubset2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusERneg) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusELneg) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusILneg) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusIRneg) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusLsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusSubset1) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffE) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffI2) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffIneg1) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffIneg2) =>
% 128.77/16.91 ((
% 128.77/16.91 (secondinupair) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairIL) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairIR) =>
% 128.77/16.91 ((
% 128.77/16.91 (kpairiskpair) =>
% 128.77/16.91 ((
% 128.77/16.91 (kpairp) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonsubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletoninpowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletoninpowunion) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairset2E) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsubunion) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairinpowunion) =>
% 128.77/16.91 ((
% 128.77/16.91 (ubforcartprodlem1) =>
% 128.77/16.91 ((
% 128.77/16.91 (ubforcartprodlem2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ubforcartprodlem3) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairin) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodmempair1) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodmempair) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionE2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionsingleton1) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionsingleton2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1E1) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1I) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1I2) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonsuniq) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjL1) =>
% 128.77/16.91 ((
% 128.77/16.91 (kfstsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (theprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (kfstpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodfstin) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjL2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjL) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR11) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR12) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR1) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairequniteq) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR) =>
% 128.77/16.91 ((
% 128.77/16.91 (ksndsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (ksndpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (kpairsurjEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodsndin) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairmemEL) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairmemER) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodmempaircEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodfstpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodsndpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairsurjEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrI) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrSub) =>
% 128.77/16.91 ((
% 128.77/16.91 (setOfPairsIsBReln) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrERa) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrEL1) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrEL2) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrER) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcImageSingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (apProp) =>
% 128.77/16.91 ((
% 128.77/16.91 (app) =>
% 128.77/16.91 ((
% 128.77/16.91 (infuncsetfunc) =>
% 128.77/16.91 ((
% 128.77/16.91 (ap2p) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcinfuncset) =>
% 128.77/16.91 ((
% 128.77/16.91 (lamProp) =>
% 128.77/16.91 ((
% 128.77/16.91 (lamp) =>
% 128.77/16.91 ((
% 128.77/16.91 (lam2p) =>
% 128.77/16.91 ((
% 128.77/16.91 (brelnall1) =>
% 128.77/16.91 ((
% 128.77/16.91 (brelnall2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1E2) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp1) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp3) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp2) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcextLem) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp4) =>
% 128.77/16.91 ((
% 128.77/16.91 (subbreln) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqbreln) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcext) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcext2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ap2apEq1) =>
% 128.77/16.91 ((
% 128.77/16.91 (ap2apEq2) =>
% 128.77/16.91 ((
% 128.77/16.91 (beta1) =>
% 128.77/16.91 ((
% 128.77/16.91 (eta1) =>
% 128.77/16.91 ((
% 128.77/16.91 (lam2lamEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (beta2) =>
% 128.77/16.91 ((
% 128.77/16.91 (eta2) =>
% 128.77/16.91 ((
% 128.77/16.91 (iffalseProp1) =>
% 128.77/16.91 ((
% 128.77/16.91 (iffalseProp2) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrueProp1) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrueProp2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ifSingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (ifp) =>
% 128.77/16.91 ((
% 128.77/16.91 (theeq) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrue) =>
% 128.77/16.91 ((
% 128.77/16.91 (iffalse) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrueorfalse) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (setextT) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetTI) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetTI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetTE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectTELcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectTERcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT1) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT2) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT3) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementSub1) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementSub2) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTnotintersectT) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementImpComplementIntersect) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementSubsetComplementIntersect) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementInPowersetComplementIntersect) =>
% 128.77/16.91 ((
% 128.77/16.91 (contraSubsetComplement) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTcontraSubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTILcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTIRcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (inIntersectImpInUnion) =>
% 128.77/16.91 ((
% 128.77/16.91 (inIntersectImpInUnion2) =>
% 128.77/16.91 ((
% 128.77/16.91 (inIntersectImpInIntersectUnions) =>
% 128.77/16.91 ((
% 128.77/16.91 (intersectInPowersetIntersectUnions) =>
% 128.77/16.91 ((
% 128.77/16.91 (inComplementUnionImpNotIn1) =>
% 128.77/16.91 ((
% 128.77/16.91 (inComplementUnionImpInComplement1) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTE) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTEcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2a1) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementUnionInPowersetComplement) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2a2) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan1a) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan1b) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan1) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2a) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2b2) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2b) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule0) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule1) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule2) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule3) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule4) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_1) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_2) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_3) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_4) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_5) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1all2) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1SetBreln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (choice2fnsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (setOfPairsIsBReln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1all1) =>
% 128.77/16.91 ((
% 128.77/16.91 (subbreln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqbreln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1invprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1invI) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1invE) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compI) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compE) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compEex) =>
% 128.77/16.91 ((
% 128.77/16.91 (!!) @ (
% 128.77/16.91 (('#B') @ (
% 128.77/16.91 !!) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#S') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#S') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 =>))) @
% 128.77/16.91 breln1)))) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 !!))) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#S') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#B') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#S') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 =>))) @
% 128.77/16.91 breln1)))))) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#C') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#B') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#B') @
% 128.77/16.91 breln1)))) @
% 128.77/16.91 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.77/16.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])).
% 128.77/16.91 thf(zip_derived_cl13, plain,
% 128.77/16.91 (~ (((powersetAx) =>
% 128.77/16.91 (((setunionAx) =>
% 128.77/16.91 (((in @ emptyset @ omega) =>
% 128.77/16.91 (((omegaSAx) =>
% 128.77/16.91 (((omegaIndAx) =>
% 128.77/16.91 (((replAx) =>
% 128.77/16.91 (((foundationAx) =>
% 128.77/16.91 (((wellorderingAx) =>
% 128.77/16.91 (((descrp) =>
% 128.77/16.91 (((dsetconstrI) =>
% 128.77/16.91 (((dsetconstrEL) =>
% 128.77/16.91 (((dsetconstrER) =>
% 128.77/16.91 (((exuE1) =>
% 128.77/16.91 (((prop2setE) =>
% 128.77/16.91 (((emptysetE) =>
% 128.77/16.91 (((emptysetimpfalse) =>
% 128.77/16.91 (((notinemptyset) =>
% 128.77/16.91 (((exuE3e) =>
% 128.77/16.91 (((setext) =>
% 128.77/16.91 (((emptyI) =>
% 128.77/16.91 (((noeltsimpempty) =>
% 128.77/16.91 (((setbeta) =>
% 128.77/16.91 (((nonemptyE1) =>
% 128.77/16.91 (((nonemptyI) =>
% 128.77/16.91 (((nonemptyI1) =>
% 128.77/16.91 (((setadjoinIL) =>
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% 128.77/16.91 emptyset @
% 128.77/16.91 (setadjoin @
% 128.77/16.91 emptyset @
% 128.77/16.91 emptyset)) =>
% 128.77/16.91 (((setadjoinIR) =>
% 128.77/16.91 (((setadjoinE) =>
% 128.77/16.91 (((setadjoinOr) =>
% 128.77/16.91 ((
% 128.77/16.91 (setoftrueEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetI) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptyinPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptyInPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetE) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionI) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionE) =>
% 128.77/16.91 ((
% 128.77/16.91 (subPowSU) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuE2) =>
% 128.77/16.91 ((
% 128.77/16.91 (nonemptyImpWitness) =>
% 128.77/16.91 ((
% 128.77/16.91 (uniqinunit) =>
% 128.77/16.91 ((
% 128.77/16.91 (notinsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqinunit) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonsswitch) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsetE) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsetIL) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsetIR) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptyE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (vacuousDall) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan1) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan2) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan3) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan4) =>
% 128.77/16.91 ((
% 128.77/16.91 (prop2setI) =>
% 128.77/16.91 ((
% 128.77/16.91 (prop2set2propI) =>
% 128.77/16.91 ((
% 128.77/16.91 (notdexE) =>
% 128.77/16.91 ((
% 128.77/16.91 (notdallE) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuI3) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuI2) =>
% 128.77/16.91 ((
% 128.77/16.91 (inCongP) =>
% 128.77/16.91 ((
% 128.77/16.91 (in__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuE3u) =>
% 128.77/16.91 ((
% 128.77/16.91 (exu__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (setadjoin__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (powerset__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunion__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuEu) =>
% 128.77/16.91 ((
% 128.77/16.91 (descr__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (dsetconstr__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqimpsubset2) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqimpsubset1) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetI2) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptysetsubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetE) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetE2) =>
% 128.77/16.91 ((
% 128.77/16.91 (notsubsetI) =>
% 128.77/16.91 ((
% 128.77/16.91 (notequalI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (notequalI2) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetRefl) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetTrans) =>
% 128.77/16.91 ((
% 128.77/16.91 (setadjoinSub) =>
% 128.77/16.91 ((
% 128.77/16.91 (setadjoinSub2) =>
% 128.77/16.91 ((
% 128.77/16.91 (subset2powerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (setextsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetemptysetimpeq) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (inPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetsubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (sepInPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (sepSubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionIL) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairset2IR) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionIR) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionEcases) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionE) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionLsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionRsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectI) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset5) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectEL) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectLsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset2) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset3) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectER) =>
% 128.77/16.91 ((
% 128.77/16.91 (disjointsetsI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectRsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset4) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset1) =>
% 128.77/16.91 ((
% 128.77/16.91 (bs114d) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusI) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusEL) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusER) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusSubset2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusERneg) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusELneg) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusILneg) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusIRneg) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusLsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusSubset1) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffE) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffI2) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffIneg1) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffIneg2) =>
% 128.77/16.91 ((
% 128.77/16.91 (secondinupair) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairIL) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairIR) =>
% 128.77/16.91 ((
% 128.77/16.91 (kpairiskpair) =>
% 128.77/16.91 ((
% 128.77/16.91 (kpairp) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonsubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletoninpowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletoninpowunion) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairset2E) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsubunion) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairinpowunion) =>
% 128.77/16.91 ((
% 128.77/16.91 (ubforcartprodlem1) =>
% 128.77/16.91 ((
% 128.77/16.91 (ubforcartprodlem2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ubforcartprodlem3) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairin) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodmempair1) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodmempair) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionE2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionsingleton1) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionsingleton2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1E1) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1I) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1I2) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonsuniq) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjL1) =>
% 128.77/16.91 ((
% 128.77/16.91 (kfstsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (theprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (kfstpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodfstin) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjL2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjL) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR11) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR12) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR1) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairequniteq) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR) =>
% 128.77/16.91 ((
% 128.77/16.91 (ksndsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (ksndpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (kpairsurjEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodsndin) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairmemEL) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairmemER) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodmempaircEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodfstpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodsndpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairsurjEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrI) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrSub) =>
% 128.77/16.91 ((
% 128.77/16.91 (setOfPairsIsBReln) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrERa) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrEL1) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrEL2) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrER) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcImageSingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (apProp) =>
% 128.77/16.91 ((
% 128.77/16.91 (app) =>
% 128.77/16.91 ((
% 128.77/16.91 (infuncsetfunc) =>
% 128.77/16.91 ((
% 128.77/16.91 (ap2p) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcinfuncset) =>
% 128.77/16.91 ((
% 128.77/16.91 (lamProp) =>
% 128.77/16.91 ((
% 128.77/16.91 (lamp) =>
% 128.77/16.91 ((
% 128.77/16.91 (lam2p) =>
% 128.77/16.91 ((
% 128.77/16.91 (brelnall1) =>
% 128.77/16.91 ((
% 128.77/16.91 (brelnall2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1E2) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp1) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp3) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp2) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcextLem) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp4) =>
% 128.77/16.91 ((
% 128.77/16.91 (subbreln) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqbreln) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcext) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcext2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ap2apEq1) =>
% 128.77/16.91 ((
% 128.77/16.91 (ap2apEq2) =>
% 128.77/16.91 ((
% 128.77/16.91 (beta1) =>
% 128.77/16.91 ((
% 128.77/16.91 (eta1) =>
% 128.77/16.91 ((
% 128.77/16.91 (lam2lamEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (beta2) =>
% 128.77/16.91 ((
% 128.77/16.91 (eta2) =>
% 128.77/16.91 ((
% 128.77/16.91 (iffalseProp1) =>
% 128.77/16.91 ((
% 128.77/16.91 (iffalseProp2) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrueProp1) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrueProp2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ifSingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (ifp) =>
% 128.77/16.91 ((
% 128.77/16.91 (theeq) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrue) =>
% 128.77/16.91 ((
% 128.77/16.91 (iffalse) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrueorfalse) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (setextT) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetTI) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetTI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetTE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectTELcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectTERcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT1) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT2) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT3) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementSub1) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementSub2) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTnotintersectT) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementImpComplementIntersect) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementSubsetComplementIntersect) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementInPowersetComplementIntersect) =>
% 128.77/16.91 ((
% 128.77/16.91 (contraSubsetComplement) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTcontraSubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTILcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTIRcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (inIntersectImpInUnion) =>
% 128.77/16.91 ((
% 128.77/16.91 (inIntersectImpInUnion2) =>
% 128.77/16.91 ((
% 128.77/16.91 (inIntersectImpInIntersectUnions) =>
% 128.77/16.91 ((
% 128.77/16.91 (intersectInPowersetIntersectUnions) =>
% 128.77/16.91 ((
% 128.77/16.91 (inComplementUnionImpNotIn1) =>
% 128.77/16.91 ((
% 128.77/16.91 (inComplementUnionImpInComplement1) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTE) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTEcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2a1) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementUnionInPowersetComplement) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2a2) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan1a) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan1b) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan1) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2a) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2b2) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2b) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule0) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule1) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule2) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule3) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule4) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_1) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_2) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_3) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_4) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_5) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1all2) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1SetBreln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (choice2fnsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (setOfPairsIsBReln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1all1) =>
% 128.77/16.91 ((
% 128.77/16.91 (subbreln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqbreln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1invprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1invI) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1invE) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compI) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compE) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compEex) =>
% 128.77/16.91 ((
% 128.77/16.91 (!!) @ (
% 128.77/16.91 (('#B') @ (
% 128.77/16.91 !!) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#S') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#S') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 =>))) @
% 128.77/16.91 breln1)))) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 !!))) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#S') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#B') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#S') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 =>))) @
% 128.77/16.91 breln1)))))) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#C') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#B') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#B') @
% 128.77/16.91 breln1)))) @
% 128.77/16.91 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.77/16.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])).
% 128.77/16.91 thf(zip_derived_cl19, plain,
% 128.77/16.91 (~ (((setunionAx) =>
% 128.77/16.91 (((in @ emptyset @ omega) =>
% 128.77/16.91 (((omegaSAx) =>
% 128.77/16.91 (((omegaIndAx) =>
% 128.77/16.91 (((replAx) =>
% 128.77/16.91 (((foundationAx) =>
% 128.77/16.91 (((wellorderingAx) =>
% 128.77/16.91 (((descrp) =>
% 128.77/16.91 (((dsetconstrI) =>
% 128.77/16.91 (((dsetconstrEL) =>
% 128.77/16.91 (((dsetconstrER) =>
% 128.77/16.91 (((exuE1) =>
% 128.77/16.91 (((prop2setE) =>
% 128.77/16.91 (((emptysetE) =>
% 128.77/16.91 (((emptysetimpfalse) =>
% 128.77/16.91 (((notinemptyset) =>
% 128.77/16.91 (((exuE3e) =>
% 128.77/16.91 (((setext) =>
% 128.77/16.91 (((emptyI) =>
% 128.77/16.91 (((noeltsimpempty) =>
% 128.77/16.91 (((setbeta) =>
% 128.77/16.91 (((nonemptyE1) =>
% 128.77/16.91 (((nonemptyI) =>
% 128.77/16.91 (((nonemptyI1) =>
% 128.77/16.91 (((setadjoinIL) =>
% 128.77/16.91 (((in @ emptyset @
% 128.77/16.91 (setadjoin @
% 128.77/16.91 emptyset @
% 128.77/16.91 emptyset)) =>
% 128.77/16.91 (((setadjoinIR) =>
% 128.77/16.91 (((setadjoinE) =>
% 128.77/16.91 (((setadjoinOr) =>
% 128.77/16.91 (((setoftrueEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetI) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptyinPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptyInPowerset) =>
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% 128.77/16.91 '#B') @
% 128.77/16.91 breln1)))) @
% 128.77/16.91 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.77/16.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])).
% 128.77/16.91 thf(zip_derived_cl25, plain,
% 128.77/16.91 (~ (((in @ emptyset @ omega) =>
% 128.77/16.91 (((omegaSAx) =>
% 128.77/16.91 (((omegaIndAx) =>
% 128.77/16.91 (((replAx) =>
% 128.77/16.91 (((foundationAx) =>
% 128.77/16.91 (((wellorderingAx) =>
% 128.77/16.91 (((descrp) =>
% 128.77/16.91 (((dsetconstrI) =>
% 128.77/16.91 (((dsetconstrEL) =>
% 128.77/16.91 (((dsetconstrER) =>
% 128.77/16.91 (((exuE1) =>
% 128.77/16.91 (((prop2setE) =>
% 128.77/16.91 (((emptysetE) =>
% 128.77/16.91 (((emptysetimpfalse) =>
% 128.77/16.91 (((notinemptyset) =>
% 128.77/16.91 (((exuE3e) =>
% 128.77/16.91 (((setext) =>
% 128.77/16.91 (((emptyI) =>
% 128.77/16.91 (((noeltsimpempty) =>
% 128.77/16.91 (((setbeta) =>
% 128.77/16.91 (((nonemptyE1) =>
% 128.77/16.91 (((nonemptyI) =>
% 128.77/16.91 (((nonemptyI1) =>
% 128.77/16.91 (((setadjoinIL) =>
% 128.77/16.91 (((in @ emptyset @
% 128.77/16.91 (setadjoin @
% 128.77/16.91 emptyset @ emptyset)) =>
% 128.77/16.91 (((setadjoinIR) =>
% 128.77/16.91 (((setadjoinE) =>
% 128.77/16.91 (((setadjoinOr) =>
% 128.77/16.91 (((setoftrueEq) =>
% 128.77/16.91 (((powersetI) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptyinPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptyInPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetE) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionI) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionE) =>
% 128.77/16.91 ((
% 128.77/16.91 (subPowSU) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuE2) =>
% 128.77/16.91 ((
% 128.77/16.91 (nonemptyImpWitness) =>
% 128.77/16.91 ((
% 128.77/16.91 (uniqinunit) =>
% 128.77/16.91 ((
% 128.77/16.91 (notinsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqinunit) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonsswitch) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsetE) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsetIL) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsetIR) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptyE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (vacuousDall) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan1) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan2) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan3) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan4) =>
% 128.77/16.91 ((
% 128.77/16.91 (prop2setI) =>
% 128.77/16.91 ((
% 128.77/16.91 (prop2set2propI) =>
% 128.77/16.91 ((
% 128.77/16.91 (notdexE) =>
% 128.77/16.91 ((
% 128.77/16.91 (notdallE) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuI3) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuI2) =>
% 128.77/16.91 ((
% 128.77/16.91 (inCongP) =>
% 128.77/16.91 ((
% 128.77/16.91 (in__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuE3u) =>
% 128.77/16.91 ((
% 128.77/16.91 (exu__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (setadjoin__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (powerset__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunion__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuEu) =>
% 128.77/16.91 ((
% 128.77/16.91 (descr__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (dsetconstr__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqimpsubset2) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqimpsubset1) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetI2) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptysetsubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetE) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetE2) =>
% 128.77/16.91 ((
% 128.77/16.91 (notsubsetI) =>
% 128.77/16.91 ((
% 128.77/16.91 (notequalI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (notequalI2) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetRefl) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetTrans) =>
% 128.77/16.91 ((
% 128.77/16.91 (setadjoinSub) =>
% 128.77/16.91 ((
% 128.77/16.91 (setadjoinSub2) =>
% 128.77/16.91 ((
% 128.77/16.91 (subset2powerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (setextsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetemptysetimpeq) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (inPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetsubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (sepInPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (sepSubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionIL) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairset2IR) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionIR) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionEcases) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionE) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionLsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionRsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectI) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset5) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectEL) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectLsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset2) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset3) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectER) =>
% 128.77/16.91 ((
% 128.77/16.91 (disjointsetsI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectRsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset4) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset1) =>
% 128.77/16.91 ((
% 128.77/16.91 (bs114d) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusI) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusEL) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusER) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusSubset2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusERneg) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusELneg) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusILneg) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusIRneg) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusLsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusSubset1) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffE) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffI2) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffIneg1) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffIneg2) =>
% 128.77/16.91 ((
% 128.77/16.91 (secondinupair) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairIL) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairIR) =>
% 128.77/16.91 ((
% 128.77/16.91 (kpairiskpair) =>
% 128.77/16.91 ((
% 128.77/16.91 (kpairp) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonsubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletoninpowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletoninpowunion) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairset2E) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsubunion) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairinpowunion) =>
% 128.77/16.91 ((
% 128.77/16.91 (ubforcartprodlem1) =>
% 128.77/16.91 ((
% 128.77/16.91 (ubforcartprodlem2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ubforcartprodlem3) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairin) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodmempair1) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodmempair) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionE2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionsingleton1) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionsingleton2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1E1) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1I) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1I2) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonsuniq) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjL1) =>
% 128.77/16.91 ((
% 128.77/16.91 (kfstsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (theprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (kfstpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodfstin) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjL2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjL) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR11) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR12) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR1) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairequniteq) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR) =>
% 128.77/16.91 ((
% 128.77/16.91 (ksndsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (ksndpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (kpairsurjEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodsndin) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairmemEL) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairmemER) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodmempaircEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodfstpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodsndpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairsurjEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrI) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrSub) =>
% 128.77/16.91 ((
% 128.77/16.91 (setOfPairsIsBReln) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrERa) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrEL1) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrEL2) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrER) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcImageSingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (apProp) =>
% 128.77/16.91 ((
% 128.77/16.91 (app) =>
% 128.77/16.91 ((
% 128.77/16.91 (infuncsetfunc) =>
% 128.77/16.91 ((
% 128.77/16.91 (ap2p) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcinfuncset) =>
% 128.77/16.91 ((
% 128.77/16.91 (lamProp) =>
% 128.77/16.91 ((
% 128.77/16.91 (lamp) =>
% 128.77/16.91 ((
% 128.77/16.91 (lam2p) =>
% 128.77/16.91 ((
% 128.77/16.91 (brelnall1) =>
% 128.77/16.91 ((
% 128.77/16.91 (brelnall2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1E2) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp1) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp3) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp2) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcextLem) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp4) =>
% 128.77/16.91 ((
% 128.77/16.91 (subbreln) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqbreln) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcext) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcext2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ap2apEq1) =>
% 128.77/16.91 ((
% 128.77/16.91 (ap2apEq2) =>
% 128.77/16.91 ((
% 128.77/16.91 (beta1) =>
% 128.77/16.91 ((
% 128.77/16.91 (eta1) =>
% 128.77/16.91 ((
% 128.77/16.91 (lam2lamEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (beta2) =>
% 128.77/16.91 ((
% 128.77/16.91 (eta2) =>
% 128.77/16.91 ((
% 128.77/16.91 (iffalseProp1) =>
% 128.77/16.91 ((
% 128.77/16.91 (iffalseProp2) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrueProp1) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrueProp2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ifSingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (ifp) =>
% 128.77/16.91 ((
% 128.77/16.91 (theeq) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrue) =>
% 128.77/16.91 ((
% 128.77/16.91 (iffalse) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrueorfalse) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (setextT) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetTI) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetTI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetTE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectTELcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectTERcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT1) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT2) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT3) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementSub1) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementSub2) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTnotintersectT) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementImpComplementIntersect) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementSubsetComplementIntersect) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementInPowersetComplementIntersect) =>
% 128.77/16.91 ((
% 128.77/16.91 (contraSubsetComplement) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTcontraSubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTILcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTIRcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (inIntersectImpInUnion) =>
% 128.77/16.91 ((
% 128.77/16.91 (inIntersectImpInUnion2) =>
% 128.77/16.91 ((
% 128.77/16.91 (inIntersectImpInIntersectUnions) =>
% 128.77/16.91 ((
% 128.77/16.91 (intersectInPowersetIntersectUnions) =>
% 128.77/16.91 ((
% 128.77/16.91 (inComplementUnionImpNotIn1) =>
% 128.77/16.91 ((
% 128.77/16.91 (inComplementUnionImpInComplement1) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTE) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTEcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2a1) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementUnionInPowersetComplement) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2a2) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan1a) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan1b) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan1) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2a) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2b2) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2b) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule0) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule1) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule2) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule3) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule4) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_1) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_2) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_3) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_4) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_5) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1all2) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1SetBreln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (choice2fnsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (setOfPairsIsBReln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1all1) =>
% 128.77/16.91 ((
% 128.77/16.91 (subbreln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqbreln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1invprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1invI) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1invE) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compI) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compE) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compEex) =>
% 128.77/16.91 ((
% 128.77/16.91 (!!) @ (
% 128.77/16.91 (('#B') @ (
% 128.77/16.91 !!) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#S') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#S') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 =>))) @
% 128.77/16.91 breln1)))) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 !!))) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#S') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#B') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#S') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 =>))) @
% 128.77/16.91 breln1)))))) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#C') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#B') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#B') @
% 128.77/16.91 breln1)))) @
% 128.77/16.91 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.77/16.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])).
% 128.77/16.91 thf(zip_derived_cl33, plain,
% 128.77/16.91 (~ (((omegaSAx) =>
% 128.77/16.91 (((omegaIndAx) =>
% 128.77/16.91 (((replAx) =>
% 128.77/16.91 (((foundationAx) =>
% 128.77/16.91 (((wellorderingAx) =>
% 128.77/16.91 (((descrp) =>
% 128.77/16.91 (((dsetconstrI) =>
% 128.77/16.91 (((dsetconstrEL) =>
% 128.77/16.91 (((dsetconstrER) =>
% 128.77/16.91 (((exuE1) =>
% 128.77/16.91 (((prop2setE) =>
% 128.77/16.91 (((emptysetE) =>
% 128.77/16.91 (((emptysetimpfalse) =>
% 128.77/16.91 (((notinemptyset) =>
% 128.77/16.91 (((exuE3e) =>
% 128.77/16.91 (((setext) =>
% 128.77/16.91 (((emptyI) =>
% 128.77/16.91 (((noeltsimpempty) =>
% 128.77/16.91 (((setbeta) =>
% 128.77/16.91 (((nonemptyE1) =>
% 128.77/16.91 (((nonemptyI) =>
% 128.77/16.91 (((nonemptyI1) =>
% 128.77/16.91 (((setadjoinIL) =>
% 128.77/16.91 (((in @ emptyset @
% 128.77/16.91 (setadjoin @
% 128.77/16.91 emptyset @ emptyset)) =>
% 128.77/16.91 (((setadjoinIR) =>
% 128.77/16.91 (((setadjoinE) =>
% 128.77/16.91 (((setadjoinOr) =>
% 128.77/16.91 (((setoftrueEq) =>
% 128.77/16.91 (((powersetI) =>
% 128.77/16.91 (((emptyinPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptyInPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetE) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionI) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionE) =>
% 128.77/16.91 ((
% 128.77/16.91 (subPowSU) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuE2) =>
% 128.77/16.91 ((
% 128.77/16.91 (nonemptyImpWitness) =>
% 128.77/16.91 ((
% 128.77/16.91 (uniqinunit) =>
% 128.77/16.91 ((
% 128.77/16.91 (notinsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqinunit) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonsswitch) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsetE) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsetIL) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsetIR) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptyE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (vacuousDall) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan1) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan2) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan3) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan4) =>
% 128.77/16.91 ((
% 128.77/16.91 (prop2setI) =>
% 128.77/16.91 ((
% 128.77/16.91 (prop2set2propI) =>
% 128.77/16.91 ((
% 128.77/16.91 (notdexE) =>
% 128.77/16.91 ((
% 128.77/16.91 (notdallE) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuI3) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuI2) =>
% 128.77/16.91 ((
% 128.77/16.91 (inCongP) =>
% 128.77/16.91 ((
% 128.77/16.91 (in__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuE3u) =>
% 128.77/16.91 ((
% 128.77/16.91 (exu__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (setadjoin__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (powerset__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunion__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuEu) =>
% 128.77/16.91 ((
% 128.77/16.91 (descr__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (dsetconstr__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqimpsubset2) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqimpsubset1) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetI2) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptysetsubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetE) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetE2) =>
% 128.77/16.91 ((
% 128.77/16.91 (notsubsetI) =>
% 128.77/16.91 ((
% 128.77/16.91 (notequalI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (notequalI2) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetRefl) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetTrans) =>
% 128.77/16.91 ((
% 128.77/16.91 (setadjoinSub) =>
% 128.77/16.91 ((
% 128.77/16.91 (setadjoinSub2) =>
% 128.77/16.91 ((
% 128.77/16.91 (subset2powerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (setextsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetemptysetimpeq) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (inPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetsubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (sepInPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (sepSubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionIL) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairset2IR) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionIR) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionEcases) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionE) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionLsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionRsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectI) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset5) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectEL) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectLsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset2) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset3) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectER) =>
% 128.77/16.91 ((
% 128.77/16.91 (disjointsetsI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectRsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset4) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectSubset1) =>
% 128.77/16.91 ((
% 128.77/16.91 (bs114d) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusI) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusEL) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusER) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusSubset2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusERneg) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusELneg) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusILneg) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusIRneg) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusLsub) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusSubset1) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffE) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffI2) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffIneg1) =>
% 128.77/16.91 ((
% 128.77/16.91 (symdiffIneg2) =>
% 128.77/16.91 ((
% 128.77/16.91 (secondinupair) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairIL) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairIR) =>
% 128.77/16.91 ((
% 128.77/16.91 (kpairiskpair) =>
% 128.77/16.91 ((
% 128.77/16.91 (kpairp) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonsubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletoninpowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletoninpowunion) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairset2E) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsubunion) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairinpowunion) =>
% 128.77/16.91 ((
% 128.77/16.91 (ubforcartprodlem1) =>
% 128.77/16.91 ((
% 128.77/16.91 (ubforcartprodlem2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ubforcartprodlem3) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairin) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodmempair1) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodmempair) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionE2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionsingleton1) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionsingleton2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1E1) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1I) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1I2) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonsuniq) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjL1) =>
% 128.77/16.91 ((
% 128.77/16.91 (kfstsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (theprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (kfstpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodfstin) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjL2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjL) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR11) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR12) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR1) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairequniteq) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR2) =>
% 128.77/16.91 ((
% 128.77/16.91 (setukpairinjR) =>
% 128.77/16.91 ((
% 128.77/16.91 (ksndsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (ksndpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (kpairsurjEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodsndin) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairmemEL) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairmemER) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodmempaircEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodfstpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodsndpairEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (cartprodpairsurjEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrI) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrSub) =>
% 128.77/16.91 ((
% 128.77/16.91 (setOfPairsIsBReln) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrERa) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrEL1) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrEL2) =>
% 128.77/16.91 ((
% 128.77/16.91 (dpsetconstrER) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcImageSingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (apProp) =>
% 128.77/16.91 ((
% 128.77/16.91 (app) =>
% 128.77/16.91 ((
% 128.77/16.91 (infuncsetfunc) =>
% 128.77/16.91 ((
% 128.77/16.91 (ap2p) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcinfuncset) =>
% 128.77/16.91 ((
% 128.77/16.91 (lamProp) =>
% 128.77/16.91 ((
% 128.77/16.91 (lamp) =>
% 128.77/16.91 ((
% 128.77/16.91 (lam2p) =>
% 128.77/16.91 ((
% 128.77/16.91 (brelnall1) =>
% 128.77/16.91 ((
% 128.77/16.91 (brelnall2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ex1E2) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp1) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp3) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp2) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcextLem) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcGraphProp4) =>
% 128.77/16.91 ((
% 128.77/16.91 (subbreln) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqbreln) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcext) =>
% 128.77/16.91 ((
% 128.77/16.91 (funcext2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ap2apEq1) =>
% 128.77/16.91 ((
% 128.77/16.91 (ap2apEq2) =>
% 128.77/16.91 ((
% 128.77/16.91 (beta1) =>
% 128.77/16.91 ((
% 128.77/16.91 (eta1) =>
% 128.77/16.91 ((
% 128.77/16.91 (lam2lamEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (beta2) =>
% 128.77/16.91 ((
% 128.77/16.91 (eta2) =>
% 128.77/16.91 ((
% 128.77/16.91 (iffalseProp1) =>
% 128.77/16.91 ((
% 128.77/16.91 (iffalseProp2) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrueProp1) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrueProp2) =>
% 128.77/16.91 ((
% 128.77/16.91 (ifSingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (ifp) =>
% 128.77/16.91 ((
% 128.77/16.91 (theeq) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrue) =>
% 128.77/16.91 ((
% 128.77/16.91 (iffalse) =>
% 128.77/16.91 ((
% 128.77/16.91 (iftrueorfalse) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (setminusT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementT_lem) =>
% 128.77/16.91 ((
% 128.77/16.91 (setextT) =>
% 128.77/16.91 ((
% 128.77/16.91 (subsetTI) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetTI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetTE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectTELcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (binintersectTERcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT1) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT2) =>
% 128.77/16.91 ((
% 128.77/16.91 (contrasubsetT3) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementSub1) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementSub2) =>
% 128.77/16.91 ((
% 128.77/16.91 (doubleComplementEq) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTnotintersectT) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementImpComplementIntersect) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementSubsetComplementIntersect) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementInPowersetComplementIntersect) =>
% 128.77/16.91 ((
% 128.77/16.91 (contraSubsetComplement) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementTcontraSubset) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTILcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTIRcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (inIntersectImpInUnion) =>
% 128.77/16.91 ((
% 128.77/16.91 (inIntersectImpInUnion2) =>
% 128.77/16.91 ((
% 128.77/16.91 (inIntersectImpInIntersectUnions) =>
% 128.77/16.91 ((
% 128.77/16.91 (intersectInPowersetIntersectUnions) =>
% 128.77/16.91 ((
% 128.77/16.91 (inComplementUnionImpNotIn1) =>
% 128.77/16.91 ((
% 128.77/16.91 (inComplementUnionImpInComplement1) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTE) =>
% 128.77/16.91 ((
% 128.77/16.91 (binunionTEcontra) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2a1) =>
% 128.77/16.91 ((
% 128.77/16.91 (complementUnionInPowersetComplement) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2a2) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan1a) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan1b) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan1) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2a) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2b2) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2b) =>
% 128.77/16.91 ((
% 128.77/16.91 (demorgan2) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule0) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule1) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule2) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule3) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz13rule4) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_1) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_2) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_3) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_4) =>
% 128.77/16.91 ((
% 128.77/16.91 (woz1_5) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1all2) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1SetBreln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (choice2fnsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (setOfPairsIsBReln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1all1) =>
% 128.77/16.91 ((
% 128.77/16.91 (subbreln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqbreln1) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1invprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1invI) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1invE) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compprop) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compI) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compE) =>
% 128.77/16.91 ((
% 128.77/16.91 (breln1compEex) =>
% 128.77/16.91 ((
% 128.77/16.91 (!!) @ (
% 128.77/16.91 (('#B') @ (
% 128.77/16.91 !!) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#S') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#S') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 =>))) @
% 128.77/16.91 breln1)))) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 !!))) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#S') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#B') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#S') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 =>))) @
% 128.77/16.91 breln1)))))) @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#C') @ (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#B') @
% 128.77/16.91 (
% 128.77/16.91 (
% 128.77/16.91 ('#B') @ (
% 128.77/16.91 '#B') @
% 128.77/16.91 breln1)))) @
% 128.77/16.91 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.77/16.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])).
% 128.77/16.91 thf(zip_derived_cl40, plain,
% 128.77/16.91 (~ (((omegaIndAx) =>
% 128.77/16.91 (((replAx) =>
% 128.77/16.91 (((foundationAx) =>
% 128.77/16.91 (((wellorderingAx) =>
% 128.77/16.91 (((descrp) =>
% 128.77/16.91 (((dsetconstrI) =>
% 128.77/16.91 (((dsetconstrEL) =>
% 128.77/16.91 (((dsetconstrER) =>
% 128.77/16.91 (((exuE1) =>
% 128.77/16.91 (((prop2setE) =>
% 128.77/16.91 (((emptysetE) =>
% 128.77/16.91 (((emptysetimpfalse) =>
% 128.77/16.91 (((notinemptyset) =>
% 128.77/16.91 (((exuE3e) =>
% 128.77/16.91 (((setext) =>
% 128.77/16.91 (((emptyI) =>
% 128.77/16.91 (((noeltsimpempty) =>
% 128.77/16.91 (((setbeta) =>
% 128.77/16.91 (((nonemptyE1) =>
% 128.77/16.91 (((nonemptyI) =>
% 128.77/16.91 (((nonemptyI1) =>
% 128.77/16.91 (((setadjoinIL) =>
% 128.77/16.91 (((in @ emptyset @
% 128.77/16.91 (setadjoin @ emptyset @
% 128.77/16.91 emptyset)) =>
% 128.77/16.91 (((setadjoinIR) =>
% 128.77/16.91 (((setadjoinE) =>
% 128.77/16.91 (((setadjoinOr) =>
% 128.77/16.91 (((setoftrueEq) =>
% 128.77/16.91 (((powersetI) =>
% 128.77/16.91 (((emptyinPowerset) =>
% 128.77/16.91 (((emptyInPowerset) =>
% 128.77/16.91 ((
% 128.77/16.91 (powersetE) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionI) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunionE) =>
% 128.77/16.91 ((
% 128.77/16.91 (subPowSU) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuE2) =>
% 128.77/16.91 ((
% 128.77/16.91 (nonemptyImpWitness) =>
% 128.77/16.91 ((
% 128.77/16.91 (uniqinunit) =>
% 128.77/16.91 ((
% 128.77/16.91 (notinsingleton) =>
% 128.77/16.91 ((
% 128.77/16.91 (eqinunit) =>
% 128.77/16.91 ((
% 128.77/16.91 (singletonsswitch) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsetE) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsetIL) =>
% 128.77/16.91 ((
% 128.77/16.91 (upairsetIR) =>
% 128.77/16.91 ((
% 128.77/16.91 (emptyE1) =>
% 128.77/16.91 ((
% 128.77/16.91 (vacuousDall) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan1) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan2) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan3) =>
% 128.77/16.91 ((
% 128.77/16.91 (quantDeMorgan4) =>
% 128.77/16.91 ((
% 128.77/16.91 (prop2setI) =>
% 128.77/16.91 ((
% 128.77/16.91 (prop2set2propI) =>
% 128.77/16.91 ((
% 128.77/16.91 (notdexE) =>
% 128.77/16.91 ((
% 128.77/16.91 (notdallE) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuI1) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuI3) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuI2) =>
% 128.77/16.91 ((
% 128.77/16.91 (inCongP) =>
% 128.77/16.91 ((
% 128.77/16.91 (in__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuE3u) =>
% 128.77/16.91 ((
% 128.77/16.91 (exu__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (setadjoin__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (powerset__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (setunion__Cong) =>
% 128.77/16.91 ((
% 128.77/16.91 (exuEu) =>
% 128.77/16.91 ((
% 128.77/16.91 (descr__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (dsetconstr__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqimpsubset2) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqimpsubset1) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetI2) =>
% 128.77/16.92 ((
% 128.77/16.92 (emptysetsubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetE) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetE2) =>
% 128.77/16.92 ((
% 128.77/16.92 (notsubsetI) =>
% 128.77/16.92 ((
% 128.77/16.92 (notequalI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (notequalI2) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetRefl) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetTrans) =>
% 128.77/16.92 ((
% 128.77/16.92 (setadjoinSub) =>
% 128.77/16.92 ((
% 128.77/16.92 (setadjoinSub2) =>
% 128.77/16.92 ((
% 128.77/16.92 (subset2powerset) =>
% 128.77/16.92 ((
% 128.77/16.92 (setextsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetemptysetimpeq) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetE1) =>
% 128.77/16.92 ((
% 128.77/16.92 (inPowerset) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetsubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (sepInPowerset) =>
% 128.77/16.92 ((
% 128.77/16.92 (sepSubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionIL) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairset2IR) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionIR) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionEcases) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionE) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionLsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionRsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectI) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset5) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectEL) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectLsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset2) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset3) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectER) =>
% 128.77/16.92 ((
% 128.77/16.92 (disjointsetsI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectRsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset4) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset1) =>
% 128.77/16.92 ((
% 128.77/16.92 (bs114d) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusI) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusEL) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusER) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusSubset2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusERneg) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusELneg) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusILneg) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusIRneg) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusLsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusSubset1) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffE) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffI2) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffIneg1) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffIneg2) =>
% 128.77/16.92 ((
% 128.77/16.92 (secondinupair) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairIL) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairIR) =>
% 128.77/16.92 ((
% 128.77/16.92 (kpairiskpair) =>
% 128.77/16.92 ((
% 128.77/16.92 (kpairp) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletonsubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletoninpowerset) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletoninpowunion) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairset2E) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairsubunion) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairinpowunion) =>
% 128.77/16.92 ((
% 128.77/16.92 (ubforcartprodlem1) =>
% 128.77/16.92 ((
% 128.77/16.92 (ubforcartprodlem2) =>
% 128.77/16.92 ((
% 128.77/16.92 (ubforcartprodlem3) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodpairin) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodmempair1) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodmempair) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionE2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionsingleton1) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionsingleton2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletonprop) =>
% 128.77/16.92 ((
% 128.77/16.92 (ex1E1) =>
% 128.77/16.92 ((
% 128.77/16.92 (ex1I) =>
% 128.77/16.92 ((
% 128.77/16.92 (ex1I2) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletonsuniq) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjL1) =>
% 128.77/16.92 ((
% 128.77/16.92 (kfstsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (theprop) =>
% 128.77/16.92 ((
% 128.77/16.92 (kfstpairEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodfstin) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjL2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjL) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR11) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR12) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR1) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairequniteq) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR) =>
% 128.77/16.92 ((
% 128.77/16.92 (ksndsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (ksndpairEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (kpairsurjEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodsndin) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodpairmemEL) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodpairmemER) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodmempaircEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodfstpairEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodsndpairEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodpairsurjEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrI) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrSub) =>
% 128.77/16.92 ((
% 128.77/16.92 (setOfPairsIsBReln) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrERa) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrEL1) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrEL2) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrER) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcImageSingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (apProp) =>
% 128.77/16.92 ((
% 128.77/16.92 (app) =>
% 128.77/16.92 ((
% 128.77/16.92 (infuncsetfunc) =>
% 128.77/16.92 ((
% 128.77/16.92 (ap2p) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcinfuncset) =>
% 128.77/16.92 ((
% 128.77/16.92 (lamProp) =>
% 128.77/16.92 ((
% 128.77/16.92 (lamp) =>
% 128.77/16.92 ((
% 128.77/16.92 (lam2p) =>
% 128.77/16.92 ((
% 128.77/16.92 (brelnall1) =>
% 128.77/16.92 ((
% 128.77/16.92 (brelnall2) =>
% 128.77/16.92 ((
% 128.77/16.92 (ex1E2) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcGraphProp1) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcGraphProp3) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcGraphProp2) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcextLem) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcGraphProp4) =>
% 128.77/16.92 ((
% 128.77/16.92 (subbreln) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqbreln) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcext) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcext2) =>
% 128.77/16.92 ((
% 128.77/16.92 (ap2apEq1) =>
% 128.77/16.92 ((
% 128.77/16.92 (ap2apEq2) =>
% 128.77/16.92 ((
% 128.77/16.92 (beta1) =>
% 128.77/16.92 ((
% 128.77/16.92 (eta1) =>
% 128.77/16.92 ((
% 128.77/16.92 (lam2lamEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (beta2) =>
% 128.77/16.92 ((
% 128.77/16.92 (eta2) =>
% 128.77/16.92 ((
% 128.77/16.92 (iffalseProp1) =>
% 128.77/16.92 ((
% 128.77/16.92 (iffalseProp2) =>
% 128.77/16.92 ((
% 128.77/16.92 (iftrueProp1) =>
% 128.77/16.92 ((
% 128.77/16.92 (iftrueProp2) =>
% 128.77/16.92 ((
% 128.77/16.92 (ifSingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (ifp) =>
% 128.77/16.92 ((
% 128.77/16.92 (theeq) =>
% 128.77/16.92 ((
% 128.77/16.92 (iftrue) =>
% 128.77/16.92 ((
% 128.77/16.92 (iffalse) =>
% 128.77/16.92 ((
% 128.77/16.92 (iftrueorfalse) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectT_lem) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionT_lem) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetT_lem) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusT_lem) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementT_lem) =>
% 128.77/16.92 ((
% 128.77/16.92 (setextT) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetTI) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetTI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetTE1) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementTI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementTE1) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectTELcontra) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectTERcontra) =>
% 128.77/16.92 ((
% 128.77/16.92 (contrasubsetT) =>
% 128.77/16.92 ((
% 128.77/16.92 (contrasubsetT1) =>
% 128.77/16.92 ((
% 128.77/16.92 (contrasubsetT2) =>
% 128.77/16.92 ((
% 128.77/16.92 (contrasubsetT3) =>
% 128.77/16.92 ((
% 128.77/16.92 (doubleComplementI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (doubleComplementE1) =>
% 128.77/16.92 ((
% 128.77/16.92 (doubleComplementSub1) =>
% 128.77/16.92 ((
% 128.77/16.92 (doubleComplementSub2) =>
% 128.77/16.92 ((
% 128.77/16.92 (doubleComplementEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementTnotintersectT) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementImpComplementIntersect) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementSubsetComplementIntersect) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementInPowersetComplementIntersect) =>
% 128.77/16.92 ((
% 128.77/16.92 (contraSubsetComplement) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementTcontraSubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionTILcontra) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionTIRcontra) =>
% 128.77/16.92 ((
% 128.77/16.92 (inIntersectImpInUnion) =>
% 128.77/16.92 ((
% 128.77/16.92 (inIntersectImpInUnion2) =>
% 128.77/16.92 ((
% 128.77/16.92 (inIntersectImpInIntersectUnions) =>
% 128.77/16.92 ((
% 128.77/16.92 (intersectInPowersetIntersectUnions) =>
% 128.77/16.92 ((
% 128.77/16.92 (inComplementUnionImpNotIn1) =>
% 128.77/16.92 ((
% 128.77/16.92 (inComplementUnionImpInComplement1) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionTE) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionTEcontra) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2a1) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementUnionInPowersetComplement) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2a2) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan1a) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan1b) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan1) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2a) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2b2) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2b) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz13rule0) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz13rule1) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz13rule2) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz13rule3) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz13rule4) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz1_1) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz1_2) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz1_3) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz1_4) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz1_5) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1all2) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1SetBreln1) =>
% 128.77/16.92 ((
% 128.77/16.92 (choice2fnsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (setOfPairsIsBReln1) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1all1) =>
% 128.77/16.92 ((
% 128.77/16.92 (subbreln1) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqbreln1) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1invprop) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1invI) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1invE) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1compprop) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1compI) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1compE) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1compEex) =>
% 128.77/16.92 ((
% 128.77/16.92 (!!) @ (
% 128.77/16.92 (('#B') @ (
% 128.77/16.92 !!) @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#S') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 '#S') @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 =>))) @
% 128.77/16.92 breln1)))) @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 !!))) @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#S') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 '#B') @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 '#S') @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 =>))) @
% 128.77/16.92 breln1)))))) @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#C') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 '#B') @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 '#B') @
% 128.77/16.92 breln1)))) @
% 128.77/16.92 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.77/16.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
% 128.77/16.92 thf(zip_derived_cl46, plain,
% 128.77/16.92 (~ (((replAx) =>
% 128.77/16.92 (((foundationAx) =>
% 128.77/16.92 (((wellorderingAx) =>
% 128.77/16.92 (((descrp) =>
% 128.77/16.92 (((dsetconstrI) =>
% 128.77/16.92 (((dsetconstrEL) =>
% 128.77/16.92 (((dsetconstrER) =>
% 128.77/16.92 (((exuE1) =>
% 128.77/16.92 (((prop2setE) =>
% 128.77/16.92 (((emptysetE) =>
% 128.77/16.92 (((emptysetimpfalse) =>
% 128.77/16.92 (((notinemptyset) =>
% 128.77/16.92 (((exuE3e) =>
% 128.77/16.92 (((setext) =>
% 128.77/16.92 (((emptyI) =>
% 128.77/16.92 (((noeltsimpempty) =>
% 128.77/16.92 (((setbeta) =>
% 128.77/16.92 (((nonemptyE1) =>
% 128.77/16.92 (((nonemptyI) =>
% 128.77/16.92 (((nonemptyI1) =>
% 128.77/16.92 (((setadjoinIL) =>
% 128.77/16.92 (((in @ emptyset @
% 128.77/16.92 (setadjoin @ emptyset @
% 128.77/16.92 emptyset)) =>
% 128.77/16.92 (((setadjoinIR) =>
% 128.77/16.92 (((setadjoinE) =>
% 128.77/16.92 (((setadjoinOr) =>
% 128.77/16.92 (((setoftrueEq) =>
% 128.77/16.92 (((powersetI) =>
% 128.77/16.92 (((emptyinPowerset) =>
% 128.77/16.92 (((emptyInPowerset) =>
% 128.77/16.92 (((powersetE) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionI) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionE) =>
% 128.77/16.92 ((
% 128.77/16.92 (subPowSU) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuE2) =>
% 128.77/16.92 ((
% 128.77/16.92 (nonemptyImpWitness) =>
% 128.77/16.92 ((
% 128.77/16.92 (uniqinunit) =>
% 128.77/16.92 ((
% 128.77/16.92 (notinsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqinunit) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletonsswitch) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairsetE) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairsetIL) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairsetIR) =>
% 128.77/16.92 ((
% 128.77/16.92 (emptyE1) =>
% 128.77/16.92 ((
% 128.77/16.92 (vacuousDall) =>
% 128.77/16.92 ((
% 128.77/16.92 (quantDeMorgan1) =>
% 128.77/16.92 ((
% 128.77/16.92 (quantDeMorgan2) =>
% 128.77/16.92 ((
% 128.77/16.92 (quantDeMorgan3) =>
% 128.77/16.92 ((
% 128.77/16.92 (quantDeMorgan4) =>
% 128.77/16.92 ((
% 128.77/16.92 (prop2setI) =>
% 128.77/16.92 ((
% 128.77/16.92 (prop2set2propI) =>
% 128.77/16.92 ((
% 128.77/16.92 (notdexE) =>
% 128.77/16.92 ((
% 128.77/16.92 (notdallE) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuI3) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuI2) =>
% 128.77/16.92 ((
% 128.77/16.92 (inCongP) =>
% 128.77/16.92 ((
% 128.77/16.92 (in__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuE3u) =>
% 128.77/16.92 ((
% 128.77/16.92 (exu__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (setadjoin__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (powerset__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunion__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuEu) =>
% 128.77/16.92 ((
% 128.77/16.92 (descr__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (dsetconstr__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqimpsubset2) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqimpsubset1) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetI2) =>
% 128.77/16.92 ((
% 128.77/16.92 (emptysetsubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetE) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetE2) =>
% 128.77/16.92 ((
% 128.77/16.92 (notsubsetI) =>
% 128.77/16.92 ((
% 128.77/16.92 (notequalI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (notequalI2) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetRefl) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetTrans) =>
% 128.77/16.92 ((
% 128.77/16.92 (setadjoinSub) =>
% 128.77/16.92 ((
% 128.77/16.92 (setadjoinSub2) =>
% 128.77/16.92 ((
% 128.77/16.92 (subset2powerset) =>
% 128.77/16.92 ((
% 128.77/16.92 (setextsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetemptysetimpeq) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetE1) =>
% 128.77/16.92 ((
% 128.77/16.92 (inPowerset) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetsubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (sepInPowerset) =>
% 128.77/16.92 ((
% 128.77/16.92 (sepSubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionIL) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairset2IR) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionIR) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionEcases) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionE) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionLsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionRsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectI) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset5) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectEL) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectLsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset2) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset3) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectER) =>
% 128.77/16.92 ((
% 128.77/16.92 (disjointsetsI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectRsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset4) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset1) =>
% 128.77/16.92 ((
% 128.77/16.92 (bs114d) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusI) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusEL) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusER) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusSubset2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusERneg) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusELneg) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusILneg) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusIRneg) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusLsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusSubset1) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffE) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffI2) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffIneg1) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffIneg2) =>
% 128.77/16.92 ((
% 128.77/16.92 (secondinupair) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairIL) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairIR) =>
% 128.77/16.92 ((
% 128.77/16.92 (kpairiskpair) =>
% 128.77/16.92 ((
% 128.77/16.92 (kpairp) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletonsubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletoninpowerset) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletoninpowunion) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairset2E) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairsubunion) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairinpowunion) =>
% 128.77/16.92 ((
% 128.77/16.92 (ubforcartprodlem1) =>
% 128.77/16.92 ((
% 128.77/16.92 (ubforcartprodlem2) =>
% 128.77/16.92 ((
% 128.77/16.92 (ubforcartprodlem3) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodpairin) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodmempair1) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodmempair) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionE2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionsingleton1) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionsingleton2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletonprop) =>
% 128.77/16.92 ((
% 128.77/16.92 (ex1E1) =>
% 128.77/16.92 ((
% 128.77/16.92 (ex1I) =>
% 128.77/16.92 ((
% 128.77/16.92 (ex1I2) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletonsuniq) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjL1) =>
% 128.77/16.92 ((
% 128.77/16.92 (kfstsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (theprop) =>
% 128.77/16.92 ((
% 128.77/16.92 (kfstpairEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodfstin) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjL2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjL) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR11) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR12) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR1) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairequniteq) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR) =>
% 128.77/16.92 ((
% 128.77/16.92 (ksndsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (ksndpairEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (kpairsurjEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodsndin) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodpairmemEL) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodpairmemER) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodmempaircEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodfstpairEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodsndpairEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodpairsurjEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrI) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrSub) =>
% 128.77/16.92 ((
% 128.77/16.92 (setOfPairsIsBReln) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrERa) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrEL1) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrEL2) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrER) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcImageSingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (apProp) =>
% 128.77/16.92 ((
% 128.77/16.92 (app) =>
% 128.77/16.92 ((
% 128.77/16.92 (infuncsetfunc) =>
% 128.77/16.92 ((
% 128.77/16.92 (ap2p) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcinfuncset) =>
% 128.77/16.92 ((
% 128.77/16.92 (lamProp) =>
% 128.77/16.92 ((
% 128.77/16.92 (lamp) =>
% 128.77/16.92 ((
% 128.77/16.92 (lam2p) =>
% 128.77/16.92 ((
% 128.77/16.92 (brelnall1) =>
% 128.77/16.92 ((
% 128.77/16.92 (brelnall2) =>
% 128.77/16.92 ((
% 128.77/16.92 (ex1E2) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcGraphProp1) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcGraphProp3) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcGraphProp2) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcextLem) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcGraphProp4) =>
% 128.77/16.92 ((
% 128.77/16.92 (subbreln) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqbreln) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcext) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcext2) =>
% 128.77/16.92 ((
% 128.77/16.92 (ap2apEq1) =>
% 128.77/16.92 ((
% 128.77/16.92 (ap2apEq2) =>
% 128.77/16.92 ((
% 128.77/16.92 (beta1) =>
% 128.77/16.92 ((
% 128.77/16.92 (eta1) =>
% 128.77/16.92 ((
% 128.77/16.92 (lam2lamEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (beta2) =>
% 128.77/16.92 ((
% 128.77/16.92 (eta2) =>
% 128.77/16.92 ((
% 128.77/16.92 (iffalseProp1) =>
% 128.77/16.92 ((
% 128.77/16.92 (iffalseProp2) =>
% 128.77/16.92 ((
% 128.77/16.92 (iftrueProp1) =>
% 128.77/16.92 ((
% 128.77/16.92 (iftrueProp2) =>
% 128.77/16.92 ((
% 128.77/16.92 (ifSingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (ifp) =>
% 128.77/16.92 ((
% 128.77/16.92 (theeq) =>
% 128.77/16.92 ((
% 128.77/16.92 (iftrue) =>
% 128.77/16.92 ((
% 128.77/16.92 (iffalse) =>
% 128.77/16.92 ((
% 128.77/16.92 (iftrueorfalse) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectT_lem) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionT_lem) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetT_lem) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusT_lem) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementT_lem) =>
% 128.77/16.92 ((
% 128.77/16.92 (setextT) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetTI) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetTI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetTE1) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementTI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementTE1) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectTELcontra) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectTERcontra) =>
% 128.77/16.92 ((
% 128.77/16.92 (contrasubsetT) =>
% 128.77/16.92 ((
% 128.77/16.92 (contrasubsetT1) =>
% 128.77/16.92 ((
% 128.77/16.92 (contrasubsetT2) =>
% 128.77/16.92 ((
% 128.77/16.92 (contrasubsetT3) =>
% 128.77/16.92 ((
% 128.77/16.92 (doubleComplementI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (doubleComplementE1) =>
% 128.77/16.92 ((
% 128.77/16.92 (doubleComplementSub1) =>
% 128.77/16.92 ((
% 128.77/16.92 (doubleComplementSub2) =>
% 128.77/16.92 ((
% 128.77/16.92 (doubleComplementEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementTnotintersectT) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementImpComplementIntersect) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementSubsetComplementIntersect) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementInPowersetComplementIntersect) =>
% 128.77/16.92 ((
% 128.77/16.92 (contraSubsetComplement) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementTcontraSubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionTILcontra) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionTIRcontra) =>
% 128.77/16.92 ((
% 128.77/16.92 (inIntersectImpInUnion) =>
% 128.77/16.92 ((
% 128.77/16.92 (inIntersectImpInUnion2) =>
% 128.77/16.92 ((
% 128.77/16.92 (inIntersectImpInIntersectUnions) =>
% 128.77/16.92 ((
% 128.77/16.92 (intersectInPowersetIntersectUnions) =>
% 128.77/16.92 ((
% 128.77/16.92 (inComplementUnionImpNotIn1) =>
% 128.77/16.92 ((
% 128.77/16.92 (inComplementUnionImpInComplement1) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionTE) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionTEcontra) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2a1) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementUnionInPowersetComplement) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2a2) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan1a) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan1b) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan1) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2a) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2b2) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2b) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz13rule0) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz13rule1) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz13rule2) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz13rule3) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz13rule4) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz1_1) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz1_2) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz1_3) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz1_4) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz1_5) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1all2) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1SetBreln1) =>
% 128.77/16.92 ((
% 128.77/16.92 (choice2fnsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (setOfPairsIsBReln1) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1all1) =>
% 128.77/16.92 ((
% 128.77/16.92 (subbreln1) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqbreln1) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1invprop) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1invI) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1invE) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1compprop) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1compI) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1compE) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1compEex) =>
% 128.77/16.92 ((
% 128.77/16.92 (!!) @ (
% 128.77/16.92 (('#B') @ (
% 128.77/16.92 !!) @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#S') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 '#S') @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 =>))) @
% 128.77/16.92 breln1)))) @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 !!))) @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#S') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 '#B') @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 '#S') @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 =>))) @
% 128.77/16.92 breln1)))))) @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#C') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 '#B') @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 '#B') @
% 128.77/16.92 breln1)))) @
% 128.77/16.92 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.77/16.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])).
% 128.77/16.92 thf(zip_derived_cl52, plain,
% 128.77/16.92 (~ (((foundationAx) =>
% 128.77/16.92 (((wellorderingAx) =>
% 128.77/16.92 (((descrp) =>
% 128.77/16.92 (((dsetconstrI) =>
% 128.77/16.92 (((dsetconstrEL) =>
% 128.77/16.92 (((dsetconstrER) =>
% 128.77/16.92 (((exuE1) =>
% 128.77/16.92 (((prop2setE) =>
% 128.77/16.92 (((emptysetE) =>
% 128.77/16.92 (((emptysetimpfalse) =>
% 128.77/16.92 (((notinemptyset) =>
% 128.77/16.92 (((exuE3e) =>
% 128.77/16.92 (((setext) =>
% 128.77/16.92 (((emptyI) =>
% 128.77/16.92 (((noeltsimpempty) =>
% 128.77/16.92 (((setbeta) =>
% 128.77/16.92 (((nonemptyE1) =>
% 128.77/16.92 (((nonemptyI) =>
% 128.77/16.92 (((nonemptyI1) =>
% 128.77/16.92 (((setadjoinIL) =>
% 128.77/16.92 (((in @ emptyset @
% 128.77/16.92 (setadjoin @ emptyset @
% 128.77/16.92 emptyset)) =>
% 128.77/16.92 (((setadjoinIR) =>
% 128.77/16.92 (((setadjoinE) =>
% 128.77/16.92 (((setadjoinOr) =>
% 128.77/16.92 (((setoftrueEq) =>
% 128.77/16.92 (((powersetI) =>
% 128.77/16.92 (((emptyinPowerset) =>
% 128.77/16.92 (((emptyInPowerset) =>
% 128.77/16.92 (((powersetE) =>
% 128.77/16.92 (((setunionI) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionE) =>
% 128.77/16.92 ((
% 128.77/16.92 (subPowSU) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuE2) =>
% 128.77/16.92 ((
% 128.77/16.92 (nonemptyImpWitness) =>
% 128.77/16.92 ((
% 128.77/16.92 (uniqinunit) =>
% 128.77/16.92 ((
% 128.77/16.92 (notinsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqinunit) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletonsswitch) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairsetE) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairsetIL) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairsetIR) =>
% 128.77/16.92 ((
% 128.77/16.92 (emptyE1) =>
% 128.77/16.92 ((
% 128.77/16.92 (vacuousDall) =>
% 128.77/16.92 ((
% 128.77/16.92 (quantDeMorgan1) =>
% 128.77/16.92 ((
% 128.77/16.92 (quantDeMorgan2) =>
% 128.77/16.92 ((
% 128.77/16.92 (quantDeMorgan3) =>
% 128.77/16.92 ((
% 128.77/16.92 (quantDeMorgan4) =>
% 128.77/16.92 ((
% 128.77/16.92 (prop2setI) =>
% 128.77/16.92 ((
% 128.77/16.92 (prop2set2propI) =>
% 128.77/16.92 ((
% 128.77/16.92 (notdexE) =>
% 128.77/16.92 ((
% 128.77/16.92 (notdallE) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuI3) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuI2) =>
% 128.77/16.92 ((
% 128.77/16.92 (inCongP) =>
% 128.77/16.92 ((
% 128.77/16.92 (in__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuE3u) =>
% 128.77/16.92 ((
% 128.77/16.92 (exu__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (setadjoin__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (powerset__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunion__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuEu) =>
% 128.77/16.92 ((
% 128.77/16.92 (descr__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (dsetconstr__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqimpsubset2) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqimpsubset1) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetI2) =>
% 128.77/16.92 ((
% 128.77/16.92 (emptysetsubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetE) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetE2) =>
% 128.77/16.92 ((
% 128.77/16.92 (notsubsetI) =>
% 128.77/16.92 ((
% 128.77/16.92 (notequalI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (notequalI2) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetRefl) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetTrans) =>
% 128.77/16.92 ((
% 128.77/16.92 (setadjoinSub) =>
% 128.77/16.92 ((
% 128.77/16.92 (setadjoinSub2) =>
% 128.77/16.92 ((
% 128.77/16.92 (subset2powerset) =>
% 128.77/16.92 ((
% 128.77/16.92 (setextsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetemptysetimpeq) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetE1) =>
% 128.77/16.92 ((
% 128.77/16.92 (inPowerset) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetsubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (sepInPowerset) =>
% 128.77/16.92 ((
% 128.77/16.92 (sepSubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionIL) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairset2IR) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionIR) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionEcases) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionE) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionLsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionRsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectI) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset5) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectEL) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectLsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset2) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset3) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectER) =>
% 128.77/16.92 ((
% 128.77/16.92 (disjointsetsI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectRsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset4) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset1) =>
% 128.77/16.92 ((
% 128.77/16.92 (bs114d) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusI) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusEL) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusER) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusSubset2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusERneg) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusELneg) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusILneg) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusIRneg) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusLsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusSubset1) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffE) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffI2) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffIneg1) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffIneg2) =>
% 128.77/16.92 ((
% 128.77/16.92 (secondinupair) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairIL) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairIR) =>
% 128.77/16.92 ((
% 128.77/16.92 (kpairiskpair) =>
% 128.77/16.92 ((
% 128.77/16.92 (kpairp) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletonsubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletoninpowerset) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletoninpowunion) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairset2E) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairsubunion) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairinpowunion) =>
% 128.77/16.92 ((
% 128.77/16.92 (ubforcartprodlem1) =>
% 128.77/16.92 ((
% 128.77/16.92 (ubforcartprodlem2) =>
% 128.77/16.92 ((
% 128.77/16.92 (ubforcartprodlem3) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodpairin) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodmempair1) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodmempair) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionE2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionsingleton1) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionsingleton2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletonprop) =>
% 128.77/16.92 ((
% 128.77/16.92 (ex1E1) =>
% 128.77/16.92 ((
% 128.77/16.92 (ex1I) =>
% 128.77/16.92 ((
% 128.77/16.92 (ex1I2) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletonsuniq) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjL1) =>
% 128.77/16.92 ((
% 128.77/16.92 (kfstsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (theprop) =>
% 128.77/16.92 ((
% 128.77/16.92 (kfstpairEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodfstin) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjL2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjL) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR11) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR12) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR1) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairequniteq) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR) =>
% 128.77/16.92 ((
% 128.77/16.92 (ksndsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (ksndpairEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (kpairsurjEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodsndin) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodpairmemEL) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodpairmemER) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodmempaircEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodfstpairEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodsndpairEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodpairsurjEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrI) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrSub) =>
% 128.77/16.92 ((
% 128.77/16.92 (setOfPairsIsBReln) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrERa) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrEL1) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrEL2) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrER) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcImageSingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (apProp) =>
% 128.77/16.92 ((
% 128.77/16.92 (app) =>
% 128.77/16.92 ((
% 128.77/16.92 (infuncsetfunc) =>
% 128.77/16.92 ((
% 128.77/16.92 (ap2p) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcinfuncset) =>
% 128.77/16.92 ((
% 128.77/16.92 (lamProp) =>
% 128.77/16.92 ((
% 128.77/16.92 (lamp) =>
% 128.77/16.92 ((
% 128.77/16.92 (lam2p) =>
% 128.77/16.92 ((
% 128.77/16.92 (brelnall1) =>
% 128.77/16.92 ((
% 128.77/16.92 (brelnall2) =>
% 128.77/16.92 ((
% 128.77/16.92 (ex1E2) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcGraphProp1) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcGraphProp3) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcGraphProp2) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcextLem) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcGraphProp4) =>
% 128.77/16.92 ((
% 128.77/16.92 (subbreln) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqbreln) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcext) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcext2) =>
% 128.77/16.92 ((
% 128.77/16.92 (ap2apEq1) =>
% 128.77/16.92 ((
% 128.77/16.92 (ap2apEq2) =>
% 128.77/16.92 ((
% 128.77/16.92 (beta1) =>
% 128.77/16.92 ((
% 128.77/16.92 (eta1) =>
% 128.77/16.92 ((
% 128.77/16.92 (lam2lamEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (beta2) =>
% 128.77/16.92 ((
% 128.77/16.92 (eta2) =>
% 128.77/16.92 ((
% 128.77/16.92 (iffalseProp1) =>
% 128.77/16.92 ((
% 128.77/16.92 (iffalseProp2) =>
% 128.77/16.92 ((
% 128.77/16.92 (iftrueProp1) =>
% 128.77/16.92 ((
% 128.77/16.92 (iftrueProp2) =>
% 128.77/16.92 ((
% 128.77/16.92 (ifSingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (ifp) =>
% 128.77/16.92 ((
% 128.77/16.92 (theeq) =>
% 128.77/16.92 ((
% 128.77/16.92 (iftrue) =>
% 128.77/16.92 ((
% 128.77/16.92 (iffalse) =>
% 128.77/16.92 ((
% 128.77/16.92 (iftrueorfalse) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectT_lem) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionT_lem) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetT_lem) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusT_lem) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementT_lem) =>
% 128.77/16.92 ((
% 128.77/16.92 (setextT) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetTI) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetTI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetTE1) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementTI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementTE1) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectTELcontra) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectTERcontra) =>
% 128.77/16.92 ((
% 128.77/16.92 (contrasubsetT) =>
% 128.77/16.92 ((
% 128.77/16.92 (contrasubsetT1) =>
% 128.77/16.92 ((
% 128.77/16.92 (contrasubsetT2) =>
% 128.77/16.92 ((
% 128.77/16.92 (contrasubsetT3) =>
% 128.77/16.92 ((
% 128.77/16.92 (doubleComplementI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (doubleComplementE1) =>
% 128.77/16.92 ((
% 128.77/16.92 (doubleComplementSub1) =>
% 128.77/16.92 ((
% 128.77/16.92 (doubleComplementSub2) =>
% 128.77/16.92 ((
% 128.77/16.92 (doubleComplementEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementTnotintersectT) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementImpComplementIntersect) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementSubsetComplementIntersect) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementInPowersetComplementIntersect) =>
% 128.77/16.92 ((
% 128.77/16.92 (contraSubsetComplement) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementTcontraSubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionTILcontra) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionTIRcontra) =>
% 128.77/16.92 ((
% 128.77/16.92 (inIntersectImpInUnion) =>
% 128.77/16.92 ((
% 128.77/16.92 (inIntersectImpInUnion2) =>
% 128.77/16.92 ((
% 128.77/16.92 (inIntersectImpInIntersectUnions) =>
% 128.77/16.92 ((
% 128.77/16.92 (intersectInPowersetIntersectUnions) =>
% 128.77/16.92 ((
% 128.77/16.92 (inComplementUnionImpNotIn1) =>
% 128.77/16.92 ((
% 128.77/16.92 (inComplementUnionImpInComplement1) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionTE) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionTEcontra) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2a1) =>
% 128.77/16.92 ((
% 128.77/16.92 (complementUnionInPowersetComplement) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2a2) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan1a) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan1b) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan1) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2a) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2b2) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2b) =>
% 128.77/16.92 ((
% 128.77/16.92 (demorgan2) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz13rule0) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz13rule1) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz13rule2) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz13rule3) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz13rule4) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz1_1) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz1_2) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz1_3) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz1_4) =>
% 128.77/16.92 ((
% 128.77/16.92 (woz1_5) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1all2) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1SetBreln1) =>
% 128.77/16.92 ((
% 128.77/16.92 (choice2fnsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (setOfPairsIsBReln1) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1all1) =>
% 128.77/16.92 ((
% 128.77/16.92 (subbreln1) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqbreln1) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1invprop) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1invI) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1invE) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1compprop) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1compI) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1compE) =>
% 128.77/16.92 ((
% 128.77/16.92 (breln1compEex) =>
% 128.77/16.92 ((
% 128.77/16.92 (!!) @ (
% 128.77/16.92 (('#B') @ (
% 128.77/16.92 !!) @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#S') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 '#S') @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 =>))) @
% 128.77/16.92 breln1)))) @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 !!))) @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#S') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 '#B') @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 '#S') @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 =>))) @
% 128.77/16.92 breln1)))))) @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#C') @ (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 '#B') @
% 128.77/16.92 (
% 128.77/16.92 (
% 128.77/16.92 ('#B') @ (
% 128.77/16.92 '#B') @
% 128.77/16.92 breln1)))) @
% 128.77/16.92 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.77/16.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])).
% 128.77/16.92 thf(zip_derived_cl58, plain,
% 128.77/16.92 (~ (((wellorderingAx) =>
% 128.77/16.92 (((descrp) =>
% 128.77/16.92 (((dsetconstrI) =>
% 128.77/16.92 (((dsetconstrEL) =>
% 128.77/16.92 (((dsetconstrER) =>
% 128.77/16.92 (((exuE1) =>
% 128.77/16.92 (((prop2setE) =>
% 128.77/16.92 (((emptysetE) =>
% 128.77/16.92 (((emptysetimpfalse) =>
% 128.77/16.92 (((notinemptyset) =>
% 128.77/16.92 (((exuE3e) =>
% 128.77/16.92 (((setext) =>
% 128.77/16.92 (((emptyI) =>
% 128.77/16.92 (((noeltsimpempty) =>
% 128.77/16.92 (((setbeta) =>
% 128.77/16.92 (((nonemptyE1) =>
% 128.77/16.92 (((nonemptyI) =>
% 128.77/16.92 (((nonemptyI1) =>
% 128.77/16.92 (((setadjoinIL) =>
% 128.77/16.92 (((in @ emptyset @
% 128.77/16.92 (setadjoin @ emptyset @
% 128.77/16.92 emptyset)) =>
% 128.77/16.92 (((setadjoinIR) =>
% 128.77/16.92 (((setadjoinE) =>
% 128.77/16.92 (((setadjoinOr) =>
% 128.77/16.92 (((setoftrueEq) =>
% 128.77/16.92 (((powersetI) =>
% 128.77/16.92 (((emptyinPowerset) =>
% 128.77/16.92 (((emptyInPowerset) =>
% 128.77/16.92 (((powersetE) =>
% 128.77/16.92 (((setunionI) =>
% 128.77/16.92 (((setunionE) =>
% 128.77/16.92 ((
% 128.77/16.92 (subPowSU) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuE2) =>
% 128.77/16.92 ((
% 128.77/16.92 (nonemptyImpWitness) =>
% 128.77/16.92 ((
% 128.77/16.92 (uniqinunit) =>
% 128.77/16.92 ((
% 128.77/16.92 (notinsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqinunit) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletonsswitch) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairsetE) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairsetIL) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairsetIR) =>
% 128.77/16.92 ((
% 128.77/16.92 (emptyE1) =>
% 128.77/16.92 ((
% 128.77/16.92 (vacuousDall) =>
% 128.77/16.92 ((
% 128.77/16.92 (quantDeMorgan1) =>
% 128.77/16.92 ((
% 128.77/16.92 (quantDeMorgan2) =>
% 128.77/16.92 ((
% 128.77/16.92 (quantDeMorgan3) =>
% 128.77/16.92 ((
% 128.77/16.92 (quantDeMorgan4) =>
% 128.77/16.92 ((
% 128.77/16.92 (prop2setI) =>
% 128.77/16.92 ((
% 128.77/16.92 (prop2set2propI) =>
% 128.77/16.92 ((
% 128.77/16.92 (notdexE) =>
% 128.77/16.92 ((
% 128.77/16.92 (notdallE) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuI3) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuI2) =>
% 128.77/16.92 ((
% 128.77/16.92 (inCongP) =>
% 128.77/16.92 ((
% 128.77/16.92 (in__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuE3u) =>
% 128.77/16.92 ((
% 128.77/16.92 (exu__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (setadjoin__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (powerset__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunion__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (exuEu) =>
% 128.77/16.92 ((
% 128.77/16.92 (descr__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (dsetconstr__Cong) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqimpsubset2) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqimpsubset1) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetI2) =>
% 128.77/16.92 ((
% 128.77/16.92 (emptysetsubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetE) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetE2) =>
% 128.77/16.92 ((
% 128.77/16.92 (notsubsetI) =>
% 128.77/16.92 ((
% 128.77/16.92 (notequalI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (notequalI2) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetRefl) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetTrans) =>
% 128.77/16.92 ((
% 128.77/16.92 (setadjoinSub) =>
% 128.77/16.92 ((
% 128.77/16.92 (setadjoinSub2) =>
% 128.77/16.92 ((
% 128.77/16.92 (subset2powerset) =>
% 128.77/16.92 ((
% 128.77/16.92 (setextsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (subsetemptysetimpeq) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetE1) =>
% 128.77/16.92 ((
% 128.77/16.92 (inPowerset) =>
% 128.77/16.92 ((
% 128.77/16.92 (powersetsubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (sepInPowerset) =>
% 128.77/16.92 ((
% 128.77/16.92 (sepSubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionIL) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairset2IR) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionIR) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionEcases) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionE) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionLsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionRsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectI) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset5) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectEL) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectLsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset2) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset3) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectER) =>
% 128.77/16.92 ((
% 128.77/16.92 (disjointsetsI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectRsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset4) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectSubset1) =>
% 128.77/16.92 ((
% 128.77/16.92 (bs114d) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusI) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusEL) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusER) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusSubset2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusERneg) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusELneg) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusILneg) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusIRneg) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusLsub) =>
% 128.77/16.92 ((
% 128.77/16.92 (setminusSubset1) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffE) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffI1) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffI2) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffIneg1) =>
% 128.77/16.92 ((
% 128.77/16.92 (symdiffIneg2) =>
% 128.77/16.92 ((
% 128.77/16.92 (secondinupair) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairIL) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairIR) =>
% 128.77/16.92 ((
% 128.77/16.92 (kpairiskpair) =>
% 128.77/16.92 ((
% 128.77/16.92 (kpairp) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletonsubset) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletoninpowerset) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletoninpowunion) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairset2E) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairsubunion) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairinpowunion) =>
% 128.77/16.92 ((
% 128.77/16.92 (ubforcartprodlem1) =>
% 128.77/16.92 ((
% 128.77/16.92 (ubforcartprodlem2) =>
% 128.77/16.92 ((
% 128.77/16.92 (ubforcartprodlem3) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodpairin) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodmempair1) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodmempair) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionE2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionsingleton1) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionsingleton2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setunionsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletonprop) =>
% 128.77/16.92 ((
% 128.77/16.92 (ex1E1) =>
% 128.77/16.92 ((
% 128.77/16.92 (ex1I) =>
% 128.77/16.92 ((
% 128.77/16.92 (ex1I2) =>
% 128.77/16.92 ((
% 128.77/16.92 (singletonsuniq) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjL1) =>
% 128.77/16.92 ((
% 128.77/16.92 (kfstsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (theprop) =>
% 128.77/16.92 ((
% 128.77/16.92 (kfstpairEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodfstin) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjL2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjL) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR11) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR12) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR1) =>
% 128.77/16.92 ((
% 128.77/16.92 (upairequniteq) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR2) =>
% 128.77/16.92 ((
% 128.77/16.92 (setukpairinjR) =>
% 128.77/16.92 ((
% 128.77/16.92 (ksndsingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (ksndpairEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (kpairsurjEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodsndin) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodpairmemEL) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodpairmemER) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodmempaircEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodfstpairEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodsndpairEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (cartprodpairsurjEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrI) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrSub) =>
% 128.77/16.92 ((
% 128.77/16.92 (setOfPairsIsBReln) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrERa) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrEL1) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrEL2) =>
% 128.77/16.92 ((
% 128.77/16.92 (dpsetconstrER) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcImageSingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (apProp) =>
% 128.77/16.92 ((
% 128.77/16.92 (app) =>
% 128.77/16.92 ((
% 128.77/16.92 (infuncsetfunc) =>
% 128.77/16.92 ((
% 128.77/16.92 (ap2p) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcinfuncset) =>
% 128.77/16.92 ((
% 128.77/16.92 (lamProp) =>
% 128.77/16.92 ((
% 128.77/16.92 (lamp) =>
% 128.77/16.92 ((
% 128.77/16.92 (lam2p) =>
% 128.77/16.92 ((
% 128.77/16.92 (brelnall1) =>
% 128.77/16.92 ((
% 128.77/16.92 (brelnall2) =>
% 128.77/16.92 ((
% 128.77/16.92 (ex1E2) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcGraphProp1) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcGraphProp3) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcGraphProp2) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcextLem) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcGraphProp4) =>
% 128.77/16.92 ((
% 128.77/16.92 (subbreln) =>
% 128.77/16.92 ((
% 128.77/16.92 (eqbreln) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcext) =>
% 128.77/16.92 ((
% 128.77/16.92 (funcext2) =>
% 128.77/16.92 ((
% 128.77/16.92 (ap2apEq1) =>
% 128.77/16.92 ((
% 128.77/16.92 (ap2apEq2) =>
% 128.77/16.92 ((
% 128.77/16.92 (beta1) =>
% 128.77/16.92 ((
% 128.77/16.92 (eta1) =>
% 128.77/16.92 ((
% 128.77/16.92 (lam2lamEq) =>
% 128.77/16.92 ((
% 128.77/16.92 (beta2) =>
% 128.77/16.92 ((
% 128.77/16.92 (eta2) =>
% 128.77/16.92 ((
% 128.77/16.92 (iffalseProp1) =>
% 128.77/16.92 ((
% 128.77/16.92 (iffalseProp2) =>
% 128.77/16.92 ((
% 128.77/16.92 (iftrueProp1) =>
% 128.77/16.92 ((
% 128.77/16.92 (iftrueProp2) =>
% 128.77/16.92 ((
% 128.77/16.92 (ifSingleton) =>
% 128.77/16.92 ((
% 128.77/16.92 (ifp) =>
% 128.77/16.92 ((
% 128.77/16.92 (theeq) =>
% 128.77/16.92 ((
% 128.77/16.92 (iftrue) =>
% 128.77/16.92 ((
% 128.77/16.92 (iffalse) =>
% 128.77/16.92 ((
% 128.77/16.92 (iftrueorfalse) =>
% 128.77/16.92 ((
% 128.77/16.92 (binintersectT_lem) =>
% 128.77/16.92 ((
% 128.77/16.92 (binunionT_lem) =>
% 128.89/16.92 ((
% 128.89/16.92 (powersetT_lem) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusT_lem) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementT_lem) =>
% 128.89/16.92 ((
% 128.89/16.92 (setextT) =>
% 128.89/16.92 ((
% 128.89/16.92 (subsetTI) =>
% 128.89/16.92 ((
% 128.89/16.92 (powersetTI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (powersetTE1) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementTI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementTE1) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectTELcontra) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectTERcontra) =>
% 128.89/16.92 ((
% 128.89/16.92 (contrasubsetT) =>
% 128.89/16.92 ((
% 128.89/16.92 (contrasubsetT1) =>
% 128.89/16.92 ((
% 128.89/16.92 (contrasubsetT2) =>
% 128.89/16.92 ((
% 128.89/16.92 (contrasubsetT3) =>
% 128.89/16.92 ((
% 128.89/16.92 (doubleComplementI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (doubleComplementE1) =>
% 128.89/16.92 ((
% 128.89/16.92 (doubleComplementSub1) =>
% 128.89/16.92 ((
% 128.89/16.92 (doubleComplementSub2) =>
% 128.89/16.92 ((
% 128.89/16.92 (doubleComplementEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementTnotintersectT) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementImpComplementIntersect) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementSubsetComplementIntersect) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementInPowersetComplementIntersect) =>
% 128.89/16.92 ((
% 128.89/16.92 (contraSubsetComplement) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementTcontraSubset) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionTILcontra) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionTIRcontra) =>
% 128.89/16.92 ((
% 128.89/16.92 (inIntersectImpInUnion) =>
% 128.89/16.92 ((
% 128.89/16.92 (inIntersectImpInUnion2) =>
% 128.89/16.92 ((
% 128.89/16.92 (inIntersectImpInIntersectUnions) =>
% 128.89/16.92 ((
% 128.89/16.92 (intersectInPowersetIntersectUnions) =>
% 128.89/16.92 ((
% 128.89/16.92 (inComplementUnionImpNotIn1) =>
% 128.89/16.92 ((
% 128.89/16.92 (inComplementUnionImpInComplement1) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionTE) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionTEcontra) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2a1) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementUnionInPowersetComplement) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2a2) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan1a) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan1b) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan1) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2a) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2b2) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2b) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz13rule0) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz13rule1) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz13rule2) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz13rule3) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz13rule4) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz1_1) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz1_2) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz1_3) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz1_4) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz1_5) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1all2) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1SetBreln1) =>
% 128.89/16.92 ((
% 128.89/16.92 (choice2fnsingleton) =>
% 128.89/16.92 ((
% 128.89/16.92 (setOfPairsIsBReln1) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1all1) =>
% 128.89/16.92 ((
% 128.89/16.92 (subbreln1) =>
% 128.89/16.92 ((
% 128.89/16.92 (eqbreln1) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1invprop) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1invI) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1invE) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1compprop) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1compI) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1compE) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1compEex) =>
% 128.89/16.92 ((
% 128.89/16.92 (!!) @ (
% 128.89/16.92 (('#B') @ (
% 128.89/16.92 !!) @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#S') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 '#S') @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 =>))) @
% 128.89/16.92 breln1)))) @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 !!))) @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#S') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 '#B') @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 '#S') @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 =>))) @
% 128.89/16.92 breln1)))))) @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#C') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 '#B') @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 '#B') @
% 128.89/16.92 breln1)))) @
% 128.89/16.92 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])).
% 128.89/16.92 thf(zip_derived_cl64, plain,
% 128.89/16.92 (~ (((descrp) =>
% 128.89/16.92 (((dsetconstrI) =>
% 128.89/16.92 (((dsetconstrEL) =>
% 128.89/16.92 (((dsetconstrER) =>
% 128.89/16.92 (((exuE1) =>
% 128.89/16.92 (((prop2setE) =>
% 128.89/16.92 (((emptysetE) =>
% 128.89/16.92 (((emptysetimpfalse) =>
% 128.89/16.92 (((notinemptyset) =>
% 128.89/16.92 (((exuE3e) =>
% 128.89/16.92 (((setext) =>
% 128.89/16.92 (((emptyI) =>
% 128.89/16.92 (((noeltsimpempty) =>
% 128.89/16.92 (((setbeta) =>
% 128.89/16.92 (((nonemptyE1) =>
% 128.89/16.92 (((nonemptyI) =>
% 128.89/16.92 (((nonemptyI1) =>
% 128.89/16.92 (((setadjoinIL) =>
% 128.89/16.92 (((in @ emptyset @
% 128.89/16.92 (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.92 (((setadjoinIR) =>
% 128.89/16.92 (((setadjoinE) =>
% 128.89/16.92 (((setadjoinOr) =>
% 128.89/16.92 (((setoftrueEq) =>
% 128.89/16.92 (((powersetI) =>
% 128.89/16.92 (((emptyinPowerset) =>
% 128.89/16.92 (((emptyInPowerset) =>
% 128.89/16.92 (((powersetE) =>
% 128.89/16.92 (((setunionI) =>
% 128.89/16.92 (((setunionE) =>
% 128.89/16.92 (((subPowSU) =>
% 128.89/16.92 ((
% 128.89/16.92 (exuE2) =>
% 128.89/16.92 ((
% 128.89/16.92 (nonemptyImpWitness) =>
% 128.89/16.92 ((
% 128.89/16.92 (uniqinunit) =>
% 128.89/16.92 ((
% 128.89/16.92 (notinsingleton) =>
% 128.89/16.92 ((
% 128.89/16.92 (eqinunit) =>
% 128.89/16.92 ((
% 128.89/16.92 (singletonsswitch) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairsetE) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairsetIL) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairsetIR) =>
% 128.89/16.92 ((
% 128.89/16.92 (emptyE1) =>
% 128.89/16.92 ((
% 128.89/16.92 (vacuousDall) =>
% 128.89/16.92 ((
% 128.89/16.92 (quantDeMorgan1) =>
% 128.89/16.92 ((
% 128.89/16.92 (quantDeMorgan2) =>
% 128.89/16.92 ((
% 128.89/16.92 (quantDeMorgan3) =>
% 128.89/16.92 ((
% 128.89/16.92 (quantDeMorgan4) =>
% 128.89/16.92 ((
% 128.89/16.92 (prop2setI) =>
% 128.89/16.92 ((
% 128.89/16.92 (prop2set2propI) =>
% 128.89/16.92 ((
% 128.89/16.92 (notdexE) =>
% 128.89/16.92 ((
% 128.89/16.92 (notdallE) =>
% 128.89/16.92 ((
% 128.89/16.92 (exuI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (exuI3) =>
% 128.89/16.92 ((
% 128.89/16.92 (exuI2) =>
% 128.89/16.92 ((
% 128.89/16.92 (inCongP) =>
% 128.89/16.92 ((
% 128.89/16.92 (in__Cong) =>
% 128.89/16.92 ((
% 128.89/16.92 (exuE3u) =>
% 128.89/16.92 ((
% 128.89/16.92 (exu__Cong) =>
% 128.89/16.92 ((
% 128.89/16.92 (setadjoin__Cong) =>
% 128.89/16.92 ((
% 128.89/16.92 (powerset__Cong) =>
% 128.89/16.92 ((
% 128.89/16.92 (setunion__Cong) =>
% 128.89/16.92 ((
% 128.89/16.92 (exuEu) =>
% 128.89/16.92 ((
% 128.89/16.92 (descr__Cong) =>
% 128.89/16.92 ((
% 128.89/16.92 (dsetconstr__Cong) =>
% 128.89/16.92 ((
% 128.89/16.92 (subsetI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (eqimpsubset2) =>
% 128.89/16.92 ((
% 128.89/16.92 (eqimpsubset1) =>
% 128.89/16.92 ((
% 128.89/16.92 (subsetI2) =>
% 128.89/16.92 ((
% 128.89/16.92 (emptysetsubset) =>
% 128.89/16.92 ((
% 128.89/16.92 (subsetE) =>
% 128.89/16.92 ((
% 128.89/16.92 (subsetE2) =>
% 128.89/16.92 ((
% 128.89/16.92 (notsubsetI) =>
% 128.89/16.92 ((
% 128.89/16.92 (notequalI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (notequalI2) =>
% 128.89/16.92 ((
% 128.89/16.92 (subsetRefl) =>
% 128.89/16.92 ((
% 128.89/16.92 (subsetTrans) =>
% 128.89/16.92 ((
% 128.89/16.92 (setadjoinSub) =>
% 128.89/16.92 ((
% 128.89/16.92 (setadjoinSub2) =>
% 128.89/16.92 ((
% 128.89/16.92 (subset2powerset) =>
% 128.89/16.92 ((
% 128.89/16.92 (setextsub) =>
% 128.89/16.92 ((
% 128.89/16.92 (subsetemptysetimpeq) =>
% 128.89/16.92 ((
% 128.89/16.92 (powersetI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (powersetE1) =>
% 128.89/16.92 ((
% 128.89/16.92 (inPowerset) =>
% 128.89/16.92 ((
% 128.89/16.92 (powersetsubset) =>
% 128.89/16.92 ((
% 128.89/16.92 (sepInPowerset) =>
% 128.89/16.92 ((
% 128.89/16.92 (sepSubset) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionIL) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairset2IR) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionIR) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionEcases) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionE) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionLsub) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionRsub) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectI) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectSubset5) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectEL) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectLsub) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectSubset2) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectSubset3) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectER) =>
% 128.89/16.92 ((
% 128.89/16.92 (disjointsetsI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectRsub) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectSubset4) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectSubset1) =>
% 128.89/16.92 ((
% 128.89/16.92 (bs114d) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusI) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusEL) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusER) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusSubset2) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusERneg) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusELneg) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusILneg) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusIRneg) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusLsub) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusSubset1) =>
% 128.89/16.92 ((
% 128.89/16.92 (symdiffE) =>
% 128.89/16.92 ((
% 128.89/16.92 (symdiffI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (symdiffI2) =>
% 128.89/16.92 ((
% 128.89/16.92 (symdiffIneg1) =>
% 128.89/16.92 ((
% 128.89/16.92 (symdiffIneg2) =>
% 128.89/16.92 ((
% 128.89/16.92 (secondinupair) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairIL) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairIR) =>
% 128.89/16.92 ((
% 128.89/16.92 (kpairiskpair) =>
% 128.89/16.92 ((
% 128.89/16.92 (kpairp) =>
% 128.89/16.92 ((
% 128.89/16.92 (singletonsubset) =>
% 128.89/16.92 ((
% 128.89/16.92 (singletoninpowerset) =>
% 128.89/16.92 ((
% 128.89/16.92 (singletoninpowunion) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairset2E) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairsubunion) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairinpowunion) =>
% 128.89/16.92 ((
% 128.89/16.92 (ubforcartprodlem1) =>
% 128.89/16.92 ((
% 128.89/16.92 (ubforcartprodlem2) =>
% 128.89/16.92 ((
% 128.89/16.92 (ubforcartprodlem3) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodpairin) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodmempair1) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodmempair) =>
% 128.89/16.92 ((
% 128.89/16.92 (setunionE2) =>
% 128.89/16.92 ((
% 128.89/16.92 (setunionsingleton1) =>
% 128.89/16.92 ((
% 128.89/16.92 (setunionsingleton2) =>
% 128.89/16.92 ((
% 128.89/16.92 (setunionsingleton) =>
% 128.89/16.92 ((
% 128.89/16.92 (singletonprop) =>
% 128.89/16.92 ((
% 128.89/16.92 (ex1E1) =>
% 128.89/16.92 ((
% 128.89/16.92 (ex1I) =>
% 128.89/16.92 ((
% 128.89/16.92 (ex1I2) =>
% 128.89/16.92 ((
% 128.89/16.92 (singletonsuniq) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairinjL1) =>
% 128.89/16.92 ((
% 128.89/16.92 (kfstsingleton) =>
% 128.89/16.92 ((
% 128.89/16.92 (theprop) =>
% 128.89/16.92 ((
% 128.89/16.92 (kfstpairEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodfstin) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairinjL2) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairinjL) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairinjR11) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairinjR12) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairinjR1) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairequniteq) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairinjR2) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairinjR) =>
% 128.89/16.92 ((
% 128.89/16.92 (ksndsingleton) =>
% 128.89/16.92 ((
% 128.89/16.92 (ksndpairEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (kpairsurjEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodsndin) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodpairmemEL) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodpairmemER) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodmempaircEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodfstpairEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodsndpairEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodpairsurjEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (dpsetconstrI) =>
% 128.89/16.92 ((
% 128.89/16.92 (dpsetconstrSub) =>
% 128.89/16.92 ((
% 128.89/16.92 (setOfPairsIsBReln) =>
% 128.89/16.92 ((
% 128.89/16.92 (dpsetconstrERa) =>
% 128.89/16.92 ((
% 128.89/16.92 (dpsetconstrEL1) =>
% 128.89/16.92 ((
% 128.89/16.92 (dpsetconstrEL2) =>
% 128.89/16.92 ((
% 128.89/16.92 (dpsetconstrER) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcImageSingleton) =>
% 128.89/16.92 ((
% 128.89/16.92 (apProp) =>
% 128.89/16.92 ((
% 128.89/16.92 (app) =>
% 128.89/16.92 ((
% 128.89/16.92 (infuncsetfunc) =>
% 128.89/16.92 ((
% 128.89/16.92 (ap2p) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcinfuncset) =>
% 128.89/16.92 ((
% 128.89/16.92 (lamProp) =>
% 128.89/16.92 ((
% 128.89/16.92 (lamp) =>
% 128.89/16.92 ((
% 128.89/16.92 (lam2p) =>
% 128.89/16.92 ((
% 128.89/16.92 (brelnall1) =>
% 128.89/16.92 ((
% 128.89/16.92 (brelnall2) =>
% 128.89/16.92 ((
% 128.89/16.92 (ex1E2) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcGraphProp1) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcGraphProp3) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcGraphProp2) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcextLem) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcGraphProp4) =>
% 128.89/16.92 ((
% 128.89/16.92 (subbreln) =>
% 128.89/16.92 ((
% 128.89/16.92 (eqbreln) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcext) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcext2) =>
% 128.89/16.92 ((
% 128.89/16.92 (ap2apEq1) =>
% 128.89/16.92 ((
% 128.89/16.92 (ap2apEq2) =>
% 128.89/16.92 ((
% 128.89/16.92 (beta1) =>
% 128.89/16.92 ((
% 128.89/16.92 (eta1) =>
% 128.89/16.92 ((
% 128.89/16.92 (lam2lamEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (beta2) =>
% 128.89/16.92 ((
% 128.89/16.92 (eta2) =>
% 128.89/16.92 ((
% 128.89/16.92 (iffalseProp1) =>
% 128.89/16.92 ((
% 128.89/16.92 (iffalseProp2) =>
% 128.89/16.92 ((
% 128.89/16.92 (iftrueProp1) =>
% 128.89/16.92 ((
% 128.89/16.92 (iftrueProp2) =>
% 128.89/16.92 ((
% 128.89/16.92 (ifSingleton) =>
% 128.89/16.92 ((
% 128.89/16.92 (ifp) =>
% 128.89/16.92 ((
% 128.89/16.92 (theeq) =>
% 128.89/16.92 ((
% 128.89/16.92 (iftrue) =>
% 128.89/16.92 ((
% 128.89/16.92 (iffalse) =>
% 128.89/16.92 ((
% 128.89/16.92 (iftrueorfalse) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectT_lem) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionT_lem) =>
% 128.89/16.92 ((
% 128.89/16.92 (powersetT_lem) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusT_lem) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementT_lem) =>
% 128.89/16.92 ((
% 128.89/16.92 (setextT) =>
% 128.89/16.92 ((
% 128.89/16.92 (subsetTI) =>
% 128.89/16.92 ((
% 128.89/16.92 (powersetTI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (powersetTE1) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementTI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementTE1) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectTELcontra) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectTERcontra) =>
% 128.89/16.92 ((
% 128.89/16.92 (contrasubsetT) =>
% 128.89/16.92 ((
% 128.89/16.92 (contrasubsetT1) =>
% 128.89/16.92 ((
% 128.89/16.92 (contrasubsetT2) =>
% 128.89/16.92 ((
% 128.89/16.92 (contrasubsetT3) =>
% 128.89/16.92 ((
% 128.89/16.92 (doubleComplementI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (doubleComplementE1) =>
% 128.89/16.92 ((
% 128.89/16.92 (doubleComplementSub1) =>
% 128.89/16.92 ((
% 128.89/16.92 (doubleComplementSub2) =>
% 128.89/16.92 ((
% 128.89/16.92 (doubleComplementEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementTnotintersectT) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementImpComplementIntersect) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementSubsetComplementIntersect) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementInPowersetComplementIntersect) =>
% 128.89/16.92 ((
% 128.89/16.92 (contraSubsetComplement) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementTcontraSubset) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionTILcontra) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionTIRcontra) =>
% 128.89/16.92 ((
% 128.89/16.92 (inIntersectImpInUnion) =>
% 128.89/16.92 ((
% 128.89/16.92 (inIntersectImpInUnion2) =>
% 128.89/16.92 ((
% 128.89/16.92 (inIntersectImpInIntersectUnions) =>
% 128.89/16.92 ((
% 128.89/16.92 (intersectInPowersetIntersectUnions) =>
% 128.89/16.92 ((
% 128.89/16.92 (inComplementUnionImpNotIn1) =>
% 128.89/16.92 ((
% 128.89/16.92 (inComplementUnionImpInComplement1) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionTE) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionTEcontra) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2a1) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementUnionInPowersetComplement) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2a2) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan1a) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan1b) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan1) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2a) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2b2) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2b) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz13rule0) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz13rule1) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz13rule2) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz13rule3) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz13rule4) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz1_1) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz1_2) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz1_3) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz1_4) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz1_5) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1all2) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1SetBreln1) =>
% 128.89/16.92 ((
% 128.89/16.92 (choice2fnsingleton) =>
% 128.89/16.92 ((
% 128.89/16.92 (setOfPairsIsBReln1) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1all1) =>
% 128.89/16.92 ((
% 128.89/16.92 (subbreln1) =>
% 128.89/16.92 ((
% 128.89/16.92 (eqbreln1) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1invprop) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1invI) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1invE) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1compprop) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1compI) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1compE) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1compEex) =>
% 128.89/16.92 ((
% 128.89/16.92 (!!) @ (
% 128.89/16.92 (('#B') @ (
% 128.89/16.92 !!) @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#S') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 '#S') @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 =>))) @
% 128.89/16.92 breln1)))) @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 !!))) @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#S') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 '#B') @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 '#S') @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 =>))) @
% 128.89/16.92 breln1)))))) @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#C') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 '#B') @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 '#B') @
% 128.89/16.92 breln1)))) @
% 128.89/16.92 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])).
% 128.89/16.92 thf(zip_derived_cl71, plain,
% 128.89/16.92 (~ (((dsetconstrI) =>
% 128.89/16.92 (((dsetconstrEL) =>
% 128.89/16.92 (((dsetconstrER) =>
% 128.89/16.92 (((exuE1) =>
% 128.89/16.92 (((prop2setE) =>
% 128.89/16.92 (((emptysetE) =>
% 128.89/16.92 (((emptysetimpfalse) =>
% 128.89/16.92 (((notinemptyset) =>
% 128.89/16.92 (((exuE3e) =>
% 128.89/16.92 (((setext) =>
% 128.89/16.92 (((emptyI) =>
% 128.89/16.92 (((noeltsimpempty) =>
% 128.89/16.92 (((setbeta) =>
% 128.89/16.92 (((nonemptyE1) =>
% 128.89/16.92 (((nonemptyI) =>
% 128.89/16.92 (((nonemptyI1) =>
% 128.89/16.92 (((setadjoinIL) =>
% 128.89/16.92 (((in @ emptyset @
% 128.89/16.92 (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.92 (((setadjoinIR) =>
% 128.89/16.92 (((setadjoinE) =>
% 128.89/16.92 (((setadjoinOr) =>
% 128.89/16.92 (((setoftrueEq) =>
% 128.89/16.92 (((powersetI) =>
% 128.89/16.92 (((emptyinPowerset) =>
% 128.89/16.92 (((emptyInPowerset) =>
% 128.89/16.92 (((powersetE) =>
% 128.89/16.92 (((setunionI) =>
% 128.89/16.92 (((setunionE) =>
% 128.89/16.92 (((subPowSU) =>
% 128.89/16.92 (((exuE2) =>
% 128.89/16.92 ((
% 128.89/16.92 (nonemptyImpWitness) =>
% 128.89/16.92 ((
% 128.89/16.92 (uniqinunit) =>
% 128.89/16.92 ((
% 128.89/16.92 (notinsingleton) =>
% 128.89/16.92 ((
% 128.89/16.92 (eqinunit) =>
% 128.89/16.92 ((
% 128.89/16.92 (singletonsswitch) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairsetE) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairsetIL) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairsetIR) =>
% 128.89/16.92 ((
% 128.89/16.92 (emptyE1) =>
% 128.89/16.92 ((
% 128.89/16.92 (vacuousDall) =>
% 128.89/16.92 ((
% 128.89/16.92 (quantDeMorgan1) =>
% 128.89/16.92 ((
% 128.89/16.92 (quantDeMorgan2) =>
% 128.89/16.92 ((
% 128.89/16.92 (quantDeMorgan3) =>
% 128.89/16.92 ((
% 128.89/16.92 (quantDeMorgan4) =>
% 128.89/16.92 ((
% 128.89/16.92 (prop2setI) =>
% 128.89/16.92 ((
% 128.89/16.92 (prop2set2propI) =>
% 128.89/16.92 ((
% 128.89/16.92 (notdexE) =>
% 128.89/16.92 ((
% 128.89/16.92 (notdallE) =>
% 128.89/16.92 ((
% 128.89/16.92 (exuI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (exuI3) =>
% 128.89/16.92 ((
% 128.89/16.92 (exuI2) =>
% 128.89/16.92 ((
% 128.89/16.92 (inCongP) =>
% 128.89/16.92 ((
% 128.89/16.92 (in__Cong) =>
% 128.89/16.92 ((
% 128.89/16.92 (exuE3u) =>
% 128.89/16.92 ((
% 128.89/16.92 (exu__Cong) =>
% 128.89/16.92 ((
% 128.89/16.92 (setadjoin__Cong) =>
% 128.89/16.92 ((
% 128.89/16.92 (powerset__Cong) =>
% 128.89/16.92 ((
% 128.89/16.92 (setunion__Cong) =>
% 128.89/16.92 ((
% 128.89/16.92 (exuEu) =>
% 128.89/16.92 ((
% 128.89/16.92 (descr__Cong) =>
% 128.89/16.92 ((
% 128.89/16.92 (dsetconstr__Cong) =>
% 128.89/16.92 ((
% 128.89/16.92 (subsetI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (eqimpsubset2) =>
% 128.89/16.92 ((
% 128.89/16.92 (eqimpsubset1) =>
% 128.89/16.92 ((
% 128.89/16.92 (subsetI2) =>
% 128.89/16.92 ((
% 128.89/16.92 (emptysetsubset) =>
% 128.89/16.92 ((
% 128.89/16.92 (subsetE) =>
% 128.89/16.92 ((
% 128.89/16.92 (subsetE2) =>
% 128.89/16.92 ((
% 128.89/16.92 (notsubsetI) =>
% 128.89/16.92 ((
% 128.89/16.92 (notequalI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (notequalI2) =>
% 128.89/16.92 ((
% 128.89/16.92 (subsetRefl) =>
% 128.89/16.92 ((
% 128.89/16.92 (subsetTrans) =>
% 128.89/16.92 ((
% 128.89/16.92 (setadjoinSub) =>
% 128.89/16.92 ((
% 128.89/16.92 (setadjoinSub2) =>
% 128.89/16.92 ((
% 128.89/16.92 (subset2powerset) =>
% 128.89/16.92 ((
% 128.89/16.92 (setextsub) =>
% 128.89/16.92 ((
% 128.89/16.92 (subsetemptysetimpeq) =>
% 128.89/16.92 ((
% 128.89/16.92 (powersetI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (powersetE1) =>
% 128.89/16.92 ((
% 128.89/16.92 (inPowerset) =>
% 128.89/16.92 ((
% 128.89/16.92 (powersetsubset) =>
% 128.89/16.92 ((
% 128.89/16.92 (sepInPowerset) =>
% 128.89/16.92 ((
% 128.89/16.92 (sepSubset) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionIL) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairset2IR) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionIR) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionEcases) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionE) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionLsub) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionRsub) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectI) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectSubset5) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectEL) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectLsub) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectSubset2) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectSubset3) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectER) =>
% 128.89/16.92 ((
% 128.89/16.92 (disjointsetsI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectRsub) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectSubset4) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectSubset1) =>
% 128.89/16.92 ((
% 128.89/16.92 (bs114d) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusI) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusEL) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusER) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusSubset2) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusERneg) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusELneg) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusILneg) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusIRneg) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusLsub) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusSubset1) =>
% 128.89/16.92 ((
% 128.89/16.92 (symdiffE) =>
% 128.89/16.92 ((
% 128.89/16.92 (symdiffI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (symdiffI2) =>
% 128.89/16.92 ((
% 128.89/16.92 (symdiffIneg1) =>
% 128.89/16.92 ((
% 128.89/16.92 (symdiffIneg2) =>
% 128.89/16.92 ((
% 128.89/16.92 (secondinupair) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairIL) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairIR) =>
% 128.89/16.92 ((
% 128.89/16.92 (kpairiskpair) =>
% 128.89/16.92 ((
% 128.89/16.92 (kpairp) =>
% 128.89/16.92 ((
% 128.89/16.92 (singletonsubset) =>
% 128.89/16.92 ((
% 128.89/16.92 (singletoninpowerset) =>
% 128.89/16.92 ((
% 128.89/16.92 (singletoninpowunion) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairset2E) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairsubunion) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairinpowunion) =>
% 128.89/16.92 ((
% 128.89/16.92 (ubforcartprodlem1) =>
% 128.89/16.92 ((
% 128.89/16.92 (ubforcartprodlem2) =>
% 128.89/16.92 ((
% 128.89/16.92 (ubforcartprodlem3) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodpairin) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodmempair1) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodmempair) =>
% 128.89/16.92 ((
% 128.89/16.92 (setunionE2) =>
% 128.89/16.92 ((
% 128.89/16.92 (setunionsingleton1) =>
% 128.89/16.92 ((
% 128.89/16.92 (setunionsingleton2) =>
% 128.89/16.92 ((
% 128.89/16.92 (setunionsingleton) =>
% 128.89/16.92 ((
% 128.89/16.92 (singletonprop) =>
% 128.89/16.92 ((
% 128.89/16.92 (ex1E1) =>
% 128.89/16.92 ((
% 128.89/16.92 (ex1I) =>
% 128.89/16.92 ((
% 128.89/16.92 (ex1I2) =>
% 128.89/16.92 ((
% 128.89/16.92 (singletonsuniq) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairinjL1) =>
% 128.89/16.92 ((
% 128.89/16.92 (kfstsingleton) =>
% 128.89/16.92 ((
% 128.89/16.92 (theprop) =>
% 128.89/16.92 ((
% 128.89/16.92 (kfstpairEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodfstin) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairinjL2) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairinjL) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairinjR11) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairinjR12) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairinjR1) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairequniteq) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairinjR2) =>
% 128.89/16.92 ((
% 128.89/16.92 (setukpairinjR) =>
% 128.89/16.92 ((
% 128.89/16.92 (ksndsingleton) =>
% 128.89/16.92 ((
% 128.89/16.92 (ksndpairEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (kpairsurjEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodsndin) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodpairmemEL) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodpairmemER) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodmempaircEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodfstpairEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodsndpairEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (cartprodpairsurjEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (dpsetconstrI) =>
% 128.89/16.92 ((
% 128.89/16.92 (dpsetconstrSub) =>
% 128.89/16.92 ((
% 128.89/16.92 (setOfPairsIsBReln) =>
% 128.89/16.92 ((
% 128.89/16.92 (dpsetconstrERa) =>
% 128.89/16.92 ((
% 128.89/16.92 (dpsetconstrEL1) =>
% 128.89/16.92 ((
% 128.89/16.92 (dpsetconstrEL2) =>
% 128.89/16.92 ((
% 128.89/16.92 (dpsetconstrER) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcImageSingleton) =>
% 128.89/16.92 ((
% 128.89/16.92 (apProp) =>
% 128.89/16.92 ((
% 128.89/16.92 (app) =>
% 128.89/16.92 ((
% 128.89/16.92 (infuncsetfunc) =>
% 128.89/16.92 ((
% 128.89/16.92 (ap2p) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcinfuncset) =>
% 128.89/16.92 ((
% 128.89/16.92 (lamProp) =>
% 128.89/16.92 ((
% 128.89/16.92 (lamp) =>
% 128.89/16.92 ((
% 128.89/16.92 (lam2p) =>
% 128.89/16.92 ((
% 128.89/16.92 (brelnall1) =>
% 128.89/16.92 ((
% 128.89/16.92 (brelnall2) =>
% 128.89/16.92 ((
% 128.89/16.92 (ex1E2) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcGraphProp1) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcGraphProp3) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcGraphProp2) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcextLem) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcGraphProp4) =>
% 128.89/16.92 ((
% 128.89/16.92 (subbreln) =>
% 128.89/16.92 ((
% 128.89/16.92 (eqbreln) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcext) =>
% 128.89/16.92 ((
% 128.89/16.92 (funcext2) =>
% 128.89/16.92 ((
% 128.89/16.92 (ap2apEq1) =>
% 128.89/16.92 ((
% 128.89/16.92 (ap2apEq2) =>
% 128.89/16.92 ((
% 128.89/16.92 (beta1) =>
% 128.89/16.92 ((
% 128.89/16.92 (eta1) =>
% 128.89/16.92 ((
% 128.89/16.92 (lam2lamEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (beta2) =>
% 128.89/16.92 ((
% 128.89/16.92 (eta2) =>
% 128.89/16.92 ((
% 128.89/16.92 (iffalseProp1) =>
% 128.89/16.92 ((
% 128.89/16.92 (iffalseProp2) =>
% 128.89/16.92 ((
% 128.89/16.92 (iftrueProp1) =>
% 128.89/16.92 ((
% 128.89/16.92 (iftrueProp2) =>
% 128.89/16.92 ((
% 128.89/16.92 (ifSingleton) =>
% 128.89/16.92 ((
% 128.89/16.92 (ifp) =>
% 128.89/16.92 ((
% 128.89/16.92 (theeq) =>
% 128.89/16.92 ((
% 128.89/16.92 (iftrue) =>
% 128.89/16.92 ((
% 128.89/16.92 (iffalse) =>
% 128.89/16.92 ((
% 128.89/16.92 (iftrueorfalse) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectT_lem) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionT_lem) =>
% 128.89/16.92 ((
% 128.89/16.92 (powersetT_lem) =>
% 128.89/16.92 ((
% 128.89/16.92 (setminusT_lem) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementT_lem) =>
% 128.89/16.92 ((
% 128.89/16.92 (setextT) =>
% 128.89/16.92 ((
% 128.89/16.92 (subsetTI) =>
% 128.89/16.92 ((
% 128.89/16.92 (powersetTI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (powersetTE1) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementTI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementTE1) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectTELcontra) =>
% 128.89/16.92 ((
% 128.89/16.92 (binintersectTERcontra) =>
% 128.89/16.92 ((
% 128.89/16.92 (contrasubsetT) =>
% 128.89/16.92 ((
% 128.89/16.92 (contrasubsetT1) =>
% 128.89/16.92 ((
% 128.89/16.92 (contrasubsetT2) =>
% 128.89/16.92 ((
% 128.89/16.92 (contrasubsetT3) =>
% 128.89/16.92 ((
% 128.89/16.92 (doubleComplementI1) =>
% 128.89/16.92 ((
% 128.89/16.92 (doubleComplementE1) =>
% 128.89/16.92 ((
% 128.89/16.92 (doubleComplementSub1) =>
% 128.89/16.92 ((
% 128.89/16.92 (doubleComplementSub2) =>
% 128.89/16.92 ((
% 128.89/16.92 (doubleComplementEq) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementTnotintersectT) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementImpComplementIntersect) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementSubsetComplementIntersect) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementInPowersetComplementIntersect) =>
% 128.89/16.92 ((
% 128.89/16.92 (contraSubsetComplement) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementTcontraSubset) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionTILcontra) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionTIRcontra) =>
% 128.89/16.92 ((
% 128.89/16.92 (inIntersectImpInUnion) =>
% 128.89/16.92 ((
% 128.89/16.92 (inIntersectImpInUnion2) =>
% 128.89/16.92 ((
% 128.89/16.92 (inIntersectImpInIntersectUnions) =>
% 128.89/16.92 ((
% 128.89/16.92 (intersectInPowersetIntersectUnions) =>
% 128.89/16.92 ((
% 128.89/16.92 (inComplementUnionImpNotIn1) =>
% 128.89/16.92 ((
% 128.89/16.92 (inComplementUnionImpInComplement1) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionTE) =>
% 128.89/16.92 ((
% 128.89/16.92 (binunionTEcontra) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2a1) =>
% 128.89/16.92 ((
% 128.89/16.92 (complementUnionInPowersetComplement) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2a2) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan1a) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan1b) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan1) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2a) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2b2) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2b) =>
% 128.89/16.92 ((
% 128.89/16.92 (demorgan2) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz13rule0) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz13rule1) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz13rule2) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz13rule3) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz13rule4) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz1_1) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz1_2) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz1_3) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz1_4) =>
% 128.89/16.92 ((
% 128.89/16.92 (woz1_5) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1all2) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1SetBreln1) =>
% 128.89/16.92 ((
% 128.89/16.92 (choice2fnsingleton) =>
% 128.89/16.92 ((
% 128.89/16.92 (setOfPairsIsBReln1) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1all1) =>
% 128.89/16.92 ((
% 128.89/16.92 (subbreln1) =>
% 128.89/16.92 ((
% 128.89/16.92 (eqbreln1) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1invprop) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1invI) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1invE) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1compprop) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1compI) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1compE) =>
% 128.89/16.92 ((
% 128.89/16.92 (breln1compEex) =>
% 128.89/16.92 ((
% 128.89/16.92 (!!) @ (
% 128.89/16.92 (('#B') @ (
% 128.89/16.92 !!) @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#S') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 '#S') @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 =>))) @
% 128.89/16.92 breln1)))) @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 !!))) @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#S') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 '#B') @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 '#S') @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 =>))) @
% 128.89/16.92 breln1)))))) @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#C') @ (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 '#B') @
% 128.89/16.92 (
% 128.89/16.92 (
% 128.89/16.92 ('#B') @ (
% 128.89/16.92 '#B') @
% 128.89/16.92 breln1)))) @
% 128.89/16.92 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])).
% 128.89/16.92 thf(zip_derived_cl79, plain,
% 128.89/16.92 (~ (((dsetconstrEL) =>
% 128.89/16.92 (((dsetconstrER) =>
% 128.89/16.92 (((exuE1) =>
% 128.89/16.92 (((prop2setE) =>
% 128.89/16.92 (((emptysetE) =>
% 128.89/16.92 (((emptysetimpfalse) =>
% 128.89/16.92 (((notinemptyset) =>
% 128.89/16.92 (((exuE3e) =>
% 128.89/16.92 (((setext) =>
% 128.89/16.92 (((emptyI) =>
% 128.89/16.92 (((noeltsimpempty) =>
% 128.89/16.92 (((setbeta) =>
% 128.89/16.92 (((nonemptyE1) =>
% 128.89/16.92 (((nonemptyI) =>
% 128.89/16.92 (((nonemptyI1) =>
% 128.89/16.92 (((setadjoinIL) =>
% 128.89/16.92 (((in @ emptyset @
% 128.89/16.92 (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.92 (((setadjoinIR) =>
% 128.89/16.92 (((setadjoinE) =>
% 128.89/16.92 (((setadjoinOr) =>
% 128.89/16.92 (((setoftrueEq) =>
% 128.89/16.92 (((powersetI) =>
% 128.89/16.92 (((emptyinPowerset) =>
% 128.89/16.92 (((emptyInPowerset) =>
% 128.89/16.92 (((powersetE) =>
% 128.89/16.92 (((setunionI) =>
% 128.89/16.92 (((setunionE) =>
% 128.89/16.92 (((subPowSU) =>
% 128.89/16.92 (((exuE2) =>
% 128.89/16.92 (((nonemptyImpWitness) =>
% 128.89/16.92 ((
% 128.89/16.92 (uniqinunit) =>
% 128.89/16.92 ((
% 128.89/16.92 (notinsingleton) =>
% 128.89/16.92 ((
% 128.89/16.92 (eqinunit) =>
% 128.89/16.92 ((
% 128.89/16.92 (singletonsswitch) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairsetE) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairsetIL) =>
% 128.89/16.92 ((
% 128.89/16.92 (upairsetIR) =>
% 128.89/16.92 ((
% 128.89/16.92 (emptyE1) =>
% 128.89/16.92 ((
% 128.89/16.92 (vacuousDall) =>
% 128.89/16.92 ((
% 128.89/16.92 (quantDeMorgan1) =>
% 128.89/16.92 ((
% 128.89/16.92 (quantDeMorgan2) =>
% 128.89/16.92 ((
% 128.89/16.92 (quantDeMorgan3) =>
% 128.89/16.92 ((
% 128.89/16.92 (quantDeMorgan4) =>
% 128.89/16.92 ((
% 128.89/16.92 (prop2setI) =>
% 128.89/16.92 ((
% 128.89/16.92 (prop2set2propI) =>
% 128.89/16.92 ((
% 128.89/16.92 (notdexE) =>
% 128.89/16.92 ((
% 128.89/16.93 (notdallE) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI3) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (inCongP) =>
% 128.89/16.93 ((
% 128.89/16.93 (in__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuE3u) =>
% 128.89/16.93 ((
% 128.89/16.93 (exu__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoin__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (powerset__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunion__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuEu) =>
% 128.89/16.93 ((
% 128.89/16.93 (descr__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (dsetconstr__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqimpsubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqimpsubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (emptysetsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetE) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetE2) =>
% 128.89/16.93 ((
% 128.89/16.93 (notsubsetI) =>
% 128.89/16.93 ((
% 128.89/16.93 (notequalI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (notequalI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetRefl) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetTrans) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoinSub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoinSub2) =>
% 128.89/16.93 ((
% 128.89/16.93 (subset2powerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (setextsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetemptysetimpeq) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (inPowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (sepInPowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (sepSubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairset2IR) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionEcases) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionE) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionRsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectI) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset5) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset3) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectER) =>
% 128.89/16.93 ((
% 128.89/16.93 (disjointsetsI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectRsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset4) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (bs114d) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusI) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusER) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusSubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusERneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusELneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusILneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusIRneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusSubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffE) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffIneg1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffIneg2) =>
% 128.89/16.93 ((
% 128.89/16.93 (secondinupair) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairiskpair) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairp) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletoninpowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletoninpowunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairset2E) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsubunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairinpowunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem3) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairin) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempair1) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempair) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionE2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton1) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1E1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1I) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1I2) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonsuniq) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL1) =>
% 128.89/16.93 ((
% 128.89/16.93 (kfstsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (theprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (kfstpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodfstin) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR11) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR12) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR1) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairequniteq) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR) =>
% 128.89/16.93 ((
% 128.89/16.93 (ksndsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (ksndpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairsurjEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodsndin) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairmemEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairmemER) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempaircEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodfstpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodsndpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairsurjEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrI) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrSub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setOfPairsIsBReln) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrERa) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrEL1) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrEL2) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrER) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcImageSingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (apProp) =>
% 128.89/16.93 ((
% 128.89/16.93 (app) =>
% 128.89/16.93 ((
% 128.89/16.93 (infuncsetfunc) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2p) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcinfuncset) =>
% 128.89/16.93 ((
% 128.89/16.93 (lamProp) =>
% 128.89/16.93 ((
% 128.89/16.93 (lamp) =>
% 128.89/16.93 ((
% 128.89/16.93 (lam2p) =>
% 128.89/16.93 ((
% 128.89/16.93 (brelnall1) =>
% 128.89/16.93 ((
% 128.89/16.93 (brelnall2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1E2) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp3) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcextLem) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp4) =>
% 128.89/16.93 ((
% 128.89/16.93 (subbreln) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqbreln) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcext) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcext2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2apEq1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2apEq2) =>
% 128.89/16.93 ((
% 128.89/16.93 (beta1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eta1) =>
% 128.89/16.93 ((
% 128.89/16.93 (lam2lamEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (beta2) =>
% 128.89/16.93 ((
% 128.89/16.93 (eta2) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalseProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalseProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ifSingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (ifp) =>
% 128.89/16.93 ((
% 128.89/16.93 (theeq) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrue) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalse) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueorfalse) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (setextT) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetTI) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetTI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetTE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectTELcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectTERcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT1) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT2) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT3) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementSub1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementSub2) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTnotintersectT) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementImpComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementSubsetComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementInPowersetComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (contraSubsetComplement) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTcontraSubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTILcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTIRcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInUnion) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInUnion2) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInIntersectUnions) =>
% 128.89/16.93 ((
% 128.89/16.93 (intersectInPowersetIntersectUnions) =>
% 128.89/16.93 ((
% 128.89/16.93 (inComplementUnionImpNotIn1) =>
% 128.89/16.93 ((
% 128.89/16.93 (inComplementUnionImpInComplement1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTE) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTEcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementUnionInPowersetComplement) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a2) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1a) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1b) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2b2) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2b) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule0) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule1) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule3) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule4) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_1) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_3) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_4) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_5) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1all2) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1SetBreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (choice2fnsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (setOfPairsIsBReln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1all1) =>
% 128.89/16.93 ((
% 128.89/16.93 (subbreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqbreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invI) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invE) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compI) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compE) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compEex) =>
% 128.89/16.93 ((
% 128.89/16.93 (!!) @ (
% 128.89/16.93 (('#B') @ (
% 128.89/16.93 !!) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#S') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#S') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 =>))) @
% 128.89/16.93 breln1)))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 !!))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#S') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#S') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 =>))) @
% 128.89/16.93 breln1)))))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#C') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 breln1)))) @
% 128.89/16.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])).
% 128.89/16.93 thf(zip_derived_cl89, plain,
% 128.89/16.93 (~ (((dsetconstrER) =>
% 128.89/16.93 (((exuE1) =>
% 128.89/16.93 (((prop2setE) =>
% 128.89/16.93 (((emptysetE) =>
% 128.89/16.93 (((emptysetimpfalse) =>
% 128.89/16.93 (((notinemptyset) =>
% 128.89/16.93 (((exuE3e) =>
% 128.89/16.93 (((setext) =>
% 128.89/16.93 (((emptyI) =>
% 128.89/16.93 (((noeltsimpempty) =>
% 128.89/16.93 (((setbeta) =>
% 128.89/16.93 (((nonemptyE1) =>
% 128.89/16.93 (((nonemptyI) =>
% 128.89/16.93 (((nonemptyI1) =>
% 128.89/16.93 (((setadjoinIL) =>
% 128.89/16.93 (((in @ emptyset @
% 128.89/16.93 (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.93 (((setadjoinIR) =>
% 128.89/16.93 (((setadjoinE) =>
% 128.89/16.93 (((setadjoinOr) =>
% 128.89/16.93 (((setoftrueEq) =>
% 128.89/16.93 (((powersetI) =>
% 128.89/16.93 (((emptyinPowerset) =>
% 128.89/16.93 (((emptyInPowerset) =>
% 128.89/16.93 (((powersetE) =>
% 128.89/16.93 (((setunionI) =>
% 128.89/16.93 (((setunionE) =>
% 128.89/16.93 (((subPowSU) =>
% 128.89/16.93 (((exuE2) =>
% 128.89/16.93 (((nonemptyImpWitness) =>
% 128.89/16.93 (((uniqinunit) =>
% 128.89/16.93 ((
% 128.89/16.93 (notinsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqinunit) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonsswitch) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsetE) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsetIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsetIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (emptyE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (vacuousDall) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan1) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan2) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan3) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan4) =>
% 128.89/16.93 ((
% 128.89/16.93 (prop2setI) =>
% 128.89/16.93 ((
% 128.89/16.93 (prop2set2propI) =>
% 128.89/16.93 ((
% 128.89/16.93 (notdexE) =>
% 128.89/16.93 ((
% 128.89/16.93 (notdallE) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI3) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (inCongP) =>
% 128.89/16.93 ((
% 128.89/16.93 (in__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuE3u) =>
% 128.89/16.93 ((
% 128.89/16.93 (exu__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoin__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (powerset__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunion__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuEu) =>
% 128.89/16.93 ((
% 128.89/16.93 (descr__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (dsetconstr__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqimpsubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqimpsubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (emptysetsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetE) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetE2) =>
% 128.89/16.93 ((
% 128.89/16.93 (notsubsetI) =>
% 128.89/16.93 ((
% 128.89/16.93 (notequalI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (notequalI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetRefl) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetTrans) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoinSub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoinSub2) =>
% 128.89/16.93 ((
% 128.89/16.93 (subset2powerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (setextsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetemptysetimpeq) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (inPowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (sepInPowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (sepSubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairset2IR) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionEcases) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionE) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionRsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectI) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset5) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset3) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectER) =>
% 128.89/16.93 ((
% 128.89/16.93 (disjointsetsI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectRsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset4) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (bs114d) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusI) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusER) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusSubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusERneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusELneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusILneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusIRneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusSubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffE) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffIneg1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffIneg2) =>
% 128.89/16.93 ((
% 128.89/16.93 (secondinupair) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairiskpair) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairp) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletoninpowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletoninpowunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairset2E) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsubunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairinpowunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem3) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairin) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempair1) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempair) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionE2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton1) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1E1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1I) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1I2) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonsuniq) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL1) =>
% 128.89/16.93 ((
% 128.89/16.93 (kfstsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (theprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (kfstpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodfstin) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR11) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR12) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR1) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairequniteq) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR) =>
% 128.89/16.93 ((
% 128.89/16.93 (ksndsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (ksndpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairsurjEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodsndin) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairmemEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairmemER) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempaircEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodfstpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodsndpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairsurjEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrI) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrSub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setOfPairsIsBReln) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrERa) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrEL1) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrEL2) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrER) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcImageSingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (apProp) =>
% 128.89/16.93 ((
% 128.89/16.93 (app) =>
% 128.89/16.93 ((
% 128.89/16.93 (infuncsetfunc) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2p) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcinfuncset) =>
% 128.89/16.93 ((
% 128.89/16.93 (lamProp) =>
% 128.89/16.93 ((
% 128.89/16.93 (lamp) =>
% 128.89/16.93 ((
% 128.89/16.93 (lam2p) =>
% 128.89/16.93 ((
% 128.89/16.93 (brelnall1) =>
% 128.89/16.93 ((
% 128.89/16.93 (brelnall2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1E2) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp3) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcextLem) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp4) =>
% 128.89/16.93 ((
% 128.89/16.93 (subbreln) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqbreln) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcext) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcext2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2apEq1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2apEq2) =>
% 128.89/16.93 ((
% 128.89/16.93 (beta1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eta1) =>
% 128.89/16.93 ((
% 128.89/16.93 (lam2lamEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (beta2) =>
% 128.89/16.93 ((
% 128.89/16.93 (eta2) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalseProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalseProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ifSingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (ifp) =>
% 128.89/16.93 ((
% 128.89/16.93 (theeq) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrue) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalse) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueorfalse) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (setextT) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetTI) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetTI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetTE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectTELcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectTERcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT1) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT2) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT3) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementSub1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementSub2) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTnotintersectT) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementImpComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementSubsetComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementInPowersetComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (contraSubsetComplement) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTcontraSubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTILcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTIRcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInUnion) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInUnion2) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInIntersectUnions) =>
% 128.89/16.93 ((
% 128.89/16.93 (intersectInPowersetIntersectUnions) =>
% 128.89/16.93 ((
% 128.89/16.93 (inComplementUnionImpNotIn1) =>
% 128.89/16.93 ((
% 128.89/16.93 (inComplementUnionImpInComplement1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTE) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTEcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementUnionInPowersetComplement) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a2) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1a) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1b) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2b2) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2b) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule0) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule1) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule3) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule4) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_1) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_3) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_4) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_5) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1all2) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1SetBreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (choice2fnsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (setOfPairsIsBReln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1all1) =>
% 128.89/16.93 ((
% 128.89/16.93 (subbreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqbreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invI) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invE) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compI) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compE) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compEex) =>
% 128.89/16.93 ((
% 128.89/16.93 (!!) @ (
% 128.89/16.93 (('#B') @ (
% 128.89/16.93 !!) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#S') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#S') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 =>))) @
% 128.89/16.93 breln1)))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 !!))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#S') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#S') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 =>))) @
% 128.89/16.93 breln1)))))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#C') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 breln1)))) @
% 128.89/16.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 128.89/16.93 thf(zip_derived_cl105, plain,
% 128.89/16.93 (~ (((exuE1) =>
% 128.89/16.93 (((prop2setE) =>
% 128.89/16.93 (((emptysetE) =>
% 128.89/16.93 (((emptysetimpfalse) =>
% 128.89/16.93 (((notinemptyset) =>
% 128.89/16.93 (((exuE3e) =>
% 128.89/16.93 (((setext) =>
% 128.89/16.93 (((emptyI) =>
% 128.89/16.93 (((noeltsimpempty) =>
% 128.89/16.93 (((setbeta) =>
% 128.89/16.93 (((nonemptyE1) =>
% 128.89/16.93 (((nonemptyI) =>
% 128.89/16.93 (((nonemptyI1) =>
% 128.89/16.93 (((setadjoinIL) =>
% 128.89/16.93 (((in @ emptyset @
% 128.89/16.93 (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.93 (((setadjoinIR) =>
% 128.89/16.93 (((setadjoinE) =>
% 128.89/16.93 (((setadjoinOr) =>
% 128.89/16.93 (((setoftrueEq) =>
% 128.89/16.93 (((powersetI) =>
% 128.89/16.93 (((emptyinPowerset) =>
% 128.89/16.93 (((emptyInPowerset) =>
% 128.89/16.93 (((powersetE) =>
% 128.89/16.93 (((setunionI) =>
% 128.89/16.93 (((setunionE) =>
% 128.89/16.93 (((subPowSU) =>
% 128.89/16.93 (((exuE2) =>
% 128.89/16.93 (((nonemptyImpWitness) =>
% 128.89/16.93 (((uniqinunit) =>
% 128.89/16.93 (((notinsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqinunit) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonsswitch) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsetE) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsetIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsetIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (emptyE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (vacuousDall) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan1) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan2) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan3) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan4) =>
% 128.89/16.93 ((
% 128.89/16.93 (prop2setI) =>
% 128.89/16.93 ((
% 128.89/16.93 (prop2set2propI) =>
% 128.89/16.93 ((
% 128.89/16.93 (notdexE) =>
% 128.89/16.93 ((
% 128.89/16.93 (notdallE) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI3) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (inCongP) =>
% 128.89/16.93 ((
% 128.89/16.93 (in__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuE3u) =>
% 128.89/16.93 ((
% 128.89/16.93 (exu__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoin__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (powerset__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunion__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuEu) =>
% 128.89/16.93 ((
% 128.89/16.93 (descr__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (dsetconstr__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqimpsubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqimpsubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (emptysetsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetE) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetE2) =>
% 128.89/16.93 ((
% 128.89/16.93 (notsubsetI) =>
% 128.89/16.93 ((
% 128.89/16.93 (notequalI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (notequalI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetRefl) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetTrans) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoinSub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoinSub2) =>
% 128.89/16.93 ((
% 128.89/16.93 (subset2powerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (setextsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetemptysetimpeq) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (inPowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (sepInPowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (sepSubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairset2IR) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionEcases) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionE) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionRsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectI) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset5) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset3) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectER) =>
% 128.89/16.93 ((
% 128.89/16.93 (disjointsetsI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectRsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset4) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (bs114d) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusI) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusER) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusSubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusERneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusELneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusILneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusIRneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusSubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffE) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffIneg1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffIneg2) =>
% 128.89/16.93 ((
% 128.89/16.93 (secondinupair) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairiskpair) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairp) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletoninpowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletoninpowunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairset2E) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsubunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairinpowunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem3) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairin) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempair1) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempair) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionE2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton1) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1E1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1I) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1I2) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonsuniq) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL1) =>
% 128.89/16.93 ((
% 128.89/16.93 (kfstsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (theprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (kfstpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodfstin) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR11) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR12) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR1) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairequniteq) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR) =>
% 128.89/16.93 ((
% 128.89/16.93 (ksndsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (ksndpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairsurjEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodsndin) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairmemEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairmemER) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempaircEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodfstpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodsndpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairsurjEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrI) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrSub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setOfPairsIsBReln) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrERa) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrEL1) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrEL2) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrER) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcImageSingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (apProp) =>
% 128.89/16.93 ((
% 128.89/16.93 (app) =>
% 128.89/16.93 ((
% 128.89/16.93 (infuncsetfunc) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2p) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcinfuncset) =>
% 128.89/16.93 ((
% 128.89/16.93 (lamProp) =>
% 128.89/16.93 ((
% 128.89/16.93 (lamp) =>
% 128.89/16.93 ((
% 128.89/16.93 (lam2p) =>
% 128.89/16.93 ((
% 128.89/16.93 (brelnall1) =>
% 128.89/16.93 ((
% 128.89/16.93 (brelnall2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1E2) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp3) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcextLem) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp4) =>
% 128.89/16.93 ((
% 128.89/16.93 (subbreln) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqbreln) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcext) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcext2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2apEq1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2apEq2) =>
% 128.89/16.93 ((
% 128.89/16.93 (beta1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eta1) =>
% 128.89/16.93 ((
% 128.89/16.93 (lam2lamEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (beta2) =>
% 128.89/16.93 ((
% 128.89/16.93 (eta2) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalseProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalseProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ifSingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (ifp) =>
% 128.89/16.93 ((
% 128.89/16.93 (theeq) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrue) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalse) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueorfalse) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (setextT) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetTI) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetTI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetTE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectTELcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectTERcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT1) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT2) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT3) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementSub1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementSub2) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTnotintersectT) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementImpComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementSubsetComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementInPowersetComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (contraSubsetComplement) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTcontraSubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTILcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTIRcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInUnion) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInUnion2) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInIntersectUnions) =>
% 128.89/16.93 ((
% 128.89/16.93 (intersectInPowersetIntersectUnions) =>
% 128.89/16.93 ((
% 128.89/16.93 (inComplementUnionImpNotIn1) =>
% 128.89/16.93 ((
% 128.89/16.93 (inComplementUnionImpInComplement1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTE) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTEcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementUnionInPowersetComplement) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a2) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1a) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1b) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2b2) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2b) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule0) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule1) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule3) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule4) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_1) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_3) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_4) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_5) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1all2) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1SetBreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (choice2fnsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (setOfPairsIsBReln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1all1) =>
% 128.89/16.93 ((
% 128.89/16.93 (subbreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqbreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invI) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invE) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compI) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compE) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compEex) =>
% 128.89/16.93 ((
% 128.89/16.93 (!!) @ (
% 128.89/16.93 (('#B') @ (
% 128.89/16.93 !!) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#S') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#S') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 =>))) @
% 128.89/16.93 breln1)))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 !!))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#S') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#S') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 =>))) @
% 128.89/16.93 breln1)))))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#C') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 breln1)))) @
% 128.89/16.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl89])).
% 128.89/16.93 thf(zip_derived_cl123, plain,
% 128.89/16.93 (~ (((prop2setE) =>
% 128.89/16.93 (((emptysetE) =>
% 128.89/16.93 (((emptysetimpfalse) =>
% 128.89/16.93 (((notinemptyset) =>
% 128.89/16.93 (((exuE3e) =>
% 128.89/16.93 (((setext) =>
% 128.89/16.93 (((emptyI) =>
% 128.89/16.93 (((noeltsimpempty) =>
% 128.89/16.93 (((setbeta) =>
% 128.89/16.93 (((nonemptyE1) =>
% 128.89/16.93 (((nonemptyI) =>
% 128.89/16.93 (((nonemptyI1) =>
% 128.89/16.93 (((setadjoinIL) =>
% 128.89/16.93 (((in @ emptyset @
% 128.89/16.93 (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.93 (((setadjoinIR) =>
% 128.89/16.93 (((setadjoinE) =>
% 128.89/16.93 (((setadjoinOr) =>
% 128.89/16.93 (((setoftrueEq) =>
% 128.89/16.93 (((powersetI) =>
% 128.89/16.93 (((emptyinPowerset) =>
% 128.89/16.93 (((emptyInPowerset) =>
% 128.89/16.93 (((powersetE) =>
% 128.89/16.93 (((setunionI) =>
% 128.89/16.93 (((setunionE) =>
% 128.89/16.93 (((subPowSU) =>
% 128.89/16.93 (((exuE2) =>
% 128.89/16.93 (((nonemptyImpWitness) =>
% 128.89/16.93 (((uniqinunit) =>
% 128.89/16.93 (((notinsingleton) =>
% 128.89/16.93 (((eqinunit) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonsswitch) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsetE) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsetIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsetIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (emptyE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (vacuousDall) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan1) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan2) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan3) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan4) =>
% 128.89/16.93 ((
% 128.89/16.93 (prop2setI) =>
% 128.89/16.93 ((
% 128.89/16.93 (prop2set2propI) =>
% 128.89/16.93 ((
% 128.89/16.93 (notdexE) =>
% 128.89/16.93 ((
% 128.89/16.93 (notdallE) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI3) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (inCongP) =>
% 128.89/16.93 ((
% 128.89/16.93 (in__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuE3u) =>
% 128.89/16.93 ((
% 128.89/16.93 (exu__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoin__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (powerset__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunion__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuEu) =>
% 128.89/16.93 ((
% 128.89/16.93 (descr__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (dsetconstr__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqimpsubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqimpsubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (emptysetsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetE) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetE2) =>
% 128.89/16.93 ((
% 128.89/16.93 (notsubsetI) =>
% 128.89/16.93 ((
% 128.89/16.93 (notequalI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (notequalI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetRefl) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetTrans) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoinSub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoinSub2) =>
% 128.89/16.93 ((
% 128.89/16.93 (subset2powerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (setextsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetemptysetimpeq) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (inPowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (sepInPowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (sepSubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairset2IR) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionEcases) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionE) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionRsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectI) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset5) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset3) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectER) =>
% 128.89/16.93 ((
% 128.89/16.93 (disjointsetsI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectRsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset4) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (bs114d) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusI) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusER) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusSubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusERneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusELneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusILneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusIRneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusSubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffE) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffIneg1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffIneg2) =>
% 128.89/16.93 ((
% 128.89/16.93 (secondinupair) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairiskpair) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairp) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletoninpowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletoninpowunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairset2E) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsubunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairinpowunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem3) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairin) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempair1) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempair) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionE2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton1) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1E1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1I) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1I2) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonsuniq) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL1) =>
% 128.89/16.93 ((
% 128.89/16.93 (kfstsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (theprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (kfstpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodfstin) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR11) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR12) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR1) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairequniteq) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR) =>
% 128.89/16.93 ((
% 128.89/16.93 (ksndsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (ksndpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairsurjEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodsndin) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairmemEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairmemER) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempaircEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodfstpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodsndpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairsurjEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrI) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrSub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setOfPairsIsBReln) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrERa) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrEL1) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrEL2) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrER) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcImageSingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (apProp) =>
% 128.89/16.93 ((
% 128.89/16.93 (app) =>
% 128.89/16.93 ((
% 128.89/16.93 (infuncsetfunc) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2p) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcinfuncset) =>
% 128.89/16.93 ((
% 128.89/16.93 (lamProp) =>
% 128.89/16.93 ((
% 128.89/16.93 (lamp) =>
% 128.89/16.93 ((
% 128.89/16.93 (lam2p) =>
% 128.89/16.93 ((
% 128.89/16.93 (brelnall1) =>
% 128.89/16.93 ((
% 128.89/16.93 (brelnall2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1E2) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp3) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcextLem) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp4) =>
% 128.89/16.93 ((
% 128.89/16.93 (subbreln) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqbreln) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcext) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcext2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2apEq1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2apEq2) =>
% 128.89/16.93 ((
% 128.89/16.93 (beta1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eta1) =>
% 128.89/16.93 ((
% 128.89/16.93 (lam2lamEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (beta2) =>
% 128.89/16.93 ((
% 128.89/16.93 (eta2) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalseProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalseProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ifSingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (ifp) =>
% 128.89/16.93 ((
% 128.89/16.93 (theeq) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrue) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalse) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueorfalse) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (setextT) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetTI) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetTI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetTE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectTELcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectTERcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT1) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT2) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT3) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementSub1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementSub2) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTnotintersectT) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementImpComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementSubsetComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementInPowersetComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (contraSubsetComplement) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTcontraSubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTILcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTIRcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInUnion) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInUnion2) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInIntersectUnions) =>
% 128.89/16.93 ((
% 128.89/16.93 (intersectInPowersetIntersectUnions) =>
% 128.89/16.93 ((
% 128.89/16.93 (inComplementUnionImpNotIn1) =>
% 128.89/16.93 ((
% 128.89/16.93 (inComplementUnionImpInComplement1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTE) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTEcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementUnionInPowersetComplement) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a2) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1a) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1b) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2b2) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2b) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule0) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule1) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule3) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule4) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_1) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_3) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_4) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_5) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1all2) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1SetBreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (choice2fnsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (setOfPairsIsBReln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1all1) =>
% 128.89/16.93 ((
% 128.89/16.93 (subbreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqbreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invI) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invE) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compI) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compE) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compEex) =>
% 128.89/16.93 ((
% 128.89/16.93 (!!) @ (
% 128.89/16.93 (('#B') @ (
% 128.89/16.93 !!) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#S') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#S') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 =>))) @
% 128.89/16.93 breln1)))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 !!))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#S') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#S') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 =>))) @
% 128.89/16.93 breln1)))))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#C') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 breln1)))) @
% 128.89/16.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])).
% 128.89/16.93 thf(zip_derived_cl142, plain,
% 128.89/16.93 (~ (((emptysetE) =>
% 128.89/16.93 (((emptysetimpfalse) =>
% 128.89/16.93 (((notinemptyset) =>
% 128.89/16.93 (((exuE3e) =>
% 128.89/16.93 (((setext) =>
% 128.89/16.93 (((emptyI) =>
% 128.89/16.93 (((noeltsimpempty) =>
% 128.89/16.93 (((setbeta) =>
% 128.89/16.93 (((nonemptyE1) =>
% 128.89/16.93 (((nonemptyI) =>
% 128.89/16.93 (((nonemptyI1) =>
% 128.89/16.93 (((setadjoinIL) =>
% 128.89/16.93 (((in @ emptyset @
% 128.89/16.93 (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.93 (((setadjoinIR) =>
% 128.89/16.93 (((setadjoinE) =>
% 128.89/16.93 (((setadjoinOr) =>
% 128.89/16.93 (((setoftrueEq) =>
% 128.89/16.93 (((powersetI) =>
% 128.89/16.93 (((emptyinPowerset) =>
% 128.89/16.93 (((emptyInPowerset) =>
% 128.89/16.93 (((powersetE) =>
% 128.89/16.93 (((setunionI) =>
% 128.89/16.93 (((setunionE) =>
% 128.89/16.93 (((subPowSU) =>
% 128.89/16.93 (((exuE2) =>
% 128.89/16.93 (((nonemptyImpWitness) =>
% 128.89/16.93 (((uniqinunit) =>
% 128.89/16.93 (((notinsingleton) =>
% 128.89/16.93 (((eqinunit) =>
% 128.89/16.93 (((singletonsswitch) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsetE) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsetIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsetIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (emptyE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (vacuousDall) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan1) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan2) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan3) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan4) =>
% 128.89/16.93 ((
% 128.89/16.93 (prop2setI) =>
% 128.89/16.93 ((
% 128.89/16.93 (prop2set2propI) =>
% 128.89/16.93 ((
% 128.89/16.93 (notdexE) =>
% 128.89/16.93 ((
% 128.89/16.93 (notdallE) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI3) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (inCongP) =>
% 128.89/16.93 ((
% 128.89/16.93 (in__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuE3u) =>
% 128.89/16.93 ((
% 128.89/16.93 (exu__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoin__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (powerset__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunion__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuEu) =>
% 128.89/16.93 ((
% 128.89/16.93 (descr__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (dsetconstr__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqimpsubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqimpsubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (emptysetsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetE) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetE2) =>
% 128.89/16.93 ((
% 128.89/16.93 (notsubsetI) =>
% 128.89/16.93 ((
% 128.89/16.93 (notequalI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (notequalI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetRefl) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetTrans) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoinSub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoinSub2) =>
% 128.89/16.93 ((
% 128.89/16.93 (subset2powerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (setextsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetemptysetimpeq) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (inPowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (sepInPowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (sepSubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairset2IR) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionEcases) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionE) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionRsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectI) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset5) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset3) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectER) =>
% 128.89/16.93 ((
% 128.89/16.93 (disjointsetsI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectRsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset4) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (bs114d) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusI) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusER) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusSubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusERneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusELneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusILneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusIRneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusSubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffE) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffIneg1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffIneg2) =>
% 128.89/16.93 ((
% 128.89/16.93 (secondinupair) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairiskpair) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairp) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletoninpowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletoninpowunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairset2E) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsubunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairinpowunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem3) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairin) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempair1) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempair) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionE2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton1) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1E1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1I) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1I2) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonsuniq) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL1) =>
% 128.89/16.93 ((
% 128.89/16.93 (kfstsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (theprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (kfstpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodfstin) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR11) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR12) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR1) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairequniteq) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR) =>
% 128.89/16.93 ((
% 128.89/16.93 (ksndsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (ksndpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairsurjEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodsndin) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairmemEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairmemER) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempaircEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodfstpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodsndpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairsurjEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrI) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrSub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setOfPairsIsBReln) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrERa) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrEL1) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrEL2) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrER) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcImageSingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (apProp) =>
% 128.89/16.93 ((
% 128.89/16.93 (app) =>
% 128.89/16.93 ((
% 128.89/16.93 (infuncsetfunc) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2p) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcinfuncset) =>
% 128.89/16.93 ((
% 128.89/16.93 (lamProp) =>
% 128.89/16.93 ((
% 128.89/16.93 (lamp) =>
% 128.89/16.93 ((
% 128.89/16.93 (lam2p) =>
% 128.89/16.93 ((
% 128.89/16.93 (brelnall1) =>
% 128.89/16.93 ((
% 128.89/16.93 (brelnall2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1E2) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp3) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcextLem) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp4) =>
% 128.89/16.93 ((
% 128.89/16.93 (subbreln) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqbreln) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcext) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcext2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2apEq1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2apEq2) =>
% 128.89/16.93 ((
% 128.89/16.93 (beta1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eta1) =>
% 128.89/16.93 ((
% 128.89/16.93 (lam2lamEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (beta2) =>
% 128.89/16.93 ((
% 128.89/16.93 (eta2) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalseProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalseProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ifSingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (ifp) =>
% 128.89/16.93 ((
% 128.89/16.93 (theeq) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrue) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalse) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueorfalse) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (setextT) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetTI) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetTI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetTE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectTELcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectTERcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT1) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT2) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT3) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementSub1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementSub2) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTnotintersectT) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementImpComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementSubsetComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementInPowersetComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (contraSubsetComplement) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTcontraSubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTILcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTIRcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInUnion) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInUnion2) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInIntersectUnions) =>
% 128.89/16.93 ((
% 128.89/16.93 (intersectInPowersetIntersectUnions) =>
% 128.89/16.93 ((
% 128.89/16.93 (inComplementUnionImpNotIn1) =>
% 128.89/16.93 ((
% 128.89/16.93 (inComplementUnionImpInComplement1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTE) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTEcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementUnionInPowersetComplement) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a2) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1a) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1b) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2b2) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2b) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule0) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule1) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule3) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule4) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_1) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_3) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_4) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_5) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1all2) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1SetBreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (choice2fnsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (setOfPairsIsBReln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1all1) =>
% 128.89/16.93 ((
% 128.89/16.93 (subbreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqbreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invI) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invE) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compI) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compE) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compEex) =>
% 128.89/16.93 ((
% 128.89/16.93 (!!) @ (
% 128.89/16.93 (('#B') @ (
% 128.89/16.93 !!) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#S') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#S') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 =>))) @
% 128.89/16.93 breln1)))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 !!))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#S') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#S') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 =>))) @
% 128.89/16.93 breln1)))))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#C') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 breln1)))) @
% 128.89/16.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])).
% 128.89/16.93 thf(zip_derived_cl158, plain,
% 128.89/16.93 (~ (((emptysetimpfalse) =>
% 128.89/16.93 (((notinemptyset) =>
% 128.89/16.93 (((exuE3e) =>
% 128.89/16.93 (((setext) =>
% 128.89/16.93 (((emptyI) =>
% 128.89/16.93 (((noeltsimpempty) =>
% 128.89/16.93 (((setbeta) =>
% 128.89/16.93 (((nonemptyE1) =>
% 128.89/16.93 (((nonemptyI) =>
% 128.89/16.93 (((nonemptyI1) =>
% 128.89/16.93 (((setadjoinIL) =>
% 128.89/16.93 (((in @ emptyset @
% 128.89/16.93 (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.93 (((setadjoinIR) =>
% 128.89/16.93 (((setadjoinE) =>
% 128.89/16.93 (((setadjoinOr) =>
% 128.89/16.93 (((setoftrueEq) =>
% 128.89/16.93 (((powersetI) =>
% 128.89/16.93 (((emptyinPowerset) =>
% 128.89/16.93 (((emptyInPowerset) =>
% 128.89/16.93 (((powersetE) =>
% 128.89/16.93 (((setunionI) =>
% 128.89/16.93 (((setunionE) =>
% 128.89/16.93 (((subPowSU) =>
% 128.89/16.93 (((exuE2) =>
% 128.89/16.93 (((nonemptyImpWitness) =>
% 128.89/16.93 (((uniqinunit) =>
% 128.89/16.93 (((notinsingleton) =>
% 128.89/16.93 (((eqinunit) =>
% 128.89/16.93 (((singletonsswitch) =>
% 128.89/16.93 (((upairsetE) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsetIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsetIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (emptyE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (vacuousDall) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan1) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan2) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan3) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan4) =>
% 128.89/16.93 ((
% 128.89/16.93 (prop2setI) =>
% 128.89/16.93 ((
% 128.89/16.93 (prop2set2propI) =>
% 128.89/16.93 ((
% 128.89/16.93 (notdexE) =>
% 128.89/16.93 ((
% 128.89/16.93 (notdallE) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI3) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (inCongP) =>
% 128.89/16.93 ((
% 128.89/16.93 (in__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuE3u) =>
% 128.89/16.93 ((
% 128.89/16.93 (exu__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoin__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (powerset__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunion__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuEu) =>
% 128.89/16.93 ((
% 128.89/16.93 (descr__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (dsetconstr__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqimpsubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqimpsubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (emptysetsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetE) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetE2) =>
% 128.89/16.93 ((
% 128.89/16.93 (notsubsetI) =>
% 128.89/16.93 ((
% 128.89/16.93 (notequalI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (notequalI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetRefl) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetTrans) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoinSub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoinSub2) =>
% 128.89/16.93 ((
% 128.89/16.93 (subset2powerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (setextsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetemptysetimpeq) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (inPowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (sepInPowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (sepSubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairset2IR) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionEcases) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionE) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionRsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectI) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset5) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset3) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectER) =>
% 128.89/16.93 ((
% 128.89/16.93 (disjointsetsI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectRsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset4) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectSubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (bs114d) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusI) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusER) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusSubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusERneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusELneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusILneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusIRneg) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusLsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusSubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffE) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffIneg1) =>
% 128.89/16.93 ((
% 128.89/16.93 (symdiffIneg2) =>
% 128.89/16.93 ((
% 128.89/16.93 (secondinupair) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairiskpair) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairp) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletoninpowerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletoninpowunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairset2E) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsubunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairinpowunion) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ubforcartprodlem3) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairin) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempair1) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempair) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionE2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton1) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunionsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1E1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1I) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1I2) =>
% 128.89/16.93 ((
% 128.89/16.93 (singletonsuniq) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL1) =>
% 128.89/16.93 ((
% 128.89/16.93 (kfstsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (theprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (kfstpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodfstin) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjL) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR11) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR12) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR1) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairequniteq) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR2) =>
% 128.89/16.93 ((
% 128.89/16.93 (setukpairinjR) =>
% 128.89/16.93 ((
% 128.89/16.93 (ksndsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (ksndpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (kpairsurjEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodsndin) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairmemEL) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairmemER) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodmempaircEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodfstpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodsndpairEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (cartprodpairsurjEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrI) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrSub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setOfPairsIsBReln) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrERa) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrEL1) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrEL2) =>
% 128.89/16.93 ((
% 128.89/16.93 (dpsetconstrER) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcImageSingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (apProp) =>
% 128.89/16.93 ((
% 128.89/16.93 (app) =>
% 128.89/16.93 ((
% 128.89/16.93 (infuncsetfunc) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2p) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcinfuncset) =>
% 128.89/16.93 ((
% 128.89/16.93 (lamProp) =>
% 128.89/16.93 ((
% 128.89/16.93 (lamp) =>
% 128.89/16.93 ((
% 128.89/16.93 (lam2p) =>
% 128.89/16.93 ((
% 128.89/16.93 (brelnall1) =>
% 128.89/16.93 ((
% 128.89/16.93 (brelnall2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ex1E2) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp3) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcextLem) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcGraphProp4) =>
% 128.89/16.93 ((
% 128.89/16.93 (subbreln) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqbreln) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcext) =>
% 128.89/16.93 ((
% 128.89/16.93 (funcext2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2apEq1) =>
% 128.89/16.93 ((
% 128.89/16.93 (ap2apEq2) =>
% 128.89/16.93 ((
% 128.89/16.93 (beta1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eta1) =>
% 128.89/16.93 ((
% 128.89/16.93 (lam2lamEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (beta2) =>
% 128.89/16.93 ((
% 128.89/16.93 (eta2) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalseProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalseProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueProp1) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueProp2) =>
% 128.89/16.93 ((
% 128.89/16.93 (ifSingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (ifp) =>
% 128.89/16.93 ((
% 128.89/16.93 (theeq) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrue) =>
% 128.89/16.93 ((
% 128.89/16.93 (iffalse) =>
% 128.89/16.93 ((
% 128.89/16.93 (iftrueorfalse) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (setminusT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementT_lem) =>
% 128.89/16.93 ((
% 128.89/16.93 (setextT) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetTI) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetTI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetTE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectTELcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (binintersectTERcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT1) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT2) =>
% 128.89/16.93 ((
% 128.89/16.93 (contrasubsetT3) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementSub1) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementSub2) =>
% 128.89/16.93 ((
% 128.89/16.93 (doubleComplementEq) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTnotintersectT) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementImpComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementSubsetComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementInPowersetComplementIntersect) =>
% 128.89/16.93 ((
% 128.89/16.93 (contraSubsetComplement) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementTcontraSubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTILcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTIRcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInUnion) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInUnion2) =>
% 128.89/16.93 ((
% 128.89/16.93 (inIntersectImpInIntersectUnions) =>
% 128.89/16.93 ((
% 128.89/16.93 (intersectInPowersetIntersectUnions) =>
% 128.89/16.93 ((
% 128.89/16.93 (inComplementUnionImpNotIn1) =>
% 128.89/16.93 ((
% 128.89/16.93 (inComplementUnionImpInComplement1) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTE) =>
% 128.89/16.93 ((
% 128.89/16.93 (binunionTEcontra) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a1) =>
% 128.89/16.93 ((
% 128.89/16.93 (complementUnionInPowersetComplement) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a2) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1a) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1b) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan1) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2a) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2b2) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2b) =>
% 128.89/16.93 ((
% 128.89/16.93 (demorgan2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule0) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule1) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule3) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz13rule4) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_1) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_2) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_3) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_4) =>
% 128.89/16.93 ((
% 128.89/16.93 (woz1_5) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1all2) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1SetBreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (choice2fnsingleton) =>
% 128.89/16.93 ((
% 128.89/16.93 (setOfPairsIsBReln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1all1) =>
% 128.89/16.93 ((
% 128.89/16.93 (subbreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqbreln1) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invI) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1invE) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compprop) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compI) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compE) =>
% 128.89/16.93 ((
% 128.89/16.93 (breln1compEex) =>
% 128.89/16.93 ((
% 128.89/16.93 (!!) @ (
% 128.89/16.93 (('#B') @ (
% 128.89/16.93 !!) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#S') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#S') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 =>))) @
% 128.89/16.93 breln1)))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 !!))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#S') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#S') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 =>))) @
% 128.89/16.93 breln1)))))) @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#C') @ (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 (
% 128.89/16.93 (
% 128.89/16.93 ('#B') @ (
% 128.89/16.93 '#B') @
% 128.89/16.93 breln1)))) @
% 128.89/16.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])).
% 128.89/16.93 thf(zip_derived_cl174, plain,
% 128.89/16.93 (~ (((notinemptyset) =>
% 128.89/16.93 (((exuE3e) =>
% 128.89/16.93 (((setext) =>
% 128.89/16.93 (((emptyI) =>
% 128.89/16.93 (((noeltsimpempty) =>
% 128.89/16.93 (((setbeta) =>
% 128.89/16.93 (((nonemptyE1) =>
% 128.89/16.93 (((nonemptyI) =>
% 128.89/16.93 (((nonemptyI1) =>
% 128.89/16.93 (((setadjoinIL) =>
% 128.89/16.93 (((in @ emptyset @
% 128.89/16.93 (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.93 (((setadjoinIR) =>
% 128.89/16.93 (((setadjoinE) =>
% 128.89/16.93 (((setadjoinOr) =>
% 128.89/16.93 (((setoftrueEq) =>
% 128.89/16.93 (((powersetI) =>
% 128.89/16.93 (((emptyinPowerset) =>
% 128.89/16.93 (((emptyInPowerset) =>
% 128.89/16.93 (((powersetE) =>
% 128.89/16.93 (((setunionI) =>
% 128.89/16.93 (((setunionE) =>
% 128.89/16.93 (((subPowSU) =>
% 128.89/16.93 (((exuE2) =>
% 128.89/16.93 (((nonemptyImpWitness) =>
% 128.89/16.93 (((uniqinunit) =>
% 128.89/16.93 (((notinsingleton) =>
% 128.89/16.93 (((eqinunit) =>
% 128.89/16.93 (((singletonsswitch) =>
% 128.89/16.93 (((upairsetE) =>
% 128.89/16.93 (((upairsetIL) =>
% 128.89/16.93 ((
% 128.89/16.93 (upairsetIR) =>
% 128.89/16.93 ((
% 128.89/16.93 (emptyE1) =>
% 128.89/16.93 ((
% 128.89/16.93 (vacuousDall) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan1) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan2) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan3) =>
% 128.89/16.93 ((
% 128.89/16.93 (quantDeMorgan4) =>
% 128.89/16.93 ((
% 128.89/16.93 (prop2setI) =>
% 128.89/16.93 ((
% 128.89/16.93 (prop2set2propI) =>
% 128.89/16.93 ((
% 128.89/16.93 (notdexE) =>
% 128.89/16.93 ((
% 128.89/16.93 (notdallE) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI3) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (inCongP) =>
% 128.89/16.93 ((
% 128.89/16.93 (in__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuE3u) =>
% 128.89/16.93 ((
% 128.89/16.93 (exu__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoin__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (powerset__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (setunion__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (exuEu) =>
% 128.89/16.93 ((
% 128.89/16.93 (descr__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (dsetconstr__Cong) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqimpsubset2) =>
% 128.89/16.93 ((
% 128.89/16.93 (eqimpsubset1) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (emptysetsubset) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetE) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetE2) =>
% 128.89/16.93 ((
% 128.89/16.93 (notsubsetI) =>
% 128.89/16.93 ((
% 128.89/16.93 (notequalI1) =>
% 128.89/16.93 ((
% 128.89/16.93 (notequalI2) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetRefl) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetTrans) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoinSub) =>
% 128.89/16.93 ((
% 128.89/16.93 (setadjoinSub2) =>
% 128.89/16.93 ((
% 128.89/16.93 (subset2powerset) =>
% 128.89/16.93 ((
% 128.89/16.93 (setextsub) =>
% 128.89/16.93 ((
% 128.89/16.93 (subsetemptysetimpeq) =>
% 128.89/16.93 ((
% 128.89/16.93 (powersetI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (inPowerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetsubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (sepInPowerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (sepSubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionIL) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairset2IR) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionIR) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionEcases) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionE) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionRsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectI) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset5) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectEL) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset2) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset3) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectER) =>
% 128.89/16.94 ((
% 128.89/16.94 (disjointsetsI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectRsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset4) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset1) =>
% 128.89/16.94 ((
% 128.89/16.94 (bs114d) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusI) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusEL) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusER) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusSubset2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusERneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusELneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusILneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusIRneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusSubset1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffE) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffIneg1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffIneg2) =>
% 128.89/16.94 ((
% 128.89/16.94 (secondinupair) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairIL) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairIR) =>
% 128.89/16.94 ((
% 128.89/16.94 (kpairiskpair) =>
% 128.89/16.94 ((
% 128.89/16.94 (kpairp) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletonsubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletoninpowerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletoninpowunion) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairset2E) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairsubunion) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairinpowunion) =>
% 128.89/16.94 ((
% 128.89/16.94 (ubforcartprodlem1) =>
% 128.89/16.94 ((
% 128.89/16.94 (ubforcartprodlem2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ubforcartprodlem3) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairin) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodmempair1) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodmempair) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionE2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionsingleton1) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionsingleton2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletonprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1E1) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1I) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1I2) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletonsuniq) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjL1) =>
% 128.89/16.94 ((
% 128.89/16.94 (kfstsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (theprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (kfstpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodfstin) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjL2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjL) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR11) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR12) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR1) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairequniteq) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR) =>
% 128.89/16.94 ((
% 128.89/16.94 (ksndsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (ksndpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (kpairsurjEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodsndin) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairmemEL) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairmemER) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodmempaircEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodfstpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodsndpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairsurjEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrI) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrSub) =>
% 128.89/16.94 ((
% 128.89/16.94 (setOfPairsIsBReln) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrERa) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrEL1) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrEL2) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrER) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcImageSingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (apProp) =>
% 128.89/16.94 ((
% 128.89/16.94 (app) =>
% 128.89/16.94 ((
% 128.89/16.94 (infuncsetfunc) =>
% 128.89/16.94 ((
% 128.89/16.94 (ap2p) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcinfuncset) =>
% 128.89/16.94 ((
% 128.89/16.94 (lamProp) =>
% 128.89/16.94 ((
% 128.89/16.94 (lamp) =>
% 128.89/16.94 ((
% 128.89/16.94 (lam2p) =>
% 128.89/16.94 ((
% 128.89/16.94 (brelnall1) =>
% 128.89/16.94 ((
% 128.89/16.94 (brelnall2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1E2) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp1) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp3) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp2) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcextLem) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp4) =>
% 128.89/16.94 ((
% 128.89/16.94 (subbreln) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqbreln) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcext) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcext2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ap2apEq1) =>
% 128.89/16.94 ((
% 128.89/16.94 (ap2apEq2) =>
% 128.89/16.94 ((
% 128.89/16.94 (beta1) =>
% 128.89/16.94 ((
% 128.89/16.94 (eta1) =>
% 128.89/16.94 ((
% 128.89/16.94 (lam2lamEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (beta2) =>
% 128.89/16.94 ((
% 128.89/16.94 (eta2) =>
% 128.89/16.94 ((
% 128.89/16.94 (iffalseProp1) =>
% 128.89/16.94 ((
% 128.89/16.94 (iffalseProp2) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrueProp1) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrueProp2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ifSingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (ifp) =>
% 128.89/16.94 ((
% 128.89/16.94 (theeq) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrue) =>
% 128.89/16.94 ((
% 128.89/16.94 (iffalse) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrueorfalse) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (setextT) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetTI) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetTI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetTE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectTELcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectTERcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT1) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT2) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT3) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementSub1) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementSub2) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTnotintersectT) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementImpComplementIntersect) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementSubsetComplementIntersect) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementInPowersetComplementIntersect) =>
% 128.89/16.94 ((
% 128.89/16.94 (contraSubsetComplement) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTcontraSubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTILcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTIRcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (inIntersectImpInUnion) =>
% 128.89/16.94 ((
% 128.89/16.94 (inIntersectImpInUnion2) =>
% 128.89/16.94 ((
% 128.89/16.94 (inIntersectImpInIntersectUnions) =>
% 128.89/16.94 ((
% 128.89/16.94 (intersectInPowersetIntersectUnions) =>
% 128.89/16.94 ((
% 128.89/16.94 (inComplementUnionImpNotIn1) =>
% 128.89/16.94 ((
% 128.89/16.94 (inComplementUnionImpInComplement1) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTE) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTEcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2a1) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementUnionInPowersetComplement) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2a2) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan1a) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan1b) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan1) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2a) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2b2) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2b) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule0) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule1) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule2) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule3) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule4) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_1) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_2) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_3) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_4) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_5) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1all2) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1SetBreln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (choice2fnsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (setOfPairsIsBReln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1all1) =>
% 128.89/16.94 ((
% 128.89/16.94 (subbreln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqbreln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1invprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1invI) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1invE) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compI) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compE) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compEex) =>
% 128.89/16.94 ((
% 128.89/16.94 (!!) @ (
% 128.89/16.94 (('#B') @ (
% 128.89/16.94 !!) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#S') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#S') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 =>))) @
% 128.89/16.94 breln1)))) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 !!))) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#S') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#B') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#S') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 =>))) @
% 128.89/16.94 breln1)))))) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#C') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#B') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#B') @
% 128.89/16.94 breln1)))) @
% 128.89/16.94 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])).
% 128.89/16.94 thf(zip_derived_cl189, plain,
% 128.89/16.94 (~ (((exuE3e) =>
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% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#B') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#B') @
% 128.89/16.94 breln1)))) @
% 128.89/16.94 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl174])).
% 128.89/16.94 thf(zip_derived_cl206, plain,
% 128.89/16.94 (~ (((setext) =>
% 128.89/16.94 (((emptyI) =>
% 128.89/16.94 (((noeltsimpempty) =>
% 128.89/16.94 (((setbeta) =>
% 128.89/16.94 (((nonemptyE1) =>
% 128.89/16.94 (((nonemptyI) =>
% 128.89/16.94 (((nonemptyI1) =>
% 128.89/16.94 (((setadjoinIL) =>
% 128.89/16.94 (((in @ emptyset @
% 128.89/16.94 (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.94 (((setadjoinIR) =>
% 128.89/16.94 (((setadjoinE) =>
% 128.89/16.94 (((setadjoinOr) =>
% 128.89/16.94 (((setoftrueEq) =>
% 128.89/16.94 (((powersetI) =>
% 128.89/16.94 (((emptyinPowerset) =>
% 128.89/16.94 (((emptyInPowerset) =>
% 128.89/16.94 (((powersetE) =>
% 128.89/16.94 (((setunionI) =>
% 128.89/16.94 (((setunionE) =>
% 128.89/16.94 (((subPowSU) =>
% 128.89/16.94 (((exuE2) =>
% 128.89/16.94 (((nonemptyImpWitness) =>
% 128.89/16.94 (((uniqinunit) =>
% 128.89/16.94 (((notinsingleton) =>
% 128.89/16.94 (((eqinunit) =>
% 128.89/16.94 (((singletonsswitch) =>
% 128.89/16.94 (((upairsetE) =>
% 128.89/16.94 (((upairsetIL) =>
% 128.89/16.94 (((upairsetIR) =>
% 128.89/16.94 (((emptyE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (vacuousDall) =>
% 128.89/16.94 ((
% 128.89/16.94 (quantDeMorgan1) =>
% 128.89/16.94 ((
% 128.89/16.94 (quantDeMorgan2) =>
% 128.89/16.94 ((
% 128.89/16.94 (quantDeMorgan3) =>
% 128.89/16.94 ((
% 128.89/16.94 (quantDeMorgan4) =>
% 128.89/16.94 ((
% 128.89/16.94 (prop2setI) =>
% 128.89/16.94 ((
% 128.89/16.94 (prop2set2propI) =>
% 128.89/16.94 ((
% 128.89/16.94 (notdexE) =>
% 128.89/16.94 ((
% 128.89/16.94 (notdallE) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuI3) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (inCongP) =>
% 128.89/16.94 ((
% 128.89/16.94 (in__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuE3u) =>
% 128.89/16.94 ((
% 128.89/16.94 (exu__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (setadjoin__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (powerset__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunion__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuEu) =>
% 128.89/16.94 ((
% 128.89/16.94 (descr__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (dsetconstr__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqimpsubset2) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqimpsubset1) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (emptysetsubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetE) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetE2) =>
% 128.89/16.94 ((
% 128.89/16.94 (notsubsetI) =>
% 128.89/16.94 ((
% 128.89/16.94 (notequalI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (notequalI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetRefl) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetTrans) =>
% 128.89/16.94 ((
% 128.89/16.94 (setadjoinSub) =>
% 128.89/16.94 ((
% 128.89/16.94 (setadjoinSub2) =>
% 128.89/16.94 ((
% 128.89/16.94 (subset2powerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (setextsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetemptysetimpeq) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (inPowerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetsubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (sepInPowerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (sepSubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionIL) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairset2IR) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionIR) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionEcases) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionE) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionRsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectI) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset5) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectEL) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset2) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset3) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectER) =>
% 128.89/16.94 ((
% 128.89/16.94 (disjointsetsI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectRsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset4) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset1) =>
% 128.89/16.94 ((
% 128.89/16.94 (bs114d) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusI) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusEL) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusER) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusSubset2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusERneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusELneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusILneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusIRneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusSubset1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffE) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffIneg1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffIneg2) =>
% 128.89/16.94 ((
% 128.89/16.94 (secondinupair) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairIL) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairIR) =>
% 128.89/16.94 ((
% 128.89/16.94 (kpairiskpair) =>
% 128.89/16.94 ((
% 128.89/16.94 (kpairp) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletonsubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletoninpowerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletoninpowunion) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairset2E) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairsubunion) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairinpowunion) =>
% 128.89/16.94 ((
% 128.89/16.94 (ubforcartprodlem1) =>
% 128.89/16.94 ((
% 128.89/16.94 (ubforcartprodlem2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ubforcartprodlem3) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairin) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodmempair1) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodmempair) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionE2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionsingleton1) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionsingleton2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletonprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1E1) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1I) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1I2) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletonsuniq) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjL1) =>
% 128.89/16.94 ((
% 128.89/16.94 (kfstsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (theprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (kfstpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodfstin) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjL2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjL) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR11) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR12) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR1) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairequniteq) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR) =>
% 128.89/16.94 ((
% 128.89/16.94 (ksndsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (ksndpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (kpairsurjEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodsndin) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairmemEL) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairmemER) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodmempaircEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodfstpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodsndpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairsurjEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrI) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrSub) =>
% 128.89/16.94 ((
% 128.89/16.94 (setOfPairsIsBReln) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrERa) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrEL1) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrEL2) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrER) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcImageSingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (apProp) =>
% 128.89/16.94 ((
% 128.89/16.94 (app) =>
% 128.89/16.94 ((
% 128.89/16.94 (infuncsetfunc) =>
% 128.89/16.94 ((
% 128.89/16.94 (ap2p) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcinfuncset) =>
% 128.89/16.94 ((
% 128.89/16.94 (lamProp) =>
% 128.89/16.94 ((
% 128.89/16.94 (lamp) =>
% 128.89/16.94 ((
% 128.89/16.94 (lam2p) =>
% 128.89/16.94 ((
% 128.89/16.94 (brelnall1) =>
% 128.89/16.94 ((
% 128.89/16.94 (brelnall2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1E2) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp1) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp3) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp2) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcextLem) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp4) =>
% 128.89/16.94 ((
% 128.89/16.94 (subbreln) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqbreln) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcext) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcext2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ap2apEq1) =>
% 128.89/16.94 ((
% 128.89/16.94 (ap2apEq2) =>
% 128.89/16.94 ((
% 128.89/16.94 (beta1) =>
% 128.89/16.94 ((
% 128.89/16.94 (eta1) =>
% 128.89/16.94 ((
% 128.89/16.94 (lam2lamEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (beta2) =>
% 128.89/16.94 ((
% 128.89/16.94 (eta2) =>
% 128.89/16.94 ((
% 128.89/16.94 (iffalseProp1) =>
% 128.89/16.94 ((
% 128.89/16.94 (iffalseProp2) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrueProp1) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrueProp2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ifSingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (ifp) =>
% 128.89/16.94 ((
% 128.89/16.94 (theeq) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrue) =>
% 128.89/16.94 ((
% 128.89/16.94 (iffalse) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrueorfalse) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (setextT) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetTI) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetTI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetTE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectTELcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectTERcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT1) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT2) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT3) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementSub1) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementSub2) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTnotintersectT) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementImpComplementIntersect) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementSubsetComplementIntersect) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementInPowersetComplementIntersect) =>
% 128.89/16.94 ((
% 128.89/16.94 (contraSubsetComplement) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTcontraSubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTILcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTIRcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (inIntersectImpInUnion) =>
% 128.89/16.94 ((
% 128.89/16.94 (inIntersectImpInUnion2) =>
% 128.89/16.94 ((
% 128.89/16.94 (inIntersectImpInIntersectUnions) =>
% 128.89/16.94 ((
% 128.89/16.94 (intersectInPowersetIntersectUnions) =>
% 128.89/16.94 ((
% 128.89/16.94 (inComplementUnionImpNotIn1) =>
% 128.89/16.94 ((
% 128.89/16.94 (inComplementUnionImpInComplement1) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTE) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTEcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2a1) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementUnionInPowersetComplement) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2a2) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan1a) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan1b) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan1) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2a) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2b2) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2b) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule0) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule1) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule2) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule3) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule4) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_1) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_2) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_3) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_4) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_5) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1all2) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1SetBreln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (choice2fnsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (setOfPairsIsBReln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1all1) =>
% 128.89/16.94 ((
% 128.89/16.94 (subbreln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqbreln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1invprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1invI) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1invE) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compI) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compE) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compEex) =>
% 128.89/16.94 ((
% 128.89/16.94 (!!) @ (
% 128.89/16.94 (('#B') @ (
% 128.89/16.94 !!) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#S') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#S') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 =>))) @
% 128.89/16.94 breln1)))) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 !!))) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#S') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#B') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#S') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 =>))) @
% 128.89/16.94 breln1)))))) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#C') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#B') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#B') @
% 128.89/16.94 breln1)))) @
% 128.89/16.94 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl189])).
% 128.89/16.94 thf(zip_derived_cl222, plain,
% 128.89/16.94 (~ (((emptyI) =>
% 128.89/16.94 (((noeltsimpempty) =>
% 128.89/16.94 (((setbeta) =>
% 128.89/16.94 (((nonemptyE1) =>
% 128.89/16.94 (((nonemptyI) =>
% 128.89/16.94 (((nonemptyI1) =>
% 128.89/16.94 (((setadjoinIL) =>
% 128.89/16.94 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.94 (((setadjoinIR) =>
% 128.89/16.94 (((setadjoinE) =>
% 128.89/16.94 (((setadjoinOr) =>
% 128.89/16.94 (((setoftrueEq) =>
% 128.89/16.94 (((powersetI) =>
% 128.89/16.94 (((emptyinPowerset) =>
% 128.89/16.94 (((emptyInPowerset) =>
% 128.89/16.94 (((powersetE) =>
% 128.89/16.94 (((setunionI) =>
% 128.89/16.94 (((setunionE) =>
% 128.89/16.94 (((subPowSU) =>
% 128.89/16.94 (((exuE2) =>
% 128.89/16.94 (((nonemptyImpWitness) =>
% 128.89/16.94 (((uniqinunit) =>
% 128.89/16.94 (((notinsingleton) =>
% 128.89/16.94 (((eqinunit) =>
% 128.89/16.94 (((singletonsswitch) =>
% 128.89/16.94 (((upairsetE) =>
% 128.89/16.94 (((upairsetIL) =>
% 128.89/16.94 (((upairsetIR) =>
% 128.89/16.94 (((emptyE1) =>
% 128.89/16.94 (((vacuousDall) =>
% 128.89/16.94 ((
% 128.89/16.94 (quantDeMorgan1) =>
% 128.89/16.94 ((
% 128.89/16.94 (quantDeMorgan2) =>
% 128.89/16.94 ((
% 128.89/16.94 (quantDeMorgan3) =>
% 128.89/16.94 ((
% 128.89/16.94 (quantDeMorgan4) =>
% 128.89/16.94 ((
% 128.89/16.94 (prop2setI) =>
% 128.89/16.94 ((
% 128.89/16.94 (prop2set2propI) =>
% 128.89/16.94 ((
% 128.89/16.94 (notdexE) =>
% 128.89/16.94 ((
% 128.89/16.94 (notdallE) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuI3) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (inCongP) =>
% 128.89/16.94 ((
% 128.89/16.94 (in__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuE3u) =>
% 128.89/16.94 ((
% 128.89/16.94 (exu__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (setadjoin__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (powerset__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunion__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuEu) =>
% 128.89/16.94 ((
% 128.89/16.94 (descr__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (dsetconstr__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqimpsubset2) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqimpsubset1) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (emptysetsubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetE) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetE2) =>
% 128.89/16.94 ((
% 128.89/16.94 (notsubsetI) =>
% 128.89/16.94 ((
% 128.89/16.94 (notequalI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (notequalI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetRefl) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetTrans) =>
% 128.89/16.94 ((
% 128.89/16.94 (setadjoinSub) =>
% 128.89/16.94 ((
% 128.89/16.94 (setadjoinSub2) =>
% 128.89/16.94 ((
% 128.89/16.94 (subset2powerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (setextsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetemptysetimpeq) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (inPowerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetsubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (sepInPowerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (sepSubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionIL) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairset2IR) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionIR) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionEcases) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionE) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionRsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectI) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset5) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectEL) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset2) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset3) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectER) =>
% 128.89/16.94 ((
% 128.89/16.94 (disjointsetsI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectRsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset4) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset1) =>
% 128.89/16.94 ((
% 128.89/16.94 (bs114d) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusI) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusEL) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusER) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusSubset2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusERneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusELneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusILneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusIRneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusSubset1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffE) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffIneg1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffIneg2) =>
% 128.89/16.94 ((
% 128.89/16.94 (secondinupair) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairIL) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairIR) =>
% 128.89/16.94 ((
% 128.89/16.94 (kpairiskpair) =>
% 128.89/16.94 ((
% 128.89/16.94 (kpairp) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletonsubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletoninpowerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletoninpowunion) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairset2E) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairsubunion) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairinpowunion) =>
% 128.89/16.94 ((
% 128.89/16.94 (ubforcartprodlem1) =>
% 128.89/16.94 ((
% 128.89/16.94 (ubforcartprodlem2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ubforcartprodlem3) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairin) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodmempair1) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodmempair) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionE2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionsingleton1) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionsingleton2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletonprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1E1) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1I) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1I2) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletonsuniq) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjL1) =>
% 128.89/16.94 ((
% 128.89/16.94 (kfstsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (theprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (kfstpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodfstin) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjL2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjL) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR11) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR12) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR1) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairequniteq) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR) =>
% 128.89/16.94 ((
% 128.89/16.94 (ksndsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (ksndpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (kpairsurjEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodsndin) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairmemEL) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairmemER) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodmempaircEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodfstpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodsndpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairsurjEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrI) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrSub) =>
% 128.89/16.94 ((
% 128.89/16.94 (setOfPairsIsBReln) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrERa) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrEL1) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrEL2) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrER) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcImageSingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (apProp) =>
% 128.89/16.94 ((
% 128.89/16.94 (app) =>
% 128.89/16.94 ((
% 128.89/16.94 (infuncsetfunc) =>
% 128.89/16.94 ((
% 128.89/16.94 (ap2p) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcinfuncset) =>
% 128.89/16.94 ((
% 128.89/16.94 (lamProp) =>
% 128.89/16.94 ((
% 128.89/16.94 (lamp) =>
% 128.89/16.94 ((
% 128.89/16.94 (lam2p) =>
% 128.89/16.94 ((
% 128.89/16.94 (brelnall1) =>
% 128.89/16.94 ((
% 128.89/16.94 (brelnall2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1E2) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp1) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp3) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp2) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcextLem) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp4) =>
% 128.89/16.94 ((
% 128.89/16.94 (subbreln) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqbreln) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcext) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcext2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ap2apEq1) =>
% 128.89/16.94 ((
% 128.89/16.94 (ap2apEq2) =>
% 128.89/16.94 ((
% 128.89/16.94 (beta1) =>
% 128.89/16.94 ((
% 128.89/16.94 (eta1) =>
% 128.89/16.94 ((
% 128.89/16.94 (lam2lamEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (beta2) =>
% 128.89/16.94 ((
% 128.89/16.94 (eta2) =>
% 128.89/16.94 ((
% 128.89/16.94 (iffalseProp1) =>
% 128.89/16.94 ((
% 128.89/16.94 (iffalseProp2) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrueProp1) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrueProp2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ifSingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (ifp) =>
% 128.89/16.94 ((
% 128.89/16.94 (theeq) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrue) =>
% 128.89/16.94 ((
% 128.89/16.94 (iffalse) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrueorfalse) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (setextT) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetTI) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetTI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetTE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectTELcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectTERcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT1) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT2) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT3) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementSub1) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementSub2) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTnotintersectT) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementImpComplementIntersect) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementSubsetComplementIntersect) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementInPowersetComplementIntersect) =>
% 128.89/16.94 ((
% 128.89/16.94 (contraSubsetComplement) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTcontraSubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTILcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTIRcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (inIntersectImpInUnion) =>
% 128.89/16.94 ((
% 128.89/16.94 (inIntersectImpInUnion2) =>
% 128.89/16.94 ((
% 128.89/16.94 (inIntersectImpInIntersectUnions) =>
% 128.89/16.94 ((
% 128.89/16.94 (intersectInPowersetIntersectUnions) =>
% 128.89/16.94 ((
% 128.89/16.94 (inComplementUnionImpNotIn1) =>
% 128.89/16.94 ((
% 128.89/16.94 (inComplementUnionImpInComplement1) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTE) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTEcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2a1) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementUnionInPowersetComplement) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2a2) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan1a) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan1b) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan1) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2a) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2b2) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2b) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule0) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule1) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule2) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule3) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule4) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_1) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_2) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_3) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_4) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_5) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1all2) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1SetBreln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (choice2fnsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (setOfPairsIsBReln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1all1) =>
% 128.89/16.94 ((
% 128.89/16.94 (subbreln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqbreln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1invprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1invI) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1invE) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compI) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compE) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compEex) =>
% 128.89/16.94 ((
% 128.89/16.94 (!!) @ (
% 128.89/16.94 (('#B') @ (
% 128.89/16.94 !!) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#S') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#S') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 =>))) @
% 128.89/16.94 breln1)))) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 !!))) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#S') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#B') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#S') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 =>))) @
% 128.89/16.94 breln1)))))) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#C') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#B') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#B') @
% 128.89/16.94 breln1)))) @
% 128.89/16.94 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])).
% 128.89/16.94 thf(zip_derived_cl236, plain,
% 128.89/16.94 (~ (((noeltsimpempty) =>
% 128.89/16.94 (((setbeta) =>
% 128.89/16.94 (((nonemptyE1) =>
% 128.89/16.94 (((nonemptyI) =>
% 128.89/16.94 (((nonemptyI1) =>
% 128.89/16.94 (((setadjoinIL) =>
% 128.89/16.94 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.94 (((setadjoinIR) =>
% 128.89/16.94 (((setadjoinE) =>
% 128.89/16.94 (((setadjoinOr) =>
% 128.89/16.94 (((setoftrueEq) =>
% 128.89/16.94 (((powersetI) =>
% 128.89/16.94 (((emptyinPowerset) =>
% 128.89/16.94 (((emptyInPowerset) =>
% 128.89/16.94 (((powersetE) =>
% 128.89/16.94 (((setunionI) =>
% 128.89/16.94 (((setunionE) =>
% 128.89/16.94 (((subPowSU) =>
% 128.89/16.94 (((exuE2) =>
% 128.89/16.94 (((nonemptyImpWitness) =>
% 128.89/16.94 (((uniqinunit) =>
% 128.89/16.94 (((notinsingleton) =>
% 128.89/16.94 (((eqinunit) =>
% 128.89/16.94 (((singletonsswitch) =>
% 128.89/16.94 (((upairsetE) =>
% 128.89/16.94 (((upairsetIL) =>
% 128.89/16.94 (((upairsetIR) =>
% 128.89/16.94 (((emptyE1) =>
% 128.89/16.94 (((vacuousDall) =>
% 128.89/16.94 (((quantDeMorgan1) =>
% 128.89/16.94 ((
% 128.89/16.94 (quantDeMorgan2) =>
% 128.89/16.94 ((
% 128.89/16.94 (quantDeMorgan3) =>
% 128.89/16.94 ((
% 128.89/16.94 (quantDeMorgan4) =>
% 128.89/16.94 ((
% 128.89/16.94 (prop2setI) =>
% 128.89/16.94 ((
% 128.89/16.94 (prop2set2propI) =>
% 128.89/16.94 ((
% 128.89/16.94 (notdexE) =>
% 128.89/16.94 ((
% 128.89/16.94 (notdallE) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuI3) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (inCongP) =>
% 128.89/16.94 ((
% 128.89/16.94 (in__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuE3u) =>
% 128.89/16.94 ((
% 128.89/16.94 (exu__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (setadjoin__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (powerset__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunion__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuEu) =>
% 128.89/16.94 ((
% 128.89/16.94 (descr__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (dsetconstr__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqimpsubset2) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqimpsubset1) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (emptysetsubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetE) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetE2) =>
% 128.89/16.94 ((
% 128.89/16.94 (notsubsetI) =>
% 128.89/16.94 ((
% 128.89/16.94 (notequalI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (notequalI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetRefl) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetTrans) =>
% 128.89/16.94 ((
% 128.89/16.94 (setadjoinSub) =>
% 128.89/16.94 ((
% 128.89/16.94 (setadjoinSub2) =>
% 128.89/16.94 ((
% 128.89/16.94 (subset2powerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (setextsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetemptysetimpeq) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (inPowerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetsubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (sepInPowerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (sepSubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionIL) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairset2IR) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionIR) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionEcases) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionE) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionRsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectI) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset5) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectEL) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset2) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset3) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectER) =>
% 128.89/16.94 ((
% 128.89/16.94 (disjointsetsI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectRsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset4) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset1) =>
% 128.89/16.94 ((
% 128.89/16.94 (bs114d) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusI) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusEL) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusER) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusSubset2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusERneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusELneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusILneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusIRneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusSubset1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffE) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffIneg1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffIneg2) =>
% 128.89/16.94 ((
% 128.89/16.94 (secondinupair) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairIL) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairIR) =>
% 128.89/16.94 ((
% 128.89/16.94 (kpairiskpair) =>
% 128.89/16.94 ((
% 128.89/16.94 (kpairp) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletonsubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletoninpowerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletoninpowunion) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairset2E) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairsubunion) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairinpowunion) =>
% 128.89/16.94 ((
% 128.89/16.94 (ubforcartprodlem1) =>
% 128.89/16.94 ((
% 128.89/16.94 (ubforcartprodlem2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ubforcartprodlem3) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairin) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodmempair1) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodmempair) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionE2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionsingleton1) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionsingleton2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletonprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1E1) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1I) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1I2) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletonsuniq) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjL1) =>
% 128.89/16.94 ((
% 128.89/16.94 (kfstsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (theprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (kfstpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodfstin) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjL2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjL) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR11) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR12) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR1) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairequniteq) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR) =>
% 128.89/16.94 ((
% 128.89/16.94 (ksndsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (ksndpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (kpairsurjEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodsndin) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairmemEL) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairmemER) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodmempaircEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodfstpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodsndpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairsurjEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrI) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrSub) =>
% 128.89/16.94 ((
% 128.89/16.94 (setOfPairsIsBReln) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrERa) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrEL1) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrEL2) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrER) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcImageSingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (apProp) =>
% 128.89/16.94 ((
% 128.89/16.94 (app) =>
% 128.89/16.94 ((
% 128.89/16.94 (infuncsetfunc) =>
% 128.89/16.94 ((
% 128.89/16.94 (ap2p) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcinfuncset) =>
% 128.89/16.94 ((
% 128.89/16.94 (lamProp) =>
% 128.89/16.94 ((
% 128.89/16.94 (lamp) =>
% 128.89/16.94 ((
% 128.89/16.94 (lam2p) =>
% 128.89/16.94 ((
% 128.89/16.94 (brelnall1) =>
% 128.89/16.94 ((
% 128.89/16.94 (brelnall2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1E2) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp1) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp3) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp2) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcextLem) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp4) =>
% 128.89/16.94 ((
% 128.89/16.94 (subbreln) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqbreln) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcext) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcext2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ap2apEq1) =>
% 128.89/16.94 ((
% 128.89/16.94 (ap2apEq2) =>
% 128.89/16.94 ((
% 128.89/16.94 (beta1) =>
% 128.89/16.94 ((
% 128.89/16.94 (eta1) =>
% 128.89/16.94 ((
% 128.89/16.94 (lam2lamEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (beta2) =>
% 128.89/16.94 ((
% 128.89/16.94 (eta2) =>
% 128.89/16.94 ((
% 128.89/16.94 (iffalseProp1) =>
% 128.89/16.94 ((
% 128.89/16.94 (iffalseProp2) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrueProp1) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrueProp2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ifSingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (ifp) =>
% 128.89/16.94 ((
% 128.89/16.94 (theeq) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrue) =>
% 128.89/16.94 ((
% 128.89/16.94 (iffalse) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrueorfalse) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (setextT) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetTI) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetTI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetTE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectTELcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectTERcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT1) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT2) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT3) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementSub1) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementSub2) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTnotintersectT) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementImpComplementIntersect) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementSubsetComplementIntersect) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementInPowersetComplementIntersect) =>
% 128.89/16.94 ((
% 128.89/16.94 (contraSubsetComplement) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTcontraSubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTILcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTIRcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (inIntersectImpInUnion) =>
% 128.89/16.94 ((
% 128.89/16.94 (inIntersectImpInUnion2) =>
% 128.89/16.94 ((
% 128.89/16.94 (inIntersectImpInIntersectUnions) =>
% 128.89/16.94 ((
% 128.89/16.94 (intersectInPowersetIntersectUnions) =>
% 128.89/16.94 ((
% 128.89/16.94 (inComplementUnionImpNotIn1) =>
% 128.89/16.94 ((
% 128.89/16.94 (inComplementUnionImpInComplement1) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTE) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTEcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2a1) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementUnionInPowersetComplement) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2a2) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan1a) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan1b) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan1) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2a) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2b2) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2b) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule0) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule1) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule2) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule3) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule4) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_1) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_2) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_3) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_4) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_5) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1all2) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1SetBreln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (choice2fnsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (setOfPairsIsBReln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1all1) =>
% 128.89/16.94 ((
% 128.89/16.94 (subbreln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqbreln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1invprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1invI) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1invE) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compI) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compE) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compEex) =>
% 128.89/16.94 ((
% 128.89/16.94 (!!) @ (
% 128.89/16.94 (('#B') @ (
% 128.89/16.94 !!) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#S') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#S') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 =>))) @
% 128.89/16.94 breln1)))) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 !!))) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#S') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#B') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#S') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 =>))) @
% 128.89/16.94 breln1)))))) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#C') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#B') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#B') @
% 128.89/16.94 breln1)))) @
% 128.89/16.94 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl222])).
% 128.89/16.94 thf(zip_derived_cl251, plain,
% 128.89/16.94 (~ (((setbeta) =>
% 128.89/16.94 (((nonemptyE1) =>
% 128.89/16.94 (((nonemptyI) =>
% 128.89/16.94 (((nonemptyI1) =>
% 128.89/16.94 (((setadjoinIL) =>
% 128.89/16.94 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.94 (((setadjoinIR) =>
% 128.89/16.94 (((setadjoinE) =>
% 128.89/16.94 (((setadjoinOr) =>
% 128.89/16.94 (((setoftrueEq) =>
% 128.89/16.94 (((powersetI) =>
% 128.89/16.94 (((emptyinPowerset) =>
% 128.89/16.94 (((emptyInPowerset) =>
% 128.89/16.94 (((powersetE) =>
% 128.89/16.94 (((setunionI) =>
% 128.89/16.94 (((setunionE) =>
% 128.89/16.94 (((subPowSU) =>
% 128.89/16.94 (((exuE2) =>
% 128.89/16.94 (((nonemptyImpWitness) =>
% 128.89/16.94 (((uniqinunit) =>
% 128.89/16.94 (((notinsingleton) =>
% 128.89/16.94 (((eqinunit) =>
% 128.89/16.94 (((singletonsswitch) =>
% 128.89/16.94 (((upairsetE) =>
% 128.89/16.94 (((upairsetIL) =>
% 128.89/16.94 (((upairsetIR) =>
% 128.89/16.94 (((emptyE1) =>
% 128.89/16.94 (((vacuousDall) =>
% 128.89/16.94 (((quantDeMorgan1) =>
% 128.89/16.94 (((quantDeMorgan2) =>
% 128.89/16.94 ((
% 128.89/16.94 (quantDeMorgan3) =>
% 128.89/16.94 ((
% 128.89/16.94 (quantDeMorgan4) =>
% 128.89/16.94 ((
% 128.89/16.94 (prop2setI) =>
% 128.89/16.94 ((
% 128.89/16.94 (prop2set2propI) =>
% 128.89/16.94 ((
% 128.89/16.94 (notdexE) =>
% 128.89/16.94 ((
% 128.89/16.94 (notdallE) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuI3) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (inCongP) =>
% 128.89/16.94 ((
% 128.89/16.94 (in__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuE3u) =>
% 128.89/16.94 ((
% 128.89/16.94 (exu__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (setadjoin__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (powerset__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunion__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuEu) =>
% 128.89/16.94 ((
% 128.89/16.94 (descr__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (dsetconstr__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqimpsubset2) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqimpsubset1) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (emptysetsubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetE) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetE2) =>
% 128.89/16.94 ((
% 128.89/16.94 (notsubsetI) =>
% 128.89/16.94 ((
% 128.89/16.94 (notequalI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (notequalI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetRefl) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetTrans) =>
% 128.89/16.94 ((
% 128.89/16.94 (setadjoinSub) =>
% 128.89/16.94 ((
% 128.89/16.94 (setadjoinSub2) =>
% 128.89/16.94 ((
% 128.89/16.94 (subset2powerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (setextsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetemptysetimpeq) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (inPowerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetsubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (sepInPowerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (sepSubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionIL) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairset2IR) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionIR) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionEcases) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionE) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionRsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectI) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset5) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectEL) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset2) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset3) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectER) =>
% 128.89/16.94 ((
% 128.89/16.94 (disjointsetsI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectRsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset4) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset1) =>
% 128.89/16.94 ((
% 128.89/16.94 (bs114d) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusI) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusEL) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusER) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusSubset2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusERneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusELneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusILneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusIRneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusSubset1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffE) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffIneg1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffIneg2) =>
% 128.89/16.94 ((
% 128.89/16.94 (secondinupair) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairIL) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairIR) =>
% 128.89/16.94 ((
% 128.89/16.94 (kpairiskpair) =>
% 128.89/16.94 ((
% 128.89/16.94 (kpairp) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletonsubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletoninpowerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletoninpowunion) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairset2E) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairsubunion) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairinpowunion) =>
% 128.89/16.94 ((
% 128.89/16.94 (ubforcartprodlem1) =>
% 128.89/16.94 ((
% 128.89/16.94 (ubforcartprodlem2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ubforcartprodlem3) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairin) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodmempair1) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodmempair) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionE2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionsingleton1) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionsingleton2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunionsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletonprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1E1) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1I) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1I2) =>
% 128.89/16.94 ((
% 128.89/16.94 (singletonsuniq) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjL1) =>
% 128.89/16.94 ((
% 128.89/16.94 (kfstsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (theprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (kfstpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodfstin) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjL2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjL) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR11) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR12) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR1) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairequniteq) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairinjR) =>
% 128.89/16.94 ((
% 128.89/16.94 (ksndsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (ksndpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (kpairsurjEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodsndin) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairmemEL) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairmemER) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodmempaircEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodfstpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodsndpairEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (cartprodpairsurjEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrI) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrSub) =>
% 128.89/16.94 ((
% 128.89/16.94 (setOfPairsIsBReln) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrERa) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrEL1) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrEL2) =>
% 128.89/16.94 ((
% 128.89/16.94 (dpsetconstrER) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcImageSingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (apProp) =>
% 128.89/16.94 ((
% 128.89/16.94 (app) =>
% 128.89/16.94 ((
% 128.89/16.94 (infuncsetfunc) =>
% 128.89/16.94 ((
% 128.89/16.94 (ap2p) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcinfuncset) =>
% 128.89/16.94 ((
% 128.89/16.94 (lamProp) =>
% 128.89/16.94 ((
% 128.89/16.94 (lamp) =>
% 128.89/16.94 ((
% 128.89/16.94 (lam2p) =>
% 128.89/16.94 ((
% 128.89/16.94 (brelnall1) =>
% 128.89/16.94 ((
% 128.89/16.94 (brelnall2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ex1E2) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp1) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp3) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp2) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcextLem) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcGraphProp4) =>
% 128.89/16.94 ((
% 128.89/16.94 (subbreln) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqbreln) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcext) =>
% 128.89/16.94 ((
% 128.89/16.94 (funcext2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ap2apEq1) =>
% 128.89/16.94 ((
% 128.89/16.94 (ap2apEq2) =>
% 128.89/16.94 ((
% 128.89/16.94 (beta1) =>
% 128.89/16.94 ((
% 128.89/16.94 (eta1) =>
% 128.89/16.94 ((
% 128.89/16.94 (lam2lamEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (beta2) =>
% 128.89/16.94 ((
% 128.89/16.94 (eta2) =>
% 128.89/16.94 ((
% 128.89/16.94 (iffalseProp1) =>
% 128.89/16.94 ((
% 128.89/16.94 (iffalseProp2) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrueProp1) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrueProp2) =>
% 128.89/16.94 ((
% 128.89/16.94 (ifSingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (ifp) =>
% 128.89/16.94 ((
% 128.89/16.94 (theeq) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrue) =>
% 128.89/16.94 ((
% 128.89/16.94 (iffalse) =>
% 128.89/16.94 ((
% 128.89/16.94 (iftrueorfalse) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementT_lem) =>
% 128.89/16.94 ((
% 128.89/16.94 (setextT) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetTI) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetTI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetTE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectTELcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectTERcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT1) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT2) =>
% 128.89/16.94 ((
% 128.89/16.94 (contrasubsetT3) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementSub1) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementSub2) =>
% 128.89/16.94 ((
% 128.89/16.94 (doubleComplementEq) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTnotintersectT) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementImpComplementIntersect) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementSubsetComplementIntersect) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementInPowersetComplementIntersect) =>
% 128.89/16.94 ((
% 128.89/16.94 (contraSubsetComplement) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementTcontraSubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTILcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTIRcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (inIntersectImpInUnion) =>
% 128.89/16.94 ((
% 128.89/16.94 (inIntersectImpInUnion2) =>
% 128.89/16.94 ((
% 128.89/16.94 (inIntersectImpInIntersectUnions) =>
% 128.89/16.94 ((
% 128.89/16.94 (intersectInPowersetIntersectUnions) =>
% 128.89/16.94 ((
% 128.89/16.94 (inComplementUnionImpNotIn1) =>
% 128.89/16.94 ((
% 128.89/16.94 (inComplementUnionImpInComplement1) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTE) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionTEcontra) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2a1) =>
% 128.89/16.94 ((
% 128.89/16.94 (complementUnionInPowersetComplement) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2a2) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan1a) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan1b) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan1) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2a) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2b2) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2b) =>
% 128.89/16.94 ((
% 128.89/16.94 (demorgan2) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule0) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule1) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule2) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule3) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz13rule4) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_1) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_2) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_3) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_4) =>
% 128.89/16.94 ((
% 128.89/16.94 (woz1_5) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1all2) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1SetBreln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (choice2fnsingleton) =>
% 128.89/16.94 ((
% 128.89/16.94 (setOfPairsIsBReln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1all1) =>
% 128.89/16.94 ((
% 128.89/16.94 (subbreln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqbreln1) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1invprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1invI) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1invE) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compprop) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compI) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compE) =>
% 128.89/16.94 ((
% 128.89/16.94 (breln1compEex) =>
% 128.89/16.94 ((
% 128.89/16.94 (!!) @ (
% 128.89/16.94 (('#B') @ (
% 128.89/16.94 !!) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#S') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#S') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 =>))) @
% 128.89/16.94 breln1)))) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 !!))) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#S') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#B') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#S') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 =>))) @
% 128.89/16.94 breln1)))))) @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#C') @ (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#B') @
% 128.89/16.94 (
% 128.89/16.94 (
% 128.89/16.94 ('#B') @ (
% 128.89/16.94 '#B') @
% 128.89/16.94 breln1)))) @
% 128.89/16.94 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl236])).
% 128.89/16.94 thf(zip_derived_cl264, plain,
% 128.89/16.94 (~ (((nonemptyE1) =>
% 128.89/16.94 (((nonemptyI) =>
% 128.89/16.94 (((nonemptyI1) =>
% 128.89/16.94 (((setadjoinIL) =>
% 128.89/16.94 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.94 (((setadjoinIR) =>
% 128.89/16.94 (((setadjoinE) =>
% 128.89/16.94 (((setadjoinOr) =>
% 128.89/16.94 (((setoftrueEq) =>
% 128.89/16.94 (((powersetI) =>
% 128.89/16.94 (((emptyinPowerset) =>
% 128.89/16.94 (((emptyInPowerset) =>
% 128.89/16.94 (((powersetE) =>
% 128.89/16.94 (((setunionI) =>
% 128.89/16.94 (((setunionE) =>
% 128.89/16.94 (((subPowSU) =>
% 128.89/16.94 (((exuE2) =>
% 128.89/16.94 (((nonemptyImpWitness) =>
% 128.89/16.94 (((uniqinunit) =>
% 128.89/16.94 (((notinsingleton) =>
% 128.89/16.94 (((eqinunit) =>
% 128.89/16.94 (((singletonsswitch) =>
% 128.89/16.94 (((upairsetE) =>
% 128.89/16.94 (((upairsetIL) =>
% 128.89/16.94 (((upairsetIR) =>
% 128.89/16.94 (((emptyE1) =>
% 128.89/16.94 (((vacuousDall) =>
% 128.89/16.94 (((quantDeMorgan1) =>
% 128.89/16.94 (((quantDeMorgan2) =>
% 128.89/16.94 (((quantDeMorgan3) =>
% 128.89/16.94 ((
% 128.89/16.94 (quantDeMorgan4) =>
% 128.89/16.94 ((
% 128.89/16.94 (prop2setI) =>
% 128.89/16.94 ((
% 128.89/16.94 (prop2set2propI) =>
% 128.89/16.94 ((
% 128.89/16.94 (notdexE) =>
% 128.89/16.94 ((
% 128.89/16.94 (notdallE) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuI3) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (inCongP) =>
% 128.89/16.94 ((
% 128.89/16.94 (in__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuE3u) =>
% 128.89/16.94 ((
% 128.89/16.94 (exu__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (setadjoin__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (powerset__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (setunion__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (exuEu) =>
% 128.89/16.94 ((
% 128.89/16.94 (descr__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (dsetconstr__Cong) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqimpsubset2) =>
% 128.89/16.94 ((
% 128.89/16.94 (eqimpsubset1) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (emptysetsubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetE) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetE2) =>
% 128.89/16.94 ((
% 128.89/16.94 (notsubsetI) =>
% 128.89/16.94 ((
% 128.89/16.94 (notequalI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (notequalI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetRefl) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetTrans) =>
% 128.89/16.94 ((
% 128.89/16.94 (setadjoinSub) =>
% 128.89/16.94 ((
% 128.89/16.94 (setadjoinSub2) =>
% 128.89/16.94 ((
% 128.89/16.94 (subset2powerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (setextsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (subsetemptysetimpeq) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetE1) =>
% 128.89/16.94 ((
% 128.89/16.94 (inPowerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (powersetsubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (sepInPowerset) =>
% 128.89/16.94 ((
% 128.89/16.94 (sepSubset) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionIL) =>
% 128.89/16.94 ((
% 128.89/16.94 (upairset2IR) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionIR) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionEcases) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionE) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binunionRsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectI) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset5) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectEL) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset2) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset3) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectER) =>
% 128.89/16.94 ((
% 128.89/16.94 (disjointsetsI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectRsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset4) =>
% 128.89/16.94 ((
% 128.89/16.94 (binintersectSubset1) =>
% 128.89/16.94 ((
% 128.89/16.94 (bs114d) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusI) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusEL) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusER) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusSubset2) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusERneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusELneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusILneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusIRneg) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusLsub) =>
% 128.89/16.94 ((
% 128.89/16.94 (setminusSubset1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffE) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffI1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffI2) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffIneg1) =>
% 128.89/16.94 ((
% 128.89/16.94 (symdiffIneg2) =>
% 128.89/16.94 ((
% 128.89/16.94 (secondinupair) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairIL) =>
% 128.89/16.94 ((
% 128.89/16.94 (setukpairIR) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairiskpair) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairp) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletoninpowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletoninpowunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairset2E) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairsubunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairinpowunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem3) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairin) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempair1) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempair) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionE2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton1) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1E1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1I) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1I2) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonsuniq) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL1) =>
% 128.89/16.95 ((
% 128.89/16.95 (kfstsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (theprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (kfstpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodfstin) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR11) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR12) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR1) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairequniteq) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR) =>
% 128.89/16.95 ((
% 128.89/16.95 (ksndsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (ksndpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairsurjEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodsndin) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairmemEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairmemER) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempaircEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodfstpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodsndpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairsurjEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrI) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrSub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setOfPairsIsBReln) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrERa) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrEL1) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrEL2) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrER) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcImageSingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (apProp) =>
% 128.89/16.95 ((
% 128.89/16.95 (app) =>
% 128.89/16.95 ((
% 128.89/16.95 (infuncsetfunc) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2p) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcinfuncset) =>
% 128.89/16.95 ((
% 128.89/16.95 (lamProp) =>
% 128.89/16.95 ((
% 128.89/16.95 (lamp) =>
% 128.89/16.95 ((
% 128.89/16.95 (lam2p) =>
% 128.89/16.95 ((
% 128.89/16.95 (brelnall1) =>
% 128.89/16.95 ((
% 128.89/16.95 (brelnall2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1E2) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp3) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcextLem) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp4) =>
% 128.89/16.95 ((
% 128.89/16.95 (subbreln) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqbreln) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcext) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcext2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2apEq1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2apEq2) =>
% 128.89/16.95 ((
% 128.89/16.95 (beta1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eta1) =>
% 128.89/16.95 ((
% 128.89/16.95 (lam2lamEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (beta2) =>
% 128.89/16.95 ((
% 128.89/16.95 (eta2) =>
% 128.89/16.95 ((
% 128.89/16.95 (iffalseProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (iffalseProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ifSingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (ifp) =>
% 128.89/16.95 ((
% 128.89/16.95 (theeq) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrue) =>
% 128.89/16.95 ((
% 128.89/16.95 (iffalse) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueorfalse) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (setextT) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetTI) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetTI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetTE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectTELcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectTERcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT1) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT2) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT3) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementSub1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementSub2) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTnotintersectT) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementImpComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementSubsetComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementInPowersetComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (contraSubsetComplement) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTcontraSubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTILcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTIRcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInUnion) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInUnion2) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInIntersectUnions) =>
% 128.89/16.95 ((
% 128.89/16.95 (intersectInPowersetIntersectUnions) =>
% 128.89/16.95 ((
% 128.89/16.95 (inComplementUnionImpNotIn1) =>
% 128.89/16.95 ((
% 128.89/16.95 (inComplementUnionImpInComplement1) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTE) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTEcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2a1) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementUnionInPowersetComplement) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2a2) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan1a) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan1b) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan1) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2a) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2b2) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2b) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule0) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule1) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule2) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule3) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule4) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_1) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_2) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_3) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_4) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_5) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1all2) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1SetBreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (choice2fnsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (setOfPairsIsBReln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1all1) =>
% 128.89/16.95 ((
% 128.89/16.95 (subbreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqbreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invI) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invE) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compI) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compE) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compEex) =>
% 128.89/16.95 ((
% 128.89/16.95 (!!) @ (
% 128.89/16.95 (('#B') @ (
% 128.89/16.95 !!) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#S') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#S') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 =>))) @
% 128.89/16.95 breln1)))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 !!))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#S') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#S') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 =>))) @
% 128.89/16.95 breln1)))))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#C') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 breln1)))) @
% 128.89/16.95 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl251])).
% 128.89/16.95 thf(zip_derived_cl280, plain,
% 128.89/16.95 (~ (((nonemptyI) =>
% 128.89/16.95 (((nonemptyI1) =>
% 128.89/16.95 (((setadjoinIL) =>
% 128.89/16.95 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.95 (((setadjoinIR) =>
% 128.89/16.95 (((setadjoinE) =>
% 128.89/16.95 (((setadjoinOr) =>
% 128.89/16.95 (((setoftrueEq) =>
% 128.89/16.95 (((powersetI) =>
% 128.89/16.95 (((emptyinPowerset) =>
% 128.89/16.95 (((emptyInPowerset) =>
% 128.89/16.95 (((powersetE) =>
% 128.89/16.95 (((setunionI) =>
% 128.89/16.95 (((setunionE) =>
% 128.89/16.95 (((subPowSU) =>
% 128.89/16.95 (((exuE2) =>
% 128.89/16.95 (((nonemptyImpWitness) =>
% 128.89/16.95 (((uniqinunit) =>
% 128.89/16.95 (((notinsingleton) =>
% 128.89/16.95 (((eqinunit) =>
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% 128.89/16.95 (((upairsetE) =>
% 128.89/16.95 (((upairsetIL) =>
% 128.89/16.95 (((upairsetIR) =>
% 128.89/16.95 (((emptyE1) =>
% 128.89/16.95 (((vacuousDall) =>
% 128.89/16.95 (((quantDeMorgan1) =>
% 128.89/16.95 (((quantDeMorgan2) =>
% 128.89/16.95 (((quantDeMorgan3) =>
% 128.89/16.95 (((quantDeMorgan4) =>
% 128.89/16.95 ((
% 128.89/16.95 (prop2setI) =>
% 128.89/16.95 ((
% 128.89/16.95 (prop2set2propI) =>
% 128.89/16.95 ((
% 128.89/16.95 (notdexE) =>
% 128.89/16.95 ((
% 128.89/16.95 (notdallE) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuI3) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (inCongP) =>
% 128.89/16.95 ((
% 128.89/16.95 (in__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuE3u) =>
% 128.89/16.95 ((
% 128.89/16.95 (exu__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (setadjoin__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (powerset__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunion__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuEu) =>
% 128.89/16.95 ((
% 128.89/16.95 (descr__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (dsetconstr__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqimpsubset2) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (subsetI2) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (subsetE) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetE2) =>
% 128.89/16.95 ((
% 128.89/16.95 (notsubsetI) =>
% 128.89/16.95 ((
% 128.89/16.95 (notequalI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (notequalI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetRefl) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetTrans) =>
% 128.89/16.95 ((
% 128.89/16.95 (setadjoinSub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setadjoinSub2) =>
% 128.89/16.95 ((
% 128.89/16.95 (subset2powerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (setextsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetemptysetimpeq) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (inPowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (sepInPowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (sepSubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionIL) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairset2IR) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionIR) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionEcases) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionE) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionRsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectI) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset5) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset2) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset3) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectER) =>
% 128.89/16.95 ((
% 128.89/16.95 (disjointsetsI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectRsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset4) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset1) =>
% 128.89/16.95 ((
% 128.89/16.95 (bs114d) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusI) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusER) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusSubset2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusERneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusELneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusILneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusIRneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusSubset1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffE) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffIneg1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffIneg2) =>
% 128.89/16.95 ((
% 128.89/16.95 (secondinupair) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairIL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairIR) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairiskpair) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairp) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletoninpowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletoninpowunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairset2E) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairsubunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairinpowunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem3) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairin) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempair1) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempair) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionE2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton1) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1E1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1I) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1I2) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonsuniq) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL1) =>
% 128.89/16.95 ((
% 128.89/16.95 (kfstsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (theprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (kfstpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodfstin) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR11) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR12) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR1) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairequniteq) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR) =>
% 128.89/16.95 ((
% 128.89/16.95 (ksndsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (ksndpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairsurjEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodsndin) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairmemEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairmemER) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempaircEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodfstpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodsndpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairsurjEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrI) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrSub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setOfPairsIsBReln) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrERa) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrEL1) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrEL2) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrER) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcImageSingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (apProp) =>
% 128.89/16.95 ((
% 128.89/16.95 (app) =>
% 128.89/16.95 ((
% 128.89/16.95 (infuncsetfunc) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2p) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcinfuncset) =>
% 128.89/16.95 ((
% 128.89/16.95 (lamProp) =>
% 128.89/16.95 ((
% 128.89/16.95 (lamp) =>
% 128.89/16.95 ((
% 128.89/16.95 (lam2p) =>
% 128.89/16.95 ((
% 128.89/16.95 (brelnall1) =>
% 128.89/16.95 ((
% 128.89/16.95 (brelnall2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1E2) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp3) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcextLem) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp4) =>
% 128.89/16.95 ((
% 128.89/16.95 (subbreln) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (funcext) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcext2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2apEq1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2apEq2) =>
% 128.89/16.95 ((
% 128.89/16.95 (beta1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eta1) =>
% 128.89/16.95 ((
% 128.89/16.95 (lam2lamEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (beta2) =>
% 128.89/16.95 ((
% 128.89/16.95 (eta2) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (iffalseProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ifSingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (ifp) =>
% 128.89/16.95 ((
% 128.89/16.95 (theeq) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrue) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (iftrueorfalse) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (binunionT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusT_lem) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (setextT) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetTI) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (powersetTE1) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (complementTE1) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (binintersectTERcontra) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT1) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT3) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementSub1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementSub2) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTnotintersectT) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementImpComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementSubsetComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementInPowersetComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (contraSubsetComplement) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTcontraSubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTILcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTIRcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInUnion) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInUnion2) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInIntersectUnions) =>
% 128.89/16.95 ((
% 128.89/16.95 (intersectInPowersetIntersectUnions) =>
% 128.89/16.95 ((
% 128.89/16.95 (inComplementUnionImpNotIn1) =>
% 128.89/16.95 ((
% 128.89/16.95 (inComplementUnionImpInComplement1) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTE) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTEcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2a1) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementUnionInPowersetComplement) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2a2) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (demorgan1) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (woz13rule4) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_1) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_2) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_3) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_4) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_5) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1all2) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1SetBreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (choice2fnsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (setOfPairsIsBReln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1all1) =>
% 128.89/16.95 ((
% 128.89/16.95 (subbreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqbreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invI) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invE) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compI) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compE) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compEex) =>
% 128.89/16.95 ((
% 128.89/16.95 (!!) @ (
% 128.89/16.95 (('#B') @ (
% 128.89/16.95 !!) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#S') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#S') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 =>))) @
% 128.89/16.95 breln1)))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 !!))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#S') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#S') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 =>))) @
% 128.89/16.95 breln1)))))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#C') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 breln1)))) @
% 128.89/16.95 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl264])).
% 128.89/16.95 thf(zip_derived_cl293, plain,
% 128.89/16.95 (~ (((nonemptyI1) =>
% 128.89/16.95 (((setadjoinIL) =>
% 128.89/16.95 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.95 (((setadjoinIR) =>
% 128.89/16.95 (((setadjoinE) =>
% 128.89/16.95 (((setadjoinOr) =>
% 128.89/16.95 (((setoftrueEq) =>
% 128.89/16.95 (((powersetI) =>
% 128.89/16.95 (((emptyinPowerset) =>
% 128.89/16.95 (((emptyInPowerset) =>
% 128.89/16.95 (((powersetE) =>
% 128.89/16.95 (((setunionI) =>
% 128.89/16.95 (((setunionE) =>
% 128.89/16.95 (((subPowSU) =>
% 128.89/16.95 (((exuE2) =>
% 128.89/16.95 (((nonemptyImpWitness) =>
% 128.89/16.95 (((uniqinunit) =>
% 128.89/16.95 (((notinsingleton) =>
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% 128.89/16.95 (((upairsetIL) =>
% 128.89/16.95 (((upairsetIR) =>
% 128.89/16.95 (((emptyE1) =>
% 128.89/16.95 (((vacuousDall) =>
% 128.89/16.95 (((quantDeMorgan1) =>
% 128.89/16.95 (((quantDeMorgan2) =>
% 128.89/16.95 (((quantDeMorgan3) =>
% 128.89/16.95 (((quantDeMorgan4) =>
% 128.89/16.95 (((prop2setI) =>
% 128.89/16.95 ((
% 128.89/16.95 (prop2set2propI) =>
% 128.89/16.95 ((
% 128.89/16.95 (notdexE) =>
% 128.89/16.95 ((
% 128.89/16.95 (notdallE) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuI3) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (inCongP) =>
% 128.89/16.95 ((
% 128.89/16.95 (in__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuE3u) =>
% 128.89/16.95 ((
% 128.89/16.95 (exu__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (setadjoin__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (powerset__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunion__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuEu) =>
% 128.89/16.95 ((
% 128.89/16.95 (descr__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (dsetconstr__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqimpsubset2) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqimpsubset1) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (emptysetsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetE) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetE2) =>
% 128.89/16.95 ((
% 128.89/16.95 (notsubsetI) =>
% 128.89/16.95 ((
% 128.89/16.95 (notequalI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (notequalI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetRefl) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetTrans) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (setadjoinSub2) =>
% 128.89/16.95 ((
% 128.89/16.95 (subset2powerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (setextsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetemptysetimpeq) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (powersetE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (inPowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (sepInPowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (sepSubset) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (upairset2IR) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionIR) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionEcases) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionE) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionRsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectI) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset5) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset2) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset3) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectER) =>
% 128.89/16.95 ((
% 128.89/16.95 (disjointsetsI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectRsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset4) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset1) =>
% 128.89/16.95 ((
% 128.89/16.95 (bs114d) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusI) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusER) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusSubset2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusERneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusELneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusILneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusIRneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusSubset1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffE) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffIneg1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffIneg2) =>
% 128.89/16.95 ((
% 128.89/16.95 (secondinupair) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairIL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairIR) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairiskpair) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairp) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletoninpowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletoninpowunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairset2E) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairsubunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairinpowunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem3) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairin) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempair1) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempair) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionE2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton1) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1E1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1I) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1I2) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonsuniq) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL1) =>
% 128.89/16.95 ((
% 128.89/16.95 (kfstsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (theprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (kfstpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodfstin) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR11) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR12) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR1) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairequniteq) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR) =>
% 128.89/16.95 ((
% 128.89/16.95 (ksndsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (ksndpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairsurjEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodsndin) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairmemEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairmemER) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempaircEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodfstpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodsndpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairsurjEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrI) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrSub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setOfPairsIsBReln) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrERa) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrEL1) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrEL2) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrER) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcImageSingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (apProp) =>
% 128.89/16.95 ((
% 128.89/16.95 (app) =>
% 128.89/16.95 ((
% 128.89/16.95 (infuncsetfunc) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2p) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcinfuncset) =>
% 128.89/16.95 ((
% 128.89/16.95 (lamProp) =>
% 128.89/16.95 ((
% 128.89/16.95 (lamp) =>
% 128.89/16.95 ((
% 128.89/16.95 (lam2p) =>
% 128.89/16.95 ((
% 128.89/16.95 (brelnall1) =>
% 128.89/16.95 ((
% 128.89/16.95 (brelnall2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1E2) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp3) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcextLem) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp4) =>
% 128.89/16.95 ((
% 128.89/16.95 (subbreln) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
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% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (ap2apEq1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2apEq2) =>
% 128.89/16.95 ((
% 128.89/16.95 (beta1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eta1) =>
% 128.89/16.95 ((
% 128.89/16.95 (lam2lamEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (beta2) =>
% 128.89/16.95 ((
% 128.89/16.95 (eta2) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (iffalseProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ifSingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (ifp) =>
% 128.89/16.95 ((
% 128.89/16.95 (theeq) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrue) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
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% 128.89/16.95 ((
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% 128.89/16.95 ((
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% 128.89/16.95 ((
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% 128.89/16.95 ((
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% 128.89/16.95 ((
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% 128.89/16.95 ((
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% 128.89/16.95 ((
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% 128.89/16.95 ((
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% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (complementTE1) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT2) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT3) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementSub1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementSub2) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTnotintersectT) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementImpComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementSubsetComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementInPowersetComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (contraSubsetComplement) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTcontraSubset) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (binunionTIRcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInUnion) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInUnion2) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInIntersectUnions) =>
% 128.89/16.95 ((
% 128.89/16.95 (intersectInPowersetIntersectUnions) =>
% 128.89/16.95 ((
% 128.89/16.95 (inComplementUnionImpNotIn1) =>
% 128.89/16.95 ((
% 128.89/16.95 (inComplementUnionImpInComplement1) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTE) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTEcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2a1) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementUnionInPowersetComplement) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2a2) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
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% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (demorgan2a) =>
% 128.89/16.95 ((
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% 128.89/16.95 ((
% 128.89/16.95 (woz13rule1) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule2) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule3) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule4) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_1) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_2) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_3) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_4) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_5) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1all2) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1SetBreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (choice2fnsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (setOfPairsIsBReln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1all1) =>
% 128.89/16.95 ((
% 128.89/16.95 (subbreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqbreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invI) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invE) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compI) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compE) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compEex) =>
% 128.89/16.95 ((
% 128.89/16.95 (!!) @ (
% 128.89/16.95 (('#B') @ (
% 128.89/16.95 !!) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#S') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#S') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 =>))) @
% 128.89/16.95 breln1)))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 !!))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#S') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#S') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 =>))) @
% 128.89/16.95 breln1)))))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#C') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 breln1)))) @
% 128.89/16.95 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl280])).
% 128.89/16.95 thf(zip_derived_cl307, plain,
% 128.89/16.95 (~ (((setadjoinIL) =>
% 128.89/16.95 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.95 (((setadjoinIR) =>
% 128.89/16.95 (((setadjoinE) =>
% 128.89/16.95 (((setadjoinOr) =>
% 128.89/16.95 (((setoftrueEq) =>
% 128.89/16.95 (((powersetI) =>
% 128.89/16.95 (((emptyinPowerset) =>
% 128.89/16.95 (((emptyInPowerset) =>
% 128.89/16.95 (((powersetE) =>
% 128.89/16.95 (((setunionI) =>
% 128.89/16.95 (((setunionE) =>
% 128.89/16.95 (((subPowSU) =>
% 128.89/16.95 (((exuE2) =>
% 128.89/16.95 (((nonemptyImpWitness) =>
% 128.89/16.95 (((uniqinunit) =>
% 128.89/16.95 (((notinsingleton) =>
% 128.89/16.95 (((eqinunit) =>
% 128.89/16.95 (((singletonsswitch) =>
% 128.89/16.95 (((upairsetE) =>
% 128.89/16.95 (((upairsetIL) =>
% 128.89/16.95 (((upairsetIR) =>
% 128.89/16.95 (((emptyE1) =>
% 128.89/16.95 (((vacuousDall) =>
% 128.89/16.95 (((quantDeMorgan1) =>
% 128.89/16.95 (((quantDeMorgan2) =>
% 128.89/16.95 (((quantDeMorgan3) =>
% 128.89/16.95 (((quantDeMorgan4) =>
% 128.89/16.95 (((prop2setI) =>
% 128.89/16.95 (((prop2set2propI) =>
% 128.89/16.95 ((
% 128.89/16.95 (notdexE) =>
% 128.89/16.95 ((
% 128.89/16.95 (notdallE) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuI3) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (inCongP) =>
% 128.89/16.95 ((
% 128.89/16.95 (in__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuE3u) =>
% 128.89/16.95 ((
% 128.89/16.95 (exu__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (setadjoin__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (powerset__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunion__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuEu) =>
% 128.89/16.95 ((
% 128.89/16.95 (descr__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (dsetconstr__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqimpsubset2) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqimpsubset1) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (emptysetsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetE) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetE2) =>
% 128.89/16.95 ((
% 128.89/16.95 (notsubsetI) =>
% 128.89/16.95 ((
% 128.89/16.95 (notequalI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (notequalI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetRefl) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetTrans) =>
% 128.89/16.95 ((
% 128.89/16.95 (setadjoinSub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setadjoinSub2) =>
% 128.89/16.95 ((
% 128.89/16.95 (subset2powerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (setextsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetemptysetimpeq) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (inPowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (sepInPowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (sepSubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionIL) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairset2IR) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionIR) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionEcases) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionE) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionRsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectI) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset5) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset2) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset3) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectER) =>
% 128.89/16.95 ((
% 128.89/16.95 (disjointsetsI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectRsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset4) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset1) =>
% 128.89/16.95 ((
% 128.89/16.95 (bs114d) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusI) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusER) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusSubset2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusERneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusELneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusILneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusIRneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusSubset1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffE) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffIneg1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffIneg2) =>
% 128.89/16.95 ((
% 128.89/16.95 (secondinupair) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairIL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairIR) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairiskpair) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairp) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletoninpowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletoninpowunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairset2E) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairsubunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairinpowunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem3) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairin) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempair1) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempair) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionE2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton1) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1E1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1I) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1I2) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonsuniq) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL1) =>
% 128.89/16.95 ((
% 128.89/16.95 (kfstsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (theprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (kfstpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodfstin) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR11) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR12) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR1) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairequniteq) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR) =>
% 128.89/16.95 ((
% 128.89/16.95 (ksndsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (ksndpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairsurjEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodsndin) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairmemEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairmemER) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempaircEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodfstpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodsndpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairsurjEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrI) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrSub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setOfPairsIsBReln) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrERa) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrEL1) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrEL2) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrER) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcImageSingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (apProp) =>
% 128.89/16.95 ((
% 128.89/16.95 (app) =>
% 128.89/16.95 ((
% 128.89/16.95 (infuncsetfunc) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2p) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcinfuncset) =>
% 128.89/16.95 ((
% 128.89/16.95 (lamProp) =>
% 128.89/16.95 ((
% 128.89/16.95 (lamp) =>
% 128.89/16.95 ((
% 128.89/16.95 (lam2p) =>
% 128.89/16.95 ((
% 128.89/16.95 (brelnall1) =>
% 128.89/16.95 ((
% 128.89/16.95 (brelnall2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1E2) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp3) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcextLem) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp4) =>
% 128.89/16.95 ((
% 128.89/16.95 (subbreln) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqbreln) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcext) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcext2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2apEq1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2apEq2) =>
% 128.89/16.95 ((
% 128.89/16.95 (beta1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eta1) =>
% 128.89/16.95 ((
% 128.89/16.95 (lam2lamEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (beta2) =>
% 128.89/16.95 ((
% 128.89/16.95 (eta2) =>
% 128.89/16.95 ((
% 128.89/16.95 (iffalseProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (iffalseProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ifSingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (ifp) =>
% 128.89/16.95 ((
% 128.89/16.95 (theeq) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrue) =>
% 128.89/16.95 ((
% 128.89/16.95 (iffalse) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueorfalse) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (setextT) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetTI) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetTI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetTE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectTELcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectTERcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT1) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT2) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT3) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementSub1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementSub2) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTnotintersectT) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementImpComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementSubsetComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementInPowersetComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (contraSubsetComplement) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTcontraSubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTILcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTIRcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInUnion) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInUnion2) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInIntersectUnions) =>
% 128.89/16.95 ((
% 128.89/16.95 (intersectInPowersetIntersectUnions) =>
% 128.89/16.95 ((
% 128.89/16.95 (inComplementUnionImpNotIn1) =>
% 128.89/16.95 ((
% 128.89/16.95 (inComplementUnionImpInComplement1) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTE) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTEcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2a1) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementUnionInPowersetComplement) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2a2) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan1a) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan1b) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan1) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2a) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2b2) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2b) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule0) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule1) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule2) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule3) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule4) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_1) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_2) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_3) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_4) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_5) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1all2) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1SetBreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (choice2fnsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (setOfPairsIsBReln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1all1) =>
% 128.89/16.95 ((
% 128.89/16.95 (subbreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqbreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invI) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invE) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compI) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compE) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compEex) =>
% 128.89/16.95 ((
% 128.89/16.95 (!!) @ (
% 128.89/16.95 (('#B') @ (
% 128.89/16.95 !!) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#S') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#S') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 =>))) @
% 128.89/16.95 breln1)))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 !!))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#S') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#S') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 =>))) @
% 128.89/16.95 breln1)))))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#C') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 breln1)))) @
% 128.89/16.95 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl293])).
% 128.89/16.95 thf(zip_derived_cl322, plain,
% 128.89/16.95 (~ (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 128.89/16.95 (((setadjoinIR) =>
% 128.89/16.95 (((setadjoinE) =>
% 128.89/16.95 (((setadjoinOr) =>
% 128.89/16.95 (((setoftrueEq) =>
% 128.89/16.95 (((powersetI) =>
% 128.89/16.95 (((emptyinPowerset) =>
% 128.89/16.95 (((emptyInPowerset) =>
% 128.89/16.95 (((powersetE) =>
% 128.89/16.95 (((setunionI) =>
% 128.89/16.95 (((setunionE) =>
% 128.89/16.95 (((subPowSU) =>
% 128.89/16.95 (((exuE2) =>
% 128.89/16.95 (((nonemptyImpWitness) =>
% 128.89/16.95 (((uniqinunit) =>
% 128.89/16.95 (((notinsingleton) =>
% 128.89/16.95 (((eqinunit) =>
% 128.89/16.95 (((singletonsswitch) =>
% 128.89/16.95 (((upairsetE) =>
% 128.89/16.95 (((upairsetIL) =>
% 128.89/16.95 (((upairsetIR) =>
% 128.89/16.95 (((emptyE1) =>
% 128.89/16.95 (((vacuousDall) =>
% 128.89/16.95 (((quantDeMorgan1) =>
% 128.89/16.95 (((quantDeMorgan2) =>
% 128.89/16.95 (((quantDeMorgan3) =>
% 128.89/16.95 (((quantDeMorgan4) =>
% 128.89/16.95 (((prop2setI) =>
% 128.89/16.95 (((prop2set2propI) =>
% 128.89/16.95 (((notdexE) =>
% 128.89/16.95 ((
% 128.89/16.95 (notdallE) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuI3) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (inCongP) =>
% 128.89/16.95 ((
% 128.89/16.95 (in__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuE3u) =>
% 128.89/16.95 ((
% 128.89/16.95 (exu__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (setadjoin__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (powerset__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunion__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuEu) =>
% 128.89/16.95 ((
% 128.89/16.95 (descr__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (dsetconstr__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqimpsubset2) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqimpsubset1) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (emptysetsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetE) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetE2) =>
% 128.89/16.95 ((
% 128.89/16.95 (notsubsetI) =>
% 128.89/16.95 ((
% 128.89/16.95 (notequalI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (notequalI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetRefl) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetTrans) =>
% 128.89/16.95 ((
% 128.89/16.95 (setadjoinSub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setadjoinSub2) =>
% 128.89/16.95 ((
% 128.89/16.95 (subset2powerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (setextsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetemptysetimpeq) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (inPowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (sepInPowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (sepSubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionIL) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairset2IR) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionIR) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionEcases) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionE) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionRsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectI) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset5) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset2) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset3) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectER) =>
% 128.89/16.95 ((
% 128.89/16.95 (disjointsetsI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectRsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset4) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset1) =>
% 128.89/16.95 ((
% 128.89/16.95 (bs114d) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusI) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusER) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusSubset2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusERneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusELneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusILneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusIRneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusSubset1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffE) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffIneg1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffIneg2) =>
% 128.89/16.95 ((
% 128.89/16.95 (secondinupair) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairIL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairIR) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairiskpair) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairp) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletoninpowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletoninpowunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairset2E) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairsubunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairinpowunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem3) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairin) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempair1) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempair) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionE2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton1) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1E1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1I) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1I2) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonsuniq) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL1) =>
% 128.89/16.95 ((
% 128.89/16.95 (kfstsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (theprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (kfstpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodfstin) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR11) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR12) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR1) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairequniteq) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR) =>
% 128.89/16.95 ((
% 128.89/16.95 (ksndsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (ksndpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairsurjEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodsndin) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairmemEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairmemER) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempaircEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodfstpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodsndpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairsurjEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrI) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrSub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setOfPairsIsBReln) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrERa) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrEL1) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrEL2) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrER) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcImageSingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (apProp) =>
% 128.89/16.95 ((
% 128.89/16.95 (app) =>
% 128.89/16.95 ((
% 128.89/16.95 (infuncsetfunc) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2p) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcinfuncset) =>
% 128.89/16.95 ((
% 128.89/16.95 (lamProp) =>
% 128.89/16.95 ((
% 128.89/16.95 (lamp) =>
% 128.89/16.95 ((
% 128.89/16.95 (lam2p) =>
% 128.89/16.95 ((
% 128.89/16.95 (brelnall1) =>
% 128.89/16.95 ((
% 128.89/16.95 (brelnall2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1E2) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp3) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcextLem) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp4) =>
% 128.89/16.95 ((
% 128.89/16.95 (subbreln) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqbreln) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcext) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcext2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2apEq1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2apEq2) =>
% 128.89/16.95 ((
% 128.89/16.95 (beta1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eta1) =>
% 128.89/16.95 ((
% 128.89/16.95 (lam2lamEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (beta2) =>
% 128.89/16.95 ((
% 128.89/16.95 (eta2) =>
% 128.89/16.95 ((
% 128.89/16.95 (iffalseProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (iffalseProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ifSingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (ifp) =>
% 128.89/16.95 ((
% 128.89/16.95 (theeq) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrue) =>
% 128.89/16.95 ((
% 128.89/16.95 (iffalse) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueorfalse) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (setextT) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetTI) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetTI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetTE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectTELcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectTERcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT1) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT2) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT3) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementSub1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementSub2) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTnotintersectT) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementImpComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementSubsetComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementInPowersetComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (contraSubsetComplement) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTcontraSubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTILcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTIRcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInUnion) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInUnion2) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInIntersectUnions) =>
% 128.89/16.95 ((
% 128.89/16.95 (intersectInPowersetIntersectUnions) =>
% 128.89/16.95 ((
% 128.89/16.95 (inComplementUnionImpNotIn1) =>
% 128.89/16.95 ((
% 128.89/16.95 (inComplementUnionImpInComplement1) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTE) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTEcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2a1) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementUnionInPowersetComplement) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2a2) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan1a) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan1b) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan1) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2a) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2b2) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2b) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule0) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule1) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule2) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule3) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule4) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_1) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_2) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_3) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_4) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_5) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1all2) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1SetBreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (choice2fnsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (setOfPairsIsBReln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1all1) =>
% 128.89/16.95 ((
% 128.89/16.95 (subbreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqbreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invI) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invE) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compI) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compE) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compEex) =>
% 128.89/16.95 ((
% 128.89/16.95 (!!) @ (
% 128.89/16.95 (('#B') @ (
% 128.89/16.95 !!) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#S') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#S') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 =>))) @
% 128.89/16.95 breln1)))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 !!))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#S') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#S') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 =>))) @
% 128.89/16.95 breln1)))))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#C') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 breln1)))) @
% 128.89/16.95 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl307])).
% 128.89/16.95 thf(zip_derived_cl337, plain,
% 128.89/16.95 (~ (((setadjoinIR) =>
% 128.89/16.95 (((setadjoinE) =>
% 128.89/16.95 (((setadjoinOr) =>
% 128.89/16.95 (((setoftrueEq) =>
% 128.89/16.95 (((powersetI) =>
% 128.89/16.95 (((emptyinPowerset) =>
% 128.89/16.95 (((emptyInPowerset) =>
% 128.89/16.95 (((powersetE) =>
% 128.89/16.95 (((setunionI) =>
% 128.89/16.95 (((setunionE) =>
% 128.89/16.95 (((subPowSU) =>
% 128.89/16.95 (((exuE2) =>
% 128.89/16.95 (((nonemptyImpWitness) =>
% 128.89/16.95 (((uniqinunit) =>
% 128.89/16.95 (((notinsingleton) =>
% 128.89/16.95 (((eqinunit) =>
% 128.89/16.95 (((singletonsswitch) =>
% 128.89/16.95 (((upairsetE) =>
% 128.89/16.95 (((upairsetIL) =>
% 128.89/16.95 (((upairsetIR) =>
% 128.89/16.95 (((emptyE1) =>
% 128.89/16.95 (((vacuousDall) =>
% 128.89/16.95 (((quantDeMorgan1) =>
% 128.89/16.95 (((quantDeMorgan2) =>
% 128.89/16.95 (((quantDeMorgan3) =>
% 128.89/16.95 (((quantDeMorgan4) =>
% 128.89/16.95 (((prop2setI) =>
% 128.89/16.95 (((prop2set2propI) =>
% 128.89/16.95 (((notdexE) =>
% 128.89/16.95 (((notdallE) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuI3) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (inCongP) =>
% 128.89/16.95 ((
% 128.89/16.95 (in__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuE3u) =>
% 128.89/16.95 ((
% 128.89/16.95 (exu__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (setadjoin__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (powerset__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunion__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuEu) =>
% 128.89/16.95 ((
% 128.89/16.95 (descr__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (dsetconstr__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqimpsubset2) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqimpsubset1) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (emptysetsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetE) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetE2) =>
% 128.89/16.95 ((
% 128.89/16.95 (notsubsetI) =>
% 128.89/16.95 ((
% 128.89/16.95 (notequalI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (notequalI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetRefl) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetTrans) =>
% 128.89/16.95 ((
% 128.89/16.95 (setadjoinSub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setadjoinSub2) =>
% 128.89/16.95 ((
% 128.89/16.95 (subset2powerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (setextsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetemptysetimpeq) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (inPowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (sepInPowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (sepSubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionIL) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairset2IR) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionIR) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionEcases) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionE) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionRsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectI) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset5) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset2) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset3) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectER) =>
% 128.89/16.95 ((
% 128.89/16.95 (disjointsetsI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectRsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset4) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset1) =>
% 128.89/16.95 ((
% 128.89/16.95 (bs114d) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusI) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusER) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusSubset2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusERneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusELneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusILneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusIRneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusSubset1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffE) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffIneg1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffIneg2) =>
% 128.89/16.95 ((
% 128.89/16.95 (secondinupair) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairIL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairIR) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairiskpair) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairp) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletoninpowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletoninpowunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairset2E) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairsubunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairinpowunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem3) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairin) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempair1) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempair) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionE2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton1) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1E1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1I) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1I2) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonsuniq) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL1) =>
% 128.89/16.95 ((
% 128.89/16.95 (kfstsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (theprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (kfstpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodfstin) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR11) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR12) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR1) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairequniteq) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR) =>
% 128.89/16.95 ((
% 128.89/16.95 (ksndsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (ksndpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairsurjEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodsndin) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairmemEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairmemER) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempaircEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodfstpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodsndpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairsurjEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrI) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrSub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setOfPairsIsBReln) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrERa) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrEL1) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrEL2) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrER) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcImageSingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (apProp) =>
% 128.89/16.95 ((
% 128.89/16.95 (app) =>
% 128.89/16.95 ((
% 128.89/16.95 (infuncsetfunc) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2p) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcinfuncset) =>
% 128.89/16.95 ((
% 128.89/16.95 (lamProp) =>
% 128.89/16.95 ((
% 128.89/16.95 (lamp) =>
% 128.89/16.95 ((
% 128.89/16.95 (lam2p) =>
% 128.89/16.95 ((
% 128.89/16.95 (brelnall1) =>
% 128.89/16.95 ((
% 128.89/16.95 (brelnall2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1E2) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp3) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcextLem) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp4) =>
% 128.89/16.95 ((
% 128.89/16.95 (subbreln) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqbreln) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcext) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcext2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2apEq1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2apEq2) =>
% 128.89/16.95 ((
% 128.89/16.95 (beta1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eta1) =>
% 128.89/16.95 ((
% 128.89/16.95 (lam2lamEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (beta2) =>
% 128.89/16.95 ((
% 128.89/16.95 (eta2) =>
% 128.89/16.95 ((
% 128.89/16.95 (iffalseProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (iffalseProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ifSingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (ifp) =>
% 128.89/16.95 ((
% 128.89/16.95 (theeq) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrue) =>
% 128.89/16.95 ((
% 128.89/16.95 (iffalse) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueorfalse) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (setextT) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetTI) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetTI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetTE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectTELcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectTERcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT1) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT2) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT3) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementSub1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementSub2) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTnotintersectT) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementImpComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementSubsetComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementInPowersetComplementIntersect) =>
% 128.89/16.95 ((
% 128.89/16.95 (contraSubsetComplement) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTcontraSubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTILcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTIRcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInUnion) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInUnion2) =>
% 128.89/16.95 ((
% 128.89/16.95 (inIntersectImpInIntersectUnions) =>
% 128.89/16.95 ((
% 128.89/16.95 (intersectInPowersetIntersectUnions) =>
% 128.89/16.95 ((
% 128.89/16.95 (inComplementUnionImpNotIn1) =>
% 128.89/16.95 ((
% 128.89/16.95 (inComplementUnionImpInComplement1) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTE) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionTEcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2a1) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementUnionInPowersetComplement) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2a2) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan1a) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan1b) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan1) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2a) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2b2) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2b) =>
% 128.89/16.95 ((
% 128.89/16.95 (demorgan2) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule0) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule1) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule2) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule3) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz13rule4) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_1) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_2) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_3) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_4) =>
% 128.89/16.95 ((
% 128.89/16.95 (woz1_5) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1all2) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1SetBreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (choice2fnsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (setOfPairsIsBReln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1all1) =>
% 128.89/16.95 ((
% 128.89/16.95 (subbreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqbreln1) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invI) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1invE) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compI) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compE) =>
% 128.89/16.95 ((
% 128.89/16.95 (breln1compEex) =>
% 128.89/16.95 ((
% 128.89/16.95 (!!) @ (
% 128.89/16.95 (('#B') @ (
% 128.89/16.95 !!) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#S') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#S') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 =>))) @
% 128.89/16.95 breln1)))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 !!))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#S') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#S') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 =>))) @
% 128.89/16.95 breln1)))))) @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#C') @ (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 (
% 128.89/16.95 (
% 128.89/16.95 ('#B') @ (
% 128.89/16.95 '#B') @
% 128.89/16.95 breln1)))) @
% 128.89/16.95 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl322])).
% 128.89/16.95 thf(zip_derived_cl349, plain,
% 128.89/16.95 (~ (((setadjoinE) =>
% 128.89/16.95 (((setadjoinOr) =>
% 128.89/16.95 (((setoftrueEq) =>
% 128.89/16.95 (((powersetI) =>
% 128.89/16.95 (((emptyinPowerset) =>
% 128.89/16.95 (((emptyInPowerset) =>
% 128.89/16.95 (((powersetE) =>
% 128.89/16.95 (((setunionI) =>
% 128.89/16.95 (((setunionE) =>
% 128.89/16.95 (((subPowSU) =>
% 128.89/16.95 (((exuE2) =>
% 128.89/16.95 (((nonemptyImpWitness) =>
% 128.89/16.95 (((uniqinunit) =>
% 128.89/16.95 (((notinsingleton) =>
% 128.89/16.95 (((eqinunit) =>
% 128.89/16.95 (((singletonsswitch) =>
% 128.89/16.95 (((upairsetE) =>
% 128.89/16.95 (((upairsetIL) =>
% 128.89/16.95 (((upairsetIR) =>
% 128.89/16.95 (((emptyE1) =>
% 128.89/16.95 (((vacuousDall) =>
% 128.89/16.95 (((quantDeMorgan1) =>
% 128.89/16.95 (((quantDeMorgan2) =>
% 128.89/16.95 (((quantDeMorgan3) =>
% 128.89/16.95 (((quantDeMorgan4) =>
% 128.89/16.95 (((prop2setI) =>
% 128.89/16.95 (((prop2set2propI) =>
% 128.89/16.95 (((notdexE) =>
% 128.89/16.95 (((notdallE) =>
% 128.89/16.95 (((exuI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuI3) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (inCongP) =>
% 128.89/16.95 ((
% 128.89/16.95 (in__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuE3u) =>
% 128.89/16.95 ((
% 128.89/16.95 (exu__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (setadjoin__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (powerset__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunion__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (exuEu) =>
% 128.89/16.95 ((
% 128.89/16.95 (descr__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (dsetconstr__Cong) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqimpsubset2) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqimpsubset1) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (emptysetsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetE) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetE2) =>
% 128.89/16.95 ((
% 128.89/16.95 (notsubsetI) =>
% 128.89/16.95 ((
% 128.89/16.95 (notequalI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (notequalI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetRefl) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetTrans) =>
% 128.89/16.95 ((
% 128.89/16.95 (setadjoinSub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setadjoinSub2) =>
% 128.89/16.95 ((
% 128.89/16.95 (subset2powerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (setextsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetemptysetimpeq) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (inPowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (sepInPowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (sepSubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionIL) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairset2IR) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionIR) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionEcases) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionE) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionRsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectI) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset5) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset2) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset3) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectER) =>
% 128.89/16.95 ((
% 128.89/16.95 (disjointsetsI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectRsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset4) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectSubset1) =>
% 128.89/16.95 ((
% 128.89/16.95 (bs114d) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusI) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusER) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusSubset2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusERneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusELneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusILneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusIRneg) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusLsub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusSubset1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffE) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffI2) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffIneg1) =>
% 128.89/16.95 ((
% 128.89/16.95 (symdiffIneg2) =>
% 128.89/16.95 ((
% 128.89/16.95 (secondinupair) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairIL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairIR) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairiskpair) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairp) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonsubset) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletoninpowerset) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletoninpowunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairset2E) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairsubunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairinpowunion) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ubforcartprodlem3) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairin) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempair1) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempair) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionE2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton1) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setunionsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1E1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1I) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1I2) =>
% 128.89/16.95 ((
% 128.89/16.95 (singletonsuniq) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL1) =>
% 128.89/16.95 ((
% 128.89/16.95 (kfstsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (theprop) =>
% 128.89/16.95 ((
% 128.89/16.95 (kfstpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodfstin) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjL) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR11) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR12) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR1) =>
% 128.89/16.95 ((
% 128.89/16.95 (upairequniteq) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR2) =>
% 128.89/16.95 ((
% 128.89/16.95 (setukpairinjR) =>
% 128.89/16.95 ((
% 128.89/16.95 (ksndsingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (ksndpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (kpairsurjEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodsndin) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairmemEL) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairmemER) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodmempaircEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodfstpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodsndpairEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (cartprodpairsurjEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrI) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrSub) =>
% 128.89/16.95 ((
% 128.89/16.95 (setOfPairsIsBReln) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrERa) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrEL1) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrEL2) =>
% 128.89/16.95 ((
% 128.89/16.95 (dpsetconstrER) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcImageSingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (apProp) =>
% 128.89/16.95 ((
% 128.89/16.95 (app) =>
% 128.89/16.95 ((
% 128.89/16.95 (infuncsetfunc) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2p) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcinfuncset) =>
% 128.89/16.95 ((
% 128.89/16.95 (lamProp) =>
% 128.89/16.95 ((
% 128.89/16.95 (lamp) =>
% 128.89/16.95 ((
% 128.89/16.95 (lam2p) =>
% 128.89/16.95 ((
% 128.89/16.95 (brelnall1) =>
% 128.89/16.95 ((
% 128.89/16.95 (brelnall2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ex1E2) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp3) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcextLem) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcGraphProp4) =>
% 128.89/16.95 ((
% 128.89/16.95 (subbreln) =>
% 128.89/16.95 ((
% 128.89/16.95 (eqbreln) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcext) =>
% 128.89/16.95 ((
% 128.89/16.95 (funcext2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2apEq1) =>
% 128.89/16.95 ((
% 128.89/16.95 (ap2apEq2) =>
% 128.89/16.95 ((
% 128.89/16.95 (beta1) =>
% 128.89/16.95 ((
% 128.89/16.95 (eta1) =>
% 128.89/16.95 ((
% 128.89/16.95 (lam2lamEq) =>
% 128.89/16.95 ((
% 128.89/16.95 (beta2) =>
% 128.89/16.95 ((
% 128.89/16.95 (eta2) =>
% 128.89/16.95 ((
% 128.89/16.95 (iffalseProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (iffalseProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueProp1) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueProp2) =>
% 128.89/16.95 ((
% 128.89/16.95 (ifSingleton) =>
% 128.89/16.95 ((
% 128.89/16.95 (ifp) =>
% 128.89/16.95 ((
% 128.89/16.95 (theeq) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrue) =>
% 128.89/16.95 ((
% 128.89/16.95 (iffalse) =>
% 128.89/16.95 ((
% 128.89/16.95 (iftrueorfalse) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (binunionT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (setminusT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementT_lem) =>
% 128.89/16.95 ((
% 128.89/16.95 (setextT) =>
% 128.89/16.95 ((
% 128.89/16.95 (subsetTI) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetTI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (powersetTE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (complementTE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectTELcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (binintersectTERcontra) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT1) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT2) =>
% 128.89/16.95 ((
% 128.89/16.95 (contrasubsetT3) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementI1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementE1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementSub1) =>
% 128.89/16.95 ((
% 128.89/16.95 (doubleComplementSub2) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTnotintersectT) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementImpComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementSubsetComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementInPowersetComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (contraSubsetComplement) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTcontraSubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTILcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTIRcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInUnion) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInUnion2) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInIntersectUnions) =>
% 128.89/16.96 ((
% 128.89/16.96 (intersectInPowersetIntersectUnions) =>
% 128.89/16.96 ((
% 128.89/16.96 (inComplementUnionImpNotIn1) =>
% 128.89/16.96 ((
% 128.89/16.96 (inComplementUnionImpInComplement1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTE) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTEcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementUnionInPowersetComplement) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a2) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1a) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1b) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2b2) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2b) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule0) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule1) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule3) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule4) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_1) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_3) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_4) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_5) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1all2) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1SetBreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (choice2fnsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (setOfPairsIsBReln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1all1) =>
% 128.89/16.96 ((
% 128.89/16.96 (subbreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqbreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invI) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invE) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compI) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compE) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compEex) =>
% 128.89/16.96 ((
% 128.89/16.96 (!!) @ (
% 128.89/16.96 (('#B') @ (
% 128.89/16.96 !!) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#S') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#S') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 =>))) @
% 128.89/16.96 breln1)))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 !!))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#S') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#S') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 =>))) @
% 128.89/16.96 breln1)))))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#C') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 breln1)))) @
% 128.89/16.96 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl337])).
% 128.89/16.96 thf(zip_derived_cl355, plain,
% 128.89/16.96 (~ (((setadjoinOr) =>
% 128.89/16.96 (((setoftrueEq) =>
% 128.89/16.96 (((powersetI) =>
% 128.89/16.96 (((emptyinPowerset) =>
% 128.89/16.96 (((emptyInPowerset) =>
% 128.89/16.96 (((powersetE) =>
% 128.89/16.96 (((setunionI) =>
% 128.89/16.96 (((setunionE) =>
% 128.89/16.96 (((subPowSU) =>
% 128.89/16.96 (((exuE2) =>
% 128.89/16.96 (((nonemptyImpWitness) =>
% 128.89/16.96 (((uniqinunit) =>
% 128.89/16.96 (((notinsingleton) =>
% 128.89/16.96 (((eqinunit) =>
% 128.89/16.96 (((singletonsswitch) =>
% 128.89/16.96 (((upairsetE) =>
% 128.89/16.96 (((upairsetIL) =>
% 128.89/16.96 (((upairsetIR) =>
% 128.89/16.96 (((emptyE1) =>
% 128.89/16.96 (((vacuousDall) =>
% 128.89/16.96 (((quantDeMorgan1) =>
% 128.89/16.96 (((quantDeMorgan2) =>
% 128.89/16.96 (((quantDeMorgan3) =>
% 128.89/16.96 (((quantDeMorgan4) =>
% 128.89/16.96 (((prop2setI) =>
% 128.89/16.96 (((prop2set2propI) =>
% 128.89/16.96 (((notdexE) =>
% 128.89/16.96 (((notdallE) =>
% 128.89/16.96 (((exuI1) =>
% 128.89/16.96 (((exuI3) =>
% 128.89/16.96 ((
% 128.89/16.96 (exuI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (inCongP) =>
% 128.89/16.96 ((
% 128.89/16.96 (in__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (exuE3u) =>
% 128.89/16.96 ((
% 128.89/16.96 (exu__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoin__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (powerset__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunion__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (exuEu) =>
% 128.89/16.96 ((
% 128.89/16.96 (descr__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (dsetconstr__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqimpsubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqimpsubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (emptysetsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetE) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetE2) =>
% 128.89/16.96 ((
% 128.89/16.96 (notsubsetI) =>
% 128.89/16.96 ((
% 128.89/16.96 (notequalI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (notequalI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetRefl) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetTrans) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoinSub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoinSub2) =>
% 128.89/16.96 ((
% 128.89/16.96 (subset2powerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (setextsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetemptysetimpeq) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (inPowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (sepInPowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (sepSubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionIL) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairset2IR) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionIR) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionEcases) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionE) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionRsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectI) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset5) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset3) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectER) =>
% 128.89/16.96 ((
% 128.89/16.96 (disjointsetsI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectRsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset4) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (bs114d) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusI) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusER) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusSubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusERneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusELneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusILneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusIRneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusSubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffE) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffIneg1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffIneg2) =>
% 128.89/16.96 ((
% 128.89/16.96 (secondinupair) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairIL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairIR) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairiskpair) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairp) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletoninpowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletoninpowunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairset2E) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairsubunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairinpowunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem3) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairin) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempair1) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempair) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionE2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton1) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1E1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1I) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1I2) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonsuniq) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL1) =>
% 128.89/16.96 ((
% 128.89/16.96 (kfstsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (theprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (kfstpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodfstin) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR11) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR12) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR1) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairequniteq) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR) =>
% 128.89/16.96 ((
% 128.89/16.96 (ksndsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (ksndpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairsurjEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodsndin) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairmemEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairmemER) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempaircEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodfstpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodsndpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairsurjEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrI) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrSub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setOfPairsIsBReln) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrERa) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrEL1) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrEL2) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrER) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcImageSingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (apProp) =>
% 128.89/16.96 ((
% 128.89/16.96 (app) =>
% 128.89/16.96 ((
% 128.89/16.96 (infuncsetfunc) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2p) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcinfuncset) =>
% 128.89/16.96 ((
% 128.89/16.96 (lamProp) =>
% 128.89/16.96 ((
% 128.89/16.96 (lamp) =>
% 128.89/16.96 ((
% 128.89/16.96 (lam2p) =>
% 128.89/16.96 ((
% 128.89/16.96 (brelnall1) =>
% 128.89/16.96 ((
% 128.89/16.96 (brelnall2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1E2) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp3) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcextLem) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp4) =>
% 128.89/16.96 ((
% 128.89/16.96 (subbreln) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqbreln) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcext) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcext2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2apEq1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2apEq2) =>
% 128.89/16.96 ((
% 128.89/16.96 (beta1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eta1) =>
% 128.89/16.96 ((
% 128.89/16.96 (lam2lamEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (beta2) =>
% 128.89/16.96 ((
% 128.89/16.96 (eta2) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalseProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalseProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ifSingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (ifp) =>
% 128.89/16.96 ((
% 128.89/16.96 (theeq) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrue) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalse) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueorfalse) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (setextT) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetTI) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetTI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetTE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectTELcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectTERcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT1) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT2) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT3) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementSub1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementSub2) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTnotintersectT) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementImpComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementSubsetComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementInPowersetComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (contraSubsetComplement) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTcontraSubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTILcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTIRcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInUnion) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInUnion2) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInIntersectUnions) =>
% 128.89/16.96 ((
% 128.89/16.96 (intersectInPowersetIntersectUnions) =>
% 128.89/16.96 ((
% 128.89/16.96 (inComplementUnionImpNotIn1) =>
% 128.89/16.96 ((
% 128.89/16.96 (inComplementUnionImpInComplement1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTE) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTEcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementUnionInPowersetComplement) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a2) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1a) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1b) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2b2) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2b) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule0) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule1) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule3) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule4) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_1) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_3) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_4) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_5) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1all2) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1SetBreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (choice2fnsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (setOfPairsIsBReln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1all1) =>
% 128.89/16.96 ((
% 128.89/16.96 (subbreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqbreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invI) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invE) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compI) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compE) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compEex) =>
% 128.89/16.96 ((
% 128.89/16.96 (!!) @ (
% 128.89/16.96 (('#B') @ (
% 128.89/16.96 !!) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#S') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#S') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 =>))) @
% 128.89/16.96 breln1)))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 !!))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#S') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#S') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 =>))) @
% 128.89/16.96 breln1)))))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#C') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 breln1)))) @
% 128.89/16.96 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl349])).
% 128.89/16.96 thf(zip_derived_cl362, plain,
% 128.89/16.96 (~ (((setoftrueEq) =>
% 128.89/16.96 (((powersetI) =>
% 128.89/16.96 (((emptyinPowerset) =>
% 128.89/16.96 (((emptyInPowerset) =>
% 128.89/16.96 (((powersetE) =>
% 128.89/16.96 (((setunionI) =>
% 128.89/16.96 (((setunionE) =>
% 128.89/16.96 (((subPowSU) =>
% 128.89/16.96 (((exuE2) =>
% 128.89/16.96 (((nonemptyImpWitness) =>
% 128.89/16.96 (((uniqinunit) =>
% 128.89/16.96 (((notinsingleton) =>
% 128.89/16.96 (((eqinunit) =>
% 128.89/16.96 (((singletonsswitch) =>
% 128.89/16.96 (((upairsetE) =>
% 128.89/16.96 (((upairsetIL) =>
% 128.89/16.96 (((upairsetIR) =>
% 128.89/16.96 (((emptyE1) =>
% 128.89/16.96 (((vacuousDall) =>
% 128.89/16.96 (((quantDeMorgan1) =>
% 128.89/16.96 (((quantDeMorgan2) =>
% 128.89/16.96 (((quantDeMorgan3) =>
% 128.89/16.96 (((quantDeMorgan4) =>
% 128.89/16.96 (((prop2setI) =>
% 128.89/16.96 (((prop2set2propI) =>
% 128.89/16.96 (((notdexE) =>
% 128.89/16.96 (((notdallE) =>
% 128.89/16.96 (((exuI1) =>
% 128.89/16.96 (((exuI3) =>
% 128.89/16.96 (((exuI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (inCongP) =>
% 128.89/16.96 ((
% 128.89/16.96 (in__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (exuE3u) =>
% 128.89/16.96 ((
% 128.89/16.96 (exu__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoin__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (powerset__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunion__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (exuEu) =>
% 128.89/16.96 ((
% 128.89/16.96 (descr__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (dsetconstr__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqimpsubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqimpsubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (emptysetsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetE) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetE2) =>
% 128.89/16.96 ((
% 128.89/16.96 (notsubsetI) =>
% 128.89/16.96 ((
% 128.89/16.96 (notequalI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (notequalI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetRefl) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetTrans) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoinSub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoinSub2) =>
% 128.89/16.96 ((
% 128.89/16.96 (subset2powerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (setextsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetemptysetimpeq) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (inPowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (sepInPowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (sepSubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionIL) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairset2IR) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionIR) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionEcases) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionE) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionRsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectI) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset5) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset3) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectER) =>
% 128.89/16.96 ((
% 128.89/16.96 (disjointsetsI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectRsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset4) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (bs114d) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusI) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusER) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusSubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusERneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusELneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusILneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusIRneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusSubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffE) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffIneg1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffIneg2) =>
% 128.89/16.96 ((
% 128.89/16.96 (secondinupair) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairIL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairIR) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairiskpair) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairp) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletoninpowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletoninpowunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairset2E) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairsubunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairinpowunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem3) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairin) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempair1) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempair) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionE2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton1) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1E1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1I) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1I2) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonsuniq) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL1) =>
% 128.89/16.96 ((
% 128.89/16.96 (kfstsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (theprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (kfstpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodfstin) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR11) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR12) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR1) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairequniteq) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR) =>
% 128.89/16.96 ((
% 128.89/16.96 (ksndsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (ksndpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairsurjEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodsndin) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairmemEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairmemER) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempaircEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodfstpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodsndpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairsurjEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrI) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrSub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setOfPairsIsBReln) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrERa) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrEL1) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrEL2) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrER) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcImageSingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (apProp) =>
% 128.89/16.96 ((
% 128.89/16.96 (app) =>
% 128.89/16.96 ((
% 128.89/16.96 (infuncsetfunc) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2p) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcinfuncset) =>
% 128.89/16.96 ((
% 128.89/16.96 (lamProp) =>
% 128.89/16.96 ((
% 128.89/16.96 (lamp) =>
% 128.89/16.96 ((
% 128.89/16.96 (lam2p) =>
% 128.89/16.96 ((
% 128.89/16.96 (brelnall1) =>
% 128.89/16.96 ((
% 128.89/16.96 (brelnall2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1E2) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp3) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcextLem) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp4) =>
% 128.89/16.96 ((
% 128.89/16.96 (subbreln) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqbreln) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcext) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcext2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2apEq1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2apEq2) =>
% 128.89/16.96 ((
% 128.89/16.96 (beta1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eta1) =>
% 128.89/16.96 ((
% 128.89/16.96 (lam2lamEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (beta2) =>
% 128.89/16.96 ((
% 128.89/16.96 (eta2) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalseProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalseProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ifSingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (ifp) =>
% 128.89/16.96 ((
% 128.89/16.96 (theeq) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrue) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalse) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueorfalse) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (setextT) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetTI) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetTI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetTE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectTELcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectTERcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT1) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT2) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT3) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementSub1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementSub2) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTnotintersectT) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementImpComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementSubsetComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementInPowersetComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (contraSubsetComplement) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTcontraSubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTILcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTIRcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInUnion) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInUnion2) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInIntersectUnions) =>
% 128.89/16.96 ((
% 128.89/16.96 (intersectInPowersetIntersectUnions) =>
% 128.89/16.96 ((
% 128.89/16.96 (inComplementUnionImpNotIn1) =>
% 128.89/16.96 ((
% 128.89/16.96 (inComplementUnionImpInComplement1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTE) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTEcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementUnionInPowersetComplement) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a2) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1a) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1b) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2b2) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2b) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule0) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule1) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule3) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule4) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_1) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_3) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_4) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_5) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1all2) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1SetBreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (choice2fnsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (setOfPairsIsBReln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1all1) =>
% 128.89/16.96 ((
% 128.89/16.96 (subbreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqbreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invI) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invE) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compI) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compE) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compEex) =>
% 128.89/16.96 ((
% 128.89/16.96 (!!) @ (
% 128.89/16.96 (('#B') @ (
% 128.89/16.96 !!) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#S') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#S') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 =>))) @
% 128.89/16.96 breln1)))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 !!))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#S') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#S') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 =>))) @
% 128.89/16.96 breln1)))))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#C') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 breln1)))) @
% 128.89/16.96 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl355])).
% 128.89/16.96 thf(zip_derived_cl369, plain,
% 128.89/16.96 (~ (((powersetI) =>
% 128.89/16.96 (((emptyinPowerset) =>
% 128.89/16.96 (((emptyInPowerset) =>
% 128.89/16.96 (((powersetE) =>
% 128.89/16.96 (((setunionI) =>
% 128.89/16.96 (((setunionE) =>
% 128.89/16.96 (((subPowSU) =>
% 128.89/16.96 (((exuE2) =>
% 128.89/16.96 (((nonemptyImpWitness) =>
% 128.89/16.96 (((uniqinunit) =>
% 128.89/16.96 (((notinsingleton) =>
% 128.89/16.96 (((eqinunit) =>
% 128.89/16.96 (((singletonsswitch) =>
% 128.89/16.96 (((upairsetE) =>
% 128.89/16.96 (((upairsetIL) =>
% 128.89/16.96 (((upairsetIR) =>
% 128.89/16.96 (((emptyE1) =>
% 128.89/16.96 (((vacuousDall) =>
% 128.89/16.96 (((quantDeMorgan1) =>
% 128.89/16.96 (((quantDeMorgan2) =>
% 128.89/16.96 (((quantDeMorgan3) =>
% 128.89/16.96 (((quantDeMorgan4) =>
% 128.89/16.96 (((prop2setI) =>
% 128.89/16.96 (((prop2set2propI) =>
% 128.89/16.96 (((notdexE) =>
% 128.89/16.96 (((notdallE) =>
% 128.89/16.96 (((exuI1) =>
% 128.89/16.96 (((exuI3) =>
% 128.89/16.96 (((exuI2) =>
% 128.89/16.96 (((inCongP) =>
% 128.89/16.96 ((
% 128.89/16.96 (in__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (exuE3u) =>
% 128.89/16.96 ((
% 128.89/16.96 (exu__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoin__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (powerset__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunion__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (exuEu) =>
% 128.89/16.96 ((
% 128.89/16.96 (descr__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (dsetconstr__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqimpsubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqimpsubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (emptysetsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetE) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetE2) =>
% 128.89/16.96 ((
% 128.89/16.96 (notsubsetI) =>
% 128.89/16.96 ((
% 128.89/16.96 (notequalI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (notequalI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetRefl) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetTrans) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoinSub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoinSub2) =>
% 128.89/16.96 ((
% 128.89/16.96 (subset2powerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (setextsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetemptysetimpeq) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (inPowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (sepInPowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (sepSubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionIL) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairset2IR) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionIR) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionEcases) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionE) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionRsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectI) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset5) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset3) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectER) =>
% 128.89/16.96 ((
% 128.89/16.96 (disjointsetsI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectRsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset4) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (bs114d) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusI) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusER) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusSubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusERneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusELneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusILneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusIRneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusSubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffE) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffIneg1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffIneg2) =>
% 128.89/16.96 ((
% 128.89/16.96 (secondinupair) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairIL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairIR) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairiskpair) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairp) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletoninpowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletoninpowunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairset2E) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairsubunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairinpowunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem3) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairin) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempair1) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempair) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionE2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton1) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1E1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1I) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1I2) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonsuniq) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL1) =>
% 128.89/16.96 ((
% 128.89/16.96 (kfstsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (theprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (kfstpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodfstin) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR11) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR12) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR1) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairequniteq) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR) =>
% 128.89/16.96 ((
% 128.89/16.96 (ksndsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (ksndpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairsurjEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodsndin) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairmemEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairmemER) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempaircEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodfstpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodsndpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairsurjEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrI) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrSub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setOfPairsIsBReln) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrERa) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrEL1) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrEL2) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrER) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcImageSingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (apProp) =>
% 128.89/16.96 ((
% 128.89/16.96 (app) =>
% 128.89/16.96 ((
% 128.89/16.96 (infuncsetfunc) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2p) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcinfuncset) =>
% 128.89/16.96 ((
% 128.89/16.96 (lamProp) =>
% 128.89/16.96 ((
% 128.89/16.96 (lamp) =>
% 128.89/16.96 ((
% 128.89/16.96 (lam2p) =>
% 128.89/16.96 ((
% 128.89/16.96 (brelnall1) =>
% 128.89/16.96 ((
% 128.89/16.96 (brelnall2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1E2) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp3) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcextLem) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp4) =>
% 128.89/16.96 ((
% 128.89/16.96 (subbreln) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqbreln) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcext) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcext2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2apEq1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2apEq2) =>
% 128.89/16.96 ((
% 128.89/16.96 (beta1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eta1) =>
% 128.89/16.96 ((
% 128.89/16.96 (lam2lamEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (beta2) =>
% 128.89/16.96 ((
% 128.89/16.96 (eta2) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalseProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalseProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ifSingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (ifp) =>
% 128.89/16.96 ((
% 128.89/16.96 (theeq) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrue) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalse) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueorfalse) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (setextT) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetTI) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetTI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetTE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectTELcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectTERcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT1) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT2) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT3) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementSub1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementSub2) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTnotintersectT) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementImpComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementSubsetComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementInPowersetComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (contraSubsetComplement) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTcontraSubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTILcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTIRcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInUnion) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInUnion2) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInIntersectUnions) =>
% 128.89/16.96 ((
% 128.89/16.96 (intersectInPowersetIntersectUnions) =>
% 128.89/16.96 ((
% 128.89/16.96 (inComplementUnionImpNotIn1) =>
% 128.89/16.96 ((
% 128.89/16.96 (inComplementUnionImpInComplement1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTE) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTEcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementUnionInPowersetComplement) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a2) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1a) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1b) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2b2) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2b) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule0) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule1) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule3) =>
% 128.89/16.96 ((
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% 128.89/16.96 ((
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% 128.89/16.96 ((
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% 128.89/16.96 ((
% 128.89/16.96 (woz1_3) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_4) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_5) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1all2) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1SetBreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (choice2fnsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (setOfPairsIsBReln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1all1) =>
% 128.89/16.96 ((
% 128.89/16.96 (subbreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqbreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invI) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invE) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compI) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compE) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compEex) =>
% 128.89/16.96 ((
% 128.89/16.96 (!!) @ (
% 128.89/16.96 (('#B') @ (
% 128.89/16.96 !!) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#S') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#S') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 =>))) @
% 128.89/16.96 breln1)))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 !!))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#S') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#S') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 =>))) @
% 128.89/16.96 breln1)))))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#C') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 breln1)))) @
% 128.89/16.96 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl362])).
% 128.89/16.96 thf(zip_derived_cl376, plain,
% 128.89/16.96 (~ (((emptyinPowerset) =>
% 128.89/16.96 (((emptyInPowerset) =>
% 128.89/16.96 (((powersetE) =>
% 128.89/16.96 (((setunionI) =>
% 128.89/16.96 (((setunionE) =>
% 128.89/16.96 (((subPowSU) =>
% 128.89/16.96 (((exuE2) =>
% 128.89/16.96 (((nonemptyImpWitness) =>
% 128.89/16.96 (((uniqinunit) =>
% 128.89/16.96 (((notinsingleton) =>
% 128.89/16.96 (((eqinunit) =>
% 128.89/16.96 (((singletonsswitch) =>
% 128.89/16.96 (((upairsetE) =>
% 128.89/16.96 (((upairsetIL) =>
% 128.89/16.96 (((upairsetIR) =>
% 128.89/16.96 (((emptyE1) =>
% 128.89/16.96 (((vacuousDall) =>
% 128.89/16.96 (((quantDeMorgan1) =>
% 128.89/16.96 (((quantDeMorgan2) =>
% 128.89/16.96 (((quantDeMorgan3) =>
% 128.89/16.96 (((quantDeMorgan4) =>
% 128.89/16.96 (((prop2setI) =>
% 128.89/16.96 (((prop2set2propI) =>
% 128.89/16.96 (((notdexE) =>
% 128.89/16.96 (((notdallE) =>
% 128.89/16.96 (((exuI1) =>
% 128.89/16.96 (((exuI3) =>
% 128.89/16.96 (((exuI2) =>
% 128.89/16.96 (((inCongP) =>
% 128.89/16.96 (((in__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (exuE3u) =>
% 128.89/16.96 ((
% 128.89/16.96 (exu__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoin__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (powerset__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunion__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (exuEu) =>
% 128.89/16.96 ((
% 128.89/16.96 (descr__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (dsetconstr__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqimpsubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqimpsubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (emptysetsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetE) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetE2) =>
% 128.89/16.96 ((
% 128.89/16.96 (notsubsetI) =>
% 128.89/16.96 ((
% 128.89/16.96 (notequalI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (notequalI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetRefl) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetTrans) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoinSub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoinSub2) =>
% 128.89/16.96 ((
% 128.89/16.96 (subset2powerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (setextsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetemptysetimpeq) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (inPowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (sepInPowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (sepSubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionIL) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairset2IR) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionIR) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionEcases) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionE) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionRsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectI) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset5) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset3) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectER) =>
% 128.89/16.96 ((
% 128.89/16.96 (disjointsetsI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectRsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset4) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (bs114d) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusI) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusER) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusSubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusERneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusELneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusILneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusIRneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusSubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffE) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffIneg1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffIneg2) =>
% 128.89/16.96 ((
% 128.89/16.96 (secondinupair) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairIL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairIR) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairiskpair) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairp) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletoninpowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletoninpowunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairset2E) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairsubunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairinpowunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem3) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairin) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempair1) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempair) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionE2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton1) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1E1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1I) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1I2) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonsuniq) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL1) =>
% 128.89/16.96 ((
% 128.89/16.96 (kfstsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (theprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (kfstpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodfstin) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR11) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR12) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR1) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairequniteq) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR) =>
% 128.89/16.96 ((
% 128.89/16.96 (ksndsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (ksndpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairsurjEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodsndin) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairmemEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairmemER) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempaircEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodfstpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodsndpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairsurjEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrI) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrSub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setOfPairsIsBReln) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrERa) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrEL1) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrEL2) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrER) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcImageSingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (apProp) =>
% 128.89/16.96 ((
% 128.89/16.96 (app) =>
% 128.89/16.96 ((
% 128.89/16.96 (infuncsetfunc) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2p) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcinfuncset) =>
% 128.89/16.96 ((
% 128.89/16.96 (lamProp) =>
% 128.89/16.96 ((
% 128.89/16.96 (lamp) =>
% 128.89/16.96 ((
% 128.89/16.96 (lam2p) =>
% 128.89/16.96 ((
% 128.89/16.96 (brelnall1) =>
% 128.89/16.96 ((
% 128.89/16.96 (brelnall2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1E2) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp3) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcextLem) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp4) =>
% 128.89/16.96 ((
% 128.89/16.96 (subbreln) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqbreln) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcext) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcext2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2apEq1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2apEq2) =>
% 128.89/16.96 ((
% 128.89/16.96 (beta1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eta1) =>
% 128.89/16.96 ((
% 128.89/16.96 (lam2lamEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (beta2) =>
% 128.89/16.96 ((
% 128.89/16.96 (eta2) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalseProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalseProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ifSingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (ifp) =>
% 128.89/16.96 ((
% 128.89/16.96 (theeq) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrue) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalse) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueorfalse) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (setextT) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetTI) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetTI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetTE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectTELcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectTERcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT1) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT2) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT3) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementSub1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementSub2) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTnotintersectT) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementImpComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementSubsetComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementInPowersetComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (contraSubsetComplement) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTcontraSubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTILcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTIRcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInUnion) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInUnion2) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInIntersectUnions) =>
% 128.89/16.96 ((
% 128.89/16.96 (intersectInPowersetIntersectUnions) =>
% 128.89/16.96 ((
% 128.89/16.96 (inComplementUnionImpNotIn1) =>
% 128.89/16.96 ((
% 128.89/16.96 (inComplementUnionImpInComplement1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTE) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTEcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementUnionInPowersetComplement) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a2) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1a) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1b) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2b2) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2b) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule0) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule1) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule3) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule4) =>
% 128.89/16.96 ((
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% 128.89/16.96 ((
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% 128.89/16.96 ((
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% 128.89/16.96 ((
% 128.89/16.96 (woz1_5) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1all2) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1SetBreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (choice2fnsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (setOfPairsIsBReln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1all1) =>
% 128.89/16.96 ((
% 128.89/16.96 (subbreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqbreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invI) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invE) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compI) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compE) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compEex) =>
% 128.89/16.96 ((
% 128.89/16.96 (!!) @ (
% 128.89/16.96 (('#B') @ (
% 128.89/16.96 !!) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#S') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#S') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 =>))) @
% 128.89/16.96 breln1)))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 !!))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#S') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#S') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 =>))) @
% 128.89/16.96 breln1)))))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#C') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 breln1)))) @
% 128.89/16.96 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl369])).
% 128.89/16.96 thf(zip_derived_cl384, plain,
% 128.89/16.96 (~ (((emptyInPowerset) =>
% 128.89/16.96 (((powersetE) =>
% 128.89/16.96 (((setunionI) =>
% 128.89/16.96 (((setunionE) =>
% 128.89/16.96 (((subPowSU) =>
% 128.89/16.96 (((exuE2) =>
% 128.89/16.96 (((nonemptyImpWitness) =>
% 128.89/16.96 (((uniqinunit) =>
% 128.89/16.96 (((notinsingleton) =>
% 128.89/16.96 (((eqinunit) =>
% 128.89/16.96 (((singletonsswitch) =>
% 128.89/16.96 (((upairsetE) =>
% 128.89/16.96 (((upairsetIL) =>
% 128.89/16.96 (((upairsetIR) =>
% 128.89/16.96 (((emptyE1) =>
% 128.89/16.96 (((vacuousDall) =>
% 128.89/16.96 (((quantDeMorgan1) =>
% 128.89/16.96 (((quantDeMorgan2) =>
% 128.89/16.96 (((quantDeMorgan3) =>
% 128.89/16.96 (((quantDeMorgan4) =>
% 128.89/16.96 (((prop2setI) =>
% 128.89/16.96 (((prop2set2propI) =>
% 128.89/16.96 (((notdexE) =>
% 128.89/16.96 (((notdallE) =>
% 128.89/16.96 (((exuI1) =>
% 128.89/16.96 (((exuI3) =>
% 128.89/16.96 (((exuI2) =>
% 128.89/16.96 (((inCongP) =>
% 128.89/16.96 (((in__Cong) =>
% 128.89/16.96 (((exuE3u) =>
% 128.89/16.96 ((
% 128.89/16.96 (exu__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoin__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (powerset__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunion__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (exuEu) =>
% 128.89/16.96 ((
% 128.89/16.96 (descr__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (dsetconstr__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqimpsubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqimpsubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (emptysetsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetE) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetE2) =>
% 128.89/16.96 ((
% 128.89/16.96 (notsubsetI) =>
% 128.89/16.96 ((
% 128.89/16.96 (notequalI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (notequalI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetRefl) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetTrans) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoinSub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoinSub2) =>
% 128.89/16.96 ((
% 128.89/16.96 (subset2powerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (setextsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetemptysetimpeq) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (inPowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (sepInPowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (sepSubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionIL) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairset2IR) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionIR) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionEcases) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionE) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionRsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectI) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset5) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset3) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectER) =>
% 128.89/16.96 ((
% 128.89/16.96 (disjointsetsI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectRsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset4) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (bs114d) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusI) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusER) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusSubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusERneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusELneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusILneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusIRneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusSubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffE) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffIneg1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffIneg2) =>
% 128.89/16.96 ((
% 128.89/16.96 (secondinupair) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairIL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairIR) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairiskpair) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairp) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletoninpowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletoninpowunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairset2E) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairsubunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairinpowunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem3) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairin) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempair1) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempair) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionE2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton1) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1E1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1I) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1I2) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonsuniq) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL1) =>
% 128.89/16.96 ((
% 128.89/16.96 (kfstsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (theprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (kfstpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodfstin) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR11) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR12) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR1) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairequniteq) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR) =>
% 128.89/16.96 ((
% 128.89/16.96 (ksndsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (ksndpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairsurjEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodsndin) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairmemEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairmemER) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempaircEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodfstpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodsndpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairsurjEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrI) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrSub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setOfPairsIsBReln) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrERa) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrEL1) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrEL2) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrER) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcImageSingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (apProp) =>
% 128.89/16.96 ((
% 128.89/16.96 (app) =>
% 128.89/16.96 ((
% 128.89/16.96 (infuncsetfunc) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2p) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcinfuncset) =>
% 128.89/16.96 ((
% 128.89/16.96 (lamProp) =>
% 128.89/16.96 ((
% 128.89/16.96 (lamp) =>
% 128.89/16.96 ((
% 128.89/16.96 (lam2p) =>
% 128.89/16.96 ((
% 128.89/16.96 (brelnall1) =>
% 128.89/16.96 ((
% 128.89/16.96 (brelnall2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1E2) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp3) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcextLem) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp4) =>
% 128.89/16.96 ((
% 128.89/16.96 (subbreln) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqbreln) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcext) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcext2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2apEq1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2apEq2) =>
% 128.89/16.96 ((
% 128.89/16.96 (beta1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eta1) =>
% 128.89/16.96 ((
% 128.89/16.96 (lam2lamEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (beta2) =>
% 128.89/16.96 ((
% 128.89/16.96 (eta2) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalseProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalseProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ifSingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (ifp) =>
% 128.89/16.96 ((
% 128.89/16.96 (theeq) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrue) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalse) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueorfalse) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (setextT) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetTI) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetTI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetTE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectTELcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectTERcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT1) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT2) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT3) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementSub1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementSub2) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTnotintersectT) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementImpComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementSubsetComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementInPowersetComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (contraSubsetComplement) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTcontraSubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTILcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTIRcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInUnion) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInUnion2) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInIntersectUnions) =>
% 128.89/16.96 ((
% 128.89/16.96 (intersectInPowersetIntersectUnions) =>
% 128.89/16.96 ((
% 128.89/16.96 (inComplementUnionImpNotIn1) =>
% 128.89/16.96 ((
% 128.89/16.96 (inComplementUnionImpInComplement1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTE) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTEcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementUnionInPowersetComplement) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a2) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1a) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1b) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2b2) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2b) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule0) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule1) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule3) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule4) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_1) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_3) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_4) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_5) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1all2) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1SetBreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (choice2fnsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (setOfPairsIsBReln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1all1) =>
% 128.89/16.96 ((
% 128.89/16.96 (subbreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqbreln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invI) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invE) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compI) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compE) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compEex) =>
% 128.89/16.96 ((
% 128.89/16.96 (!!) @ (
% 128.89/16.96 (('#B') @ (
% 128.89/16.96 !!) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#S') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#S') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 =>))) @
% 128.89/16.96 breln1)))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 !!))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#S') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#S') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 =>))) @
% 128.89/16.96 breln1)))))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#C') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 breln1)))) @
% 128.89/16.96 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl376])).
% 128.89/16.96 thf(zip_derived_cl392, plain,
% 128.89/16.96 (~ (((powersetE) =>
% 128.89/16.96 (((setunionI) =>
% 128.89/16.96 (((setunionE) =>
% 128.89/16.96 (((subPowSU) =>
% 128.89/16.96 (((exuE2) =>
% 128.89/16.96 (((nonemptyImpWitness) =>
% 128.89/16.96 (((uniqinunit) =>
% 128.89/16.96 (((notinsingleton) =>
% 128.89/16.96 (((eqinunit) =>
% 128.89/16.96 (((singletonsswitch) =>
% 128.89/16.96 (((upairsetE) =>
% 128.89/16.96 (((upairsetIL) =>
% 128.89/16.96 (((upairsetIR) =>
% 128.89/16.96 (((emptyE1) =>
% 128.89/16.96 (((vacuousDall) =>
% 128.89/16.96 (((quantDeMorgan1) =>
% 128.89/16.96 (((quantDeMorgan2) =>
% 128.89/16.96 (((quantDeMorgan3) =>
% 128.89/16.96 (((quantDeMorgan4) =>
% 128.89/16.96 (((prop2setI) =>
% 128.89/16.96 (((prop2set2propI) =>
% 128.89/16.96 (((notdexE) =>
% 128.89/16.96 (((notdallE) =>
% 128.89/16.96 (((exuI1) =>
% 128.89/16.96 (((exuI3) =>
% 128.89/16.96 (((exuI2) =>
% 128.89/16.96 (((inCongP) =>
% 128.89/16.96 (((in__Cong) =>
% 128.89/16.96 (((exuE3u) =>
% 128.89/16.96 (((exu__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoin__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (powerset__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunion__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (exuEu) =>
% 128.89/16.96 ((
% 128.89/16.96 (descr__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (dsetconstr__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqimpsubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqimpsubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (emptysetsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetE) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetE2) =>
% 128.89/16.96 ((
% 128.89/16.96 (notsubsetI) =>
% 128.89/16.96 ((
% 128.89/16.96 (notequalI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (notequalI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetRefl) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetTrans) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoinSub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoinSub2) =>
% 128.89/16.96 ((
% 128.89/16.96 (subset2powerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (setextsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetemptysetimpeq) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (inPowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (sepInPowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (sepSubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionIL) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairset2IR) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionIR) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionEcases) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionE) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionRsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectI) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset5) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset3) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectER) =>
% 128.89/16.96 ((
% 128.89/16.96 (disjointsetsI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectRsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset4) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (bs114d) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusI) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusER) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusSubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusERneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusELneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusILneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusIRneg) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusSubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffE) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffIneg1) =>
% 128.89/16.96 ((
% 128.89/16.96 (symdiffIneg2) =>
% 128.89/16.96 ((
% 128.89/16.96 (secondinupair) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairIL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairIR) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairiskpair) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairp) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletoninpowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletoninpowunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairset2E) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairsubunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairinpowunion) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ubforcartprodlem3) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairin) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempair1) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempair) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionE2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton1) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunionsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1E1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1I) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1I2) =>
% 128.89/16.96 ((
% 128.89/16.96 (singletonsuniq) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL1) =>
% 128.89/16.96 ((
% 128.89/16.96 (kfstsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (theprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (kfstpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodfstin) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjL) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR11) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR12) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR1) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairequniteq) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR2) =>
% 128.89/16.96 ((
% 128.89/16.96 (setukpairinjR) =>
% 128.89/16.96 ((
% 128.89/16.96 (ksndsingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (ksndpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (kpairsurjEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodsndin) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairmemEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairmemER) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodmempaircEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodfstpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodsndpairEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (cartprodpairsurjEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrI) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrSub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setOfPairsIsBReln) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrERa) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrEL1) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrEL2) =>
% 128.89/16.96 ((
% 128.89/16.96 (dpsetconstrER) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcImageSingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (apProp) =>
% 128.89/16.96 ((
% 128.89/16.96 (app) =>
% 128.89/16.96 ((
% 128.89/16.96 (infuncsetfunc) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2p) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcinfuncset) =>
% 128.89/16.96 ((
% 128.89/16.96 (lamProp) =>
% 128.89/16.96 ((
% 128.89/16.96 (lamp) =>
% 128.89/16.96 ((
% 128.89/16.96 (lam2p) =>
% 128.89/16.96 ((
% 128.89/16.96 (brelnall1) =>
% 128.89/16.96 ((
% 128.89/16.96 (brelnall2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ex1E2) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp3) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcextLem) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcGraphProp4) =>
% 128.89/16.96 ((
% 128.89/16.96 (subbreln) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqbreln) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcext) =>
% 128.89/16.96 ((
% 128.89/16.96 (funcext2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2apEq1) =>
% 128.89/16.96 ((
% 128.89/16.96 (ap2apEq2) =>
% 128.89/16.96 ((
% 128.89/16.96 (beta1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eta1) =>
% 128.89/16.96 ((
% 128.89/16.96 (lam2lamEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (beta2) =>
% 128.89/16.96 ((
% 128.89/16.96 (eta2) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalseProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalseProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueProp1) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueProp2) =>
% 128.89/16.96 ((
% 128.89/16.96 (ifSingleton) =>
% 128.89/16.96 ((
% 128.89/16.96 (ifp) =>
% 128.89/16.96 ((
% 128.89/16.96 (theeq) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrue) =>
% 128.89/16.96 ((
% 128.89/16.96 (iffalse) =>
% 128.89/16.96 ((
% 128.89/16.96 (iftrueorfalse) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (setminusT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementT_lem) =>
% 128.89/16.96 ((
% 128.89/16.96 (setextT) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetTI) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetTI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetTE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectTELcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectTERcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT1) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT2) =>
% 128.89/16.96 ((
% 128.89/16.96 (contrasubsetT3) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementSub1) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementSub2) =>
% 128.89/16.96 ((
% 128.89/16.96 (doubleComplementEq) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTnotintersectT) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementImpComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementSubsetComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementInPowersetComplementIntersect) =>
% 128.89/16.96 ((
% 128.89/16.96 (contraSubsetComplement) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementTcontraSubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTILcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTIRcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInUnion) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInUnion2) =>
% 128.89/16.96 ((
% 128.89/16.96 (inIntersectImpInIntersectUnions) =>
% 128.89/16.96 ((
% 128.89/16.96 (intersectInPowersetIntersectUnions) =>
% 128.89/16.96 ((
% 128.89/16.96 (inComplementUnionImpNotIn1) =>
% 128.89/16.96 ((
% 128.89/16.96 (inComplementUnionImpInComplement1) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTE) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionTEcontra) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a1) =>
% 128.89/16.96 ((
% 128.89/16.96 (complementUnionInPowersetComplement) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a2) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1a) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1b) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan1) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2a) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2b2) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2b) =>
% 128.89/16.96 ((
% 128.89/16.96 (demorgan2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule0) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule1) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule2) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule3) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz13rule4) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_1) =>
% 128.89/16.96 ((
% 128.89/16.96 (woz1_2) =>
% 128.89/16.96 ((
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% 128.89/16.96 ((
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% 128.89/16.96 ((
% 128.89/16.96 (woz1_5) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1all2) =>
% 128.89/16.96 ((
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% 128.89/16.96 ((
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% 128.89/16.96 ((
% 128.89/16.96 (setOfPairsIsBReln1) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1all1) =>
% 128.89/16.96 ((
% 128.89/16.96 (subbreln1) =>
% 128.89/16.96 ((
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% 128.89/16.96 ((
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% 128.89/16.96 ((
% 128.89/16.96 (breln1invI) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1invE) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compprop) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compI) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compE) =>
% 128.89/16.96 ((
% 128.89/16.96 (breln1compEex) =>
% 128.89/16.96 ((
% 128.89/16.96 (!!) @ (
% 128.89/16.96 (('#B') @ (
% 128.89/16.96 !!) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#S') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#S') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 =>))) @
% 128.89/16.96 breln1)))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 !!))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#S') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#S') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 =>))) @
% 128.89/16.96 breln1)))))) @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#C') @ (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 (
% 128.89/16.96 (
% 128.89/16.96 ('#B') @ (
% 128.89/16.96 '#B') @
% 128.89/16.96 breln1)))) @
% 128.89/16.96 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl384])).
% 128.89/16.96 thf(zip_derived_cl400, plain,
% 128.89/16.96 (~ (((setunionI) =>
% 128.89/16.96 (((setunionE) =>
% 128.89/16.96 (((subPowSU) =>
% 128.89/16.96 (((exuE2) =>
% 128.89/16.96 (((nonemptyImpWitness) =>
% 128.89/16.96 (((uniqinunit) =>
% 128.89/16.96 (((notinsingleton) =>
% 128.89/16.96 (((eqinunit) =>
% 128.89/16.96 (((singletonsswitch) =>
% 128.89/16.96 (((upairsetE) =>
% 128.89/16.96 (((upairsetIL) =>
% 128.89/16.96 (((upairsetIR) =>
% 128.89/16.96 (((emptyE1) =>
% 128.89/16.96 (((vacuousDall) =>
% 128.89/16.96 (((quantDeMorgan1) =>
% 128.89/16.96 (((quantDeMorgan2) =>
% 128.89/16.96 (((quantDeMorgan3) =>
% 128.89/16.96 (((quantDeMorgan4) =>
% 128.89/16.96 (((prop2setI) =>
% 128.89/16.96 (((prop2set2propI) =>
% 128.89/16.96 (((notdexE) =>
% 128.89/16.96 (((notdallE) =>
% 128.89/16.96 (((exuI1) =>
% 128.89/16.96 (((exuI3) =>
% 128.89/16.96 (((exuI2) =>
% 128.89/16.96 (((inCongP) =>
% 128.89/16.96 (((in__Cong) =>
% 128.89/16.96 (((exuE3u) =>
% 128.89/16.96 (((exu__Cong) =>
% 128.89/16.96 (((setadjoin__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (powerset__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (setunion__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (exuEu) =>
% 128.89/16.96 ((
% 128.89/16.96 (descr__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (dsetconstr__Cong) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqimpsubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (eqimpsubset1) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (emptysetsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetE) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetE2) =>
% 128.89/16.96 ((
% 128.89/16.96 (notsubsetI) =>
% 128.89/16.96 ((
% 128.89/16.96 (notequalI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (notequalI2) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetRefl) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetTrans) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoinSub) =>
% 128.89/16.96 ((
% 128.89/16.96 (setadjoinSub2) =>
% 128.89/16.96 ((
% 128.89/16.96 (subset2powerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (setextsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (subsetemptysetimpeq) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetI1) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetE1) =>
% 128.89/16.96 ((
% 128.89/16.96 (inPowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (powersetsubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (sepInPowerset) =>
% 128.89/16.96 ((
% 128.89/16.96 (sepSubset) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionIL) =>
% 128.89/16.96 ((
% 128.89/16.96 (upairset2IR) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionIR) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionEcases) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionE) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binunionRsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectI) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset5) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectEL) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectLsub) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset2) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectSubset3) =>
% 128.89/16.96 ((
% 128.89/16.96 (binintersectER) =>
% 128.89/16.96 ((
% 128.89/16.96 (disjointsetsI1) =>
% 128.89/16.96 ((
% 128.89/16.97 (binintersectRsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset4) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (bs114d) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusI) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusER) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusSubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusERneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusELneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusILneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusIRneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusSubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffE) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffIneg1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffIneg2) =>
% 128.89/16.97 ((
% 128.89/16.97 (secondinupair) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairIL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairIR) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairiskpair) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairp) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletoninpowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletoninpowunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairset2E) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairsubunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairinpowunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem3) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairin) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempair1) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempair) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionE2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton1) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1E1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1I) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1I2) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonsuniq) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL1) =>
% 128.89/16.97 ((
% 128.89/16.97 (kfstsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (theprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (kfstpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodfstin) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR11) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR12) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR1) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairequniteq) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR) =>
% 128.89/16.97 ((
% 128.89/16.97 (ksndsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (ksndpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairsurjEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodsndin) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairmemEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairmemER) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempaircEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodfstpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodsndpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairsurjEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrI) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrSub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setOfPairsIsBReln) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrERa) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrEL1) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrEL2) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrER) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcImageSingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (apProp) =>
% 128.89/16.97 ((
% 128.89/16.97 (app) =>
% 128.89/16.97 ((
% 128.89/16.97 (infuncsetfunc) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2p) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcinfuncset) =>
% 128.89/16.97 ((
% 128.89/16.97 (lamProp) =>
% 128.89/16.97 ((
% 128.89/16.97 (lamp) =>
% 128.89/16.97 ((
% 128.89/16.97 (lam2p) =>
% 128.89/16.97 ((
% 128.89/16.97 (brelnall1) =>
% 128.89/16.97 ((
% 128.89/16.97 (brelnall2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1E2) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp3) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcextLem) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp4) =>
% 128.89/16.97 ((
% 128.89/16.97 (subbreln) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqbreln) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcext) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcext2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2apEq1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2apEq2) =>
% 128.89/16.97 ((
% 128.89/16.97 (beta1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eta1) =>
% 128.89/16.97 ((
% 128.89/16.97 (lam2lamEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (beta2) =>
% 128.89/16.97 ((
% 128.89/16.97 (eta2) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalseProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalseProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ifSingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (ifp) =>
% 128.89/16.97 ((
% 128.89/16.97 (theeq) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrue) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalse) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueorfalse) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (setextT) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetTI) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetTI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetTE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectTELcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectTERcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT1) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT2) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT3) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementSub1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementSub2) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTnotintersectT) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementImpComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementSubsetComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementInPowersetComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (contraSubsetComplement) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTcontraSubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTILcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTIRcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInUnion) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInUnion2) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInIntersectUnions) =>
% 128.89/16.97 ((
% 128.89/16.97 (intersectInPowersetIntersectUnions) =>
% 128.89/16.97 ((
% 128.89/16.97 (inComplementUnionImpNotIn1) =>
% 128.89/16.97 ((
% 128.89/16.97 (inComplementUnionImpInComplement1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTE) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTEcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementUnionInPowersetComplement) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a2) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1a) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1b) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2b2) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2b) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule0) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule1) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule3) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule4) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_1) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_3) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_4) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_5) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1all2) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1SetBreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (choice2fnsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (setOfPairsIsBReln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1all1) =>
% 128.89/16.97 ((
% 128.89/16.97 (subbreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqbreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invI) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invE) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compI) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compE) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compEex) =>
% 128.89/16.97 ((
% 128.89/16.97 (!!) @ (
% 128.89/16.97 (('#B') @ (
% 128.89/16.97 !!) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#S') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#S') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 =>))) @
% 128.89/16.97 breln1)))) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 !!))) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#S') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#B') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#S') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 =>))) @
% 128.89/16.97 breln1)))))) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#C') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#B') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#B') @
% 128.89/16.97 breln1)))) @
% 128.89/16.97 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl392])).
% 128.89/16.97 thf(zip_derived_cl408, plain,
% 128.89/16.97 (~ (((setunionE) =>
% 128.89/16.97 (((subPowSU) =>
% 128.89/16.97 (((exuE2) =>
% 128.89/16.97 (((nonemptyImpWitness) =>
% 128.89/16.97 (((uniqinunit) =>
% 128.89/16.97 (((notinsingleton) =>
% 128.89/16.97 (((eqinunit) =>
% 128.89/16.97 (((singletonsswitch) =>
% 128.89/16.97 (((upairsetE) =>
% 128.89/16.97 (((upairsetIL) =>
% 128.89/16.97 (((upairsetIR) =>
% 128.89/16.97 (((emptyE1) =>
% 128.89/16.97 (((vacuousDall) =>
% 128.89/16.97 (((quantDeMorgan1) =>
% 128.89/16.97 (((quantDeMorgan2) =>
% 128.89/16.97 (((quantDeMorgan3) =>
% 128.89/16.97 (((quantDeMorgan4) =>
% 128.89/16.97 (((prop2setI) =>
% 128.89/16.97 (((prop2set2propI) =>
% 128.89/16.97 (((notdexE) =>
% 128.89/16.97 (((notdallE) =>
% 128.89/16.97 (((exuI1) =>
% 128.89/16.97 (((exuI3) =>
% 128.89/16.97 (((exuI2) =>
% 128.89/16.97 (((inCongP) =>
% 128.89/16.97 (((in__Cong) =>
% 128.89/16.97 (((exuE3u) =>
% 128.89/16.97 (((exu__Cong) =>
% 128.89/16.97 (((setadjoin__Cong) =>
% 128.89/16.97 (((powerset__Cong) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunion__Cong) =>
% 128.89/16.97 ((
% 128.89/16.97 (exuEu) =>
% 128.89/16.97 ((
% 128.89/16.97 (descr__Cong) =>
% 128.89/16.97 ((
% 128.89/16.97 (dsetconstr__Cong) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqimpsubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqimpsubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (emptysetsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetE) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetE2) =>
% 128.89/16.97 ((
% 128.89/16.97 (notsubsetI) =>
% 128.89/16.97 ((
% 128.89/16.97 (notequalI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (notequalI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetRefl) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetTrans) =>
% 128.89/16.97 ((
% 128.89/16.97 (setadjoinSub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setadjoinSub2) =>
% 128.89/16.97 ((
% 128.89/16.97 (subset2powerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (setextsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetemptysetimpeq) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (inPowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (sepInPowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (sepSubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionIL) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairset2IR) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionIR) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionEcases) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionE) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionRsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectI) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset5) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset3) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectER) =>
% 128.89/16.97 ((
% 128.89/16.97 (disjointsetsI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectRsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset4) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (bs114d) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusI) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusER) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusSubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusERneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusELneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusILneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusIRneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusSubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffE) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffIneg1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffIneg2) =>
% 128.89/16.97 ((
% 128.89/16.97 (secondinupair) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairIL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairIR) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairiskpair) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairp) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletoninpowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletoninpowunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairset2E) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairsubunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairinpowunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem3) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairin) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempair1) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempair) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionE2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton1) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1E1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1I) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1I2) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonsuniq) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL1) =>
% 128.89/16.97 ((
% 128.89/16.97 (kfstsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (theprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (kfstpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodfstin) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR11) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR12) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR1) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairequniteq) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR) =>
% 128.89/16.97 ((
% 128.89/16.97 (ksndsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (ksndpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairsurjEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodsndin) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairmemEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairmemER) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempaircEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodfstpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodsndpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairsurjEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrI) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrSub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setOfPairsIsBReln) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrERa) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrEL1) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrEL2) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrER) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcImageSingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (apProp) =>
% 128.89/16.97 ((
% 128.89/16.97 (app) =>
% 128.89/16.97 ((
% 128.89/16.97 (infuncsetfunc) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2p) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcinfuncset) =>
% 128.89/16.97 ((
% 128.89/16.97 (lamProp) =>
% 128.89/16.97 ((
% 128.89/16.97 (lamp) =>
% 128.89/16.97 ((
% 128.89/16.97 (lam2p) =>
% 128.89/16.97 ((
% 128.89/16.97 (brelnall1) =>
% 128.89/16.97 ((
% 128.89/16.97 (brelnall2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1E2) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp3) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcextLem) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp4) =>
% 128.89/16.97 ((
% 128.89/16.97 (subbreln) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqbreln) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcext) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcext2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2apEq1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2apEq2) =>
% 128.89/16.97 ((
% 128.89/16.97 (beta1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eta1) =>
% 128.89/16.97 ((
% 128.89/16.97 (lam2lamEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (beta2) =>
% 128.89/16.97 ((
% 128.89/16.97 (eta2) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalseProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalseProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ifSingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (ifp) =>
% 128.89/16.97 ((
% 128.89/16.97 (theeq) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrue) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalse) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueorfalse) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (setextT) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetTI) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetTI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetTE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectTELcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectTERcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT1) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT2) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT3) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementSub1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementSub2) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTnotintersectT) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementImpComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementSubsetComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementInPowersetComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (contraSubsetComplement) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTcontraSubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTILcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTIRcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInUnion) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInUnion2) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInIntersectUnions) =>
% 128.89/16.97 ((
% 128.89/16.97 (intersectInPowersetIntersectUnions) =>
% 128.89/16.97 ((
% 128.89/16.97 (inComplementUnionImpNotIn1) =>
% 128.89/16.97 ((
% 128.89/16.97 (inComplementUnionImpInComplement1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTE) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTEcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementUnionInPowersetComplement) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a2) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1a) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1b) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2b2) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2b) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule0) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule1) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule3) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule4) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_1) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_3) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_4) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_5) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1all2) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1SetBreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (choice2fnsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (setOfPairsIsBReln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1all1) =>
% 128.89/16.97 ((
% 128.89/16.97 (subbreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqbreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invI) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invE) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compI) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compE) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compEex) =>
% 128.89/16.97 ((
% 128.89/16.97 (!!) @ (
% 128.89/16.97 (('#B') @ (
% 128.89/16.97 !!) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#S') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#S') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 =>))) @
% 128.89/16.97 breln1)))) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 !!))) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#S') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#B') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#S') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 =>))) @
% 128.89/16.97 breln1)))))) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#C') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#B') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#B') @
% 128.89/16.97 breln1)))) @
% 128.89/16.97 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl400])).
% 128.89/16.97 thf(zip_derived_cl417, plain,
% 128.89/16.97 (~ (((subPowSU) =>
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% 128.89/16.97 (((notinsingleton) =>
% 128.89/16.97 (((eqinunit) =>
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% 128.89/16.97 (((upairsetIR) =>
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% 128.89/16.97 (((vacuousDall) =>
% 128.89/16.97 (((quantDeMorgan1) =>
% 128.89/16.97 (((quantDeMorgan2) =>
% 128.89/16.97 (((quantDeMorgan3) =>
% 128.89/16.97 (((quantDeMorgan4) =>
% 128.89/16.97 (((prop2setI) =>
% 128.89/16.97 (((prop2set2propI) =>
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% 128.89/16.97 (((notdallE) =>
% 128.89/16.97 (((exuI1) =>
% 128.89/16.97 (((exuI3) =>
% 128.89/16.97 (((exuI2) =>
% 128.89/16.97 (((inCongP) =>
% 128.89/16.97 (((in__Cong) =>
% 128.89/16.97 (((exuE3u) =>
% 128.89/16.97 (((exu__Cong) =>
% 128.89/16.97 (((setadjoin__Cong) =>
% 128.89/16.97 (((powerset__Cong) =>
% 128.89/16.97 (((setunion__Cong) =>
% 128.89/16.97 ((
% 128.89/16.97 (exuEu) =>
% 128.89/16.97 ((
% 128.89/16.97 (descr__Cong) =>
% 128.89/16.97 ((
% 128.89/16.97 (dsetconstr__Cong) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqimpsubset2) =>
% 128.89/16.97 ((
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% 128.89/16.97 ((
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% 128.89/16.97 ((
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% 128.89/16.97 ((
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% 128.89/16.97 ((
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% 128.89/16.97 ((
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% 128.89/16.97 ((
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% 128.89/16.97 ((
% 128.89/16.97 (notequalI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetRefl) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetTrans) =>
% 128.89/16.97 ((
% 128.89/16.97 (setadjoinSub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setadjoinSub2) =>
% 128.89/16.97 ((
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% 128.89/16.97 ((
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% 128.89/16.97 ((
% 128.89/16.97 (powersetE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (inPowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (sepInPowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (sepSubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionIL) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairset2IR) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionIR) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionEcases) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionE) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionRsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectI) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset5) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset3) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectER) =>
% 128.89/16.97 ((
% 128.89/16.97 (disjointsetsI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectRsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset4) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (bs114d) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusI) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusER) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusSubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusERneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusELneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusILneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusIRneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusSubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffE) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffIneg1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffIneg2) =>
% 128.89/16.97 ((
% 128.89/16.97 (secondinupair) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairIL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairIR) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairiskpair) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairp) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletoninpowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletoninpowunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairset2E) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairsubunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairinpowunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem3) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairin) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempair1) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempair) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionE2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton1) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1E1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1I) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1I2) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonsuniq) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL1) =>
% 128.89/16.97 ((
% 128.89/16.97 (kfstsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (theprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (kfstpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodfstin) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR11) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR12) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR1) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairequniteq) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR) =>
% 128.89/16.97 ((
% 128.89/16.97 (ksndsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (ksndpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairsurjEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodsndin) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairmemEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairmemER) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempaircEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodfstpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodsndpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairsurjEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrI) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrSub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setOfPairsIsBReln) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrERa) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrEL1) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrEL2) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrER) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcImageSingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (apProp) =>
% 128.89/16.97 ((
% 128.89/16.97 (app) =>
% 128.89/16.97 ((
% 128.89/16.97 (infuncsetfunc) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2p) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcinfuncset) =>
% 128.89/16.97 ((
% 128.89/16.97 (lamProp) =>
% 128.89/16.97 ((
% 128.89/16.97 (lamp) =>
% 128.89/16.97 ((
% 128.89/16.97 (lam2p) =>
% 128.89/16.97 ((
% 128.89/16.97 (brelnall1) =>
% 128.89/16.97 ((
% 128.89/16.97 (brelnall2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1E2) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp3) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcextLem) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp4) =>
% 128.89/16.97 ((
% 128.89/16.97 (subbreln) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqbreln) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcext) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcext2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2apEq1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2apEq2) =>
% 128.89/16.97 ((
% 128.89/16.97 (beta1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eta1) =>
% 128.89/16.97 ((
% 128.89/16.97 (lam2lamEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (beta2) =>
% 128.89/16.97 ((
% 128.89/16.97 (eta2) =>
% 128.89/16.97 ((
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% 128.89/16.97 ((
% 128.89/16.97 (iffalseProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ifSingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (ifp) =>
% 128.89/16.97 ((
% 128.89/16.97 (theeq) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrue) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalse) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueorfalse) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusT_lem) =>
% 128.89/16.97 ((
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% 128.89/16.97 ((
% 128.89/16.97 (setextT) =>
% 128.89/16.97 ((
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% 128.89/16.97 ((
% 128.89/16.97 (powersetTI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetTE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectTELcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectTERcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT) =>
% 128.89/16.97 ((
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% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT2) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT3) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementSub1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementSub2) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTnotintersectT) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementImpComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementSubsetComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementInPowersetComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (contraSubsetComplement) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTcontraSubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTILcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTIRcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInUnion) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInUnion2) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInIntersectUnions) =>
% 128.89/16.97 ((
% 128.89/16.97 (intersectInPowersetIntersectUnions) =>
% 128.89/16.97 ((
% 128.89/16.97 (inComplementUnionImpNotIn1) =>
% 128.89/16.97 ((
% 128.89/16.97 (inComplementUnionImpInComplement1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTE) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTEcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementUnionInPowersetComplement) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a2) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1a) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1b) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2b2) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2b) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule0) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule1) =>
% 128.89/16.97 ((
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% 128.89/16.97 ((
% 128.89/16.97 (woz13rule3) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule4) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_1) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_2) =>
% 128.89/16.97 ((
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% 128.89/16.97 ((
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% 128.89/16.97 ((
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% 128.89/16.97 ((
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% 128.89/16.97 breln1)))) @
% 128.89/16.97 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl408])).
% 128.89/16.97 thf(zip_derived_cl428, plain,
% 128.89/16.97 (~ (((exuE2) =>
% 128.89/16.97 (((nonemptyImpWitness) =>
% 128.89/16.97 (((uniqinunit) =>
% 128.89/16.97 (((notinsingleton) =>
% 128.89/16.97 (((eqinunit) =>
% 128.89/16.97 (((singletonsswitch) =>
% 128.89/16.97 (((upairsetE) =>
% 128.89/16.97 (((upairsetIL) =>
% 128.89/16.97 (((upairsetIR) =>
% 128.89/16.97 (((emptyE1) =>
% 128.89/16.97 (((vacuousDall) =>
% 128.89/16.97 (((quantDeMorgan1) =>
% 128.89/16.97 (((quantDeMorgan2) =>
% 128.89/16.97 (((quantDeMorgan3) =>
% 128.89/16.97 (((quantDeMorgan4) =>
% 128.89/16.97 (((prop2setI) =>
% 128.89/16.97 (((prop2set2propI) =>
% 128.89/16.97 (((notdexE) =>
% 128.89/16.97 (((notdallE) =>
% 128.89/16.97 (((exuI1) =>
% 128.89/16.97 (((exuI3) =>
% 128.89/16.97 (((exuI2) =>
% 128.89/16.97 (((inCongP) =>
% 128.89/16.97 (((in__Cong) =>
% 128.89/16.97 (((exuE3u) =>
% 128.89/16.97 (((exu__Cong) =>
% 128.89/16.97 (((setadjoin__Cong) =>
% 128.89/16.97 (((powerset__Cong) =>
% 128.89/16.97 (((setunion__Cong) =>
% 128.89/16.97 (((exuEu) =>
% 128.89/16.97 ((
% 128.89/16.97 (descr__Cong) =>
% 128.89/16.97 ((
% 128.89/16.97 (dsetconstr__Cong) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqimpsubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqimpsubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (emptysetsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetE) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetE2) =>
% 128.89/16.97 ((
% 128.89/16.97 (notsubsetI) =>
% 128.89/16.97 ((
% 128.89/16.97 (notequalI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (notequalI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetRefl) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetTrans) =>
% 128.89/16.97 ((
% 128.89/16.97 (setadjoinSub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setadjoinSub2) =>
% 128.89/16.97 ((
% 128.89/16.97 (subset2powerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (setextsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetemptysetimpeq) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (inPowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (sepInPowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (sepSubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionIL) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairset2IR) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionIR) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionEcases) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionE) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionRsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectI) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset5) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset3) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectER) =>
% 128.89/16.97 ((
% 128.89/16.97 (disjointsetsI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectRsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset4) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (bs114d) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusI) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusER) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusSubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusERneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusELneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusILneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusIRneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusSubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffE) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffIneg1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffIneg2) =>
% 128.89/16.97 ((
% 128.89/16.97 (secondinupair) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairIL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairIR) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairiskpair) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairp) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletoninpowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletoninpowunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairset2E) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairsubunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairinpowunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem3) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairin) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempair1) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempair) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionE2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton1) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1E1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1I) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1I2) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonsuniq) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL1) =>
% 128.89/16.97 ((
% 128.89/16.97 (kfstsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (theprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (kfstpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodfstin) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR11) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR12) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR1) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairequniteq) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR) =>
% 128.89/16.97 ((
% 128.89/16.97 (ksndsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (ksndpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairsurjEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodsndin) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairmemEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairmemER) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempaircEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodfstpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodsndpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairsurjEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrI) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrSub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setOfPairsIsBReln) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrERa) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrEL1) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrEL2) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrER) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcImageSingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (apProp) =>
% 128.89/16.97 ((
% 128.89/16.97 (app) =>
% 128.89/16.97 ((
% 128.89/16.97 (infuncsetfunc) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2p) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcinfuncset) =>
% 128.89/16.97 ((
% 128.89/16.97 (lamProp) =>
% 128.89/16.97 ((
% 128.89/16.97 (lamp) =>
% 128.89/16.97 ((
% 128.89/16.97 (lam2p) =>
% 128.89/16.97 ((
% 128.89/16.97 (brelnall1) =>
% 128.89/16.97 ((
% 128.89/16.97 (brelnall2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1E2) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp3) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcextLem) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp4) =>
% 128.89/16.97 ((
% 128.89/16.97 (subbreln) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqbreln) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcext) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcext2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2apEq1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2apEq2) =>
% 128.89/16.97 ((
% 128.89/16.97 (beta1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eta1) =>
% 128.89/16.97 ((
% 128.89/16.97 (lam2lamEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (beta2) =>
% 128.89/16.97 ((
% 128.89/16.97 (eta2) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalseProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalseProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ifSingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (ifp) =>
% 128.89/16.97 ((
% 128.89/16.97 (theeq) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrue) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalse) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueorfalse) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (setextT) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetTI) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetTI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetTE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectTELcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectTERcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT1) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT2) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT3) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementSub1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementSub2) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTnotintersectT) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementImpComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementSubsetComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementInPowersetComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (contraSubsetComplement) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTcontraSubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTILcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTIRcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInUnion) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInUnion2) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInIntersectUnions) =>
% 128.89/16.97 ((
% 128.89/16.97 (intersectInPowersetIntersectUnions) =>
% 128.89/16.97 ((
% 128.89/16.97 (inComplementUnionImpNotIn1) =>
% 128.89/16.97 ((
% 128.89/16.97 (inComplementUnionImpInComplement1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTE) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTEcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementUnionInPowersetComplement) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a2) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1a) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1b) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2b2) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2b) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule0) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule1) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule3) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule4) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_1) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_3) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_4) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_5) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1all2) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1SetBreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (choice2fnsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (setOfPairsIsBReln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1all1) =>
% 128.89/16.97 ((
% 128.89/16.97 (subbreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqbreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invI) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invE) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compI) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compE) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compEex) =>
% 128.89/16.97 ((
% 128.89/16.97 (!!) @ (
% 128.89/16.97 (('#B') @ (
% 128.89/16.97 !!) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#S') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#S') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 =>))) @
% 128.89/16.97 breln1)))) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 !!))) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#S') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#B') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#S') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 =>))) @
% 128.89/16.97 breln1)))))) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#C') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#B') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#B') @
% 128.89/16.97 breln1)))) @
% 128.89/16.97 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl417])).
% 128.89/16.97 thf(zip_derived_cl439, plain,
% 128.89/16.97 (~ (((nonemptyImpWitness) =>
% 128.89/16.97 (((uniqinunit) =>
% 128.89/16.97 (((notinsingleton) =>
% 128.89/16.97 (((eqinunit) =>
% 128.89/16.97 (((singletonsswitch) =>
% 128.89/16.97 (((upairsetE) =>
% 128.89/16.97 (((upairsetIL) =>
% 128.89/16.97 (((upairsetIR) =>
% 128.89/16.97 (((emptyE1) =>
% 128.89/16.97 (((vacuousDall) =>
% 128.89/16.97 (((quantDeMorgan1) =>
% 128.89/16.97 (((quantDeMorgan2) =>
% 128.89/16.97 (((quantDeMorgan3) =>
% 128.89/16.97 (((quantDeMorgan4) =>
% 128.89/16.97 (((prop2setI) =>
% 128.89/16.97 (((prop2set2propI) =>
% 128.89/16.97 (((notdexE) =>
% 128.89/16.97 (((notdallE) =>
% 128.89/16.97 (((exuI1) =>
% 128.89/16.97 (((exuI3) =>
% 128.89/16.97 (((exuI2) =>
% 128.89/16.97 (((inCongP) =>
% 128.89/16.97 (((in__Cong) =>
% 128.89/16.97 (((exuE3u) =>
% 128.89/16.97 (((exu__Cong) =>
% 128.89/16.97 (((setadjoin__Cong) =>
% 128.89/16.97 (((powerset__Cong) =>
% 128.89/16.97 (((setunion__Cong) =>
% 128.89/16.97 (((exuEu) =>
% 128.89/16.97 (((descr__Cong) =>
% 128.89/16.97 ((
% 128.89/16.97 (dsetconstr__Cong) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqimpsubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqimpsubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (emptysetsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetE) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetE2) =>
% 128.89/16.97 ((
% 128.89/16.97 (notsubsetI) =>
% 128.89/16.97 ((
% 128.89/16.97 (notequalI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (notequalI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetRefl) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetTrans) =>
% 128.89/16.97 ((
% 128.89/16.97 (setadjoinSub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setadjoinSub2) =>
% 128.89/16.97 ((
% 128.89/16.97 (subset2powerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (setextsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetemptysetimpeq) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (inPowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (sepInPowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (sepSubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionIL) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairset2IR) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionIR) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionEcases) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionE) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionRsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectI) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset5) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset3) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectER) =>
% 128.89/16.97 ((
% 128.89/16.97 (disjointsetsI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectRsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset4) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (bs114d) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusI) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusER) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusSubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusERneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusELneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusILneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusIRneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusSubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffE) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffIneg1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffIneg2) =>
% 128.89/16.97 ((
% 128.89/16.97 (secondinupair) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairIL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairIR) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairiskpair) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairp) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletoninpowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletoninpowunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairset2E) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairsubunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairinpowunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem3) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairin) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempair1) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempair) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionE2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton1) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1E1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1I) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1I2) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonsuniq) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL1) =>
% 128.89/16.97 ((
% 128.89/16.97 (kfstsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (theprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (kfstpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodfstin) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR11) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR12) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR1) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairequniteq) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR) =>
% 128.89/16.97 ((
% 128.89/16.97 (ksndsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (ksndpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairsurjEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodsndin) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairmemEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairmemER) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempaircEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodfstpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodsndpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairsurjEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrI) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrSub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setOfPairsIsBReln) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrERa) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrEL1) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrEL2) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrER) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcImageSingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (apProp) =>
% 128.89/16.97 ((
% 128.89/16.97 (app) =>
% 128.89/16.97 ((
% 128.89/16.97 (infuncsetfunc) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2p) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcinfuncset) =>
% 128.89/16.97 ((
% 128.89/16.97 (lamProp) =>
% 128.89/16.97 ((
% 128.89/16.97 (lamp) =>
% 128.89/16.97 ((
% 128.89/16.97 (lam2p) =>
% 128.89/16.97 ((
% 128.89/16.97 (brelnall1) =>
% 128.89/16.97 ((
% 128.89/16.97 (brelnall2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1E2) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp3) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcextLem) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp4) =>
% 128.89/16.97 ((
% 128.89/16.97 (subbreln) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqbreln) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcext) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcext2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2apEq1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2apEq2) =>
% 128.89/16.97 ((
% 128.89/16.97 (beta1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eta1) =>
% 128.89/16.97 ((
% 128.89/16.97 (lam2lamEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (beta2) =>
% 128.89/16.97 ((
% 128.89/16.97 (eta2) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalseProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalseProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ifSingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (ifp) =>
% 128.89/16.97 ((
% 128.89/16.97 (theeq) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrue) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalse) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueorfalse) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (setextT) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetTI) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetTI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetTE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectTELcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectTERcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT1) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT2) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT3) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementSub1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementSub2) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTnotintersectT) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementImpComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementSubsetComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementInPowersetComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (contraSubsetComplement) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTcontraSubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTILcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTIRcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInUnion) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInUnion2) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInIntersectUnions) =>
% 128.89/16.97 ((
% 128.89/16.97 (intersectInPowersetIntersectUnions) =>
% 128.89/16.97 ((
% 128.89/16.97 (inComplementUnionImpNotIn1) =>
% 128.89/16.97 ((
% 128.89/16.97 (inComplementUnionImpInComplement1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTE) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTEcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementUnionInPowersetComplement) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a2) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1a) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1b) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2b2) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2b) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule0) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule1) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule3) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule4) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_1) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_3) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_4) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_5) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1all2) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1SetBreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (choice2fnsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (setOfPairsIsBReln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1all1) =>
% 128.89/16.97 ((
% 128.89/16.97 (subbreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqbreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invI) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invE) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compI) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compE) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compEex) =>
% 128.89/16.97 ((
% 128.89/16.97 (!!) @ (
% 128.89/16.97 (('#B') @ (
% 128.89/16.97 !!) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#S') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#S') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 =>))) @
% 128.89/16.97 breln1)))) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 !!))) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#S') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#B') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#S') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 =>))) @
% 128.89/16.97 breln1)))))) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#C') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#B') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#B') @
% 128.89/16.97 breln1)))) @
% 128.89/16.97 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])).
% 128.89/16.97 thf(zip_derived_cl449, plain,
% 128.89/16.97 (~ (((uniqinunit) =>
% 128.89/16.97 (((notinsingleton) =>
% 128.89/16.97 (((eqinunit) =>
% 128.89/16.97 (((singletonsswitch) =>
% 128.89/16.97 (((upairsetE) =>
% 128.89/16.97 (((upairsetIL) =>
% 128.89/16.97 (((upairsetIR) =>
% 128.89/16.97 (((emptyE1) =>
% 128.89/16.97 (((vacuousDall) =>
% 128.89/16.97 (((quantDeMorgan1) =>
% 128.89/16.97 (((quantDeMorgan2) =>
% 128.89/16.97 (((quantDeMorgan3) =>
% 128.89/16.97 (((quantDeMorgan4) =>
% 128.89/16.97 (((prop2setI) =>
% 128.89/16.97 (((prop2set2propI) =>
% 128.89/16.97 (((notdexE) =>
% 128.89/16.97 (((notdallE) =>
% 128.89/16.97 (((exuI1) =>
% 128.89/16.97 (((exuI3) =>
% 128.89/16.97 (((exuI2) =>
% 128.89/16.97 (((inCongP) =>
% 128.89/16.97 (((in__Cong) =>
% 128.89/16.97 (((exuE3u) =>
% 128.89/16.97 (((exu__Cong) =>
% 128.89/16.97 (((setadjoin__Cong) =>
% 128.89/16.97 (((powerset__Cong) =>
% 128.89/16.97 (((setunion__Cong) =>
% 128.89/16.97 (((exuEu) =>
% 128.89/16.97 (((descr__Cong) =>
% 128.89/16.97 (((dsetconstr__Cong) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqimpsubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqimpsubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (emptysetsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetE) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetE2) =>
% 128.89/16.97 ((
% 128.89/16.97 (notsubsetI) =>
% 128.89/16.97 ((
% 128.89/16.97 (notequalI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (notequalI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetRefl) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetTrans) =>
% 128.89/16.97 ((
% 128.89/16.97 (setadjoinSub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setadjoinSub2) =>
% 128.89/16.97 ((
% 128.89/16.97 (subset2powerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (setextsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetemptysetimpeq) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (inPowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (sepInPowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (sepSubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionIL) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairset2IR) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionIR) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionEcases) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionE) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionRsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectI) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset5) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset3) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectER) =>
% 128.89/16.97 ((
% 128.89/16.97 (disjointsetsI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectRsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset4) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (bs114d) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusI) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusER) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusSubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusERneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusELneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusILneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusIRneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusSubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffE) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffIneg1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffIneg2) =>
% 128.89/16.97 ((
% 128.89/16.97 (secondinupair) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairIL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairIR) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairiskpair) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairp) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletoninpowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletoninpowunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairset2E) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairsubunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairinpowunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem3) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairin) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempair1) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempair) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionE2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton1) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1E1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1I) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1I2) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonsuniq) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL1) =>
% 128.89/16.97 ((
% 128.89/16.97 (kfstsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (theprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (kfstpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodfstin) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR11) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR12) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR1) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairequniteq) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR) =>
% 128.89/16.97 ((
% 128.89/16.97 (ksndsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (ksndpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairsurjEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodsndin) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairmemEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairmemER) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempaircEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodfstpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodsndpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairsurjEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrI) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrSub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setOfPairsIsBReln) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrERa) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrEL1) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrEL2) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrER) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcImageSingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (apProp) =>
% 128.89/16.97 ((
% 128.89/16.97 (app) =>
% 128.89/16.97 ((
% 128.89/16.97 (infuncsetfunc) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2p) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcinfuncset) =>
% 128.89/16.97 ((
% 128.89/16.97 (lamProp) =>
% 128.89/16.97 ((
% 128.89/16.97 (lamp) =>
% 128.89/16.97 ((
% 128.89/16.97 (lam2p) =>
% 128.89/16.97 ((
% 128.89/16.97 (brelnall1) =>
% 128.89/16.97 ((
% 128.89/16.97 (brelnall2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1E2) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp3) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcextLem) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp4) =>
% 128.89/16.97 ((
% 128.89/16.97 (subbreln) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqbreln) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcext) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcext2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2apEq1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2apEq2) =>
% 128.89/16.97 ((
% 128.89/16.97 (beta1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eta1) =>
% 128.89/16.97 ((
% 128.89/16.97 (lam2lamEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (beta2) =>
% 128.89/16.97 ((
% 128.89/16.97 (eta2) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalseProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalseProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ifSingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (ifp) =>
% 128.89/16.97 ((
% 128.89/16.97 (theeq) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrue) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalse) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueorfalse) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (setextT) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetTI) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetTI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetTE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectTELcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectTERcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT1) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT2) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT3) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementSub1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementSub2) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTnotintersectT) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementImpComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementSubsetComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementInPowersetComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (contraSubsetComplement) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTcontraSubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTILcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTIRcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInUnion) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInUnion2) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInIntersectUnions) =>
% 128.89/16.97 ((
% 128.89/16.97 (intersectInPowersetIntersectUnions) =>
% 128.89/16.97 ((
% 128.89/16.97 (inComplementUnionImpNotIn1) =>
% 128.89/16.97 ((
% 128.89/16.97 (inComplementUnionImpInComplement1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTE) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTEcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementUnionInPowersetComplement) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a2) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1a) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1b) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2b2) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2b) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule0) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule1) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule3) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule4) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_1) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_3) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_4) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_5) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1all2) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1SetBreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (choice2fnsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (setOfPairsIsBReln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1all1) =>
% 128.89/16.97 ((
% 128.89/16.97 (subbreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqbreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invI) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invE) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compI) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compE) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compEex) =>
% 128.89/16.97 ((
% 128.89/16.97 (!!) @ (
% 128.89/16.97 (('#B') @ (
% 128.89/16.97 !!) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#S') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#S') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 =>))) @
% 128.89/16.97 breln1)))) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 !!))) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#S') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#B') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#S') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 =>))) @
% 128.89/16.97 breln1)))))) @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#C') @ (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#B') @
% 128.89/16.97 (
% 128.89/16.97 (
% 128.89/16.97 ('#B') @ (
% 128.89/16.97 '#B') @
% 128.89/16.97 breln1)))) @
% 128.89/16.97 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl439])).
% 128.89/16.97 thf(zip_derived_cl458, plain,
% 128.89/16.97 (~ (((notinsingleton) =>
% 128.89/16.97 (((eqinunit) =>
% 128.89/16.97 (((singletonsswitch) =>
% 128.89/16.97 (((upairsetE) =>
% 128.89/16.97 (((upairsetIL) =>
% 128.89/16.97 (((upairsetIR) =>
% 128.89/16.97 (((emptyE1) =>
% 128.89/16.97 (((vacuousDall) =>
% 128.89/16.97 (((quantDeMorgan1) =>
% 128.89/16.97 (((quantDeMorgan2) =>
% 128.89/16.97 (((quantDeMorgan3) =>
% 128.89/16.97 (((quantDeMorgan4) =>
% 128.89/16.97 (((prop2setI) =>
% 128.89/16.97 (((prop2set2propI) =>
% 128.89/16.97 (((notdexE) =>
% 128.89/16.97 (((notdallE) =>
% 128.89/16.97 (((exuI1) =>
% 128.89/16.97 (((exuI3) =>
% 128.89/16.97 (((exuI2) =>
% 128.89/16.97 (((inCongP) =>
% 128.89/16.97 (((in__Cong) =>
% 128.89/16.97 (((exuE3u) =>
% 128.89/16.97 (((exu__Cong) =>
% 128.89/16.97 (((setadjoin__Cong) =>
% 128.89/16.97 (((powerset__Cong) =>
% 128.89/16.97 (((setunion__Cong) =>
% 128.89/16.97 (((exuEu) =>
% 128.89/16.97 (((descr__Cong) =>
% 128.89/16.97 (((dsetconstr__Cong) =>
% 128.89/16.97 (((subsetI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqimpsubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqimpsubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (emptysetsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetE) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetE2) =>
% 128.89/16.97 ((
% 128.89/16.97 (notsubsetI) =>
% 128.89/16.97 ((
% 128.89/16.97 (notequalI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (notequalI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetRefl) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetTrans) =>
% 128.89/16.97 ((
% 128.89/16.97 (setadjoinSub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setadjoinSub2) =>
% 128.89/16.97 ((
% 128.89/16.97 (subset2powerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (setextsub) =>
% 128.89/16.97 ((
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% 128.89/16.97 ((
% 128.89/16.97 (powersetI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (inPowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (sepInPowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (sepSubset) =>
% 128.89/16.97 ((
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% 128.89/16.97 ((
% 128.89/16.97 (upairset2IR) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionIR) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionEcases) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionE) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionRsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectI) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset5) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset3) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectER) =>
% 128.89/16.97 ((
% 128.89/16.97 (disjointsetsI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectRsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset4) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectSubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (bs114d) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusI) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusER) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusSubset2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusERneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusELneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusILneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusIRneg) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusLsub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusSubset1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffE) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffI2) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffIneg1) =>
% 128.89/16.97 ((
% 128.89/16.97 (symdiffIneg2) =>
% 128.89/16.97 ((
% 128.89/16.97 (secondinupair) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairIL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairIR) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairiskpair) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairp) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonsubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletoninpowerset) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletoninpowunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairset2E) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairsubunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairinpowunion) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ubforcartprodlem3) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairin) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempair1) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempair) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionE2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton1) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setunionsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1E1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1I) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1I2) =>
% 128.89/16.97 ((
% 128.89/16.97 (singletonsuniq) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL1) =>
% 128.89/16.97 ((
% 128.89/16.97 (kfstsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (theprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (kfstpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodfstin) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjL) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR11) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR12) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR1) =>
% 128.89/16.97 ((
% 128.89/16.97 (upairequniteq) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR2) =>
% 128.89/16.97 ((
% 128.89/16.97 (setukpairinjR) =>
% 128.89/16.97 ((
% 128.89/16.97 (ksndsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (ksndpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (kpairsurjEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodsndin) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairmemEL) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairmemER) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodmempaircEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodfstpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodsndpairEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (cartprodpairsurjEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrI) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrSub) =>
% 128.89/16.97 ((
% 128.89/16.97 (setOfPairsIsBReln) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrERa) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrEL1) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrEL2) =>
% 128.89/16.97 ((
% 128.89/16.97 (dpsetconstrER) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcImageSingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (apProp) =>
% 128.89/16.97 ((
% 128.89/16.97 (app) =>
% 128.89/16.97 ((
% 128.89/16.97 (infuncsetfunc) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2p) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcinfuncset) =>
% 128.89/16.97 ((
% 128.89/16.97 (lamProp) =>
% 128.89/16.97 ((
% 128.89/16.97 (lamp) =>
% 128.89/16.97 ((
% 128.89/16.97 (lam2p) =>
% 128.89/16.97 ((
% 128.89/16.97 (brelnall1) =>
% 128.89/16.97 ((
% 128.89/16.97 (brelnall2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ex1E2) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp3) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcextLem) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcGraphProp4) =>
% 128.89/16.97 ((
% 128.89/16.97 (subbreln) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqbreln) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcext) =>
% 128.89/16.97 ((
% 128.89/16.97 (funcext2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2apEq1) =>
% 128.89/16.97 ((
% 128.89/16.97 (ap2apEq2) =>
% 128.89/16.97 ((
% 128.89/16.97 (beta1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eta1) =>
% 128.89/16.97 ((
% 128.89/16.97 (lam2lamEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (beta2) =>
% 128.89/16.97 ((
% 128.89/16.97 (eta2) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalseProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalseProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueProp1) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueProp2) =>
% 128.89/16.97 ((
% 128.89/16.97 (ifSingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (ifp) =>
% 128.89/16.97 ((
% 128.89/16.97 (theeq) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrue) =>
% 128.89/16.97 ((
% 128.89/16.97 (iffalse) =>
% 128.89/16.97 ((
% 128.89/16.97 (iftrueorfalse) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (setminusT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementT_lem) =>
% 128.89/16.97 ((
% 128.89/16.97 (setextT) =>
% 128.89/16.97 ((
% 128.89/16.97 (subsetTI) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetTI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (powersetTE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectTELcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (binintersectTERcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT1) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT2) =>
% 128.89/16.97 ((
% 128.89/16.97 (contrasubsetT3) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementI1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementE1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementSub1) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementSub2) =>
% 128.89/16.97 ((
% 128.89/16.97 (doubleComplementEq) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTnotintersectT) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementImpComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementSubsetComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementInPowersetComplementIntersect) =>
% 128.89/16.97 ((
% 128.89/16.97 (contraSubsetComplement) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementTcontraSubset) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTILcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTIRcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInUnion) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInUnion2) =>
% 128.89/16.97 ((
% 128.89/16.97 (inIntersectImpInIntersectUnions) =>
% 128.89/16.97 ((
% 128.89/16.97 (intersectInPowersetIntersectUnions) =>
% 128.89/16.97 ((
% 128.89/16.97 (inComplementUnionImpNotIn1) =>
% 128.89/16.97 ((
% 128.89/16.97 (inComplementUnionImpInComplement1) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTE) =>
% 128.89/16.97 ((
% 128.89/16.97 (binunionTEcontra) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a1) =>
% 128.89/16.97 ((
% 128.89/16.97 (complementUnionInPowersetComplement) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a2) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1a) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1b) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan1) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2a) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2b2) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2b) =>
% 128.89/16.97 ((
% 128.89/16.97 (demorgan2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule0) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule1) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule3) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz13rule4) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_1) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_2) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_3) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_4) =>
% 128.89/16.97 ((
% 128.89/16.97 (woz1_5) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1all2) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1SetBreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (choice2fnsingleton) =>
% 128.89/16.97 ((
% 128.89/16.97 (setOfPairsIsBReln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1all1) =>
% 128.89/16.97 ((
% 128.89/16.97 (subbreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (eqbreln1) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invI) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1invE) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compprop) =>
% 128.89/16.97 ((
% 128.89/16.97 (breln1compI) =>
% 128.89/16.97 ((
% 128.89/16.98 (breln1compE) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compEex) =>
% 128.89/16.98 ((
% 128.89/16.98 (!!) @ (
% 128.89/16.98 (('#B') @ (
% 128.89/16.98 !!) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#S') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#S') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 =>))) @
% 128.89/16.98 breln1)))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 !!))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#S') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#S') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 =>))) @
% 128.89/16.98 breln1)))))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#C') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 breln1)))) @
% 128.89/16.98 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl449])).
% 128.89/16.98 thf(zip_derived_cl467, plain,
% 128.89/16.98 (~ (((eqinunit) =>
% 128.89/16.98 (((singletonsswitch) =>
% 128.89/16.98 (((upairsetE) =>
% 128.89/16.98 (((upairsetIL) =>
% 128.89/16.98 (((upairsetIR) =>
% 128.89/16.98 (((emptyE1) =>
% 128.89/16.98 (((vacuousDall) =>
% 128.89/16.98 (((quantDeMorgan1) =>
% 128.89/16.98 (((quantDeMorgan2) =>
% 128.89/16.98 (((quantDeMorgan3) =>
% 128.89/16.98 (((quantDeMorgan4) =>
% 128.89/16.98 (((prop2setI) =>
% 128.89/16.98 (((prop2set2propI) =>
% 128.89/16.98 (((notdexE) =>
% 128.89/16.98 (((notdallE) =>
% 128.89/16.98 (((exuI1) =>
% 128.89/16.98 (((exuI3) =>
% 128.89/16.98 (((exuI2) =>
% 128.89/16.98 (((inCongP) =>
% 128.89/16.98 (((in__Cong) =>
% 128.89/16.98 (((exuE3u) =>
% 128.89/16.98 (((exu__Cong) =>
% 128.89/16.98 (((setadjoin__Cong) =>
% 128.89/16.98 (((powerset__Cong) =>
% 128.89/16.98 (((setunion__Cong) =>
% 128.89/16.98 (((exuEu) =>
% 128.89/16.98 (((descr__Cong) =>
% 128.89/16.98 (((dsetconstr__Cong) =>
% 128.89/16.98 (((subsetI1) =>
% 128.89/16.98 (((eqimpsubset2) =>
% 128.89/16.98 ((
% 128.89/16.98 (eqimpsubset1) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetI2) =>
% 128.89/16.98 ((
% 128.89/16.98 (emptysetsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetE) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetE2) =>
% 128.89/16.98 ((
% 128.89/16.98 (notsubsetI) =>
% 128.89/16.98 ((
% 128.89/16.98 (notequalI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (notequalI2) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetRefl) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetTrans) =>
% 128.89/16.98 ((
% 128.89/16.98 (setadjoinSub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setadjoinSub2) =>
% 128.89/16.98 ((
% 128.89/16.98 (subset2powerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (setextsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetemptysetimpeq) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (inPowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (sepInPowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (sepSubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionIL) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairset2IR) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionIR) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionEcases) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionE) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionRsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectI) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset5) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset2) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset3) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectER) =>
% 128.89/16.98 ((
% 128.89/16.98 (disjointsetsI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectRsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset4) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset1) =>
% 128.89/16.98 ((
% 128.89/16.98 (bs114d) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusI) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusER) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusSubset2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusERneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusELneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusILneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusIRneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusSubset1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffE) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffI2) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffIneg1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffIneg2) =>
% 128.89/16.98 ((
% 128.89/16.98 (secondinupair) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairIL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairIR) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairiskpair) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairp) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletoninpowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletoninpowunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairset2E) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairsubunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairinpowunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem3) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairin) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempair1) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempair) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionE2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton1) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1E1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1I) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1I2) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonsuniq) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL1) =>
% 128.89/16.98 ((
% 128.89/16.98 (kfstsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (theprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (kfstpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodfstin) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR11) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR12) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR1) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairequniteq) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR) =>
% 128.89/16.98 ((
% 128.89/16.98 (ksndsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (ksndpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairsurjEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodsndin) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairmemEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairmemER) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempaircEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodfstpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodsndpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairsurjEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrI) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrSub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setOfPairsIsBReln) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrERa) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrEL1) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrEL2) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrER) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcImageSingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (apProp) =>
% 128.89/16.98 ((
% 128.89/16.98 (app) =>
% 128.89/16.98 ((
% 128.89/16.98 (infuncsetfunc) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2p) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcinfuncset) =>
% 128.89/16.98 ((
% 128.89/16.98 (lamProp) =>
% 128.89/16.98 ((
% 128.89/16.98 (lamp) =>
% 128.89/16.98 ((
% 128.89/16.98 (lam2p) =>
% 128.89/16.98 ((
% 128.89/16.98 (brelnall1) =>
% 128.89/16.98 ((
% 128.89/16.98 (brelnall2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1E2) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp3) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcextLem) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp4) =>
% 128.89/16.98 ((
% 128.89/16.98 (subbreln) =>
% 128.89/16.98 ((
% 128.89/16.98 (eqbreln) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcext) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcext2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2apEq1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2apEq2) =>
% 128.89/16.98 ((
% 128.89/16.98 (beta1) =>
% 128.89/16.98 ((
% 128.89/16.98 (eta1) =>
% 128.89/16.98 ((
% 128.89/16.98 (lam2lamEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (beta2) =>
% 128.89/16.98 ((
% 128.89/16.98 (eta2) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalseProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalseProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ifSingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (ifp) =>
% 128.89/16.98 ((
% 128.89/16.98 (theeq) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrue) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalse) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueorfalse) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (setextT) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetTI) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetTI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetTE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectTELcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectTERcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT1) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT2) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT3) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementSub1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementSub2) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTnotintersectT) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementImpComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementSubsetComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementInPowersetComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (contraSubsetComplement) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTcontraSubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTILcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTIRcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInUnion) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInUnion2) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInIntersectUnions) =>
% 128.89/16.98 ((
% 128.89/16.98 (intersectInPowersetIntersectUnions) =>
% 128.89/16.98 ((
% 128.89/16.98 (inComplementUnionImpNotIn1) =>
% 128.89/16.98 ((
% 128.89/16.98 (inComplementUnionImpInComplement1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTE) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTEcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementUnionInPowersetComplement) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a2) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1a) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1b) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2b2) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2b) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule0) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule1) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule3) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule4) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_1) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_3) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_4) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_5) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1all2) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1SetBreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (choice2fnsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (setOfPairsIsBReln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1all1) =>
% 128.89/16.98 ((
% 128.89/16.98 (subbreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (eqbreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invI) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invE) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compI) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compE) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compEex) =>
% 128.89/16.98 ((
% 128.89/16.98 (!!) @ (
% 128.89/16.98 (('#B') @ (
% 128.89/16.98 !!) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#S') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#S') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 =>))) @
% 128.89/16.98 breln1)))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 !!))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#S') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#S') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 =>))) @
% 128.89/16.98 breln1)))))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#C') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 breln1)))) @
% 128.89/16.98 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl458])).
% 128.89/16.98 thf(zip_derived_cl475, plain,
% 128.89/16.98 (~ (((singletonsswitch) =>
% 128.89/16.98 (((upairsetE) =>
% 128.89/16.98 (((upairsetIL) =>
% 128.89/16.98 (((upairsetIR) =>
% 128.89/16.98 (((emptyE1) =>
% 128.89/16.98 (((vacuousDall) =>
% 128.89/16.98 (((quantDeMorgan1) =>
% 128.89/16.98 (((quantDeMorgan2) =>
% 128.89/16.98 (((quantDeMorgan3) =>
% 128.89/16.98 (((quantDeMorgan4) =>
% 128.89/16.98 (((prop2setI) =>
% 128.89/16.98 (((prop2set2propI) =>
% 128.89/16.98 (((notdexE) =>
% 128.89/16.98 (((notdallE) =>
% 128.89/16.98 (((exuI1) =>
% 128.89/16.98 (((exuI3) =>
% 128.89/16.98 (((exuI2) =>
% 128.89/16.98 (((inCongP) =>
% 128.89/16.98 (((in__Cong) =>
% 128.89/16.98 (((exuE3u) =>
% 128.89/16.98 (((exu__Cong) =>
% 128.89/16.98 (((setadjoin__Cong) =>
% 128.89/16.98 (((powerset__Cong) =>
% 128.89/16.98 (((setunion__Cong) =>
% 128.89/16.98 (((exuEu) =>
% 128.89/16.98 (((descr__Cong) =>
% 128.89/16.98 (((dsetconstr__Cong) =>
% 128.89/16.98 (((subsetI1) =>
% 128.89/16.98 (((eqimpsubset2) =>
% 128.89/16.98 (((eqimpsubset1) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetI2) =>
% 128.89/16.98 ((
% 128.89/16.98 (emptysetsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetE) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetE2) =>
% 128.89/16.98 ((
% 128.89/16.98 (notsubsetI) =>
% 128.89/16.98 ((
% 128.89/16.98 (notequalI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (notequalI2) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetRefl) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetTrans) =>
% 128.89/16.98 ((
% 128.89/16.98 (setadjoinSub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setadjoinSub2) =>
% 128.89/16.98 ((
% 128.89/16.98 (subset2powerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (setextsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetemptysetimpeq) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (inPowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (sepInPowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (sepSubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionIL) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairset2IR) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionIR) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionEcases) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionE) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionRsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectI) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset5) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset2) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset3) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectER) =>
% 128.89/16.98 ((
% 128.89/16.98 (disjointsetsI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectRsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset4) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset1) =>
% 128.89/16.98 ((
% 128.89/16.98 (bs114d) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusI) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusER) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusSubset2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusERneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusELneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusILneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusIRneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusSubset1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffE) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffI2) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffIneg1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffIneg2) =>
% 128.89/16.98 ((
% 128.89/16.98 (secondinupair) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairIL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairIR) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairiskpair) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairp) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletoninpowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletoninpowunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairset2E) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairsubunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairinpowunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem3) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairin) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempair1) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempair) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionE2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton1) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1E1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1I) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1I2) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonsuniq) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL1) =>
% 128.89/16.98 ((
% 128.89/16.98 (kfstsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (theprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (kfstpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodfstin) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR11) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR12) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR1) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairequniteq) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR) =>
% 128.89/16.98 ((
% 128.89/16.98 (ksndsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (ksndpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairsurjEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodsndin) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairmemEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairmemER) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempaircEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodfstpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodsndpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairsurjEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrI) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrSub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setOfPairsIsBReln) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrERa) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrEL1) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrEL2) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrER) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcImageSingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (apProp) =>
% 128.89/16.98 ((
% 128.89/16.98 (app) =>
% 128.89/16.98 ((
% 128.89/16.98 (infuncsetfunc) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2p) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcinfuncset) =>
% 128.89/16.98 ((
% 128.89/16.98 (lamProp) =>
% 128.89/16.98 ((
% 128.89/16.98 (lamp) =>
% 128.89/16.98 ((
% 128.89/16.98 (lam2p) =>
% 128.89/16.98 ((
% 128.89/16.98 (brelnall1) =>
% 128.89/16.98 ((
% 128.89/16.98 (brelnall2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1E2) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp3) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcextLem) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp4) =>
% 128.89/16.98 ((
% 128.89/16.98 (subbreln) =>
% 128.89/16.98 ((
% 128.89/16.98 (eqbreln) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcext) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcext2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2apEq1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2apEq2) =>
% 128.89/16.98 ((
% 128.89/16.98 (beta1) =>
% 128.89/16.98 ((
% 128.89/16.98 (eta1) =>
% 128.89/16.98 ((
% 128.89/16.98 (lam2lamEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (beta2) =>
% 128.89/16.98 ((
% 128.89/16.98 (eta2) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalseProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalseProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ifSingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (ifp) =>
% 128.89/16.98 ((
% 128.89/16.98 (theeq) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrue) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalse) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueorfalse) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (setextT) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetTI) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetTI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetTE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectTELcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectTERcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT1) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT2) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT3) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementSub1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementSub2) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTnotintersectT) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementImpComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementSubsetComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementInPowersetComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (contraSubsetComplement) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTcontraSubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTILcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTIRcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInUnion) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInUnion2) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInIntersectUnions) =>
% 128.89/16.98 ((
% 128.89/16.98 (intersectInPowersetIntersectUnions) =>
% 128.89/16.98 ((
% 128.89/16.98 (inComplementUnionImpNotIn1) =>
% 128.89/16.98 ((
% 128.89/16.98 (inComplementUnionImpInComplement1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTE) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTEcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementUnionInPowersetComplement) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a2) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1a) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1b) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2b2) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2b) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule0) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule1) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule3) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule4) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_1) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_3) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_4) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_5) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1all2) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1SetBreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (choice2fnsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (setOfPairsIsBReln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1all1) =>
% 128.89/16.98 ((
% 128.89/16.98 (subbreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (eqbreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invI) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invE) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compI) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compE) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compEex) =>
% 128.89/16.98 ((
% 128.89/16.98 (!!) @ (
% 128.89/16.98 (('#B') @ (
% 128.89/16.98 !!) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#S') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#S') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 =>))) @
% 128.89/16.98 breln1)))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 !!))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#S') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#S') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 =>))) @
% 128.89/16.98 breln1)))))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#C') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 breln1)))) @
% 128.89/16.98 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl467])).
% 128.89/16.98 thf(zip_derived_cl485, plain,
% 128.89/16.98 (~ (((upairsetE) =>
% 128.89/16.98 (((upairsetIL) =>
% 128.89/16.98 (((upairsetIR) =>
% 128.89/16.98 (((emptyE1) =>
% 128.89/16.98 (((vacuousDall) =>
% 128.89/16.98 (((quantDeMorgan1) =>
% 128.89/16.98 (((quantDeMorgan2) =>
% 128.89/16.98 (((quantDeMorgan3) =>
% 128.89/16.98 (((quantDeMorgan4) =>
% 128.89/16.98 (((prop2setI) =>
% 128.89/16.98 (((prop2set2propI) =>
% 128.89/16.98 (((notdexE) =>
% 128.89/16.98 (((notdallE) =>
% 128.89/16.98 (((exuI1) =>
% 128.89/16.98 (((exuI3) =>
% 128.89/16.98 (((exuI2) =>
% 128.89/16.98 (((inCongP) =>
% 128.89/16.98 (((in__Cong) =>
% 128.89/16.98 (((exuE3u) =>
% 128.89/16.98 (((exu__Cong) =>
% 128.89/16.98 (((setadjoin__Cong) =>
% 128.89/16.98 (((powerset__Cong) =>
% 128.89/16.98 (((setunion__Cong) =>
% 128.89/16.98 (((exuEu) =>
% 128.89/16.98 (((descr__Cong) =>
% 128.89/16.98 (((dsetconstr__Cong) =>
% 128.89/16.98 (((subsetI1) =>
% 128.89/16.98 (((eqimpsubset2) =>
% 128.89/16.98 (((eqimpsubset1) =>
% 128.89/16.98 (((subsetI2) =>
% 128.89/16.98 ((
% 128.89/16.98 (emptysetsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetE) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetE2) =>
% 128.89/16.98 ((
% 128.89/16.98 (notsubsetI) =>
% 128.89/16.98 ((
% 128.89/16.98 (notequalI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (notequalI2) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetRefl) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetTrans) =>
% 128.89/16.98 ((
% 128.89/16.98 (setadjoinSub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setadjoinSub2) =>
% 128.89/16.98 ((
% 128.89/16.98 (subset2powerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (setextsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetemptysetimpeq) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (inPowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (sepInPowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (sepSubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionIL) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairset2IR) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionIR) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionEcases) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionE) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionRsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectI) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset5) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset2) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset3) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectER) =>
% 128.89/16.98 ((
% 128.89/16.98 (disjointsetsI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectRsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset4) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset1) =>
% 128.89/16.98 ((
% 128.89/16.98 (bs114d) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusI) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusER) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusSubset2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusERneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusELneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusILneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusIRneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusSubset1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffE) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffI2) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffIneg1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffIneg2) =>
% 128.89/16.98 ((
% 128.89/16.98 (secondinupair) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairIL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairIR) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairiskpair) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairp) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletoninpowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletoninpowunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairset2E) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairsubunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairinpowunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem3) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairin) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempair1) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempair) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionE2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton1) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1E1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1I) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1I2) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonsuniq) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL1) =>
% 128.89/16.98 ((
% 128.89/16.98 (kfstsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (theprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (kfstpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodfstin) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR11) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR12) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR1) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairequniteq) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR) =>
% 128.89/16.98 ((
% 128.89/16.98 (ksndsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (ksndpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairsurjEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodsndin) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairmemEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairmemER) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempaircEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodfstpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodsndpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairsurjEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrI) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrSub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setOfPairsIsBReln) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrERa) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrEL1) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrEL2) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrER) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcImageSingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (apProp) =>
% 128.89/16.98 ((
% 128.89/16.98 (app) =>
% 128.89/16.98 ((
% 128.89/16.98 (infuncsetfunc) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2p) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcinfuncset) =>
% 128.89/16.98 ((
% 128.89/16.98 (lamProp) =>
% 128.89/16.98 ((
% 128.89/16.98 (lamp) =>
% 128.89/16.98 ((
% 128.89/16.98 (lam2p) =>
% 128.89/16.98 ((
% 128.89/16.98 (brelnall1) =>
% 128.89/16.98 ((
% 128.89/16.98 (brelnall2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1E2) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp3) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcextLem) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp4) =>
% 128.89/16.98 ((
% 128.89/16.98 (subbreln) =>
% 128.89/16.98 ((
% 128.89/16.98 (eqbreln) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcext) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcext2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2apEq1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2apEq2) =>
% 128.89/16.98 ((
% 128.89/16.98 (beta1) =>
% 128.89/16.98 ((
% 128.89/16.98 (eta1) =>
% 128.89/16.98 ((
% 128.89/16.98 (lam2lamEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (beta2) =>
% 128.89/16.98 ((
% 128.89/16.98 (eta2) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalseProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalseProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ifSingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (ifp) =>
% 128.89/16.98 ((
% 128.89/16.98 (theeq) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrue) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalse) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueorfalse) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (setextT) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetTI) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetTI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetTE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectTELcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectTERcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT1) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT2) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT3) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementSub1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementSub2) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTnotintersectT) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementImpComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementSubsetComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementInPowersetComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (contraSubsetComplement) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTcontraSubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTILcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTIRcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInUnion) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInUnion2) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInIntersectUnions) =>
% 128.89/16.98 ((
% 128.89/16.98 (intersectInPowersetIntersectUnions) =>
% 128.89/16.98 ((
% 128.89/16.98 (inComplementUnionImpNotIn1) =>
% 128.89/16.98 ((
% 128.89/16.98 (inComplementUnionImpInComplement1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTE) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTEcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementUnionInPowersetComplement) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a2) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1a) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1b) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2b2) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2b) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule0) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule1) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule3) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule4) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_1) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_3) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_4) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_5) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1all2) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1SetBreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (choice2fnsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (setOfPairsIsBReln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1all1) =>
% 128.89/16.98 ((
% 128.89/16.98 (subbreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (eqbreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invI) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invE) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compI) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compE) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compEex) =>
% 128.89/16.98 ((
% 128.89/16.98 (!!) @ (
% 128.89/16.98 (('#B') @ (
% 128.89/16.98 !!) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#S') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#S') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 =>))) @
% 128.89/16.98 breln1)))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 !!))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#S') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#S') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 =>))) @
% 128.89/16.98 breln1)))))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#C') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 breln1)))) @
% 128.89/16.98 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl475])).
% 128.89/16.98 thf(zip_derived_cl496, plain,
% 128.89/16.98 (~ (((upairsetIL) =>
% 128.89/16.98 (((upairsetIR) =>
% 128.89/16.98 (((emptyE1) =>
% 128.89/16.98 (((vacuousDall) =>
% 128.89/16.98 (((quantDeMorgan1) =>
% 128.89/16.98 (((quantDeMorgan2) =>
% 128.89/16.98 (((quantDeMorgan3) =>
% 128.89/16.98 (((quantDeMorgan4) =>
% 128.89/16.98 (((prop2setI) =>
% 128.89/16.98 (((prop2set2propI) =>
% 128.89/16.98 (((notdexE) =>
% 128.89/16.98 (((notdallE) =>
% 128.89/16.98 (((exuI1) =>
% 128.89/16.98 (((exuI3) =>
% 128.89/16.98 (((exuI2) =>
% 128.89/16.98 (((inCongP) =>
% 128.89/16.98 (((in__Cong) =>
% 128.89/16.98 (((exuE3u) =>
% 128.89/16.98 (((exu__Cong) =>
% 128.89/16.98 (((setadjoin__Cong) =>
% 128.89/16.98 (((powerset__Cong) =>
% 128.89/16.98 (((setunion__Cong) =>
% 128.89/16.98 (((exuEu) =>
% 128.89/16.98 (((descr__Cong) =>
% 128.89/16.98 (((dsetconstr__Cong) =>
% 128.89/16.98 (((subsetI1) =>
% 128.89/16.98 (((eqimpsubset2) =>
% 128.89/16.98 (((eqimpsubset1) =>
% 128.89/16.98 (((subsetI2) =>
% 128.89/16.98 (((emptysetsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetE) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetE2) =>
% 128.89/16.98 ((
% 128.89/16.98 (notsubsetI) =>
% 128.89/16.98 ((
% 128.89/16.98 (notequalI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (notequalI2) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetRefl) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetTrans) =>
% 128.89/16.98 ((
% 128.89/16.98 (setadjoinSub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setadjoinSub2) =>
% 128.89/16.98 ((
% 128.89/16.98 (subset2powerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (setextsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetemptysetimpeq) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (inPowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (sepInPowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (sepSubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionIL) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairset2IR) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionIR) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionEcases) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionE) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionRsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectI) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset5) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset2) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset3) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectER) =>
% 128.89/16.98 ((
% 128.89/16.98 (disjointsetsI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectRsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset4) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset1) =>
% 128.89/16.98 ((
% 128.89/16.98 (bs114d) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusI) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusER) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusSubset2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusERneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusELneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusILneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusIRneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusSubset1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffE) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffI2) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffIneg1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffIneg2) =>
% 128.89/16.98 ((
% 128.89/16.98 (secondinupair) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairIL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairIR) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairiskpair) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairp) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletoninpowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletoninpowunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairset2E) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairsubunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairinpowunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem3) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairin) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempair1) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempair) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionE2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton1) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1E1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1I) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1I2) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonsuniq) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL1) =>
% 128.89/16.98 ((
% 128.89/16.98 (kfstsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (theprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (kfstpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodfstin) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR11) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR12) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR1) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairequniteq) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR) =>
% 128.89/16.98 ((
% 128.89/16.98 (ksndsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (ksndpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairsurjEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodsndin) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairmemEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairmemER) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempaircEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodfstpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodsndpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairsurjEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrI) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrSub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setOfPairsIsBReln) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrERa) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrEL1) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrEL2) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrER) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcImageSingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (apProp) =>
% 128.89/16.98 ((
% 128.89/16.98 (app) =>
% 128.89/16.98 ((
% 128.89/16.98 (infuncsetfunc) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2p) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcinfuncset) =>
% 128.89/16.98 ((
% 128.89/16.98 (lamProp) =>
% 128.89/16.98 ((
% 128.89/16.98 (lamp) =>
% 128.89/16.98 ((
% 128.89/16.98 (lam2p) =>
% 128.89/16.98 ((
% 128.89/16.98 (brelnall1) =>
% 128.89/16.98 ((
% 128.89/16.98 (brelnall2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1E2) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp3) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcextLem) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp4) =>
% 128.89/16.98 ((
% 128.89/16.98 (subbreln) =>
% 128.89/16.98 ((
% 128.89/16.98 (eqbreln) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcext) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcext2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2apEq1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2apEq2) =>
% 128.89/16.98 ((
% 128.89/16.98 (beta1) =>
% 128.89/16.98 ((
% 128.89/16.98 (eta1) =>
% 128.89/16.98 ((
% 128.89/16.98 (lam2lamEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (beta2) =>
% 128.89/16.98 ((
% 128.89/16.98 (eta2) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalseProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalseProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ifSingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (ifp) =>
% 128.89/16.98 ((
% 128.89/16.98 (theeq) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrue) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalse) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueorfalse) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (setextT) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetTI) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetTI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetTE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectTELcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectTERcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT1) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT2) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT3) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementSub1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementSub2) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTnotintersectT) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementImpComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementSubsetComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementInPowersetComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (contraSubsetComplement) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTcontraSubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTILcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTIRcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInUnion) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInUnion2) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInIntersectUnions) =>
% 128.89/16.98 ((
% 128.89/16.98 (intersectInPowersetIntersectUnions) =>
% 128.89/16.98 ((
% 128.89/16.98 (inComplementUnionImpNotIn1) =>
% 128.89/16.98 ((
% 128.89/16.98 (inComplementUnionImpInComplement1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTE) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTEcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementUnionInPowersetComplement) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a2) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1a) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1b) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2b2) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2b) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule0) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule1) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule3) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule4) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_1) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_3) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_4) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_5) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1all2) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1SetBreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (choice2fnsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (setOfPairsIsBReln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1all1) =>
% 128.89/16.98 ((
% 128.89/16.98 (subbreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (eqbreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invI) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invE) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compI) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compE) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compEex) =>
% 128.89/16.98 ((
% 128.89/16.98 (!!) @ (
% 128.89/16.98 (('#B') @ (
% 128.89/16.98 !!) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#S') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#S') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 =>))) @
% 128.89/16.98 breln1)))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 !!))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#S') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#S') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 =>))) @
% 128.89/16.98 breln1)))))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#C') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 breln1)))) @
% 128.89/16.98 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl485])).
% 128.89/16.98 thf(zip_derived_cl507, plain,
% 128.89/16.98 (~ (((upairsetIR) =>
% 128.89/16.98 (((emptyE1) =>
% 128.89/16.98 (((vacuousDall) =>
% 128.89/16.98 (((quantDeMorgan1) =>
% 128.89/16.98 (((quantDeMorgan2) =>
% 128.89/16.98 (((quantDeMorgan3) =>
% 128.89/16.98 (((quantDeMorgan4) =>
% 128.89/16.98 (((prop2setI) =>
% 128.89/16.98 (((prop2set2propI) =>
% 128.89/16.98 (((notdexE) =>
% 128.89/16.98 (((notdallE) =>
% 128.89/16.98 (((exuI1) =>
% 128.89/16.98 (((exuI3) =>
% 128.89/16.98 (((exuI2) =>
% 128.89/16.98 (((inCongP) =>
% 128.89/16.98 (((in__Cong) =>
% 128.89/16.98 (((exuE3u) =>
% 128.89/16.98 (((exu__Cong) =>
% 128.89/16.98 (((setadjoin__Cong) =>
% 128.89/16.98 (((powerset__Cong) =>
% 128.89/16.98 (((setunion__Cong) =>
% 128.89/16.98 (((exuEu) =>
% 128.89/16.98 (((descr__Cong) =>
% 128.89/16.98 (((dsetconstr__Cong) =>
% 128.89/16.98 (((subsetI1) =>
% 128.89/16.98 (((eqimpsubset2) =>
% 128.89/16.98 (((eqimpsubset1) =>
% 128.89/16.98 (((subsetI2) =>
% 128.89/16.98 (((emptysetsubset) =>
% 128.89/16.98 (((subsetE) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetE2) =>
% 128.89/16.98 ((
% 128.89/16.98 (notsubsetI) =>
% 128.89/16.98 ((
% 128.89/16.98 (notequalI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (notequalI2) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetRefl) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetTrans) =>
% 128.89/16.98 ((
% 128.89/16.98 (setadjoinSub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setadjoinSub2) =>
% 128.89/16.98 ((
% 128.89/16.98 (subset2powerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (setextsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetemptysetimpeq) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (inPowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (sepInPowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (sepSubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionIL) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairset2IR) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionIR) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionEcases) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionE) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionRsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectI) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset5) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset2) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset3) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectER) =>
% 128.89/16.98 ((
% 128.89/16.98 (disjointsetsI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectRsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset4) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset1) =>
% 128.89/16.98 ((
% 128.89/16.98 (bs114d) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusI) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusER) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusSubset2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusERneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusELneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusILneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusIRneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusSubset1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffE) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffI2) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffIneg1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffIneg2) =>
% 128.89/16.98 ((
% 128.89/16.98 (secondinupair) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairIL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairIR) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairiskpair) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairp) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletoninpowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletoninpowunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairset2E) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairsubunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairinpowunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem3) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairin) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempair1) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempair) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionE2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton1) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1E1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1I) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1I2) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonsuniq) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL1) =>
% 128.89/16.98 ((
% 128.89/16.98 (kfstsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (theprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (kfstpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodfstin) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR11) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR12) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR1) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairequniteq) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR) =>
% 128.89/16.98 ((
% 128.89/16.98 (ksndsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (ksndpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairsurjEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodsndin) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairmemEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairmemER) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempaircEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodfstpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodsndpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairsurjEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrI) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrSub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setOfPairsIsBReln) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrERa) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrEL1) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrEL2) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrER) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcImageSingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (apProp) =>
% 128.89/16.98 ((
% 128.89/16.98 (app) =>
% 128.89/16.98 ((
% 128.89/16.98 (infuncsetfunc) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2p) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcinfuncset) =>
% 128.89/16.98 ((
% 128.89/16.98 (lamProp) =>
% 128.89/16.98 ((
% 128.89/16.98 (lamp) =>
% 128.89/16.98 ((
% 128.89/16.98 (lam2p) =>
% 128.89/16.98 ((
% 128.89/16.98 (brelnall1) =>
% 128.89/16.98 ((
% 128.89/16.98 (brelnall2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1E2) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp3) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcextLem) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp4) =>
% 128.89/16.98 ((
% 128.89/16.98 (subbreln) =>
% 128.89/16.98 ((
% 128.89/16.98 (eqbreln) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcext) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcext2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2apEq1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2apEq2) =>
% 128.89/16.98 ((
% 128.89/16.98 (beta1) =>
% 128.89/16.98 ((
% 128.89/16.98 (eta1) =>
% 128.89/16.98 ((
% 128.89/16.98 (lam2lamEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (beta2) =>
% 128.89/16.98 ((
% 128.89/16.98 (eta2) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalseProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalseProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ifSingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (ifp) =>
% 128.89/16.98 ((
% 128.89/16.98 (theeq) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrue) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalse) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueorfalse) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (setextT) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetTI) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetTI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetTE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectTELcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectTERcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT1) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT2) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT3) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementSub1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementSub2) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTnotintersectT) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementImpComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementSubsetComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementInPowersetComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (contraSubsetComplement) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTcontraSubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTILcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTIRcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInUnion) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInUnion2) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInIntersectUnions) =>
% 128.89/16.98 ((
% 128.89/16.98 (intersectInPowersetIntersectUnions) =>
% 128.89/16.98 ((
% 128.89/16.98 (inComplementUnionImpNotIn1) =>
% 128.89/16.98 ((
% 128.89/16.98 (inComplementUnionImpInComplement1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTE) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTEcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementUnionInPowersetComplement) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a2) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1a) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1b) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2b2) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2b) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule0) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule1) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule3) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule4) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_1) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_3) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_4) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_5) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1all2) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1SetBreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (choice2fnsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (setOfPairsIsBReln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1all1) =>
% 128.89/16.98 ((
% 128.89/16.98 (subbreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (eqbreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invI) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invE) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compI) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compE) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compEex) =>
% 128.89/16.98 ((
% 128.89/16.98 (!!) @ (
% 128.89/16.98 (('#B') @ (
% 128.89/16.98 !!) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#S') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#S') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 =>))) @
% 128.89/16.98 breln1)))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 !!))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#S') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#S') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 =>))) @
% 128.89/16.98 breln1)))))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#C') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 breln1)))) @
% 128.89/16.98 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl496])).
% 128.89/16.98 thf(zip_derived_cl517, plain,
% 128.89/16.98 (~ (((emptyE1) =>
% 128.89/16.98 (((vacuousDall) =>
% 128.89/16.98 (((quantDeMorgan1) =>
% 128.89/16.98 (((quantDeMorgan2) =>
% 128.89/16.98 (((quantDeMorgan3) =>
% 128.89/16.98 (((quantDeMorgan4) =>
% 128.89/16.98 (((prop2setI) =>
% 128.89/16.98 (((prop2set2propI) =>
% 128.89/16.98 (((notdexE) =>
% 128.89/16.98 (((notdallE) =>
% 128.89/16.98 (((exuI1) =>
% 128.89/16.98 (((exuI3) =>
% 128.89/16.98 (((exuI2) =>
% 128.89/16.98 (((inCongP) =>
% 128.89/16.98 (((in__Cong) =>
% 128.89/16.98 (((exuE3u) =>
% 128.89/16.98 (((exu__Cong) =>
% 128.89/16.98 (((setadjoin__Cong) =>
% 128.89/16.98 (((powerset__Cong) =>
% 128.89/16.98 (((setunion__Cong) =>
% 128.89/16.98 (((exuEu) =>
% 128.89/16.98 (((descr__Cong) =>
% 128.89/16.98 (((dsetconstr__Cong) =>
% 128.89/16.98 (((subsetI1) =>
% 128.89/16.98 (((eqimpsubset2) =>
% 128.89/16.98 (((eqimpsubset1) =>
% 128.89/16.98 (((subsetI2) =>
% 128.89/16.98 (((emptysetsubset) =>
% 128.89/16.98 (((subsetE) =>
% 128.89/16.98 (((subsetE2) =>
% 128.89/16.98 ((
% 128.89/16.98 (notsubsetI) =>
% 128.89/16.98 ((
% 128.89/16.98 (notequalI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (notequalI2) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetRefl) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetTrans) =>
% 128.89/16.98 ((
% 128.89/16.98 (setadjoinSub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setadjoinSub2) =>
% 128.89/16.98 ((
% 128.89/16.98 (subset2powerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (setextsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetemptysetimpeq) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (inPowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (sepInPowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (sepSubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionIL) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairset2IR) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionIR) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionEcases) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionE) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionRsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectI) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset5) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset2) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset3) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectER) =>
% 128.89/16.98 ((
% 128.89/16.98 (disjointsetsI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectRsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset4) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset1) =>
% 128.89/16.98 ((
% 128.89/16.98 (bs114d) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusI) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusER) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusSubset2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusERneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusELneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusILneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusIRneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusSubset1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffE) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffI2) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffIneg1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffIneg2) =>
% 128.89/16.98 ((
% 128.89/16.98 (secondinupair) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairIL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairIR) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairiskpair) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairp) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletoninpowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletoninpowunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairset2E) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairsubunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairinpowunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem3) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairin) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempair1) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempair) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionE2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton1) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1E1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1I) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1I2) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonsuniq) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL1) =>
% 128.89/16.98 ((
% 128.89/16.98 (kfstsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (theprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (kfstpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodfstin) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR11) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR12) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR1) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairequniteq) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR) =>
% 128.89/16.98 ((
% 128.89/16.98 (ksndsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (ksndpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairsurjEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodsndin) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairmemEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairmemER) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempaircEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodfstpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodsndpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairsurjEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrI) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrSub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setOfPairsIsBReln) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrERa) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrEL1) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrEL2) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrER) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcImageSingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (apProp) =>
% 128.89/16.98 ((
% 128.89/16.98 (app) =>
% 128.89/16.98 ((
% 128.89/16.98 (infuncsetfunc) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2p) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcinfuncset) =>
% 128.89/16.98 ((
% 128.89/16.98 (lamProp) =>
% 128.89/16.98 ((
% 128.89/16.98 (lamp) =>
% 128.89/16.98 ((
% 128.89/16.98 (lam2p) =>
% 128.89/16.98 ((
% 128.89/16.98 (brelnall1) =>
% 128.89/16.98 ((
% 128.89/16.98 (brelnall2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1E2) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp3) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcextLem) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp4) =>
% 128.89/16.98 ((
% 128.89/16.98 (subbreln) =>
% 128.89/16.98 ((
% 128.89/16.98 (eqbreln) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcext) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcext2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2apEq1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2apEq2) =>
% 128.89/16.98 ((
% 128.89/16.98 (beta1) =>
% 128.89/16.98 ((
% 128.89/16.98 (eta1) =>
% 128.89/16.98 ((
% 128.89/16.98 (lam2lamEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (beta2) =>
% 128.89/16.98 ((
% 128.89/16.98 (eta2) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalseProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalseProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ifSingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (ifp) =>
% 128.89/16.98 ((
% 128.89/16.98 (theeq) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrue) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalse) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueorfalse) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (setextT) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetTI) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetTI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetTE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectTELcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectTERcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT1) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT2) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT3) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementSub1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementSub2) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTnotintersectT) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementImpComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementSubsetComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementInPowersetComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (contraSubsetComplement) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTcontraSubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTILcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTIRcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInUnion) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInUnion2) =>
% 128.89/16.98 ((
% 128.89/16.98 (inIntersectImpInIntersectUnions) =>
% 128.89/16.98 ((
% 128.89/16.98 (intersectInPowersetIntersectUnions) =>
% 128.89/16.98 ((
% 128.89/16.98 (inComplementUnionImpNotIn1) =>
% 128.89/16.98 ((
% 128.89/16.98 (inComplementUnionImpInComplement1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTE) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTEcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementUnionInPowersetComplement) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a2) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1a) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1b) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan1) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2a) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2b2) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2b) =>
% 128.89/16.98 ((
% 128.89/16.98 (demorgan2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule0) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule1) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule3) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz13rule4) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_1) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_2) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_3) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_4) =>
% 128.89/16.98 ((
% 128.89/16.98 (woz1_5) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1all2) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1SetBreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (choice2fnsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (setOfPairsIsBReln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1all1) =>
% 128.89/16.98 ((
% 128.89/16.98 (subbreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (eqbreln1) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invI) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1invE) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compI) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compE) =>
% 128.89/16.98 ((
% 128.89/16.98 (breln1compEex) =>
% 128.89/16.98 ((
% 128.89/16.98 (!!) @ (
% 128.89/16.98 (('#B') @ (
% 128.89/16.98 !!) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#S') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#S') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 =>))) @
% 128.89/16.98 breln1)))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 !!))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#S') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#S') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 =>))) @
% 128.89/16.98 breln1)))))) @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#C') @ (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 (
% 128.89/16.98 (
% 128.89/16.98 ('#B') @ (
% 128.89/16.98 '#B') @
% 128.89/16.98 breln1)))) @
% 128.89/16.98 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl507])).
% 128.89/16.98 thf(zip_derived_cl528, plain,
% 128.89/16.98 (~ (((vacuousDall) =>
% 128.89/16.98 (((quantDeMorgan1) =>
% 128.89/16.98 (((quantDeMorgan2) =>
% 128.89/16.98 (((quantDeMorgan3) =>
% 128.89/16.98 (((quantDeMorgan4) =>
% 128.89/16.98 (((prop2setI) =>
% 128.89/16.98 (((prop2set2propI) =>
% 128.89/16.98 (((notdexE) =>
% 128.89/16.98 (((notdallE) =>
% 128.89/16.98 (((exuI1) =>
% 128.89/16.98 (((exuI3) =>
% 128.89/16.98 (((exuI2) =>
% 128.89/16.98 (((inCongP) =>
% 128.89/16.98 (((in__Cong) =>
% 128.89/16.98 (((exuE3u) =>
% 128.89/16.98 (((exu__Cong) =>
% 128.89/16.98 (((setadjoin__Cong) =>
% 128.89/16.98 (((powerset__Cong) =>
% 128.89/16.98 (((setunion__Cong) =>
% 128.89/16.98 (((exuEu) =>
% 128.89/16.98 (((descr__Cong) =>
% 128.89/16.98 (((dsetconstr__Cong) =>
% 128.89/16.98 (((subsetI1) =>
% 128.89/16.98 (((eqimpsubset2) =>
% 128.89/16.98 (((eqimpsubset1) =>
% 128.89/16.98 (((subsetI2) =>
% 128.89/16.98 (((emptysetsubset) =>
% 128.89/16.98 (((subsetE) =>
% 128.89/16.98 (((subsetE2) =>
% 128.89/16.98 (((notsubsetI) =>
% 128.89/16.98 ((
% 128.89/16.98 (notequalI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (notequalI2) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetRefl) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetTrans) =>
% 128.89/16.98 ((
% 128.89/16.98 (setadjoinSub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setadjoinSub2) =>
% 128.89/16.98 ((
% 128.89/16.98 (subset2powerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (setextsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetemptysetimpeq) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (inPowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (sepInPowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (sepSubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionIL) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairset2IR) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionIR) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionEcases) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionE) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionRsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectI) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset5) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset2) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset3) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectER) =>
% 128.89/16.98 ((
% 128.89/16.98 (disjointsetsI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectRsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset4) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectSubset1) =>
% 128.89/16.98 ((
% 128.89/16.98 (bs114d) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusI) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusER) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusSubset2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusERneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusELneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusILneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusIRneg) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusLsub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusSubset1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffE) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffI2) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffIneg1) =>
% 128.89/16.98 ((
% 128.89/16.98 (symdiffIneg2) =>
% 128.89/16.98 ((
% 128.89/16.98 (secondinupair) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairIL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairIR) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairiskpair) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairp) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonsubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletoninpowerset) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletoninpowunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairset2E) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairsubunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairinpowunion) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ubforcartprodlem3) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairin) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempair1) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempair) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionE2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton1) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setunionsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1E1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1I) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1I2) =>
% 128.89/16.98 ((
% 128.89/16.98 (singletonsuniq) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL1) =>
% 128.89/16.98 ((
% 128.89/16.98 (kfstsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (theprop) =>
% 128.89/16.98 ((
% 128.89/16.98 (kfstpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodfstin) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjL) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR11) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR12) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR1) =>
% 128.89/16.98 ((
% 128.89/16.98 (upairequniteq) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR2) =>
% 128.89/16.98 ((
% 128.89/16.98 (setukpairinjR) =>
% 128.89/16.98 ((
% 128.89/16.98 (ksndsingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (ksndpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (kpairsurjEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodsndin) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairmemEL) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairmemER) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodmempaircEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodfstpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodsndpairEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (cartprodpairsurjEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrI) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrSub) =>
% 128.89/16.98 ((
% 128.89/16.98 (setOfPairsIsBReln) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrERa) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrEL1) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrEL2) =>
% 128.89/16.98 ((
% 128.89/16.98 (dpsetconstrER) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcImageSingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (apProp) =>
% 128.89/16.98 ((
% 128.89/16.98 (app) =>
% 128.89/16.98 ((
% 128.89/16.98 (infuncsetfunc) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2p) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcinfuncset) =>
% 128.89/16.98 ((
% 128.89/16.98 (lamProp) =>
% 128.89/16.98 ((
% 128.89/16.98 (lamp) =>
% 128.89/16.98 ((
% 128.89/16.98 (lam2p) =>
% 128.89/16.98 ((
% 128.89/16.98 (brelnall1) =>
% 128.89/16.98 ((
% 128.89/16.98 (brelnall2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ex1E2) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp3) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcextLem) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcGraphProp4) =>
% 128.89/16.98 ((
% 128.89/16.98 (subbreln) =>
% 128.89/16.98 ((
% 128.89/16.98 (eqbreln) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcext) =>
% 128.89/16.98 ((
% 128.89/16.98 (funcext2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2apEq1) =>
% 128.89/16.98 ((
% 128.89/16.98 (ap2apEq2) =>
% 128.89/16.98 ((
% 128.89/16.98 (beta1) =>
% 128.89/16.98 ((
% 128.89/16.98 (eta1) =>
% 128.89/16.98 ((
% 128.89/16.98 (lam2lamEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (beta2) =>
% 128.89/16.98 ((
% 128.89/16.98 (eta2) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalseProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalseProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueProp1) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueProp2) =>
% 128.89/16.98 ((
% 128.89/16.98 (ifSingleton) =>
% 128.89/16.98 ((
% 128.89/16.98 (ifp) =>
% 128.89/16.98 ((
% 128.89/16.98 (theeq) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrue) =>
% 128.89/16.98 ((
% 128.89/16.98 (iffalse) =>
% 128.89/16.98 ((
% 128.89/16.98 (iftrueorfalse) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (setminusT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementT_lem) =>
% 128.89/16.98 ((
% 128.89/16.98 (setextT) =>
% 128.89/16.98 ((
% 128.89/16.98 (subsetTI) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetTI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (powersetTE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectTELcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (binintersectTERcontra) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT1) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT2) =>
% 128.89/16.98 ((
% 128.89/16.98 (contrasubsetT3) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementI1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementE1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementSub1) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementSub2) =>
% 128.89/16.98 ((
% 128.89/16.98 (doubleComplementEq) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTnotintersectT) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementImpComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementSubsetComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementInPowersetComplementIntersect) =>
% 128.89/16.98 ((
% 128.89/16.98 (contraSubsetComplement) =>
% 128.89/16.98 ((
% 128.89/16.98 (complementTcontraSubset) =>
% 128.89/16.98 ((
% 128.89/16.98 (binunionTILcontra) =>
% 128.89/16.98 ((
% 128.89/16.99 (binunionTIRcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInUnion) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInUnion2) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInIntersectUnions) =>
% 128.89/16.99 ((
% 128.89/16.99 (intersectInPowersetIntersectUnions) =>
% 128.89/16.99 ((
% 128.89/16.99 (inComplementUnionImpNotIn1) =>
% 128.89/16.99 ((
% 128.89/16.99 (inComplementUnionImpInComplement1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTE) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTEcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementUnionInPowersetComplement) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a2) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1a) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1b) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2b2) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2b) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule0) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule1) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule3) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule4) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_1) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_3) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_4) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_5) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1all2) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1SetBreln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (choice2fnsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (setOfPairsIsBReln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1all1) =>
% 128.89/16.99 ((
% 128.89/16.99 (subbreln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (eqbreln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1invprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1invI) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1invE) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compI) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compE) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compEex) =>
% 128.89/16.99 ((
% 128.89/16.99 (!!) @ (
% 128.89/16.99 (('#B') @ (
% 128.89/16.99 !!) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#S') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#S') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 =>))) @
% 128.89/16.99 breln1)))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 !!))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#S') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#S') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 =>))) @
% 128.89/16.99 breln1)))))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#C') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 breln1)))) @
% 128.89/16.99 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl517])).
% 128.89/16.99 thf(zip_derived_cl537, plain,
% 128.89/16.99 (~ (((quantDeMorgan1) =>
% 128.89/16.99 (((quantDeMorgan2) =>
% 128.89/16.99 (((quantDeMorgan3) =>
% 128.89/16.99 (((quantDeMorgan4) =>
% 128.89/16.99 (((prop2setI) =>
% 128.89/16.99 (((prop2set2propI) =>
% 128.89/16.99 (((notdexE) =>
% 128.89/16.99 (((notdallE) =>
% 128.89/16.99 (((exuI1) =>
% 128.89/16.99 (((exuI3) =>
% 128.89/16.99 (((exuI2) =>
% 128.89/16.99 (((inCongP) =>
% 128.89/16.99 (((in__Cong) =>
% 128.89/16.99 (((exuE3u) =>
% 128.89/16.99 (((exu__Cong) =>
% 128.89/16.99 (((setadjoin__Cong) =>
% 128.89/16.99 (((powerset__Cong) =>
% 128.89/16.99 (((setunion__Cong) =>
% 128.89/16.99 (((exuEu) =>
% 128.89/16.99 (((descr__Cong) =>
% 128.89/16.99 (((dsetconstr__Cong) =>
% 128.89/16.99 (((subsetI1) =>
% 128.89/16.99 (((eqimpsubset2) =>
% 128.89/16.99 (((eqimpsubset1) =>
% 128.89/16.99 (((subsetI2) =>
% 128.89/16.99 (((emptysetsubset) =>
% 128.89/16.99 (((subsetE) =>
% 128.89/16.99 (((subsetE2) =>
% 128.89/16.99 (((notsubsetI) =>
% 128.89/16.99 (((notequalI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (notequalI2) =>
% 128.89/16.99 ((
% 128.89/16.99 (subsetRefl) =>
% 128.89/16.99 ((
% 128.89/16.99 (subsetTrans) =>
% 128.89/16.99 ((
% 128.89/16.99 (setadjoinSub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setadjoinSub2) =>
% 128.89/16.99 ((
% 128.89/16.99 (subset2powerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (setextsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (subsetemptysetimpeq) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (inPowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetsubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (sepInPowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (sepSubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionIL) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairset2IR) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionIR) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionEcases) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionE) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionRsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectI) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset5) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset2) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset3) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectER) =>
% 128.89/16.99 ((
% 128.89/16.99 (disjointsetsI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectRsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset4) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset1) =>
% 128.89/16.99 ((
% 128.89/16.99 (bs114d) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusI) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusER) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusSubset2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusERneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusELneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusILneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusIRneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusSubset1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffE) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffI2) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffIneg1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffIneg2) =>
% 128.89/16.99 ((
% 128.89/16.99 (secondinupair) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairIL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairIR) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairiskpair) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairp) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonsubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletoninpowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletoninpowunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairset2E) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairsubunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairinpowunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem3) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairin) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempair1) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempair) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionE2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton1) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1E1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1I) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1I2) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonsuniq) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL1) =>
% 128.89/16.99 ((
% 128.89/16.99 (kfstsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (theprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (kfstpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodfstin) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR11) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR12) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR1) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairequniteq) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR) =>
% 128.89/16.99 ((
% 128.89/16.99 (ksndsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (ksndpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairsurjEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodsndin) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairmemEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairmemER) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempaircEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodfstpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodsndpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairsurjEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrI) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrSub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setOfPairsIsBReln) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrERa) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrEL1) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrEL2) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrER) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcImageSingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (apProp) =>
% 128.89/16.99 ((
% 128.89/16.99 (app) =>
% 128.89/16.99 ((
% 128.89/16.99 (infuncsetfunc) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2p) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcinfuncset) =>
% 128.89/16.99 ((
% 128.89/16.99 (lamProp) =>
% 128.89/16.99 ((
% 128.89/16.99 (lamp) =>
% 128.89/16.99 ((
% 128.89/16.99 (lam2p) =>
% 128.89/16.99 ((
% 128.89/16.99 (brelnall1) =>
% 128.89/16.99 ((
% 128.89/16.99 (brelnall2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1E2) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp3) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcextLem) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp4) =>
% 128.89/16.99 ((
% 128.89/16.99 (subbreln) =>
% 128.89/16.99 ((
% 128.89/16.99 (eqbreln) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcext) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcext2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2apEq1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2apEq2) =>
% 128.89/16.99 ((
% 128.89/16.99 (beta1) =>
% 128.89/16.99 ((
% 128.89/16.99 (eta1) =>
% 128.89/16.99 ((
% 128.89/16.99 (lam2lamEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (beta2) =>
% 128.89/16.99 ((
% 128.89/16.99 (eta2) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalseProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalseProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ifSingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (ifp) =>
% 128.89/16.99 ((
% 128.89/16.99 (theeq) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrue) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalse) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueorfalse) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (setextT) =>
% 128.89/16.99 ((
% 128.89/16.99 (subsetTI) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetTI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetTE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectTELcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectTERcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT1) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT2) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT3) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementSub1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementSub2) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTnotintersectT) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementImpComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementSubsetComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementInPowersetComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (contraSubsetComplement) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTcontraSubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTILcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTIRcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInUnion) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInUnion2) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInIntersectUnions) =>
% 128.89/16.99 ((
% 128.89/16.99 (intersectInPowersetIntersectUnions) =>
% 128.89/16.99 ((
% 128.89/16.99 (inComplementUnionImpNotIn1) =>
% 128.89/16.99 ((
% 128.89/16.99 (inComplementUnionImpInComplement1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTE) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTEcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementUnionInPowersetComplement) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a2) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1a) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1b) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2b2) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2b) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule0) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule1) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule3) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule4) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_1) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_3) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_4) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_5) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1all2) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1SetBreln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (choice2fnsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (setOfPairsIsBReln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1all1) =>
% 128.89/16.99 ((
% 128.89/16.99 (subbreln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (eqbreln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1invprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1invI) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1invE) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compI) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compE) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compEex) =>
% 128.89/16.99 ((
% 128.89/16.99 (!!) @ (
% 128.89/16.99 (('#B') @ (
% 128.89/16.99 !!) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#S') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#S') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 =>))) @
% 128.89/16.99 breln1)))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 !!))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#S') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#S') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 =>))) @
% 128.89/16.99 breln1)))))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#C') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 breln1)))) @
% 128.89/16.99 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl528])).
% 128.89/16.99 thf(zip_derived_cl546, plain,
% 128.89/16.99 (~ (((quantDeMorgan2) =>
% 128.89/16.99 (((quantDeMorgan3) =>
% 128.89/16.99 (((quantDeMorgan4) =>
% 128.89/16.99 (((prop2setI) =>
% 128.89/16.99 (((prop2set2propI) =>
% 128.89/16.99 (((notdexE) =>
% 128.89/16.99 (((notdallE) =>
% 128.89/16.99 (((exuI1) =>
% 128.89/16.99 (((exuI3) =>
% 128.89/16.99 (((exuI2) =>
% 128.89/16.99 (((inCongP) =>
% 128.89/16.99 (((in__Cong) =>
% 128.89/16.99 (((exuE3u) =>
% 128.89/16.99 (((exu__Cong) =>
% 128.89/16.99 (((setadjoin__Cong) =>
% 128.89/16.99 (((powerset__Cong) =>
% 128.89/16.99 (((setunion__Cong) =>
% 128.89/16.99 (((exuEu) =>
% 128.89/16.99 (((descr__Cong) =>
% 128.89/16.99 (((dsetconstr__Cong) =>
% 128.89/16.99 (((subsetI1) =>
% 128.89/16.99 (((eqimpsubset2) =>
% 128.89/16.99 (((eqimpsubset1) =>
% 128.89/16.99 (((subsetI2) =>
% 128.89/16.99 (((emptysetsubset) =>
% 128.89/16.99 (((subsetE) =>
% 128.89/16.99 (((subsetE2) =>
% 128.89/16.99 (((notsubsetI) =>
% 128.89/16.99 (((notequalI1) =>
% 128.89/16.99 (((notequalI2) =>
% 128.89/16.99 ((
% 128.89/16.99 (subsetRefl) =>
% 128.89/16.99 ((
% 128.89/16.99 (subsetTrans) =>
% 128.89/16.99 ((
% 128.89/16.99 (setadjoinSub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setadjoinSub2) =>
% 128.89/16.99 ((
% 128.89/16.99 (subset2powerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (setextsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (subsetemptysetimpeq) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (inPowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetsubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (sepInPowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (sepSubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionIL) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairset2IR) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionIR) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionEcases) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionE) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionRsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectI) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset5) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset2) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset3) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectER) =>
% 128.89/16.99 ((
% 128.89/16.99 (disjointsetsI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectRsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset4) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset1) =>
% 128.89/16.99 ((
% 128.89/16.99 (bs114d) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusI) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusER) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusSubset2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusERneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusELneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusILneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusIRneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusSubset1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffE) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffI2) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffIneg1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffIneg2) =>
% 128.89/16.99 ((
% 128.89/16.99 (secondinupair) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairIL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairIR) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairiskpair) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairp) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonsubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletoninpowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletoninpowunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairset2E) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairsubunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairinpowunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem3) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairin) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempair1) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempair) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionE2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton1) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1E1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1I) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1I2) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonsuniq) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL1) =>
% 128.89/16.99 ((
% 128.89/16.99 (kfstsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (theprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (kfstpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodfstin) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR11) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR12) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR1) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairequniteq) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR) =>
% 128.89/16.99 ((
% 128.89/16.99 (ksndsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (ksndpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairsurjEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodsndin) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairmemEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairmemER) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempaircEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodfstpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodsndpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairsurjEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrI) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrSub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setOfPairsIsBReln) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrERa) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrEL1) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrEL2) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrER) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcImageSingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (apProp) =>
% 128.89/16.99 ((
% 128.89/16.99 (app) =>
% 128.89/16.99 ((
% 128.89/16.99 (infuncsetfunc) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2p) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcinfuncset) =>
% 128.89/16.99 ((
% 128.89/16.99 (lamProp) =>
% 128.89/16.99 ((
% 128.89/16.99 (lamp) =>
% 128.89/16.99 ((
% 128.89/16.99 (lam2p) =>
% 128.89/16.99 ((
% 128.89/16.99 (brelnall1) =>
% 128.89/16.99 ((
% 128.89/16.99 (brelnall2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1E2) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp3) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcextLem) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp4) =>
% 128.89/16.99 ((
% 128.89/16.99 (subbreln) =>
% 128.89/16.99 ((
% 128.89/16.99 (eqbreln) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcext) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcext2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2apEq1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2apEq2) =>
% 128.89/16.99 ((
% 128.89/16.99 (beta1) =>
% 128.89/16.99 ((
% 128.89/16.99 (eta1) =>
% 128.89/16.99 ((
% 128.89/16.99 (lam2lamEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (beta2) =>
% 128.89/16.99 ((
% 128.89/16.99 (eta2) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalseProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalseProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ifSingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (ifp) =>
% 128.89/16.99 ((
% 128.89/16.99 (theeq) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrue) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalse) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueorfalse) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (setextT) =>
% 128.89/16.99 ((
% 128.89/16.99 (subsetTI) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetTI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetTE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectTELcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectTERcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT1) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT2) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT3) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementSub1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementSub2) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTnotintersectT) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementImpComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementSubsetComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementInPowersetComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (contraSubsetComplement) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTcontraSubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTILcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTIRcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInUnion) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInUnion2) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInIntersectUnions) =>
% 128.89/16.99 ((
% 128.89/16.99 (intersectInPowersetIntersectUnions) =>
% 128.89/16.99 ((
% 128.89/16.99 (inComplementUnionImpNotIn1) =>
% 128.89/16.99 ((
% 128.89/16.99 (inComplementUnionImpInComplement1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTE) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTEcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementUnionInPowersetComplement) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a2) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1a) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1b) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2b2) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2b) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule0) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule1) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule3) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule4) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_1) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_3) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_4) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_5) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1all2) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1SetBreln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (choice2fnsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (setOfPairsIsBReln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1all1) =>
% 128.89/16.99 ((
% 128.89/16.99 (subbreln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (eqbreln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1invprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1invI) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1invE) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compI) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compE) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compEex) =>
% 128.89/16.99 ((
% 128.89/16.99 (!!) @ (
% 128.89/16.99 (('#B') @ (
% 128.89/16.99 !!) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#S') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#S') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 =>))) @
% 128.89/16.99 breln1)))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 !!))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#S') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#S') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 =>))) @
% 128.89/16.99 breln1)))))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#C') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 breln1)))) @
% 128.89/16.99 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl537])).
% 128.89/16.99 thf(zip_derived_cl553, plain,
% 128.89/16.99 (~ (((quantDeMorgan3) =>
% 128.89/16.99 (((quantDeMorgan4) =>
% 128.89/16.99 (((prop2setI) =>
% 128.89/16.99 (((prop2set2propI) =>
% 128.89/16.99 (((notdexE) =>
% 128.89/16.99 (((notdallE) =>
% 128.89/16.99 (((exuI1) =>
% 128.89/16.99 (((exuI3) =>
% 128.89/16.99 (((exuI2) =>
% 128.89/16.99 (((inCongP) =>
% 128.89/16.99 (((in__Cong) =>
% 128.89/16.99 (((exuE3u) =>
% 128.89/16.99 (((exu__Cong) =>
% 128.89/16.99 (((setadjoin__Cong) =>
% 128.89/16.99 (((powerset__Cong) =>
% 128.89/16.99 (((setunion__Cong) =>
% 128.89/16.99 (((exuEu) =>
% 128.89/16.99 (((descr__Cong) =>
% 128.89/16.99 (((dsetconstr__Cong) =>
% 128.89/16.99 (((subsetI1) =>
% 128.89/16.99 (((eqimpsubset2) =>
% 128.89/16.99 (((eqimpsubset1) =>
% 128.89/16.99 (((subsetI2) =>
% 128.89/16.99 (((emptysetsubset) =>
% 128.89/16.99 (((subsetE) =>
% 128.89/16.99 (((subsetE2) =>
% 128.89/16.99 (((notsubsetI) =>
% 128.89/16.99 (((notequalI1) =>
% 128.89/16.99 (((notequalI2) =>
% 128.89/16.99 (((subsetRefl) =>
% 128.89/16.99 ((
% 128.89/16.99 (subsetTrans) =>
% 128.89/16.99 ((
% 128.89/16.99 (setadjoinSub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setadjoinSub2) =>
% 128.89/16.99 ((
% 128.89/16.99 (subset2powerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (setextsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (subsetemptysetimpeq) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (inPowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetsubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (sepInPowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (sepSubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionIL) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairset2IR) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionIR) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionEcases) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionE) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionRsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectI) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset5) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset2) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset3) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectER) =>
% 128.89/16.99 ((
% 128.89/16.99 (disjointsetsI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectRsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset4) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset1) =>
% 128.89/16.99 ((
% 128.89/16.99 (bs114d) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusI) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusER) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusSubset2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusERneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusELneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusILneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusIRneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusSubset1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffE) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffI2) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffIneg1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffIneg2) =>
% 128.89/16.99 ((
% 128.89/16.99 (secondinupair) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairIL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairIR) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairiskpair) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairp) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonsubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletoninpowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletoninpowunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairset2E) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairsubunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairinpowunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem3) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairin) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempair1) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempair) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionE2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton1) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1E1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1I) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1I2) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonsuniq) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL1) =>
% 128.89/16.99 ((
% 128.89/16.99 (kfstsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (theprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (kfstpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodfstin) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR11) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR12) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR1) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairequniteq) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR) =>
% 128.89/16.99 ((
% 128.89/16.99 (ksndsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (ksndpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairsurjEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodsndin) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairmemEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairmemER) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempaircEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodfstpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodsndpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairsurjEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrI) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrSub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setOfPairsIsBReln) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrERa) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrEL1) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrEL2) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrER) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcImageSingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (apProp) =>
% 128.89/16.99 ((
% 128.89/16.99 (app) =>
% 128.89/16.99 ((
% 128.89/16.99 (infuncsetfunc) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2p) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcinfuncset) =>
% 128.89/16.99 ((
% 128.89/16.99 (lamProp) =>
% 128.89/16.99 ((
% 128.89/16.99 (lamp) =>
% 128.89/16.99 ((
% 128.89/16.99 (lam2p) =>
% 128.89/16.99 ((
% 128.89/16.99 (brelnall1) =>
% 128.89/16.99 ((
% 128.89/16.99 (brelnall2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1E2) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp3) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcextLem) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp4) =>
% 128.89/16.99 ((
% 128.89/16.99 (subbreln) =>
% 128.89/16.99 ((
% 128.89/16.99 (eqbreln) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcext) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcext2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2apEq1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2apEq2) =>
% 128.89/16.99 ((
% 128.89/16.99 (beta1) =>
% 128.89/16.99 ((
% 128.89/16.99 (eta1) =>
% 128.89/16.99 ((
% 128.89/16.99 (lam2lamEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (beta2) =>
% 128.89/16.99 ((
% 128.89/16.99 (eta2) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalseProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalseProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ifSingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (ifp) =>
% 128.89/16.99 ((
% 128.89/16.99 (theeq) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrue) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalse) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueorfalse) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (setextT) =>
% 128.89/16.99 ((
% 128.89/16.99 (subsetTI) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetTI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetTE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectTELcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectTERcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT1) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT2) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT3) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementSub1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementSub2) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTnotintersectT) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementImpComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementSubsetComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementInPowersetComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (contraSubsetComplement) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTcontraSubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTILcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTIRcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInUnion) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInUnion2) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInIntersectUnions) =>
% 128.89/16.99 ((
% 128.89/16.99 (intersectInPowersetIntersectUnions) =>
% 128.89/16.99 ((
% 128.89/16.99 (inComplementUnionImpNotIn1) =>
% 128.89/16.99 ((
% 128.89/16.99 (inComplementUnionImpInComplement1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTE) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTEcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementUnionInPowersetComplement) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a2) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1a) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1b) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2b2) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2b) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule0) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule1) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule3) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule4) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_1) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_3) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_4) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_5) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1all2) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1SetBreln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (choice2fnsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (setOfPairsIsBReln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1all1) =>
% 128.89/16.99 ((
% 128.89/16.99 (subbreln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (eqbreln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1invprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1invI) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1invE) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compI) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compE) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compEex) =>
% 128.89/16.99 ((
% 128.89/16.99 (!!) @ (
% 128.89/16.99 (('#B') @ (
% 128.89/16.99 !!) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#S') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#S') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 =>))) @
% 128.89/16.99 breln1)))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 !!))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#S') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#S') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 =>))) @
% 128.89/16.99 breln1)))))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#C') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 breln1)))) @
% 128.89/16.99 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl546])).
% 128.89/16.99 thf(zip_derived_cl561, plain,
% 128.89/16.99 (~ (((quantDeMorgan4) =>
% 128.89/16.99 (((prop2setI) =>
% 128.89/16.99 (((prop2set2propI) =>
% 128.89/16.99 (((notdexE) =>
% 128.89/16.99 (((notdallE) =>
% 128.89/16.99 (((exuI1) =>
% 128.89/16.99 (((exuI3) =>
% 128.89/16.99 (((exuI2) =>
% 128.89/16.99 (((inCongP) =>
% 128.89/16.99 (((in__Cong) =>
% 128.89/16.99 (((exuE3u) =>
% 128.89/16.99 (((exu__Cong) =>
% 128.89/16.99 (((setadjoin__Cong) =>
% 128.89/16.99 (((powerset__Cong) =>
% 128.89/16.99 (((setunion__Cong) =>
% 128.89/16.99 (((exuEu) =>
% 128.89/16.99 (((descr__Cong) =>
% 128.89/16.99 (((dsetconstr__Cong) =>
% 128.89/16.99 (((subsetI1) =>
% 128.89/16.99 (((eqimpsubset2) =>
% 128.89/16.99 (((eqimpsubset1) =>
% 128.89/16.99 (((subsetI2) =>
% 128.89/16.99 (((emptysetsubset) =>
% 128.89/16.99 (((subsetE) =>
% 128.89/16.99 (((subsetE2) =>
% 128.89/16.99 (((notsubsetI) =>
% 128.89/16.99 (((notequalI1) =>
% 128.89/16.99 (((notequalI2) =>
% 128.89/16.99 (((subsetRefl) =>
% 128.89/16.99 (((subsetTrans) =>
% 128.89/16.99 ((
% 128.89/16.99 (setadjoinSub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setadjoinSub2) =>
% 128.89/16.99 ((
% 128.89/16.99 (subset2powerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (setextsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (subsetemptysetimpeq) =>
% 128.89/16.99 ((
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% 128.89/16.99 ((
% 128.89/16.99 (powersetE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (inPowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetsubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (sepInPowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (sepSubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionIL) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairset2IR) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionIR) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionEcases) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionE) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionRsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectI) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset5) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset2) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset3) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectER) =>
% 128.89/16.99 ((
% 128.89/16.99 (disjointsetsI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectRsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset4) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset1) =>
% 128.89/16.99 ((
% 128.89/16.99 (bs114d) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusI) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusER) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusSubset2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusERneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusELneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusILneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusIRneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusSubset1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffE) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffI2) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffIneg1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffIneg2) =>
% 128.89/16.99 ((
% 128.89/16.99 (secondinupair) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairIL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairIR) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairiskpair) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairp) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonsubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletoninpowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletoninpowunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairset2E) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairsubunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairinpowunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem3) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairin) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempair1) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempair) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionE2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton1) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1E1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1I) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1I2) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonsuniq) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL1) =>
% 128.89/16.99 ((
% 128.89/16.99 (kfstsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (theprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (kfstpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodfstin) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR11) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR12) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR1) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairequniteq) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR) =>
% 128.89/16.99 ((
% 128.89/16.99 (ksndsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (ksndpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairsurjEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodsndin) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairmemEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairmemER) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempaircEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodfstpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodsndpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairsurjEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrI) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrSub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setOfPairsIsBReln) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrERa) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrEL1) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrEL2) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrER) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcImageSingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (apProp) =>
% 128.89/16.99 ((
% 128.89/16.99 (app) =>
% 128.89/16.99 ((
% 128.89/16.99 (infuncsetfunc) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2p) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcinfuncset) =>
% 128.89/16.99 ((
% 128.89/16.99 (lamProp) =>
% 128.89/16.99 ((
% 128.89/16.99 (lamp) =>
% 128.89/16.99 ((
% 128.89/16.99 (lam2p) =>
% 128.89/16.99 ((
% 128.89/16.99 (brelnall1) =>
% 128.89/16.99 ((
% 128.89/16.99 (brelnall2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1E2) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp3) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcextLem) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp4) =>
% 128.89/16.99 ((
% 128.89/16.99 (subbreln) =>
% 128.89/16.99 ((
% 128.89/16.99 (eqbreln) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcext) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcext2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2apEq1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2apEq2) =>
% 128.89/16.99 ((
% 128.89/16.99 (beta1) =>
% 128.89/16.99 ((
% 128.89/16.99 (eta1) =>
% 128.89/16.99 ((
% 128.89/16.99 (lam2lamEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (beta2) =>
% 128.89/16.99 ((
% 128.89/16.99 (eta2) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalseProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalseProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ifSingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (ifp) =>
% 128.89/16.99 ((
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% 128.89/16.99 ((
% 128.89/16.99 (iftrue) =>
% 128.89/16.99 ((
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% 128.89/16.99 ((
% 128.89/16.99 (iftrueorfalse) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectT_lem) =>
% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
% 128.89/16.99 (setminusT_lem) =>
% 128.89/16.99 ((
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% 128.89/16.99 ((
% 128.89/16.99 (setextT) =>
% 128.89/16.99 ((
% 128.89/16.99 (subsetTI) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetTI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetTE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTE1) =>
% 128.89/16.99 ((
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% 128.89/16.99 ((
% 128.89/16.99 (binintersectTERcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT1) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT2) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT3) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementSub1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementSub2) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTnotintersectT) =>
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% 128.89/16.99 (complementImpComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementSubsetComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementInPowersetComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (contraSubsetComplement) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTcontraSubset) =>
% 128.89/16.99 ((
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% 128.89/16.99 ((
% 128.89/16.99 (binunionTIRcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInUnion) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInUnion2) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInIntersectUnions) =>
% 128.89/16.99 ((
% 128.89/16.99 (intersectInPowersetIntersectUnions) =>
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% 128.89/16.99 (inComplementUnionImpNotIn1) =>
% 128.89/16.99 ((
% 128.89/16.99 (inComplementUnionImpInComplement1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTE) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTEcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementUnionInPowersetComplement) =>
% 128.89/16.99 ((
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% 128.89/16.99 ((
% 128.89/16.99 (demorgan1a) =>
% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
% 128.89/16.99 (demorgan2) =>
% 128.89/16.99 ((
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% 128.89/16.99 ((
% 128.89/16.99 (woz13rule1) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule2) =>
% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 =>))) @
% 128.89/16.99 breln1)))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 !!))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#S') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#S') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 =>))) @
% 128.89/16.99 breln1)))))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#C') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 breln1)))) @
% 128.89/16.99 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl553])).
% 128.89/16.99 thf(zip_derived_cl570, plain,
% 128.89/16.99 (~ (((prop2setI) =>
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% 128.89/16.99 (((inCongP) =>
% 128.89/16.99 (((in__Cong) =>
% 128.89/16.99 (((exuE3u) =>
% 128.89/16.99 (((exu__Cong) =>
% 128.89/16.99 (((setadjoin__Cong) =>
% 128.89/16.99 (((powerset__Cong) =>
% 128.89/16.99 (((setunion__Cong) =>
% 128.89/16.99 (((exuEu) =>
% 128.89/16.99 (((descr__Cong) =>
% 128.89/16.99 (((dsetconstr__Cong) =>
% 128.89/16.99 (((subsetI1) =>
% 128.89/16.99 (((eqimpsubset2) =>
% 128.89/16.99 (((eqimpsubset1) =>
% 128.89/16.99 (((subsetI2) =>
% 128.89/16.99 (((emptysetsubset) =>
% 128.89/16.99 (((subsetE) =>
% 128.89/16.99 (((subsetE2) =>
% 128.89/16.99 (((notsubsetI) =>
% 128.89/16.99 (((notequalI1) =>
% 128.89/16.99 (((notequalI2) =>
% 128.89/16.99 (((subsetRefl) =>
% 128.89/16.99 (((subsetTrans) =>
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% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
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% 128.89/16.99 ((
% 128.89/16.99 (upairset2IR) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionIR) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionEcases) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionE) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionRsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectI) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset5) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectEL) =>
% 128.89/16.99 ((
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% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset2) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset3) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectER) =>
% 128.89/16.99 ((
% 128.89/16.99 (disjointsetsI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectRsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset4) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset1) =>
% 128.89/16.99 ((
% 128.89/16.99 (bs114d) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusI) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusER) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusSubset2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusERneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusELneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusILneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusIRneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusSubset1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffE) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffI2) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffIneg1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffIneg2) =>
% 128.89/16.99 ((
% 128.89/16.99 (secondinupair) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairIL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairIR) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairiskpair) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairp) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonsubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletoninpowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletoninpowunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairset2E) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairsubunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairinpowunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem3) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairin) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempair1) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempair) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionE2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton1) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1E1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1I) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1I2) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonsuniq) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL1) =>
% 128.89/16.99 ((
% 128.89/16.99 (kfstsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (theprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (kfstpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodfstin) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR11) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR12) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR1) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairequniteq) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR) =>
% 128.89/16.99 ((
% 128.89/16.99 (ksndsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (ksndpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairsurjEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodsndin) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairmemEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairmemER) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempaircEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodfstpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodsndpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairsurjEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrI) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrSub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setOfPairsIsBReln) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrERa) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrEL1) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrEL2) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrER) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcImageSingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (apProp) =>
% 128.89/16.99 ((
% 128.89/16.99 (app) =>
% 128.89/16.99 ((
% 128.89/16.99 (infuncsetfunc) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2p) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcinfuncset) =>
% 128.89/16.99 ((
% 128.89/16.99 (lamProp) =>
% 128.89/16.99 ((
% 128.89/16.99 (lamp) =>
% 128.89/16.99 ((
% 128.89/16.99 (lam2p) =>
% 128.89/16.99 ((
% 128.89/16.99 (brelnall1) =>
% 128.89/16.99 ((
% 128.89/16.99 (brelnall2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1E2) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp3) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcextLem) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp4) =>
% 128.89/16.99 ((
% 128.89/16.99 (subbreln) =>
% 128.89/16.99 ((
% 128.89/16.99 (eqbreln) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcext) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcext2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2apEq1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2apEq2) =>
% 128.89/16.99 ((
% 128.89/16.99 (beta1) =>
% 128.89/16.99 ((
% 128.89/16.99 (eta1) =>
% 128.89/16.99 ((
% 128.89/16.99 (lam2lamEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (beta2) =>
% 128.89/16.99 ((
% 128.89/16.99 (eta2) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalseProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalseProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ifSingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (ifp) =>
% 128.89/16.99 ((
% 128.89/16.99 (theeq) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrue) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalse) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueorfalse) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (setextT) =>
% 128.89/16.99 ((
% 128.89/16.99 (subsetTI) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetTI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetTE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectTELcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectTERcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT1) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT2) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT3) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementSub1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementSub2) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTnotintersectT) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementImpComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementSubsetComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementInPowersetComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (contraSubsetComplement) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTcontraSubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTILcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTIRcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInUnion) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInUnion2) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInIntersectUnions) =>
% 128.89/16.99 ((
% 128.89/16.99 (intersectInPowersetIntersectUnions) =>
% 128.89/16.99 ((
% 128.89/16.99 (inComplementUnionImpNotIn1) =>
% 128.89/16.99 ((
% 128.89/16.99 (inComplementUnionImpInComplement1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTE) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTEcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementUnionInPowersetComplement) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a2) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1a) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1b) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2b2) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2b) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule0) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule1) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule3) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule4) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_1) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_3) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_4) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_5) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1all2) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1SetBreln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (choice2fnsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (setOfPairsIsBReln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1all1) =>
% 128.89/16.99 ((
% 128.89/16.99 (subbreln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (eqbreln1) =>
% 128.89/16.99 ((
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% 128.89/16.99 ((
% 128.89/16.99 (breln1invI) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1invE) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compI) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compE) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compEex) =>
% 128.89/16.99 ((
% 128.89/16.99 (!!) @ (
% 128.89/16.99 (('#B') @ (
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% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#S') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
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% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
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% 128.89/16.99 ('#B') @ (
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% 128.89/16.99 breln1)))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
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% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#S') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
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% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 =>))) @
% 128.89/16.99 breln1)))))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#C') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 breln1)))) @
% 128.89/16.99 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl561])).
% 128.89/16.99 thf(zip_derived_cl578, plain,
% 128.89/16.99 (~ (((prop2set2propI) =>
% 128.89/16.99 (((notdexE) =>
% 128.89/16.99 (((notdallE) =>
% 128.89/16.99 (((exuI1) =>
% 128.89/16.99 (((exuI3) =>
% 128.89/16.99 (((exuI2) =>
% 128.89/16.99 (((inCongP) =>
% 128.89/16.99 (((in__Cong) =>
% 128.89/16.99 (((exuE3u) =>
% 128.89/16.99 (((exu__Cong) =>
% 128.89/16.99 (((setadjoin__Cong) =>
% 128.89/16.99 (((powerset__Cong) =>
% 128.89/16.99 (((setunion__Cong) =>
% 128.89/16.99 (((exuEu) =>
% 128.89/16.99 (((descr__Cong) =>
% 128.89/16.99 (((dsetconstr__Cong) =>
% 128.89/16.99 (((subsetI1) =>
% 128.89/16.99 (((eqimpsubset2) =>
% 128.89/16.99 (((eqimpsubset1) =>
% 128.89/16.99 (((subsetI2) =>
% 128.89/16.99 (((emptysetsubset) =>
% 128.89/16.99 (((subsetE) =>
% 128.89/16.99 (((subsetE2) =>
% 128.89/16.99 (((notsubsetI) =>
% 128.89/16.99 (((notequalI1) =>
% 128.89/16.99 (((notequalI2) =>
% 128.89/16.99 (((subsetRefl) =>
% 128.89/16.99 (((subsetTrans) =>
% 128.89/16.99 (((setadjoinSub) =>
% 128.89/16.99 (((setadjoinSub2) =>
% 128.89/16.99 ((
% 128.89/16.99 (subset2powerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (setextsub) =>
% 128.89/16.99 ((
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% 128.89/16.99 ((
% 128.89/16.99 (powersetI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (inPowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetsubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (sepInPowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (sepSubset) =>
% 128.89/16.99 ((
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% 128.89/16.99 ((
% 128.89/16.99 (upairset2IR) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionIR) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionEcases) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionE) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionRsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectI) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset5) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset2) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset3) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectER) =>
% 128.89/16.99 ((
% 128.89/16.99 (disjointsetsI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectRsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset4) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset1) =>
% 128.89/16.99 ((
% 128.89/16.99 (bs114d) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusI) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusER) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusSubset2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusERneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusELneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusILneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusIRneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusSubset1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffE) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffI2) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffIneg1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffIneg2) =>
% 128.89/16.99 ((
% 128.89/16.99 (secondinupair) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairIL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairIR) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairiskpair) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairp) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonsubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletoninpowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletoninpowunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairset2E) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairsubunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairinpowunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem3) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairin) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempair1) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempair) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionE2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton1) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1E1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1I) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1I2) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonsuniq) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL1) =>
% 128.89/16.99 ((
% 128.89/16.99 (kfstsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (theprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (kfstpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodfstin) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR11) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR12) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR1) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairequniteq) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR) =>
% 128.89/16.99 ((
% 128.89/16.99 (ksndsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (ksndpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairsurjEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodsndin) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairmemEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairmemER) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempaircEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodfstpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodsndpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairsurjEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrI) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrSub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setOfPairsIsBReln) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrERa) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrEL1) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrEL2) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrER) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcImageSingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (apProp) =>
% 128.89/16.99 ((
% 128.89/16.99 (app) =>
% 128.89/16.99 ((
% 128.89/16.99 (infuncsetfunc) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2p) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcinfuncset) =>
% 128.89/16.99 ((
% 128.89/16.99 (lamProp) =>
% 128.89/16.99 ((
% 128.89/16.99 (lamp) =>
% 128.89/16.99 ((
% 128.89/16.99 (lam2p) =>
% 128.89/16.99 ((
% 128.89/16.99 (brelnall1) =>
% 128.89/16.99 ((
% 128.89/16.99 (brelnall2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1E2) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp3) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcextLem) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp4) =>
% 128.89/16.99 ((
% 128.89/16.99 (subbreln) =>
% 128.89/16.99 ((
% 128.89/16.99 (eqbreln) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcext) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcext2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2apEq1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2apEq2) =>
% 128.89/16.99 ((
% 128.89/16.99 (beta1) =>
% 128.89/16.99 ((
% 128.89/16.99 (eta1) =>
% 128.89/16.99 ((
% 128.89/16.99 (lam2lamEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (beta2) =>
% 128.89/16.99 ((
% 128.89/16.99 (eta2) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalseProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalseProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ifSingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (ifp) =>
% 128.89/16.99 ((
% 128.89/16.99 (theeq) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrue) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalse) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueorfalse) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (setextT) =>
% 128.89/16.99 ((
% 128.89/16.99 (subsetTI) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetTI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetTE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectTELcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectTERcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT1) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT2) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT3) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementSub1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementSub2) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTnotintersectT) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementImpComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementSubsetComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementInPowersetComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (contraSubsetComplement) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTcontraSubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTILcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTIRcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInUnion) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInUnion2) =>
% 128.89/16.99 ((
% 128.89/16.99 (inIntersectImpInIntersectUnions) =>
% 128.89/16.99 ((
% 128.89/16.99 (intersectInPowersetIntersectUnions) =>
% 128.89/16.99 ((
% 128.89/16.99 (inComplementUnionImpNotIn1) =>
% 128.89/16.99 ((
% 128.89/16.99 (inComplementUnionImpInComplement1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTE) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTEcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementUnionInPowersetComplement) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a2) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1a) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1b) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan1) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2a) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2b2) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2b) =>
% 128.89/16.99 ((
% 128.89/16.99 (demorgan2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule0) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule1) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule3) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz13rule4) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_1) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_2) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_3) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_4) =>
% 128.89/16.99 ((
% 128.89/16.99 (woz1_5) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1all2) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1SetBreln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (choice2fnsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (setOfPairsIsBReln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1all1) =>
% 128.89/16.99 ((
% 128.89/16.99 (subbreln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (eqbreln1) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1invprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1invI) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1invE) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compI) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compE) =>
% 128.89/16.99 ((
% 128.89/16.99 (breln1compEex) =>
% 128.89/16.99 ((
% 128.89/16.99 (!!) @ (
% 128.89/16.99 (('#B') @ (
% 128.89/16.99 !!) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#S') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#S') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 =>))) @
% 128.89/16.99 breln1)))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 !!))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#S') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#S') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 =>))) @
% 128.89/16.99 breln1)))))) @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#C') @ (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 (
% 128.89/16.99 (
% 128.89/16.99 ('#B') @ (
% 128.89/16.99 '#B') @
% 128.89/16.99 breln1)))) @
% 128.89/16.99 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/16.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl570])).
% 128.89/16.99 thf(zip_derived_cl586, plain,
% 128.89/16.99 (~ (((notdexE) =>
% 128.89/16.99 (((notdallE) =>
% 128.89/16.99 (((exuI1) =>
% 128.89/16.99 (((exuI3) =>
% 128.89/16.99 (((exuI2) =>
% 128.89/16.99 (((inCongP) =>
% 128.89/16.99 (((in__Cong) =>
% 128.89/16.99 (((exuE3u) =>
% 128.89/16.99 (((exu__Cong) =>
% 128.89/16.99 (((setadjoin__Cong) =>
% 128.89/16.99 (((powerset__Cong) =>
% 128.89/16.99 (((setunion__Cong) =>
% 128.89/16.99 (((exuEu) =>
% 128.89/16.99 (((descr__Cong) =>
% 128.89/16.99 (((dsetconstr__Cong) =>
% 128.89/16.99 (((subsetI1) =>
% 128.89/16.99 (((eqimpsubset2) =>
% 128.89/16.99 (((eqimpsubset1) =>
% 128.89/16.99 (((subsetI2) =>
% 128.89/16.99 (((emptysetsubset) =>
% 128.89/16.99 (((subsetE) =>
% 128.89/16.99 (((subsetE2) =>
% 128.89/16.99 (((notsubsetI) =>
% 128.89/16.99 (((notequalI1) =>
% 128.89/16.99 (((notequalI2) =>
% 128.89/16.99 (((subsetRefl) =>
% 128.89/16.99 (((subsetTrans) =>
% 128.89/16.99 (((setadjoinSub) =>
% 128.89/16.99 (((setadjoinSub2) =>
% 128.89/16.99 (((subset2powerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (setextsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (subsetemptysetimpeq) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (inPowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetsubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (sepInPowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (sepSubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionIL) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairset2IR) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionIR) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionEcases) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionE) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionRsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectI) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset5) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset2) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset3) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectER) =>
% 128.89/16.99 ((
% 128.89/16.99 (disjointsetsI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectRsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset4) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectSubset1) =>
% 128.89/16.99 ((
% 128.89/16.99 (bs114d) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusI) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusER) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusSubset2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusERneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusELneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusILneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusIRneg) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusLsub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusSubset1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffE) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffI2) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffIneg1) =>
% 128.89/16.99 ((
% 128.89/16.99 (symdiffIneg2) =>
% 128.89/16.99 ((
% 128.89/16.99 (secondinupair) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairIL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairIR) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairiskpair) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairp) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonsubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletoninpowerset) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletoninpowunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairset2E) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairsubunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairinpowunion) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ubforcartprodlem3) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairin) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempair1) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempair) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionE2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton1) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setunionsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1E1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1I) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1I2) =>
% 128.89/16.99 ((
% 128.89/16.99 (singletonsuniq) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL1) =>
% 128.89/16.99 ((
% 128.89/16.99 (kfstsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (theprop) =>
% 128.89/16.99 ((
% 128.89/16.99 (kfstpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodfstin) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjL) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR11) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR12) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR1) =>
% 128.89/16.99 ((
% 128.89/16.99 (upairequniteq) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR2) =>
% 128.89/16.99 ((
% 128.89/16.99 (setukpairinjR) =>
% 128.89/16.99 ((
% 128.89/16.99 (ksndsingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (ksndpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (kpairsurjEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodsndin) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairmemEL) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairmemER) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodmempaircEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodfstpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodsndpairEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (cartprodpairsurjEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrI) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrSub) =>
% 128.89/16.99 ((
% 128.89/16.99 (setOfPairsIsBReln) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrERa) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrEL1) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrEL2) =>
% 128.89/16.99 ((
% 128.89/16.99 (dpsetconstrER) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcImageSingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (apProp) =>
% 128.89/16.99 ((
% 128.89/16.99 (app) =>
% 128.89/16.99 ((
% 128.89/16.99 (infuncsetfunc) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2p) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcinfuncset) =>
% 128.89/16.99 ((
% 128.89/16.99 (lamProp) =>
% 128.89/16.99 ((
% 128.89/16.99 (lamp) =>
% 128.89/16.99 ((
% 128.89/16.99 (lam2p) =>
% 128.89/16.99 ((
% 128.89/16.99 (brelnall1) =>
% 128.89/16.99 ((
% 128.89/16.99 (brelnall2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ex1E2) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp3) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcextLem) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcGraphProp4) =>
% 128.89/16.99 ((
% 128.89/16.99 (subbreln) =>
% 128.89/16.99 ((
% 128.89/16.99 (eqbreln) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcext) =>
% 128.89/16.99 ((
% 128.89/16.99 (funcext2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2apEq1) =>
% 128.89/16.99 ((
% 128.89/16.99 (ap2apEq2) =>
% 128.89/16.99 ((
% 128.89/16.99 (beta1) =>
% 128.89/16.99 ((
% 128.89/16.99 (eta1) =>
% 128.89/16.99 ((
% 128.89/16.99 (lam2lamEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (beta2) =>
% 128.89/16.99 ((
% 128.89/16.99 (eta2) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalseProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalseProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueProp1) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueProp2) =>
% 128.89/16.99 ((
% 128.89/16.99 (ifSingleton) =>
% 128.89/16.99 ((
% 128.89/16.99 (ifp) =>
% 128.89/16.99 ((
% 128.89/16.99 (theeq) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrue) =>
% 128.89/16.99 ((
% 128.89/16.99 (iffalse) =>
% 128.89/16.99 ((
% 128.89/16.99 (iftrueorfalse) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (setminusT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementT_lem) =>
% 128.89/16.99 ((
% 128.89/16.99 (setextT) =>
% 128.89/16.99 ((
% 128.89/16.99 (subsetTI) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetTI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (powersetTE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectTELcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (binintersectTERcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT1) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT2) =>
% 128.89/16.99 ((
% 128.89/16.99 (contrasubsetT3) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementI1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementE1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementSub1) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementSub2) =>
% 128.89/16.99 ((
% 128.89/16.99 (doubleComplementEq) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTnotintersectT) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementImpComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementSubsetComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementInPowersetComplementIntersect) =>
% 128.89/16.99 ((
% 128.89/16.99 (contraSubsetComplement) =>
% 128.89/16.99 ((
% 128.89/16.99 (complementTcontraSubset) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTILcontra) =>
% 128.89/16.99 ((
% 128.89/16.99 (binunionTIRcontra) =>
% 128.89/16.99 ((
% 128.89/17.00 (inIntersectImpInUnion) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInUnion2) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInIntersectUnions) =>
% 128.89/17.00 ((
% 128.89/17.00 (intersectInPowersetIntersectUnions) =>
% 128.89/17.00 ((
% 128.89/17.00 (inComplementUnionImpNotIn1) =>
% 128.89/17.00 ((
% 128.89/17.00 (inComplementUnionImpInComplement1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTE) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTEcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementUnionInPowersetComplement) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a2) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1a) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1b) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2b2) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2b) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule0) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule1) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule3) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule4) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_1) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_3) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_4) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_5) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1all2) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1SetBreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (choice2fnsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (setOfPairsIsBReln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1all1) =>
% 128.89/17.00 ((
% 128.89/17.00 (subbreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (eqbreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invI) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invE) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compI) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compE) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compEex) =>
% 128.89/17.00 ((
% 128.89/17.00 (!!) @ (
% 128.89/17.00 (('#B') @ (
% 128.89/17.00 !!) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#S') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#S') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 =>))) @
% 128.89/17.00 breln1)))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 !!))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#S') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#S') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 =>))) @
% 128.89/17.00 breln1)))))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#C') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 breln1)))) @
% 128.89/17.00 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/17.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
% 128.89/17.00 thf(zip_derived_cl595, plain,
% 128.89/17.00 (~ (((notdallE) =>
% 128.89/17.00 (((exuI1) =>
% 128.89/17.00 (((exuI3) =>
% 128.89/17.00 (((exuI2) =>
% 128.89/17.00 (((inCongP) =>
% 128.89/17.00 (((in__Cong) =>
% 128.89/17.00 (((exuE3u) =>
% 128.89/17.00 (((exu__Cong) =>
% 128.89/17.00 (((setadjoin__Cong) =>
% 128.89/17.00 (((powerset__Cong) =>
% 128.89/17.00 (((setunion__Cong) =>
% 128.89/17.00 (((exuEu) =>
% 128.89/17.00 (((descr__Cong) =>
% 128.89/17.00 (((dsetconstr__Cong) =>
% 128.89/17.00 (((subsetI1) =>
% 128.89/17.00 (((eqimpsubset2) =>
% 128.89/17.00 (((eqimpsubset1) =>
% 128.89/17.00 (((subsetI2) =>
% 128.89/17.00 (((emptysetsubset) =>
% 128.89/17.00 (((subsetE) =>
% 128.89/17.00 (((subsetE2) =>
% 128.89/17.00 (((notsubsetI) =>
% 128.89/17.00 (((notequalI1) =>
% 128.89/17.00 (((notequalI2) =>
% 128.89/17.00 (((subsetRefl) =>
% 128.89/17.00 (((subsetTrans) =>
% 128.89/17.00 (((setadjoinSub) =>
% 128.89/17.00 (((setadjoinSub2) =>
% 128.89/17.00 (((subset2powerset) =>
% 128.89/17.00 (((setextsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (subsetemptysetimpeq) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (inPowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetsubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (sepInPowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (sepSubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionIL) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairset2IR) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionIR) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionEcases) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionE) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionRsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectI) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset5) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset2) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset3) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectER) =>
% 128.89/17.00 ((
% 128.89/17.00 (disjointsetsI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectRsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset4) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset1) =>
% 128.89/17.00 ((
% 128.89/17.00 (bs114d) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusI) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusER) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusSubset2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusERneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusELneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusILneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusIRneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusSubset1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffE) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffI2) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffIneg1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffIneg2) =>
% 128.89/17.00 ((
% 128.89/17.00 (secondinupair) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairIL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairIR) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairiskpair) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairp) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonsubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletoninpowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletoninpowunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairset2E) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairsubunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairinpowunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem3) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairin) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempair1) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempair) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionE2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton1) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1E1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1I) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1I2) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonsuniq) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL1) =>
% 128.89/17.00 ((
% 128.89/17.00 (kfstsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (theprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (kfstpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodfstin) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR11) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR12) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR1) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairequniteq) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR) =>
% 128.89/17.00 ((
% 128.89/17.00 (ksndsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (ksndpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairsurjEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodsndin) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairmemEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairmemER) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempaircEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodfstpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodsndpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairsurjEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrI) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrSub) =>
% 128.89/17.00 ((
% 128.89/17.00 (setOfPairsIsBReln) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrERa) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrEL1) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrEL2) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrER) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcImageSingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (apProp) =>
% 128.89/17.00 ((
% 128.89/17.00 (app) =>
% 128.89/17.00 ((
% 128.89/17.00 (infuncsetfunc) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2p) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcinfuncset) =>
% 128.89/17.00 ((
% 128.89/17.00 (lamProp) =>
% 128.89/17.00 ((
% 128.89/17.00 (lamp) =>
% 128.89/17.00 ((
% 128.89/17.00 (lam2p) =>
% 128.89/17.00 ((
% 128.89/17.00 (brelnall1) =>
% 128.89/17.00 ((
% 128.89/17.00 (brelnall2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1E2) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp3) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcextLem) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp4) =>
% 128.89/17.00 ((
% 128.89/17.00 (subbreln) =>
% 128.89/17.00 ((
% 128.89/17.00 (eqbreln) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcext) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcext2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2apEq1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2apEq2) =>
% 128.89/17.00 ((
% 128.89/17.00 (beta1) =>
% 128.89/17.00 ((
% 128.89/17.00 (eta1) =>
% 128.89/17.00 ((
% 128.89/17.00 (lam2lamEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (beta2) =>
% 128.89/17.00 ((
% 128.89/17.00 (eta2) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalseProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalseProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ifSingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (ifp) =>
% 128.89/17.00 ((
% 128.89/17.00 (theeq) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrue) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalse) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueorfalse) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (setextT) =>
% 128.89/17.00 ((
% 128.89/17.00 (subsetTI) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetTI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetTE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectTELcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectTERcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT1) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT2) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT3) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementSub1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementSub2) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTnotintersectT) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementImpComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementSubsetComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementInPowersetComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (contraSubsetComplement) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTcontraSubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTILcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTIRcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInUnion) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInUnion2) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInIntersectUnions) =>
% 128.89/17.00 ((
% 128.89/17.00 (intersectInPowersetIntersectUnions) =>
% 128.89/17.00 ((
% 128.89/17.00 (inComplementUnionImpNotIn1) =>
% 128.89/17.00 ((
% 128.89/17.00 (inComplementUnionImpInComplement1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTE) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTEcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementUnionInPowersetComplement) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a2) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1a) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1b) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2b2) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2b) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule0) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule1) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule3) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule4) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_1) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_3) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_4) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_5) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1all2) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1SetBreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (choice2fnsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (setOfPairsIsBReln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1all1) =>
% 128.89/17.00 ((
% 128.89/17.00 (subbreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (eqbreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invI) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invE) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compI) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compE) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compEex) =>
% 128.89/17.00 ((
% 128.89/17.00 (!!) @ (
% 128.89/17.00 (('#B') @ (
% 128.89/17.00 !!) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#S') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#S') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 =>))) @
% 128.89/17.00 breln1)))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 !!))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#S') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#S') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 =>))) @
% 128.89/17.00 breln1)))))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#C') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 breln1)))) @
% 128.89/17.00 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/17.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl586])).
% 128.89/17.00 thf(zip_derived_cl606, plain,
% 128.89/17.00 (~ (((exuI1) =>
% 128.89/17.00 (((exuI3) =>
% 128.89/17.00 (((exuI2) =>
% 128.89/17.00 (((inCongP) =>
% 128.89/17.00 (((in__Cong) =>
% 128.89/17.00 (((exuE3u) =>
% 128.89/17.00 (((exu__Cong) =>
% 128.89/17.00 (((setadjoin__Cong) =>
% 128.89/17.00 (((powerset__Cong) =>
% 128.89/17.00 (((setunion__Cong) =>
% 128.89/17.00 (((exuEu) =>
% 128.89/17.00 (((descr__Cong) =>
% 128.89/17.00 (((dsetconstr__Cong) =>
% 128.89/17.00 (((subsetI1) =>
% 128.89/17.00 (((eqimpsubset2) =>
% 128.89/17.00 (((eqimpsubset1) =>
% 128.89/17.00 (((subsetI2) =>
% 128.89/17.00 (((emptysetsubset) =>
% 128.89/17.00 (((subsetE) =>
% 128.89/17.00 (((subsetE2) =>
% 128.89/17.00 (((notsubsetI) =>
% 128.89/17.00 (((notequalI1) =>
% 128.89/17.00 (((notequalI2) =>
% 128.89/17.00 (((subsetRefl) =>
% 128.89/17.00 (((subsetTrans) =>
% 128.89/17.00 (((setadjoinSub) =>
% 128.89/17.00 (((setadjoinSub2) =>
% 128.89/17.00 (((subset2powerset) =>
% 128.89/17.00 (((setextsub) =>
% 128.89/17.00 (((subsetemptysetimpeq) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (inPowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetsubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (sepInPowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (sepSubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionIL) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairset2IR) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionIR) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionEcases) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionE) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionRsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectI) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset5) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset2) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset3) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectER) =>
% 128.89/17.00 ((
% 128.89/17.00 (disjointsetsI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectRsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset4) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset1) =>
% 128.89/17.00 ((
% 128.89/17.00 (bs114d) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusI) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusER) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusSubset2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusERneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusELneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusILneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusIRneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusSubset1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffE) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffI2) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffIneg1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffIneg2) =>
% 128.89/17.00 ((
% 128.89/17.00 (secondinupair) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairIL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairIR) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairiskpair) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairp) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonsubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletoninpowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletoninpowunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairset2E) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairsubunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairinpowunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem3) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairin) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempair1) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempair) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionE2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton1) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1E1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1I) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1I2) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonsuniq) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL1) =>
% 128.89/17.00 ((
% 128.89/17.00 (kfstsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (theprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (kfstpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodfstin) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR11) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR12) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR1) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairequniteq) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR) =>
% 128.89/17.00 ((
% 128.89/17.00 (ksndsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (ksndpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairsurjEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodsndin) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairmemEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairmemER) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempaircEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodfstpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodsndpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairsurjEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrI) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrSub) =>
% 128.89/17.00 ((
% 128.89/17.00 (setOfPairsIsBReln) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrERa) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrEL1) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrEL2) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrER) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcImageSingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (apProp) =>
% 128.89/17.00 ((
% 128.89/17.00 (app) =>
% 128.89/17.00 ((
% 128.89/17.00 (infuncsetfunc) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2p) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcinfuncset) =>
% 128.89/17.00 ((
% 128.89/17.00 (lamProp) =>
% 128.89/17.00 ((
% 128.89/17.00 (lamp) =>
% 128.89/17.00 ((
% 128.89/17.00 (lam2p) =>
% 128.89/17.00 ((
% 128.89/17.00 (brelnall1) =>
% 128.89/17.00 ((
% 128.89/17.00 (brelnall2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1E2) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp3) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcextLem) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp4) =>
% 128.89/17.00 ((
% 128.89/17.00 (subbreln) =>
% 128.89/17.00 ((
% 128.89/17.00 (eqbreln) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcext) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcext2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2apEq1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2apEq2) =>
% 128.89/17.00 ((
% 128.89/17.00 (beta1) =>
% 128.89/17.00 ((
% 128.89/17.00 (eta1) =>
% 128.89/17.00 ((
% 128.89/17.00 (lam2lamEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (beta2) =>
% 128.89/17.00 ((
% 128.89/17.00 (eta2) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalseProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalseProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ifSingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (ifp) =>
% 128.89/17.00 ((
% 128.89/17.00 (theeq) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrue) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalse) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueorfalse) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (setextT) =>
% 128.89/17.00 ((
% 128.89/17.00 (subsetTI) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetTI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetTE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectTELcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectTERcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT1) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT2) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT3) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementSub1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementSub2) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTnotintersectT) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementImpComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementSubsetComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementInPowersetComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (contraSubsetComplement) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTcontraSubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTILcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTIRcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInUnion) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInUnion2) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInIntersectUnions) =>
% 128.89/17.00 ((
% 128.89/17.00 (intersectInPowersetIntersectUnions) =>
% 128.89/17.00 ((
% 128.89/17.00 (inComplementUnionImpNotIn1) =>
% 128.89/17.00 ((
% 128.89/17.00 (inComplementUnionImpInComplement1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTE) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTEcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementUnionInPowersetComplement) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a2) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1a) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1b) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2b2) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2b) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule0) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule1) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule3) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule4) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_1) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_3) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_4) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_5) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1all2) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1SetBreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (choice2fnsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (setOfPairsIsBReln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1all1) =>
% 128.89/17.00 ((
% 128.89/17.00 (subbreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (eqbreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invI) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invE) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compI) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compE) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compEex) =>
% 128.89/17.00 ((
% 128.89/17.00 (!!) @ (
% 128.89/17.00 (('#B') @ (
% 128.89/17.00 !!) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#S') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#S') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 =>))) @
% 128.89/17.00 breln1)))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 !!))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#S') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#S') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 =>))) @
% 128.89/17.00 breln1)))))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#C') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 breln1)))) @
% 128.89/17.00 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/17.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl595])).
% 128.89/17.00 thf(zip_derived_cl619, plain,
% 128.89/17.00 (~ (((exuI3) =>
% 128.89/17.00 (((exuI2) =>
% 128.89/17.00 (((inCongP) =>
% 128.89/17.00 (((in__Cong) =>
% 128.89/17.00 (((exuE3u) =>
% 128.89/17.00 (((exu__Cong) =>
% 128.89/17.00 (((setadjoin__Cong) =>
% 128.89/17.00 (((powerset__Cong) =>
% 128.89/17.00 (((setunion__Cong) =>
% 128.89/17.00 (((exuEu) =>
% 128.89/17.00 (((descr__Cong) =>
% 128.89/17.00 (((dsetconstr__Cong) =>
% 128.89/17.00 (((subsetI1) =>
% 128.89/17.00 (((eqimpsubset2) =>
% 128.89/17.00 (((eqimpsubset1) =>
% 128.89/17.00 (((subsetI2) =>
% 128.89/17.00 (((emptysetsubset) =>
% 128.89/17.00 (((subsetE) =>
% 128.89/17.00 (((subsetE2) =>
% 128.89/17.00 (((notsubsetI) =>
% 128.89/17.00 (((notequalI1) =>
% 128.89/17.00 (((notequalI2) =>
% 128.89/17.00 (((subsetRefl) =>
% 128.89/17.00 (((subsetTrans) =>
% 128.89/17.00 (((setadjoinSub) =>
% 128.89/17.00 (((setadjoinSub2) =>
% 128.89/17.00 (((subset2powerset) =>
% 128.89/17.00 (((setextsub) =>
% 128.89/17.00 (((subsetemptysetimpeq) =>
% 128.89/17.00 (((powersetI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (inPowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetsubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (sepInPowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (sepSubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionIL) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairset2IR) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionIR) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionEcases) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionE) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionRsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectI) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset5) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset2) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset3) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectER) =>
% 128.89/17.00 ((
% 128.89/17.00 (disjointsetsI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectRsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset4) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset1) =>
% 128.89/17.00 ((
% 128.89/17.00 (bs114d) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusI) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusER) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusSubset2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusERneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusELneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusILneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusIRneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusSubset1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffE) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffI2) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffIneg1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffIneg2) =>
% 128.89/17.00 ((
% 128.89/17.00 (secondinupair) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairIL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairIR) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairiskpair) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairp) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonsubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletoninpowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletoninpowunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairset2E) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairsubunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairinpowunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem3) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairin) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempair1) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempair) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionE2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton1) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1E1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1I) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1I2) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonsuniq) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL1) =>
% 128.89/17.00 ((
% 128.89/17.00 (kfstsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (theprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (kfstpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodfstin) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR11) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR12) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR1) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairequniteq) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR) =>
% 128.89/17.00 ((
% 128.89/17.00 (ksndsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (ksndpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairsurjEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodsndin) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairmemEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairmemER) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempaircEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodfstpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodsndpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairsurjEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrI) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrSub) =>
% 128.89/17.00 ((
% 128.89/17.00 (setOfPairsIsBReln) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrERa) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrEL1) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrEL2) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrER) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcImageSingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (apProp) =>
% 128.89/17.00 ((
% 128.89/17.00 (app) =>
% 128.89/17.00 ((
% 128.89/17.00 (infuncsetfunc) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2p) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcinfuncset) =>
% 128.89/17.00 ((
% 128.89/17.00 (lamProp) =>
% 128.89/17.00 ((
% 128.89/17.00 (lamp) =>
% 128.89/17.00 ((
% 128.89/17.00 (lam2p) =>
% 128.89/17.00 ((
% 128.89/17.00 (brelnall1) =>
% 128.89/17.00 ((
% 128.89/17.00 (brelnall2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1E2) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp3) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcextLem) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp4) =>
% 128.89/17.00 ((
% 128.89/17.00 (subbreln) =>
% 128.89/17.00 ((
% 128.89/17.00 (eqbreln) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcext) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcext2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2apEq1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2apEq2) =>
% 128.89/17.00 ((
% 128.89/17.00 (beta1) =>
% 128.89/17.00 ((
% 128.89/17.00 (eta1) =>
% 128.89/17.00 ((
% 128.89/17.00 (lam2lamEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (beta2) =>
% 128.89/17.00 ((
% 128.89/17.00 (eta2) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalseProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalseProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ifSingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (ifp) =>
% 128.89/17.00 ((
% 128.89/17.00 (theeq) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrue) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalse) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueorfalse) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (setextT) =>
% 128.89/17.00 ((
% 128.89/17.00 (subsetTI) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetTI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetTE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectTELcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectTERcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT1) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT2) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT3) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementSub1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementSub2) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTnotintersectT) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementImpComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementSubsetComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementInPowersetComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (contraSubsetComplement) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTcontraSubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTILcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTIRcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInUnion) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInUnion2) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInIntersectUnions) =>
% 128.89/17.00 ((
% 128.89/17.00 (intersectInPowersetIntersectUnions) =>
% 128.89/17.00 ((
% 128.89/17.00 (inComplementUnionImpNotIn1) =>
% 128.89/17.00 ((
% 128.89/17.00 (inComplementUnionImpInComplement1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTE) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTEcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementUnionInPowersetComplement) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a2) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1a) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1b) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2b2) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2b) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule0) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule1) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule3) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule4) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_1) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_3) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_4) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_5) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1all2) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1SetBreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (choice2fnsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (setOfPairsIsBReln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1all1) =>
% 128.89/17.00 ((
% 128.89/17.00 (subbreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (eqbreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invI) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invE) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compI) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compE) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compEex) =>
% 128.89/17.00 ((
% 128.89/17.00 (!!) @ (
% 128.89/17.00 (('#B') @ (
% 128.89/17.00 !!) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#S') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#S') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 =>))) @
% 128.89/17.00 breln1)))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 !!))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#S') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#S') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 =>))) @
% 128.89/17.00 breln1)))))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#C') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 breln1)))) @
% 128.89/17.00 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/17.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl606])).
% 128.89/17.00 thf(zip_derived_cl630, plain,
% 128.89/17.00 (~ (((exuI2) =>
% 128.89/17.00 (((inCongP) =>
% 128.89/17.00 (((in__Cong) =>
% 128.89/17.00 (((exuE3u) =>
% 128.89/17.00 (((exu__Cong) =>
% 128.89/17.00 (((setadjoin__Cong) =>
% 128.89/17.00 (((powerset__Cong) =>
% 128.89/17.00 (((setunion__Cong) =>
% 128.89/17.00 (((exuEu) =>
% 128.89/17.00 (((descr__Cong) =>
% 128.89/17.00 (((dsetconstr__Cong) =>
% 128.89/17.00 (((subsetI1) =>
% 128.89/17.00 (((eqimpsubset2) =>
% 128.89/17.00 (((eqimpsubset1) =>
% 128.89/17.00 (((subsetI2) =>
% 128.89/17.00 (((emptysetsubset) =>
% 128.89/17.00 (((subsetE) =>
% 128.89/17.00 (((subsetE2) =>
% 128.89/17.00 (((notsubsetI) =>
% 128.89/17.00 (((notequalI1) =>
% 128.89/17.00 (((notequalI2) =>
% 128.89/17.00 (((subsetRefl) =>
% 128.89/17.00 (((subsetTrans) =>
% 128.89/17.00 (((setadjoinSub) =>
% 128.89/17.00 (((setadjoinSub2) =>
% 128.89/17.00 (((subset2powerset) =>
% 128.89/17.00 (((setextsub) =>
% 128.89/17.00 (((subsetemptysetimpeq) =>
% 128.89/17.00 (((powersetI1) =>
% 128.89/17.00 (((powersetE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (inPowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetsubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (sepInPowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (sepSubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionIL) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairset2IR) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionIR) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionEcases) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionE) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionRsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectI) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset5) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset2) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset3) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectER) =>
% 128.89/17.00 ((
% 128.89/17.00 (disjointsetsI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectRsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset4) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset1) =>
% 128.89/17.00 ((
% 128.89/17.00 (bs114d) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusI) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusER) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusSubset2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusERneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusELneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusILneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusIRneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusSubset1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffE) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffI2) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffIneg1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffIneg2) =>
% 128.89/17.00 ((
% 128.89/17.00 (secondinupair) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairIL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairIR) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairiskpair) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairp) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonsubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletoninpowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletoninpowunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairset2E) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairsubunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairinpowunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem3) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairin) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempair1) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempair) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionE2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton1) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1E1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1I) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1I2) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonsuniq) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL1) =>
% 128.89/17.00 ((
% 128.89/17.00 (kfstsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (theprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (kfstpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodfstin) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR11) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR12) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR1) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairequniteq) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR) =>
% 128.89/17.00 ((
% 128.89/17.00 (ksndsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (ksndpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairsurjEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodsndin) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairmemEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairmemER) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempaircEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodfstpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodsndpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairsurjEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrI) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrSub) =>
% 128.89/17.00 ((
% 128.89/17.00 (setOfPairsIsBReln) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrERa) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrEL1) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrEL2) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrER) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcImageSingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (apProp) =>
% 128.89/17.00 ((
% 128.89/17.00 (app) =>
% 128.89/17.00 ((
% 128.89/17.00 (infuncsetfunc) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2p) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcinfuncset) =>
% 128.89/17.00 ((
% 128.89/17.00 (lamProp) =>
% 128.89/17.00 ((
% 128.89/17.00 (lamp) =>
% 128.89/17.00 ((
% 128.89/17.00 (lam2p) =>
% 128.89/17.00 ((
% 128.89/17.00 (brelnall1) =>
% 128.89/17.00 ((
% 128.89/17.00 (brelnall2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1E2) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp3) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcextLem) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp4) =>
% 128.89/17.00 ((
% 128.89/17.00 (subbreln) =>
% 128.89/17.00 ((
% 128.89/17.00 (eqbreln) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcext) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcext2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2apEq1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2apEq2) =>
% 128.89/17.00 ((
% 128.89/17.00 (beta1) =>
% 128.89/17.00 ((
% 128.89/17.00 (eta1) =>
% 128.89/17.00 ((
% 128.89/17.00 (lam2lamEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (beta2) =>
% 128.89/17.00 ((
% 128.89/17.00 (eta2) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalseProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalseProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ifSingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (ifp) =>
% 128.89/17.00 ((
% 128.89/17.00 (theeq) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrue) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalse) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueorfalse) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (setextT) =>
% 128.89/17.00 ((
% 128.89/17.00 (subsetTI) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetTI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetTE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectTELcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectTERcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT1) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT2) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT3) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementSub1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementSub2) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTnotintersectT) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementImpComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementSubsetComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementInPowersetComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (contraSubsetComplement) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTcontraSubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTILcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTIRcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInUnion) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInUnion2) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInIntersectUnions) =>
% 128.89/17.00 ((
% 128.89/17.00 (intersectInPowersetIntersectUnions) =>
% 128.89/17.00 ((
% 128.89/17.00 (inComplementUnionImpNotIn1) =>
% 128.89/17.00 ((
% 128.89/17.00 (inComplementUnionImpInComplement1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTE) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTEcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementUnionInPowersetComplement) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a2) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1a) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1b) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2b2) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2b) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule0) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule1) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule3) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule4) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_1) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_3) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_4) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_5) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1all2) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1SetBreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (choice2fnsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (setOfPairsIsBReln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1all1) =>
% 128.89/17.00 ((
% 128.89/17.00 (subbreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (eqbreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invI) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invE) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compI) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compE) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compEex) =>
% 128.89/17.00 ((
% 128.89/17.00 (!!) @ (
% 128.89/17.00 (('#B') @ (
% 128.89/17.00 !!) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#S') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#S') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 =>))) @
% 128.89/17.00 breln1)))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 !!))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#S') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#S') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 =>))) @
% 128.89/17.00 breln1)))))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#C') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 breln1)))) @
% 128.89/17.00 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/17.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl619])).
% 128.89/17.00 thf(zip_derived_cl640, plain,
% 128.89/17.00 (~ (((inCongP) =>
% 128.89/17.00 (((in__Cong) =>
% 128.89/17.00 (((exuE3u) =>
% 128.89/17.00 (((exu__Cong) =>
% 128.89/17.00 (((setadjoin__Cong) =>
% 128.89/17.00 (((powerset__Cong) =>
% 128.89/17.00 (((setunion__Cong) =>
% 128.89/17.00 (((exuEu) =>
% 128.89/17.00 (((descr__Cong) =>
% 128.89/17.00 (((dsetconstr__Cong) =>
% 128.89/17.00 (((subsetI1) =>
% 128.89/17.00 (((eqimpsubset2) =>
% 128.89/17.00 (((eqimpsubset1) =>
% 128.89/17.00 (((subsetI2) =>
% 128.89/17.00 (((emptysetsubset) =>
% 128.89/17.00 (((subsetE) =>
% 128.89/17.00 (((subsetE2) =>
% 128.89/17.00 (((notsubsetI) =>
% 128.89/17.00 (((notequalI1) =>
% 128.89/17.00 (((notequalI2) =>
% 128.89/17.00 (((subsetRefl) =>
% 128.89/17.00 (((subsetTrans) =>
% 128.89/17.00 (((setadjoinSub) =>
% 128.89/17.00 (((setadjoinSub2) =>
% 128.89/17.00 (((subset2powerset) =>
% 128.89/17.00 (((setextsub) =>
% 128.89/17.00 (((subsetemptysetimpeq) =>
% 128.89/17.00 (((powersetI1) =>
% 128.89/17.00 (((powersetE1) =>
% 128.89/17.00 (((inPowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetsubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (sepInPowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (sepSubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionIL) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairset2IR) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionIR) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionEcases) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionE) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionRsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectI) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset5) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset2) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset3) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectER) =>
% 128.89/17.00 ((
% 128.89/17.00 (disjointsetsI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectRsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset4) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset1) =>
% 128.89/17.00 ((
% 128.89/17.00 (bs114d) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusI) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusER) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusSubset2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusERneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusELneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusILneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusIRneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusSubset1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffE) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffI2) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffIneg1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffIneg2) =>
% 128.89/17.00 ((
% 128.89/17.00 (secondinupair) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairIL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairIR) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairiskpair) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairp) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonsubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletoninpowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletoninpowunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairset2E) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairsubunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairinpowunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem3) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairin) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempair1) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempair) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionE2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton1) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1E1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1I) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1I2) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonsuniq) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL1) =>
% 128.89/17.00 ((
% 128.89/17.00 (kfstsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (theprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (kfstpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodfstin) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR11) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR12) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR1) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairequniteq) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR) =>
% 128.89/17.00 ((
% 128.89/17.00 (ksndsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (ksndpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairsurjEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodsndin) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairmemEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairmemER) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempaircEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodfstpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodsndpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairsurjEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrI) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrSub) =>
% 128.89/17.00 ((
% 128.89/17.00 (setOfPairsIsBReln) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrERa) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrEL1) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrEL2) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrER) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcImageSingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (apProp) =>
% 128.89/17.00 ((
% 128.89/17.00 (app) =>
% 128.89/17.00 ((
% 128.89/17.00 (infuncsetfunc) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2p) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcinfuncset) =>
% 128.89/17.00 ((
% 128.89/17.00 (lamProp) =>
% 128.89/17.00 ((
% 128.89/17.00 (lamp) =>
% 128.89/17.00 ((
% 128.89/17.00 (lam2p) =>
% 128.89/17.00 ((
% 128.89/17.00 (brelnall1) =>
% 128.89/17.00 ((
% 128.89/17.00 (brelnall2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1E2) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp3) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcextLem) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp4) =>
% 128.89/17.00 ((
% 128.89/17.00 (subbreln) =>
% 128.89/17.00 ((
% 128.89/17.00 (eqbreln) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcext) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcext2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2apEq1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2apEq2) =>
% 128.89/17.00 ((
% 128.89/17.00 (beta1) =>
% 128.89/17.00 ((
% 128.89/17.00 (eta1) =>
% 128.89/17.00 ((
% 128.89/17.00 (lam2lamEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (beta2) =>
% 128.89/17.00 ((
% 128.89/17.00 (eta2) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalseProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalseProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ifSingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (ifp) =>
% 128.89/17.00 ((
% 128.89/17.00 (theeq) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrue) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalse) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueorfalse) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (setextT) =>
% 128.89/17.00 ((
% 128.89/17.00 (subsetTI) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetTI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetTE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectTELcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectTERcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT1) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT2) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT3) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementSub1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementSub2) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTnotintersectT) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementImpComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementSubsetComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementInPowersetComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (contraSubsetComplement) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTcontraSubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTILcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTIRcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInUnion) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInUnion2) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInIntersectUnions) =>
% 128.89/17.00 ((
% 128.89/17.00 (intersectInPowersetIntersectUnions) =>
% 128.89/17.00 ((
% 128.89/17.00 (inComplementUnionImpNotIn1) =>
% 128.89/17.00 ((
% 128.89/17.00 (inComplementUnionImpInComplement1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTE) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTEcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementUnionInPowersetComplement) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a2) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1a) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1b) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2b2) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2b) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule0) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule1) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule3) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule4) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_1) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_3) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_4) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_5) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1all2) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1SetBreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (choice2fnsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (setOfPairsIsBReln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1all1) =>
% 128.89/17.00 ((
% 128.89/17.00 (subbreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (eqbreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invI) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invE) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compI) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compE) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compEex) =>
% 128.89/17.00 ((
% 128.89/17.00 (!!) @ (
% 128.89/17.00 (('#B') @ (
% 128.89/17.00 !!) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#S') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#S') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 =>))) @
% 128.89/17.00 breln1)))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 !!))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#S') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#S') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 =>))) @
% 128.89/17.00 breln1)))))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#C') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 breln1)))) @
% 128.89/17.00 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/17.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl630])).
% 128.89/17.00 thf(zip_derived_cl650, plain,
% 128.89/17.00 (~ (((in__Cong) =>
% 128.89/17.00 (((exuE3u) =>
% 128.89/17.00 (((exu__Cong) =>
% 128.89/17.00 (((setadjoin__Cong) =>
% 128.89/17.00 (((powerset__Cong) =>
% 128.89/17.00 (((setunion__Cong) =>
% 128.89/17.00 (((exuEu) =>
% 128.89/17.00 (((descr__Cong) =>
% 128.89/17.00 (((dsetconstr__Cong) =>
% 128.89/17.00 (((subsetI1) =>
% 128.89/17.00 (((eqimpsubset2) =>
% 128.89/17.00 (((eqimpsubset1) =>
% 128.89/17.00 (((subsetI2) =>
% 128.89/17.00 (((emptysetsubset) =>
% 128.89/17.00 (((subsetE) =>
% 128.89/17.00 (((subsetE2) =>
% 128.89/17.00 (((notsubsetI) =>
% 128.89/17.00 (((notequalI1) =>
% 128.89/17.00 (((notequalI2) =>
% 128.89/17.00 (((subsetRefl) =>
% 128.89/17.00 (((subsetTrans) =>
% 128.89/17.00 (((setadjoinSub) =>
% 128.89/17.00 (((setadjoinSub2) =>
% 128.89/17.00 (((subset2powerset) =>
% 128.89/17.00 (((setextsub) =>
% 128.89/17.00 (((subsetemptysetimpeq) =>
% 128.89/17.00 (((powersetI1) =>
% 128.89/17.00 (((powersetE1) =>
% 128.89/17.00 (((inPowerset) =>
% 128.89/17.00 (((powersetsubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (sepInPowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (sepSubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionIL) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairset2IR) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionIR) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionEcases) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionE) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionRsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectI) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset5) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset2) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset3) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectER) =>
% 128.89/17.00 ((
% 128.89/17.00 (disjointsetsI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectRsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset4) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset1) =>
% 128.89/17.00 ((
% 128.89/17.00 (bs114d) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusI) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusER) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusSubset2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusERneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusELneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusILneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusIRneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusSubset1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffE) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffI2) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffIneg1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffIneg2) =>
% 128.89/17.00 ((
% 128.89/17.00 (secondinupair) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairIL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairIR) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairiskpair) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairp) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonsubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletoninpowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletoninpowunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairset2E) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairsubunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairinpowunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem3) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairin) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempair1) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempair) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionE2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton1) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1E1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1I) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1I2) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonsuniq) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL1) =>
% 128.89/17.00 ((
% 128.89/17.00 (kfstsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (theprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (kfstpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodfstin) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR11) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR12) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR1) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairequniteq) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR) =>
% 128.89/17.00 ((
% 128.89/17.00 (ksndsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (ksndpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairsurjEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodsndin) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairmemEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairmemER) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempaircEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodfstpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodsndpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairsurjEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrI) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrSub) =>
% 128.89/17.00 ((
% 128.89/17.00 (setOfPairsIsBReln) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrERa) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrEL1) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrEL2) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrER) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcImageSingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (apProp) =>
% 128.89/17.00 ((
% 128.89/17.00 (app) =>
% 128.89/17.00 ((
% 128.89/17.00 (infuncsetfunc) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2p) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcinfuncset) =>
% 128.89/17.00 ((
% 128.89/17.00 (lamProp) =>
% 128.89/17.00 ((
% 128.89/17.00 (lamp) =>
% 128.89/17.00 ((
% 128.89/17.00 (lam2p) =>
% 128.89/17.00 ((
% 128.89/17.00 (brelnall1) =>
% 128.89/17.00 ((
% 128.89/17.00 (brelnall2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1E2) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp3) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcextLem) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp4) =>
% 128.89/17.00 ((
% 128.89/17.00 (subbreln) =>
% 128.89/17.00 ((
% 128.89/17.00 (eqbreln) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcext) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcext2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2apEq1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2apEq2) =>
% 128.89/17.00 ((
% 128.89/17.00 (beta1) =>
% 128.89/17.00 ((
% 128.89/17.00 (eta1) =>
% 128.89/17.00 ((
% 128.89/17.00 (lam2lamEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (beta2) =>
% 128.89/17.00 ((
% 128.89/17.00 (eta2) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalseProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalseProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ifSingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (ifp) =>
% 128.89/17.00 ((
% 128.89/17.00 (theeq) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrue) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalse) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueorfalse) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (setextT) =>
% 128.89/17.00 ((
% 128.89/17.00 (subsetTI) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetTI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetTE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectTELcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectTERcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT1) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT2) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT3) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementSub1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementSub2) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTnotintersectT) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementImpComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementSubsetComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementInPowersetComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (contraSubsetComplement) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTcontraSubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTILcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTIRcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInUnion) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInUnion2) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInIntersectUnions) =>
% 128.89/17.00 ((
% 128.89/17.00 (intersectInPowersetIntersectUnions) =>
% 128.89/17.00 ((
% 128.89/17.00 (inComplementUnionImpNotIn1) =>
% 128.89/17.00 ((
% 128.89/17.00 (inComplementUnionImpInComplement1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTE) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTEcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementUnionInPowersetComplement) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a2) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1a) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1b) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2b2) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2b) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule0) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule1) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule3) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule4) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_1) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_3) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_4) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_5) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1all2) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1SetBreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (choice2fnsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (setOfPairsIsBReln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1all1) =>
% 128.89/17.00 ((
% 128.89/17.00 (subbreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (eqbreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invI) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invE) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compI) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compE) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compEex) =>
% 128.89/17.00 ((
% 128.89/17.00 (!!) @ (
% 128.89/17.00 (('#B') @ (
% 128.89/17.00 !!) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#S') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#S') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 =>))) @
% 128.89/17.00 breln1)))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 !!))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#S') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#S') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 =>))) @
% 128.89/17.00 breln1)))))) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#C') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#B') @
% 128.89/17.00 breln1)))) @
% 128.89/17.00 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/17.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl640])).
% 128.89/17.00 thf(zip_derived_cl660, plain,
% 128.89/17.00 (~ (((exuE3u) =>
% 128.89/17.00 (((exu__Cong) =>
% 128.89/17.00 (((setadjoin__Cong) =>
% 128.89/17.00 (((powerset__Cong) =>
% 128.89/17.00 (((setunion__Cong) =>
% 128.89/17.00 (((exuEu) =>
% 128.89/17.00 (((descr__Cong) =>
% 128.89/17.00 (((dsetconstr__Cong) =>
% 128.89/17.00 (((subsetI1) =>
% 128.89/17.00 (((eqimpsubset2) =>
% 128.89/17.00 (((eqimpsubset1) =>
% 128.89/17.00 (((subsetI2) =>
% 128.89/17.00 (((emptysetsubset) =>
% 128.89/17.00 (((subsetE) =>
% 128.89/17.00 (((subsetE2) =>
% 128.89/17.00 (((notsubsetI) =>
% 128.89/17.00 (((notequalI1) =>
% 128.89/17.00 (((notequalI2) =>
% 128.89/17.00 (((subsetRefl) =>
% 128.89/17.00 (((subsetTrans) =>
% 128.89/17.00 (((setadjoinSub) =>
% 128.89/17.00 (((setadjoinSub2) =>
% 128.89/17.00 (((subset2powerset) =>
% 128.89/17.00 (((setextsub) =>
% 128.89/17.00 (((subsetemptysetimpeq) =>
% 128.89/17.00 (((powersetI1) =>
% 128.89/17.00 (((powersetE1) =>
% 128.89/17.00 (((inPowerset) =>
% 128.89/17.00 (((powersetsubset) =>
% 128.89/17.00 (((sepInPowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (sepSubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionIL) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairset2IR) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionIR) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionEcases) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionE) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionRsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectI) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset5) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset2) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset3) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectER) =>
% 128.89/17.00 ((
% 128.89/17.00 (disjointsetsI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectRsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset4) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectSubset1) =>
% 128.89/17.00 ((
% 128.89/17.00 (bs114d) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusI) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusER) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusSubset2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusERneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusELneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusILneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusIRneg) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusLsub) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusSubset1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffE) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffI2) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffIneg1) =>
% 128.89/17.00 ((
% 128.89/17.00 (symdiffIneg2) =>
% 128.89/17.00 ((
% 128.89/17.00 (secondinupair) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairIL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairIR) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairiskpair) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairp) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonsubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletoninpowerset) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletoninpowunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairset2E) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairsubunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairinpowunion) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ubforcartprodlem3) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairin) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempair1) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempair) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionE2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton1) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setunionsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1E1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1I) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1I2) =>
% 128.89/17.00 ((
% 128.89/17.00 (singletonsuniq) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL1) =>
% 128.89/17.00 ((
% 128.89/17.00 (kfstsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (theprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (kfstpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodfstin) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjL) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR11) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR12) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR1) =>
% 128.89/17.00 ((
% 128.89/17.00 (upairequniteq) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR2) =>
% 128.89/17.00 ((
% 128.89/17.00 (setukpairinjR) =>
% 128.89/17.00 ((
% 128.89/17.00 (ksndsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (ksndpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (kpairsurjEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodsndin) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairmemEL) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairmemER) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodmempaircEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodfstpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodsndpairEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (cartprodpairsurjEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrI) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrSub) =>
% 128.89/17.00 ((
% 128.89/17.00 (setOfPairsIsBReln) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrERa) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrEL1) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrEL2) =>
% 128.89/17.00 ((
% 128.89/17.00 (dpsetconstrER) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcImageSingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (apProp) =>
% 128.89/17.00 ((
% 128.89/17.00 (app) =>
% 128.89/17.00 ((
% 128.89/17.00 (infuncsetfunc) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2p) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcinfuncset) =>
% 128.89/17.00 ((
% 128.89/17.00 (lamProp) =>
% 128.89/17.00 ((
% 128.89/17.00 (lamp) =>
% 128.89/17.00 ((
% 128.89/17.00 (lam2p) =>
% 128.89/17.00 ((
% 128.89/17.00 (brelnall1) =>
% 128.89/17.00 ((
% 128.89/17.00 (brelnall2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ex1E2) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp3) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcextLem) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcGraphProp4) =>
% 128.89/17.00 ((
% 128.89/17.00 (subbreln) =>
% 128.89/17.00 ((
% 128.89/17.00 (eqbreln) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcext) =>
% 128.89/17.00 ((
% 128.89/17.00 (funcext2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2apEq1) =>
% 128.89/17.00 ((
% 128.89/17.00 (ap2apEq2) =>
% 128.89/17.00 ((
% 128.89/17.00 (beta1) =>
% 128.89/17.00 ((
% 128.89/17.00 (eta1) =>
% 128.89/17.00 ((
% 128.89/17.00 (lam2lamEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (beta2) =>
% 128.89/17.00 ((
% 128.89/17.00 (eta2) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalseProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalseProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueProp1) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueProp2) =>
% 128.89/17.00 ((
% 128.89/17.00 (ifSingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (ifp) =>
% 128.89/17.00 ((
% 128.89/17.00 (theeq) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrue) =>
% 128.89/17.00 ((
% 128.89/17.00 (iffalse) =>
% 128.89/17.00 ((
% 128.89/17.00 (iftrueorfalse) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (setminusT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementT_lem) =>
% 128.89/17.00 ((
% 128.89/17.00 (setextT) =>
% 128.89/17.00 ((
% 128.89/17.00 (subsetTI) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetTI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (powersetTE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectTELcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (binintersectTERcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT1) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT2) =>
% 128.89/17.00 ((
% 128.89/17.00 (contrasubsetT3) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementI1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementE1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementSub1) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementSub2) =>
% 128.89/17.00 ((
% 128.89/17.00 (doubleComplementEq) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTnotintersectT) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementImpComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementSubsetComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementInPowersetComplementIntersect) =>
% 128.89/17.00 ((
% 128.89/17.00 (contraSubsetComplement) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementTcontraSubset) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTILcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTIRcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInUnion) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInUnion2) =>
% 128.89/17.00 ((
% 128.89/17.00 (inIntersectImpInIntersectUnions) =>
% 128.89/17.00 ((
% 128.89/17.00 (intersectInPowersetIntersectUnions) =>
% 128.89/17.00 ((
% 128.89/17.00 (inComplementUnionImpNotIn1) =>
% 128.89/17.00 ((
% 128.89/17.00 (inComplementUnionImpInComplement1) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTE) =>
% 128.89/17.00 ((
% 128.89/17.00 (binunionTEcontra) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a1) =>
% 128.89/17.00 ((
% 128.89/17.00 (complementUnionInPowersetComplement) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a2) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1a) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1b) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan1) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2a) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2b2) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2b) =>
% 128.89/17.00 ((
% 128.89/17.00 (demorgan2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule0) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule1) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule3) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz13rule4) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_1) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_2) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_3) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_4) =>
% 128.89/17.00 ((
% 128.89/17.00 (woz1_5) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1all2) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1SetBreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (choice2fnsingleton) =>
% 128.89/17.00 ((
% 128.89/17.00 (setOfPairsIsBReln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1all1) =>
% 128.89/17.00 ((
% 128.89/17.00 (subbreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (eqbreln1) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invI) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1invE) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compprop) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compI) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compE) =>
% 128.89/17.00 ((
% 128.89/17.00 (breln1compEex) =>
% 128.89/17.00 ((
% 128.89/17.00 (!!) @ (
% 128.89/17.00 (('#B') @ (
% 128.89/17.00 !!) @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#S') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 '#S') @
% 128.89/17.00 (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 (
% 128.89/17.00 ('#B') @ (
% 128.89/17.00 =>))) @
% 128.89/17.01 breln1)))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 !!))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#S') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#S') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 =>))) @
% 128.89/17.01 breln1)))))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#C') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 breln1)))) @
% 128.89/17.01 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/17.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl650])).
% 128.89/17.01 thf(zip_derived_cl672, plain,
% 128.89/17.01 (~ (((exu__Cong) =>
% 128.89/17.01 (((setadjoin__Cong) =>
% 128.89/17.01 (((powerset__Cong) =>
% 128.89/17.01 (((setunion__Cong) =>
% 128.89/17.01 (((exuEu) =>
% 128.89/17.01 (((descr__Cong) =>
% 128.89/17.01 (((dsetconstr__Cong) =>
% 128.89/17.01 (((subsetI1) =>
% 128.89/17.01 (((eqimpsubset2) =>
% 128.89/17.01 (((eqimpsubset1) =>
% 128.89/17.01 (((subsetI2) =>
% 128.89/17.01 (((emptysetsubset) =>
% 128.89/17.01 (((subsetE) =>
% 128.89/17.01 (((subsetE2) =>
% 128.89/17.01 (((notsubsetI) =>
% 128.89/17.01 (((notequalI1) =>
% 128.89/17.01 (((notequalI2) =>
% 128.89/17.01 (((subsetRefl) =>
% 128.89/17.01 (((subsetTrans) =>
% 128.89/17.01 (((setadjoinSub) =>
% 128.89/17.01 (((setadjoinSub2) =>
% 128.89/17.01 (((subset2powerset) =>
% 128.89/17.01 (((setextsub) =>
% 128.89/17.01 (((subsetemptysetimpeq) =>
% 128.89/17.01 (((powersetI1) =>
% 128.89/17.01 (((powersetE1) =>
% 128.89/17.01 (((inPowerset) =>
% 128.89/17.01 (((powersetsubset) =>
% 128.89/17.01 (((sepInPowerset) =>
% 128.89/17.01 (((sepSubset) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionIL) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairset2IR) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionIR) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionEcases) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionE) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionRsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectI) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset5) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset2) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset3) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectER) =>
% 128.89/17.01 ((
% 128.89/17.01 (disjointsetsI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectRsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset4) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset1) =>
% 128.89/17.01 ((
% 128.89/17.01 (bs114d) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusI) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusER) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusSubset2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusERneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusELneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusILneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusIRneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusSubset1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffE) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffI2) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffIneg1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffIneg2) =>
% 128.89/17.01 ((
% 128.89/17.01 (secondinupair) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairIL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairIR) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairiskpair) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairp) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonsubset) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletoninpowerset) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletoninpowunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairset2E) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairsubunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairinpowunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem3) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairin) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempair1) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempair) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionE2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton1) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1E1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1I) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1I2) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonsuniq) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL1) =>
% 128.89/17.01 ((
% 128.89/17.01 (kfstsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (theprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (kfstpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodfstin) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR11) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR12) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR1) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairequniteq) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR) =>
% 128.89/17.01 ((
% 128.89/17.01 (ksndsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (ksndpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairsurjEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodsndin) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairmemEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairmemER) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempaircEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodfstpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodsndpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairsurjEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrI) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrSub) =>
% 128.89/17.01 ((
% 128.89/17.01 (setOfPairsIsBReln) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrERa) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrEL1) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrEL2) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrER) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcImageSingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (apProp) =>
% 128.89/17.01 ((
% 128.89/17.01 (app) =>
% 128.89/17.01 ((
% 128.89/17.01 (infuncsetfunc) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2p) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcinfuncset) =>
% 128.89/17.01 ((
% 128.89/17.01 (lamProp) =>
% 128.89/17.01 ((
% 128.89/17.01 (lamp) =>
% 128.89/17.01 ((
% 128.89/17.01 (lam2p) =>
% 128.89/17.01 ((
% 128.89/17.01 (brelnall1) =>
% 128.89/17.01 ((
% 128.89/17.01 (brelnall2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1E2) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp3) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcextLem) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp4) =>
% 128.89/17.01 ((
% 128.89/17.01 (subbreln) =>
% 128.89/17.01 ((
% 128.89/17.01 (eqbreln) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcext) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcext2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2apEq1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2apEq2) =>
% 128.89/17.01 ((
% 128.89/17.01 (beta1) =>
% 128.89/17.01 ((
% 128.89/17.01 (eta1) =>
% 128.89/17.01 ((
% 128.89/17.01 (lam2lamEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (beta2) =>
% 128.89/17.01 ((
% 128.89/17.01 (eta2) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalseProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalseProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ifSingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (ifp) =>
% 128.89/17.01 ((
% 128.89/17.01 (theeq) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrue) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalse) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueorfalse) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (setextT) =>
% 128.89/17.01 ((
% 128.89/17.01 (subsetTI) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetTI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetTE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectTELcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectTERcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT1) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT2) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT3) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementSub1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementSub2) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTnotintersectT) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementImpComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementSubsetComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementInPowersetComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (contraSubsetComplement) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTcontraSubset) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTILcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTIRcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInUnion) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInUnion2) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInIntersectUnions) =>
% 128.89/17.01 ((
% 128.89/17.01 (intersectInPowersetIntersectUnions) =>
% 128.89/17.01 ((
% 128.89/17.01 (inComplementUnionImpNotIn1) =>
% 128.89/17.01 ((
% 128.89/17.01 (inComplementUnionImpInComplement1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTE) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTEcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementUnionInPowersetComplement) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a2) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1a) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1b) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2b2) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2b) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule0) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule1) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule3) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule4) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_1) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_3) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_4) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_5) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1all2) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1SetBreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (choice2fnsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (setOfPairsIsBReln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1all1) =>
% 128.89/17.01 ((
% 128.89/17.01 (subbreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (eqbreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invI) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invE) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compI) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compE) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compEex) =>
% 128.89/17.01 ((
% 128.89/17.01 (!!) @ (
% 128.89/17.01 (('#B') @ (
% 128.89/17.01 !!) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#S') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#S') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 =>))) @
% 128.89/17.01 breln1)))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 !!))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#S') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#S') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 =>))) @
% 128.89/17.01 breln1)))))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#C') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 breln1)))) @
% 128.89/17.01 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/17.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl660])).
% 128.89/17.01 thf(zip_derived_cl685, plain,
% 128.89/17.01 (~ (((setadjoin__Cong) =>
% 128.89/17.01 (((powerset__Cong) =>
% 128.89/17.01 (((setunion__Cong) =>
% 128.89/17.01 (((exuEu) =>
% 128.89/17.01 (((descr__Cong) =>
% 128.89/17.01 (((dsetconstr__Cong) =>
% 128.89/17.01 (((subsetI1) =>
% 128.89/17.01 (((eqimpsubset2) =>
% 128.89/17.01 (((eqimpsubset1) =>
% 128.89/17.01 (((subsetI2) =>
% 128.89/17.01 (((emptysetsubset) =>
% 128.89/17.01 (((subsetE) =>
% 128.89/17.01 (((subsetE2) =>
% 128.89/17.01 (((notsubsetI) =>
% 128.89/17.01 (((notequalI1) =>
% 128.89/17.01 (((notequalI2) =>
% 128.89/17.01 (((subsetRefl) =>
% 128.89/17.01 (((subsetTrans) =>
% 128.89/17.01 (((setadjoinSub) =>
% 128.89/17.01 (((setadjoinSub2) =>
% 128.89/17.01 (((subset2powerset) =>
% 128.89/17.01 (((setextsub) =>
% 128.89/17.01 (((subsetemptysetimpeq) =>
% 128.89/17.01 (((powersetI1) =>
% 128.89/17.01 (((powersetE1) =>
% 128.89/17.01 (((inPowerset) =>
% 128.89/17.01 (((powersetsubset) =>
% 128.89/17.01 (((sepInPowerset) =>
% 128.89/17.01 (((sepSubset) =>
% 128.89/17.01 (((binunionIL) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairset2IR) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionIR) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionEcases) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionE) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionRsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectI) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset5) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset2) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset3) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectER) =>
% 128.89/17.01 ((
% 128.89/17.01 (disjointsetsI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectRsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset4) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset1) =>
% 128.89/17.01 ((
% 128.89/17.01 (bs114d) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusI) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusER) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusSubset2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusERneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusELneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusILneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusIRneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusSubset1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffE) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffI2) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffIneg1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffIneg2) =>
% 128.89/17.01 ((
% 128.89/17.01 (secondinupair) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairIL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairIR) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairiskpair) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairp) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonsubset) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletoninpowerset) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletoninpowunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairset2E) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairsubunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairinpowunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem3) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairin) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempair1) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempair) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionE2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton1) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1E1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1I) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1I2) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonsuniq) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL1) =>
% 128.89/17.01 ((
% 128.89/17.01 (kfstsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (theprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (kfstpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodfstin) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR11) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR12) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR1) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairequniteq) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR) =>
% 128.89/17.01 ((
% 128.89/17.01 (ksndsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (ksndpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairsurjEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodsndin) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairmemEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairmemER) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempaircEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodfstpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodsndpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairsurjEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrI) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrSub) =>
% 128.89/17.01 ((
% 128.89/17.01 (setOfPairsIsBReln) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrERa) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrEL1) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrEL2) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrER) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcImageSingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (apProp) =>
% 128.89/17.01 ((
% 128.89/17.01 (app) =>
% 128.89/17.01 ((
% 128.89/17.01 (infuncsetfunc) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2p) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcinfuncset) =>
% 128.89/17.01 ((
% 128.89/17.01 (lamProp) =>
% 128.89/17.01 ((
% 128.89/17.01 (lamp) =>
% 128.89/17.01 ((
% 128.89/17.01 (lam2p) =>
% 128.89/17.01 ((
% 128.89/17.01 (brelnall1) =>
% 128.89/17.01 ((
% 128.89/17.01 (brelnall2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1E2) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp3) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcextLem) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp4) =>
% 128.89/17.01 ((
% 128.89/17.01 (subbreln) =>
% 128.89/17.01 ((
% 128.89/17.01 (eqbreln) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcext) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcext2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2apEq1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2apEq2) =>
% 128.89/17.01 ((
% 128.89/17.01 (beta1) =>
% 128.89/17.01 ((
% 128.89/17.01 (eta1) =>
% 128.89/17.01 ((
% 128.89/17.01 (lam2lamEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (beta2) =>
% 128.89/17.01 ((
% 128.89/17.01 (eta2) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalseProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalseProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ifSingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (ifp) =>
% 128.89/17.01 ((
% 128.89/17.01 (theeq) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrue) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalse) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueorfalse) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (setextT) =>
% 128.89/17.01 ((
% 128.89/17.01 (subsetTI) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetTI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetTE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectTELcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectTERcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT1) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT2) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT3) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementSub1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementSub2) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTnotintersectT) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementImpComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementSubsetComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementInPowersetComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (contraSubsetComplement) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTcontraSubset) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTILcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTIRcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInUnion) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInUnion2) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInIntersectUnions) =>
% 128.89/17.01 ((
% 128.89/17.01 (intersectInPowersetIntersectUnions) =>
% 128.89/17.01 ((
% 128.89/17.01 (inComplementUnionImpNotIn1) =>
% 128.89/17.01 ((
% 128.89/17.01 (inComplementUnionImpInComplement1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTE) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTEcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementUnionInPowersetComplement) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a2) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1a) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1b) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2b2) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2b) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule0) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule1) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule3) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule4) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_1) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_3) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_4) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_5) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1all2) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1SetBreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (choice2fnsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (setOfPairsIsBReln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1all1) =>
% 128.89/17.01 ((
% 128.89/17.01 (subbreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (eqbreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invI) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invE) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compI) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compE) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compEex) =>
% 128.89/17.01 ((
% 128.89/17.01 (!!) @ (
% 128.89/17.01 (('#B') @ (
% 128.89/17.01 !!) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#S') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#S') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 =>))) @
% 128.89/17.01 breln1)))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 !!))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#S') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#S') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 =>))) @
% 128.89/17.01 breln1)))))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#C') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 breln1)))) @
% 128.89/17.01 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/17.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl672])).
% 128.89/17.01 thf(zip_derived_cl699, plain,
% 128.89/17.01 (~ (((powerset__Cong) =>
% 128.89/17.01 (((setunion__Cong) =>
% 128.89/17.01 (((exuEu) =>
% 128.89/17.01 (((descr__Cong) =>
% 128.89/17.01 (((dsetconstr__Cong) =>
% 128.89/17.01 (((subsetI1) =>
% 128.89/17.01 (((eqimpsubset2) =>
% 128.89/17.01 (((eqimpsubset1) =>
% 128.89/17.01 (((subsetI2) =>
% 128.89/17.01 (((emptysetsubset) =>
% 128.89/17.01 (((subsetE) =>
% 128.89/17.01 (((subsetE2) =>
% 128.89/17.01 (((notsubsetI) =>
% 128.89/17.01 (((notequalI1) =>
% 128.89/17.01 (((notequalI2) =>
% 128.89/17.01 (((subsetRefl) =>
% 128.89/17.01 (((subsetTrans) =>
% 128.89/17.01 (((setadjoinSub) =>
% 128.89/17.01 (((setadjoinSub2) =>
% 128.89/17.01 (((subset2powerset) =>
% 128.89/17.01 (((setextsub) =>
% 128.89/17.01 (((subsetemptysetimpeq) =>
% 128.89/17.01 (((powersetI1) =>
% 128.89/17.01 (((powersetE1) =>
% 128.89/17.01 (((inPowerset) =>
% 128.89/17.01 (((powersetsubset) =>
% 128.89/17.01 (((sepInPowerset) =>
% 128.89/17.01 (((sepSubset) =>
% 128.89/17.01 (((binunionIL) =>
% 128.89/17.01 (((upairset2IR) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionIR) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionEcases) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionE) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionRsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectI) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset5) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset2) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset3) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectER) =>
% 128.89/17.01 ((
% 128.89/17.01 (disjointsetsI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectRsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset4) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset1) =>
% 128.89/17.01 ((
% 128.89/17.01 (bs114d) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusI) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusER) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusSubset2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusERneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusELneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusILneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusIRneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusSubset1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffE) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffI2) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffIneg1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffIneg2) =>
% 128.89/17.01 ((
% 128.89/17.01 (secondinupair) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairIL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairIR) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairiskpair) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairp) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonsubset) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletoninpowerset) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletoninpowunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairset2E) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairsubunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairinpowunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem3) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairin) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempair1) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempair) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionE2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton1) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1E1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1I) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1I2) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonsuniq) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL1) =>
% 128.89/17.01 ((
% 128.89/17.01 (kfstsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (theprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (kfstpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodfstin) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR11) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR12) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR1) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairequniteq) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR) =>
% 128.89/17.01 ((
% 128.89/17.01 (ksndsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (ksndpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairsurjEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodsndin) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairmemEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairmemER) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempaircEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodfstpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodsndpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairsurjEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrI) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrSub) =>
% 128.89/17.01 ((
% 128.89/17.01 (setOfPairsIsBReln) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrERa) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrEL1) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrEL2) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrER) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcImageSingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (apProp) =>
% 128.89/17.01 ((
% 128.89/17.01 (app) =>
% 128.89/17.01 ((
% 128.89/17.01 (infuncsetfunc) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2p) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcinfuncset) =>
% 128.89/17.01 ((
% 128.89/17.01 (lamProp) =>
% 128.89/17.01 ((
% 128.89/17.01 (lamp) =>
% 128.89/17.01 ((
% 128.89/17.01 (lam2p) =>
% 128.89/17.01 ((
% 128.89/17.01 (brelnall1) =>
% 128.89/17.01 ((
% 128.89/17.01 (brelnall2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1E2) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp3) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcextLem) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp4) =>
% 128.89/17.01 ((
% 128.89/17.01 (subbreln) =>
% 128.89/17.01 ((
% 128.89/17.01 (eqbreln) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcext) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcext2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2apEq1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2apEq2) =>
% 128.89/17.01 ((
% 128.89/17.01 (beta1) =>
% 128.89/17.01 ((
% 128.89/17.01 (eta1) =>
% 128.89/17.01 ((
% 128.89/17.01 (lam2lamEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (beta2) =>
% 128.89/17.01 ((
% 128.89/17.01 (eta2) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalseProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalseProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ifSingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (ifp) =>
% 128.89/17.01 ((
% 128.89/17.01 (theeq) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrue) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalse) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueorfalse) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (setextT) =>
% 128.89/17.01 ((
% 128.89/17.01 (subsetTI) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetTI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetTE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectTELcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectTERcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT1) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT2) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT3) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementSub1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementSub2) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTnotintersectT) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementImpComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementSubsetComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementInPowersetComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (contraSubsetComplement) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTcontraSubset) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTILcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTIRcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInUnion) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInUnion2) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInIntersectUnions) =>
% 128.89/17.01 ((
% 128.89/17.01 (intersectInPowersetIntersectUnions) =>
% 128.89/17.01 ((
% 128.89/17.01 (inComplementUnionImpNotIn1) =>
% 128.89/17.01 ((
% 128.89/17.01 (inComplementUnionImpInComplement1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTE) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTEcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementUnionInPowersetComplement) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a2) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1a) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1b) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2b2) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2b) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule0) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule1) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule3) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule4) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_1) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_3) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_4) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_5) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1all2) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1SetBreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (choice2fnsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (setOfPairsIsBReln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1all1) =>
% 128.89/17.01 ((
% 128.89/17.01 (subbreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (eqbreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invI) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invE) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compI) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compE) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compEex) =>
% 128.89/17.01 ((
% 128.89/17.01 (!!) @ (
% 128.89/17.01 (('#B') @ (
% 128.89/17.01 !!) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#S') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#S') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 =>))) @
% 128.89/17.01 breln1)))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 !!))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#S') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#S') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 =>))) @
% 128.89/17.01 breln1)))))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#C') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 breln1)))) @
% 128.89/17.01 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/17.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl685])).
% 128.89/17.01 thf(zip_derived_cl714, plain,
% 128.89/17.01 (~ (((setunion__Cong) =>
% 128.89/17.01 (((exuEu) =>
% 128.89/17.01 (((descr__Cong) =>
% 128.89/17.01 (((dsetconstr__Cong) =>
% 128.89/17.01 (((subsetI1) =>
% 128.89/17.01 (((eqimpsubset2) =>
% 128.89/17.01 (((eqimpsubset1) =>
% 128.89/17.01 (((subsetI2) =>
% 128.89/17.01 (((emptysetsubset) =>
% 128.89/17.01 (((subsetE) =>
% 128.89/17.01 (((subsetE2) =>
% 128.89/17.01 (((notsubsetI) =>
% 128.89/17.01 (((notequalI1) =>
% 128.89/17.01 (((notequalI2) =>
% 128.89/17.01 (((subsetRefl) =>
% 128.89/17.01 (((subsetTrans) =>
% 128.89/17.01 (((setadjoinSub) =>
% 128.89/17.01 (((setadjoinSub2) =>
% 128.89/17.01 (((subset2powerset) =>
% 128.89/17.01 (((setextsub) =>
% 128.89/17.01 (((subsetemptysetimpeq) =>
% 128.89/17.01 (((powersetI1) =>
% 128.89/17.01 (((powersetE1) =>
% 128.89/17.01 (((inPowerset) =>
% 128.89/17.01 (((powersetsubset) =>
% 128.89/17.01 (((sepInPowerset) =>
% 128.89/17.01 (((sepSubset) =>
% 128.89/17.01 (((binunionIL) =>
% 128.89/17.01 (((upairset2IR) =>
% 128.89/17.01 (((binunionIR) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionEcases) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionE) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionRsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectI) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset5) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset2) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset3) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectER) =>
% 128.89/17.01 ((
% 128.89/17.01 (disjointsetsI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectRsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset4) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset1) =>
% 128.89/17.01 ((
% 128.89/17.01 (bs114d) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusI) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusER) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusSubset2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusERneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusELneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusILneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusIRneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusSubset1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffE) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffI2) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffIneg1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffIneg2) =>
% 128.89/17.01 ((
% 128.89/17.01 (secondinupair) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairIL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairIR) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairiskpair) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairp) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonsubset) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletoninpowerset) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletoninpowunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairset2E) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairsubunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairinpowunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem3) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairin) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempair1) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempair) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionE2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton1) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1E1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1I) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1I2) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonsuniq) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL1) =>
% 128.89/17.01 ((
% 128.89/17.01 (kfstsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (theprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (kfstpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodfstin) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR11) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR12) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR1) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairequniteq) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR) =>
% 128.89/17.01 ((
% 128.89/17.01 (ksndsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (ksndpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairsurjEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodsndin) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairmemEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairmemER) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempaircEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodfstpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodsndpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairsurjEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrI) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrSub) =>
% 128.89/17.01 ((
% 128.89/17.01 (setOfPairsIsBReln) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrERa) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrEL1) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrEL2) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrER) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcImageSingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (apProp) =>
% 128.89/17.01 ((
% 128.89/17.01 (app) =>
% 128.89/17.01 ((
% 128.89/17.01 (infuncsetfunc) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2p) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcinfuncset) =>
% 128.89/17.01 ((
% 128.89/17.01 (lamProp) =>
% 128.89/17.01 ((
% 128.89/17.01 (lamp) =>
% 128.89/17.01 ((
% 128.89/17.01 (lam2p) =>
% 128.89/17.01 ((
% 128.89/17.01 (brelnall1) =>
% 128.89/17.01 ((
% 128.89/17.01 (brelnall2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1E2) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp3) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcextLem) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp4) =>
% 128.89/17.01 ((
% 128.89/17.01 (subbreln) =>
% 128.89/17.01 ((
% 128.89/17.01 (eqbreln) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcext) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcext2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2apEq1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2apEq2) =>
% 128.89/17.01 ((
% 128.89/17.01 (beta1) =>
% 128.89/17.01 ((
% 128.89/17.01 (eta1) =>
% 128.89/17.01 ((
% 128.89/17.01 (lam2lamEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (beta2) =>
% 128.89/17.01 ((
% 128.89/17.01 (eta2) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalseProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalseProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ifSingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (ifp) =>
% 128.89/17.01 ((
% 128.89/17.01 (theeq) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrue) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalse) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueorfalse) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (setextT) =>
% 128.89/17.01 ((
% 128.89/17.01 (subsetTI) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetTI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetTE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectTELcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectTERcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT1) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT2) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT3) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementSub1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementSub2) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTnotintersectT) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementImpComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementSubsetComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementInPowersetComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (contraSubsetComplement) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTcontraSubset) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTILcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTIRcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInUnion) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInUnion2) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInIntersectUnions) =>
% 128.89/17.01 ((
% 128.89/17.01 (intersectInPowersetIntersectUnions) =>
% 128.89/17.01 ((
% 128.89/17.01 (inComplementUnionImpNotIn1) =>
% 128.89/17.01 ((
% 128.89/17.01 (inComplementUnionImpInComplement1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTE) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTEcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementUnionInPowersetComplement) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a2) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1a) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1b) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2b2) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2b) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule0) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule1) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule3) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule4) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_1) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_3) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_4) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_5) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1all2) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1SetBreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (choice2fnsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (setOfPairsIsBReln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1all1) =>
% 128.89/17.01 ((
% 128.89/17.01 (subbreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (eqbreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invI) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invE) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compI) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compE) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compEex) =>
% 128.89/17.01 ((
% 128.89/17.01 (!!) @ (
% 128.89/17.01 (('#B') @ (
% 128.89/17.01 !!) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#S') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#S') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 =>))) @
% 128.89/17.01 breln1)))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 !!))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#S') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#S') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 =>))) @
% 128.89/17.01 breln1)))))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#C') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 breln1)))) @
% 128.89/17.01 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/17.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl699])).
% 128.89/17.01 thf(zip_derived_cl731, plain,
% 128.89/17.01 (~ (((exuEu) =>
% 128.89/17.01 (((descr__Cong) =>
% 128.89/17.01 (((dsetconstr__Cong) =>
% 128.89/17.01 (((subsetI1) =>
% 128.89/17.01 (((eqimpsubset2) =>
% 128.89/17.01 (((eqimpsubset1) =>
% 128.89/17.01 (((subsetI2) =>
% 128.89/17.01 (((emptysetsubset) =>
% 128.89/17.01 (((subsetE) =>
% 128.89/17.01 (((subsetE2) =>
% 128.89/17.01 (((notsubsetI) =>
% 128.89/17.01 (((notequalI1) =>
% 128.89/17.01 (((notequalI2) =>
% 128.89/17.01 (((subsetRefl) =>
% 128.89/17.01 (((subsetTrans) =>
% 128.89/17.01 (((setadjoinSub) =>
% 128.89/17.01 (((setadjoinSub2) =>
% 128.89/17.01 (((subset2powerset) =>
% 128.89/17.01 (((setextsub) =>
% 128.89/17.01 (((subsetemptysetimpeq) =>
% 128.89/17.01 (((powersetI1) =>
% 128.89/17.01 (((powersetE1) =>
% 128.89/17.01 (((inPowerset) =>
% 128.89/17.01 (((powersetsubset) =>
% 128.89/17.01 (((sepInPowerset) =>
% 128.89/17.01 (((sepSubset) =>
% 128.89/17.01 (((binunionIL) =>
% 128.89/17.01 (((upairset2IR) =>
% 128.89/17.01 (((binunionIR) =>
% 128.89/17.01 (((binunionEcases) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionE) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionRsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectI) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset5) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset2) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset3) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectER) =>
% 128.89/17.01 ((
% 128.89/17.01 (disjointsetsI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectRsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset4) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset1) =>
% 128.89/17.01 ((
% 128.89/17.01 (bs114d) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusI) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusER) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusSubset2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusERneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusELneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusILneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusIRneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusSubset1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffE) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffI2) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffIneg1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffIneg2) =>
% 128.89/17.01 ((
% 128.89/17.01 (secondinupair) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairIL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairIR) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairiskpair) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairp) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonsubset) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletoninpowerset) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletoninpowunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairset2E) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairsubunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairinpowunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem3) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairin) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempair1) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempair) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionE2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton1) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1E1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1I) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1I2) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonsuniq) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL1) =>
% 128.89/17.01 ((
% 128.89/17.01 (kfstsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (theprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (kfstpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodfstin) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR11) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR12) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR1) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairequniteq) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR) =>
% 128.89/17.01 ((
% 128.89/17.01 (ksndsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (ksndpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairsurjEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodsndin) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairmemEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairmemER) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempaircEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodfstpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodsndpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairsurjEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrI) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrSub) =>
% 128.89/17.01 ((
% 128.89/17.01 (setOfPairsIsBReln) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrERa) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrEL1) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrEL2) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrER) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcImageSingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (apProp) =>
% 128.89/17.01 ((
% 128.89/17.01 (app) =>
% 128.89/17.01 ((
% 128.89/17.01 (infuncsetfunc) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2p) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcinfuncset) =>
% 128.89/17.01 ((
% 128.89/17.01 (lamProp) =>
% 128.89/17.01 ((
% 128.89/17.01 (lamp) =>
% 128.89/17.01 ((
% 128.89/17.01 (lam2p) =>
% 128.89/17.01 ((
% 128.89/17.01 (brelnall1) =>
% 128.89/17.01 ((
% 128.89/17.01 (brelnall2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1E2) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp3) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcextLem) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp4) =>
% 128.89/17.01 ((
% 128.89/17.01 (subbreln) =>
% 128.89/17.01 ((
% 128.89/17.01 (eqbreln) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcext) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcext2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2apEq1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2apEq2) =>
% 128.89/17.01 ((
% 128.89/17.01 (beta1) =>
% 128.89/17.01 ((
% 128.89/17.01 (eta1) =>
% 128.89/17.01 ((
% 128.89/17.01 (lam2lamEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (beta2) =>
% 128.89/17.01 ((
% 128.89/17.01 (eta2) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalseProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalseProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ifSingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (ifp) =>
% 128.89/17.01 ((
% 128.89/17.01 (theeq) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrue) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalse) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueorfalse) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (setextT) =>
% 128.89/17.01 ((
% 128.89/17.01 (subsetTI) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetTI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetTE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectTELcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectTERcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT1) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT2) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT3) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementSub1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementSub2) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTnotintersectT) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementImpComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementSubsetComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementInPowersetComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (contraSubsetComplement) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTcontraSubset) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTILcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTIRcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInUnion) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInUnion2) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInIntersectUnions) =>
% 128.89/17.01 ((
% 128.89/17.01 (intersectInPowersetIntersectUnions) =>
% 128.89/17.01 ((
% 128.89/17.01 (inComplementUnionImpNotIn1) =>
% 128.89/17.01 ((
% 128.89/17.01 (inComplementUnionImpInComplement1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTE) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTEcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementUnionInPowersetComplement) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a2) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1a) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1b) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2b2) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2b) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule0) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule1) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule3) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule4) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_1) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_3) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_4) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_5) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1all2) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1SetBreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (choice2fnsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (setOfPairsIsBReln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1all1) =>
% 128.89/17.01 ((
% 128.89/17.01 (subbreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (eqbreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invI) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invE) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compI) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compE) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compEex) =>
% 128.89/17.01 ((
% 128.89/17.01 (!!) @ (
% 128.89/17.01 (('#B') @ (
% 128.89/17.01 !!) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#S') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#S') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 =>))) @
% 128.89/17.01 breln1)))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 !!))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#S') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#S') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 =>))) @
% 128.89/17.01 breln1)))))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#C') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 breln1)))) @
% 128.89/17.01 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/17.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl714])).
% 128.89/17.01 thf(zip_derived_cl749, plain,
% 128.89/17.01 (~ (((descr__Cong) =>
% 128.89/17.01 (((dsetconstr__Cong) =>
% 128.89/17.01 (((subsetI1) =>
% 128.89/17.01 (((eqimpsubset2) =>
% 128.89/17.01 (((eqimpsubset1) =>
% 128.89/17.01 (((subsetI2) =>
% 128.89/17.01 (((emptysetsubset) =>
% 128.89/17.01 (((subsetE) =>
% 128.89/17.01 (((subsetE2) =>
% 128.89/17.01 (((notsubsetI) =>
% 128.89/17.01 (((notequalI1) =>
% 128.89/17.01 (((notequalI2) =>
% 128.89/17.01 (((subsetRefl) =>
% 128.89/17.01 (((subsetTrans) =>
% 128.89/17.01 (((setadjoinSub) =>
% 128.89/17.01 (((setadjoinSub2) =>
% 128.89/17.01 (((subset2powerset) =>
% 128.89/17.01 (((setextsub) =>
% 128.89/17.01 (((subsetemptysetimpeq) =>
% 128.89/17.01 (((powersetI1) =>
% 128.89/17.01 (((powersetE1) =>
% 128.89/17.01 (((inPowerset) =>
% 128.89/17.01 (((powersetsubset) =>
% 128.89/17.01 (((sepInPowerset) =>
% 128.89/17.01 (((sepSubset) =>
% 128.89/17.01 (((binunionIL) =>
% 128.89/17.01 (((upairset2IR) =>
% 128.89/17.01 (((binunionIR) =>
% 128.89/17.01 (((binunionEcases) =>
% 128.89/17.01 (((binunionE) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionRsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectI) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset5) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset2) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset3) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectER) =>
% 128.89/17.01 ((
% 128.89/17.01 (disjointsetsI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectRsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset4) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset1) =>
% 128.89/17.01 ((
% 128.89/17.01 (bs114d) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusI) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusER) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusSubset2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusERneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusELneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusILneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusIRneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusSubset1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffE) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffI2) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffIneg1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffIneg2) =>
% 128.89/17.01 ((
% 128.89/17.01 (secondinupair) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairIL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairIR) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairiskpair) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairp) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonsubset) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletoninpowerset) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletoninpowunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairset2E) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairsubunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairinpowunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem3) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairin) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempair1) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempair) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionE2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton1) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1E1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1I) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1I2) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonsuniq) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL1) =>
% 128.89/17.01 ((
% 128.89/17.01 (kfstsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (theprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (kfstpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodfstin) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR11) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR12) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR1) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairequniteq) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR) =>
% 128.89/17.01 ((
% 128.89/17.01 (ksndsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (ksndpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairsurjEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodsndin) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairmemEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairmemER) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempaircEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodfstpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodsndpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairsurjEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrI) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrSub) =>
% 128.89/17.01 ((
% 128.89/17.01 (setOfPairsIsBReln) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrERa) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrEL1) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrEL2) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrER) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcImageSingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (apProp) =>
% 128.89/17.01 ((
% 128.89/17.01 (app) =>
% 128.89/17.01 ((
% 128.89/17.01 (infuncsetfunc) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2p) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcinfuncset) =>
% 128.89/17.01 ((
% 128.89/17.01 (lamProp) =>
% 128.89/17.01 ((
% 128.89/17.01 (lamp) =>
% 128.89/17.01 ((
% 128.89/17.01 (lam2p) =>
% 128.89/17.01 ((
% 128.89/17.01 (brelnall1) =>
% 128.89/17.01 ((
% 128.89/17.01 (brelnall2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1E2) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp3) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcextLem) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp4) =>
% 128.89/17.01 ((
% 128.89/17.01 (subbreln) =>
% 128.89/17.01 ((
% 128.89/17.01 (eqbreln) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcext) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcext2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2apEq1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2apEq2) =>
% 128.89/17.01 ((
% 128.89/17.01 (beta1) =>
% 128.89/17.01 ((
% 128.89/17.01 (eta1) =>
% 128.89/17.01 ((
% 128.89/17.01 (lam2lamEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (beta2) =>
% 128.89/17.01 ((
% 128.89/17.01 (eta2) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalseProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalseProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ifSingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (ifp) =>
% 128.89/17.01 ((
% 128.89/17.01 (theeq) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrue) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalse) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueorfalse) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (setextT) =>
% 128.89/17.01 ((
% 128.89/17.01 (subsetTI) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetTI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetTE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectTELcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectTERcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT1) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT2) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT3) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementSub1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementSub2) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTnotintersectT) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementImpComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementSubsetComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementInPowersetComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (contraSubsetComplement) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTcontraSubset) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTILcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTIRcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInUnion) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInUnion2) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInIntersectUnions) =>
% 128.89/17.01 ((
% 128.89/17.01 (intersectInPowersetIntersectUnions) =>
% 128.89/17.01 ((
% 128.89/17.01 (inComplementUnionImpNotIn1) =>
% 128.89/17.01 ((
% 128.89/17.01 (inComplementUnionImpInComplement1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTE) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTEcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementUnionInPowersetComplement) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a2) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1a) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1b) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2b2) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2b) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule0) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule1) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule3) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule4) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_1) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_3) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_4) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_5) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1all2) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1SetBreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (choice2fnsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (setOfPairsIsBReln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1all1) =>
% 128.89/17.01 ((
% 128.89/17.01 (subbreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (eqbreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invI) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invE) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compI) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compE) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compEex) =>
% 128.89/17.01 ((
% 128.89/17.01 (!!) @ (
% 128.89/17.01 (('#B') @ (
% 128.89/17.01 !!) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#S') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#S') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 =>))) @
% 128.89/17.01 breln1)))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 !!))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#S') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#S') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 =>))) @
% 128.89/17.01 breln1)))))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#C') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 breln1)))) @
% 128.89/17.01 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/17.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl731])).
% 128.89/17.01 thf(zip_derived_cl769, plain,
% 128.89/17.01 (~ (((dsetconstr__Cong) =>
% 128.89/17.01 (((subsetI1) =>
% 128.89/17.01 (((eqimpsubset2) =>
% 128.89/17.01 (((eqimpsubset1) =>
% 128.89/17.01 (((subsetI2) =>
% 128.89/17.01 (((emptysetsubset) =>
% 128.89/17.01 (((subsetE) =>
% 128.89/17.01 (((subsetE2) =>
% 128.89/17.01 (((notsubsetI) =>
% 128.89/17.01 (((notequalI1) =>
% 128.89/17.01 (((notequalI2) =>
% 128.89/17.01 (((subsetRefl) =>
% 128.89/17.01 (((subsetTrans) =>
% 128.89/17.01 (((setadjoinSub) =>
% 128.89/17.01 (((setadjoinSub2) =>
% 128.89/17.01 (((subset2powerset) =>
% 128.89/17.01 (((setextsub) =>
% 128.89/17.01 (((subsetemptysetimpeq) =>
% 128.89/17.01 (((powersetI1) =>
% 128.89/17.01 (((powersetE1) =>
% 128.89/17.01 (((inPowerset) =>
% 128.89/17.01 (((powersetsubset) =>
% 128.89/17.01 (((sepInPowerset) =>
% 128.89/17.01 (((sepSubset) =>
% 128.89/17.01 (((binunionIL) =>
% 128.89/17.01 (((upairset2IR) =>
% 128.89/17.01 (((binunionIR) =>
% 128.89/17.01 (((binunionEcases) =>
% 128.89/17.01 (((binunionE) =>
% 128.89/17.01 (((binunionLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionRsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectI) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset5) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset2) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset3) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectER) =>
% 128.89/17.01 ((
% 128.89/17.01 (disjointsetsI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectRsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset4) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset1) =>
% 128.89/17.01 ((
% 128.89/17.01 (bs114d) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusI) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusER) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusSubset2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusERneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusELneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusILneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusIRneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusSubset1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffE) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffI2) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffIneg1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffIneg2) =>
% 128.89/17.01 ((
% 128.89/17.01 (secondinupair) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairIL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairIR) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairiskpair) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairp) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonsubset) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletoninpowerset) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletoninpowunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairset2E) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairsubunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairinpowunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem3) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairin) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempair1) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempair) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionE2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton1) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1E1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1I) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1I2) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonsuniq) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL1) =>
% 128.89/17.01 ((
% 128.89/17.01 (kfstsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (theprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (kfstpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodfstin) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR11) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR12) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR1) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairequniteq) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjR) =>
% 128.89/17.01 ((
% 128.89/17.01 (ksndsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (ksndpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairsurjEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodsndin) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairmemEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairmemER) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempaircEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodfstpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodsndpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairsurjEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrI) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrSub) =>
% 128.89/17.01 ((
% 128.89/17.01 (setOfPairsIsBReln) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrERa) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrEL1) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrEL2) =>
% 128.89/17.01 ((
% 128.89/17.01 (dpsetconstrER) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcImageSingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (apProp) =>
% 128.89/17.01 ((
% 128.89/17.01 (app) =>
% 128.89/17.01 ((
% 128.89/17.01 (infuncsetfunc) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2p) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcinfuncset) =>
% 128.89/17.01 ((
% 128.89/17.01 (lamProp) =>
% 128.89/17.01 ((
% 128.89/17.01 (lamp) =>
% 128.89/17.01 ((
% 128.89/17.01 (lam2p) =>
% 128.89/17.01 ((
% 128.89/17.01 (brelnall1) =>
% 128.89/17.01 ((
% 128.89/17.01 (brelnall2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1E2) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp3) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcextLem) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcGraphProp4) =>
% 128.89/17.01 ((
% 128.89/17.01 (subbreln) =>
% 128.89/17.01 ((
% 128.89/17.01 (eqbreln) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcext) =>
% 128.89/17.01 ((
% 128.89/17.01 (funcext2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2apEq1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ap2apEq2) =>
% 128.89/17.01 ((
% 128.89/17.01 (beta1) =>
% 128.89/17.01 ((
% 128.89/17.01 (eta1) =>
% 128.89/17.01 ((
% 128.89/17.01 (lam2lamEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (beta2) =>
% 128.89/17.01 ((
% 128.89/17.01 (eta2) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalseProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalseProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueProp1) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueProp2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ifSingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (ifp) =>
% 128.89/17.01 ((
% 128.89/17.01 (theeq) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrue) =>
% 128.89/17.01 ((
% 128.89/17.01 (iffalse) =>
% 128.89/17.01 ((
% 128.89/17.01 (iftrueorfalse) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementT_lem) =>
% 128.89/17.01 ((
% 128.89/17.01 (setextT) =>
% 128.89/17.01 ((
% 128.89/17.01 (subsetTI) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetTI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (powersetTE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectTELcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectTERcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT1) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT2) =>
% 128.89/17.01 ((
% 128.89/17.01 (contrasubsetT3) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementE1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementSub1) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementSub2) =>
% 128.89/17.01 ((
% 128.89/17.01 (doubleComplementEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTnotintersectT) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementImpComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementSubsetComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementInPowersetComplementIntersect) =>
% 128.89/17.01 ((
% 128.89/17.01 (contraSubsetComplement) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementTcontraSubset) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTILcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTIRcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInUnion) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInUnion2) =>
% 128.89/17.01 ((
% 128.89/17.01 (inIntersectImpInIntersectUnions) =>
% 128.89/17.01 ((
% 128.89/17.01 (intersectInPowersetIntersectUnions) =>
% 128.89/17.01 ((
% 128.89/17.01 (inComplementUnionImpNotIn1) =>
% 128.89/17.01 ((
% 128.89/17.01 (inComplementUnionImpInComplement1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTE) =>
% 128.89/17.01 ((
% 128.89/17.01 (binunionTEcontra) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a1) =>
% 128.89/17.01 ((
% 128.89/17.01 (complementUnionInPowersetComplement) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a2) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1a) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1b) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan1) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2a) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2b2) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2b) =>
% 128.89/17.01 ((
% 128.89/17.01 (demorgan2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule0) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule1) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule3) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz13rule4) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_1) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_2) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_3) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_4) =>
% 128.89/17.01 ((
% 128.89/17.01 (woz1_5) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1all2) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1SetBreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (choice2fnsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (setOfPairsIsBReln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1all1) =>
% 128.89/17.01 ((
% 128.89/17.01 (subbreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (eqbreln1) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invI) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1invE) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compI) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compE) =>
% 128.89/17.01 ((
% 128.89/17.01 (breln1compEex) =>
% 128.89/17.01 ((
% 128.89/17.01 (!!) @ (
% 128.89/17.01 (('#B') @ (
% 128.89/17.01 !!) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#S') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#S') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 =>))) @
% 128.89/17.01 breln1)))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 !!))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#S') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#S') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 =>))) @
% 128.89/17.01 breln1)))))) @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#C') @ (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 (
% 128.89/17.01 (
% 128.89/17.01 ('#B') @ (
% 128.89/17.01 '#B') @
% 128.89/17.01 breln1)))) @
% 128.89/17.01 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/17.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl749])).
% 128.89/17.01 thf(zip_derived_cl789, plain,
% 128.89/17.01 (~ (((subsetI1) =>
% 128.89/17.01 (((eqimpsubset2) =>
% 128.89/17.01 (((eqimpsubset1) =>
% 128.89/17.01 (((subsetI2) =>
% 128.89/17.01 (((emptysetsubset) =>
% 128.89/17.01 (((subsetE) =>
% 128.89/17.01 (((subsetE2) =>
% 128.89/17.01 (((notsubsetI) =>
% 128.89/17.01 (((notequalI1) =>
% 128.89/17.01 (((notequalI2) =>
% 128.89/17.01 (((subsetRefl) =>
% 128.89/17.01 (((subsetTrans) =>
% 128.89/17.01 (((setadjoinSub) =>
% 128.89/17.01 (((setadjoinSub2) =>
% 128.89/17.01 (((subset2powerset) =>
% 128.89/17.01 (((setextsub) =>
% 128.89/17.01 (((subsetemptysetimpeq) =>
% 128.89/17.01 (((powersetI1) =>
% 128.89/17.01 (((powersetE1) =>
% 128.89/17.01 (((inPowerset) =>
% 128.89/17.01 (((powersetsubset) =>
% 128.89/17.01 (((sepInPowerset) =>
% 128.89/17.01 (((sepSubset) =>
% 128.89/17.01 (((binunionIL) =>
% 128.89/17.01 (((upairset2IR) =>
% 128.89/17.01 (((binunionIR) =>
% 128.89/17.01 (((binunionEcases) =>
% 128.89/17.01 (((binunionE) =>
% 128.89/17.01 (((binunionLsub) =>
% 128.89/17.01 (((binunionRsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectI) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset5) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset2) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset3) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectER) =>
% 128.89/17.01 ((
% 128.89/17.01 (disjointsetsI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectRsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset4) =>
% 128.89/17.01 ((
% 128.89/17.01 (binintersectSubset1) =>
% 128.89/17.01 ((
% 128.89/17.01 (bs114d) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusI) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusEL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusER) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusSubset2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusERneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusELneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusILneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusIRneg) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusLsub) =>
% 128.89/17.01 ((
% 128.89/17.01 (setminusSubset1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffE) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffI1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffI2) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffIneg1) =>
% 128.89/17.01 ((
% 128.89/17.01 (symdiffIneg2) =>
% 128.89/17.01 ((
% 128.89/17.01 (secondinupair) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairIL) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairIR) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairiskpair) =>
% 128.89/17.01 ((
% 128.89/17.01 (kpairp) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonsubset) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletoninpowerset) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletoninpowunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairset2E) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairsubunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (upairinpowunion) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem2) =>
% 128.89/17.01 ((
% 128.89/17.01 (ubforcartprodlem3) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodpairin) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempair1) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodmempair) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionE2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton1) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setunionsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1E1) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1I) =>
% 128.89/17.01 ((
% 128.89/17.01 (ex1I2) =>
% 128.89/17.01 ((
% 128.89/17.01 (singletonsuniq) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL1) =>
% 128.89/17.01 ((
% 128.89/17.01 (kfstsingleton) =>
% 128.89/17.01 ((
% 128.89/17.01 (theprop) =>
% 128.89/17.01 ((
% 128.89/17.01 (kfstpairEq) =>
% 128.89/17.01 ((
% 128.89/17.01 (cartprodfstin) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL2) =>
% 128.89/17.01 ((
% 128.89/17.01 (setukpairinjL) =>
% 128.89/17.02 ((
% 128.89/17.02 (setukpairinjR11) =>
% 128.89/17.02 ((
% 128.89/17.02 (setukpairinjR12) =>
% 128.89/17.02 ((
% 128.89/17.02 (setukpairinjR1) =>
% 128.89/17.02 ((
% 128.89/17.02 (upairequniteq) =>
% 128.89/17.02 ((
% 128.89/17.02 (setukpairinjR2) =>
% 128.89/17.02 ((
% 128.89/17.02 (setukpairinjR) =>
% 128.89/17.02 ((
% 128.89/17.02 (ksndsingleton) =>
% 128.89/17.02 ((
% 128.89/17.02 (ksndpairEq) =>
% 128.89/17.02 ((
% 128.89/17.02 (kpairsurjEq) =>
% 128.89/17.02 ((
% 128.89/17.02 (cartprodsndin) =>
% 128.89/17.02 ((
% 128.89/17.02 (cartprodpairmemEL) =>
% 128.89/17.02 ((
% 128.89/17.02 (cartprodpairmemER) =>
% 128.89/17.02 ((
% 128.89/17.02 (cartprodmempaircEq) =>
% 128.89/17.02 ((
% 128.89/17.02 (cartprodfstpairEq) =>
% 128.89/17.02 ((
% 128.89/17.02 (cartprodsndpairEq) =>
% 128.89/17.02 ((
% 128.89/17.02 (cartprodpairsurjEq) =>
% 128.89/17.02 ((
% 128.89/17.02 (dpsetconstrI) =>
% 128.89/17.02 ((
% 128.89/17.02 (dpsetconstrSub) =>
% 128.89/17.02 ((
% 128.89/17.02 (setOfPairsIsBReln) =>
% 128.89/17.02 ((
% 128.89/17.02 (dpsetconstrERa) =>
% 128.89/17.02 ((
% 128.89/17.02 (dpsetconstrEL1) =>
% 128.89/17.02 ((
% 128.89/17.02 (dpsetconstrEL2) =>
% 128.89/17.02 ((
% 128.89/17.02 (dpsetconstrER) =>
% 128.89/17.02 ((
% 128.89/17.02 (funcImageSingleton) =>
% 128.89/17.02 ((
% 128.89/17.02 (apProp) =>
% 128.89/17.02 ((
% 128.89/17.02 (app) =>
% 128.89/17.02 ((
% 128.89/17.02 (infuncsetfunc) =>
% 128.89/17.02 ((
% 128.89/17.02 (ap2p) =>
% 128.89/17.02 ((
% 128.89/17.02 (funcinfuncset) =>
% 128.89/17.02 ((
% 128.89/17.02 (lamProp) =>
% 128.89/17.02 ((
% 128.89/17.02 (lamp) =>
% 128.89/17.02 ((
% 128.89/17.02 (lam2p) =>
% 128.89/17.02 ((
% 128.89/17.02 (brelnall1) =>
% 128.89/17.02 ((
% 128.89/17.02 (brelnall2) =>
% 128.89/17.02 ((
% 128.89/17.02 (ex1E2) =>
% 128.89/17.02 ((
% 128.89/17.02 (funcGraphProp1) =>
% 128.89/17.02 ((
% 128.89/17.02 (funcGraphProp3) =>
% 128.89/17.02 ((
% 128.89/17.02 (funcGraphProp2) =>
% 128.89/17.02 ((
% 128.89/17.02 (funcextLem) =>
% 128.89/17.02 ((
% 128.89/17.02 (funcGraphProp4) =>
% 128.89/17.02 ((
% 128.89/17.02 (subbreln) =>
% 128.89/17.02 ((
% 128.89/17.02 (eqbreln) =>
% 128.89/17.02 ((
% 128.89/17.02 (funcext) =>
% 128.89/17.02 ((
% 128.89/17.02 (funcext2) =>
% 128.89/17.02 ((
% 128.89/17.02 (ap2apEq1) =>
% 128.89/17.02 ((
% 128.89/17.02 (ap2apEq2) =>
% 128.89/17.02 ((
% 128.89/17.02 (beta1) =>
% 128.89/17.02 ((
% 128.89/17.02 (eta1) =>
% 128.89/17.02 ((
% 128.89/17.02 (lam2lamEq) =>
% 128.89/17.02 ((
% 128.89/17.02 (beta2) =>
% 128.89/17.02 ((
% 128.89/17.02 (eta2) =>
% 128.89/17.02 ((
% 128.89/17.02 (iffalseProp1) =>
% 128.89/17.02 ((
% 128.89/17.02 (iffalseProp2) =>
% 128.89/17.02 ((
% 128.89/17.02 (iftrueProp1) =>
% 128.89/17.02 ((
% 128.89/17.02 (iftrueProp2) =>
% 128.89/17.02 ((
% 128.89/17.02 (ifSingleton) =>
% 128.89/17.02 ((
% 128.89/17.02 (ifp) =>
% 128.89/17.02 ((
% 128.89/17.02 (theeq) =>
% 128.89/17.02 ((
% 128.89/17.02 (iftrue) =>
% 128.89/17.02 ((
% 128.89/17.02 (iffalse) =>
% 128.89/17.02 ((
% 128.89/17.02 (iftrueorfalse) =>
% 128.89/17.02 ((
% 128.89/17.02 (binintersectT_lem) =>
% 128.89/17.02 ((
% 128.89/17.02 (binunionT_lem) =>
% 128.89/17.02 ((
% 128.89/17.02 (powersetT_lem) =>
% 128.89/17.02 ((
% 128.89/17.02 (setminusT_lem) =>
% 128.89/17.02 ((
% 128.89/17.02 (complementT_lem) =>
% 128.89/17.02 ((
% 128.89/17.02 (setextT) =>
% 128.89/17.02 ((
% 128.89/17.02 (subsetTI) =>
% 128.89/17.02 ((
% 128.89/17.02 (powersetTI1) =>
% 128.89/17.02 ((
% 128.89/17.02 (powersetTE1) =>
% 128.89/17.02 ((
% 128.89/17.02 (complementTI1) =>
% 128.89/17.02 ((
% 128.89/17.02 (complementTE1) =>
% 128.89/17.02 ((
% 128.89/17.02 (binintersectTELcontra) =>
% 128.89/17.02 ((
% 128.89/17.02 (binintersectTERcontra) =>
% 128.89/17.02 ((
% 128.89/17.02 (contrasubsetT) =>
% 128.89/17.02 ((
% 128.89/17.02 (contrasubsetT1) =>
% 128.89/17.02 ((
% 128.89/17.02 (contrasubsetT2) =>
% 128.89/17.02 ((
% 128.89/17.02 (contrasubsetT3) =>
% 128.89/17.02 ((
% 128.89/17.02 (doubleComplementI1) =>
% 128.89/17.02 ((
% 128.89/17.02 (doubleComplementE1) =>
% 128.89/17.02 ((
% 128.89/17.02 (doubleComplementSub1) =>
% 128.89/17.02 ((
% 128.89/17.02 (doubleComplementSub2) =>
% 128.89/17.02 ((
% 128.89/17.02 (doubleComplementEq) =>
% 128.89/17.02 ((
% 128.89/17.02 (complementTnotintersectT) =>
% 128.89/17.02 ((
% 128.89/17.02 (complementImpComplementIntersect) =>
% 128.89/17.02 ((
% 128.89/17.02 (complementSubsetComplementIntersect) =>
% 128.89/17.02 ((
% 128.89/17.02 (complementInPowersetComplementIntersect) =>
% 128.89/17.02 ((
% 128.89/17.02 (contraSubsetComplement) =>
% 128.89/17.02 ((
% 128.89/17.02 (complementTcontraSubset) =>
% 128.89/17.02 ((
% 128.89/17.02 (binunionTILcontra) =>
% 128.89/17.02 ((
% 128.89/17.02 (binunionTIRcontra) =>
% 128.89/17.02 ((
% 128.89/17.02 (inIntersectImpInUnion) =>
% 128.89/17.02 ((
% 128.89/17.02 (inIntersectImpInUnion2) =>
% 128.89/17.02 ((
% 128.89/17.02 (inIntersectImpInIntersectUnions) =>
% 128.89/17.02 ((
% 128.89/17.02 (intersectInPowersetIntersectUnions) =>
% 128.89/17.02 ((
% 128.89/17.02 (inComplementUnionImpNotIn1) =>
% 128.89/17.02 ((
% 128.89/17.02 (inComplementUnionImpInComplement1) =>
% 128.89/17.02 ((
% 128.89/17.02 (binunionTE) =>
% 128.89/17.02 ((
% 128.89/17.02 (binunionTEcontra) =>
% 128.89/17.02 ((
% 128.89/17.02 (demorgan2a1) =>
% 128.89/17.02 ((
% 128.89/17.02 (complementUnionInPowersetComplement) =>
% 128.89/17.02 ((
% 128.89/17.02 (demorgan2a2) =>
% 128.89/17.02 ((
% 128.89/17.02 (demorgan1a) =>
% 128.89/17.02 ((
% 128.89/17.02 (demorgan1b) =>
% 128.89/17.02 ((
% 128.89/17.02 (demorgan1) =>
% 128.89/17.02 ((
% 128.89/17.02 (demorgan2a) =>
% 128.89/17.02 ((
% 128.89/17.02 (demorgan2b2) =>
% 128.89/17.02 ((
% 128.89/17.02 (demorgan2b) =>
% 128.89/17.02 ((
% 128.89/17.02 (demorgan2) =>
% 128.89/17.02 ((
% 128.89/17.02 (woz13rule0) =>
% 128.89/17.02 ((
% 128.89/17.02 (woz13rule1) =>
% 128.89/17.02 ((
% 128.89/17.02 (woz13rule2) =>
% 128.89/17.02 ((
% 128.89/17.02 (woz13rule3) =>
% 128.89/17.02 ((
% 128.89/17.02 (woz13rule4) =>
% 128.89/17.02 ((
% 128.89/17.02 (woz1_1) =>
% 128.89/17.02 ((
% 128.89/17.02 (woz1_2) =>
% 128.89/17.02 ((
% 128.89/17.02 (woz1_3) =>
% 128.89/17.02 ((
% 128.89/17.02 (woz1_4) =>
% 128.89/17.02 ((
% 128.89/17.02 (woz1_5) =>
% 128.89/17.02 ((
% 128.89/17.02 (breln1all2) =>
% 128.89/17.02 ((
% 128.89/17.02 (breln1SetBreln1) =>
% 128.89/17.02 ((
% 128.89/17.02 (choice2fnsingleton) =>
% 128.89/17.02 ((
% 128.89/17.02 (setOfPairsIsBReln1) =>
% 128.89/17.02 ((
% 128.89/17.02 (breln1all1) =>
% 128.89/17.02 ((
% 128.89/17.02 (subbreln1) =>
% 128.89/17.02 ((
% 128.89/17.02 (eqbreln1) =>
% 128.89/17.02 ((
% 128.89/17.02 (breln1invprop) =>
% 128.89/17.02 ((
% 128.89/17.02 (breln1invI) =>
% 128.89/17.02 ((
% 128.89/17.02 (breln1invE) =>
% 128.89/17.02 ((
% 128.89/17.02 (breln1compprop) =>
% 128.89/17.02 ((
% 128.89/17.02 (breln1compI) =>
% 128.89/17.02 ((
% 128.89/17.02 (breln1compE) =>
% 128.89/17.02 ((
% 128.89/17.02 (breln1compEex) =>
% 128.89/17.02 ((
% 128.89/17.02 (!!) @ (
% 128.89/17.02 (('#B') @ (
% 128.89/17.02 !!) @
% 128.89/17.02 (
% 128.89/17.02 (
% 128.89/17.02 ('#S') @ (
% 128.89/17.02 (
% 128.89/17.02 ('#B') @ (
% 128.89/17.02 '#S') @
% 128.89/17.02 (
% 128.89/17.02 (
% 128.89/17.02 ('#B') @ (
% 128.89/17.02 (
% 128.89/17.02 ('#B') @ (
% 128.89/17.02 =>))) @
% 128.89/17.02 breln1)))) @
% 128.89/17.02 (
% 128.89/17.02 (
% 128.89/17.02 ('#B') @ (
% 128.89/17.02 (
% 128.89/17.02 ('#B') @ (
% 128.89/17.02 !!))) @
% 128.89/17.02 (
% 128.89/17.02 (
% 128.89/17.02 ('#S') @ (
% 128.89/17.02 (
% 128.89/17.02 ('#B') @ (
% 128.89/17.02 '#B') @
% 128.89/17.02 (
% 128.89/17.02 (
% 128.89/17.02 ('#B') @ (
% 128.89/17.02 '#S') @
% 128.89/17.02 (
% 128.89/17.02 (
% 128.89/17.02 ('#B') @ (
% 128.89/17.02 (
% 128.89/17.02 ('#B') @ (
% 128.89/17.02 =>))) @
% 128.89/17.02 breln1)))))) @
% 128.89/17.02 (
% 128.89/17.02 (
% 128.89/17.02 ('#C') @ (
% 128.89/17.02 (
% 128.89/17.02 ('#B') @ (
% 128.89/17.02 '#B') @
% 128.89/17.02 (
% 128.89/17.02 (
% 128.89/17.02 ('#B') @ (
% 128.89/17.02 '#B') @
% 128.89/17.02 breln1)))) @
% 128.89/17.02 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 128.89/17.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl769])).
% 128.89/17.02 thf(zip_derived_cl807, plain,
% 128.89/17.02 (~ (((eqimpsubset2) =>
% 128.89/17.02 (((eqimpsubset1) =>
% 128.89/17.02 (((subsetI2) =>
% 128.89/17.02 (((emptysetsubset) =>
% 128.89/17.02 (((subsetE) =>
% 128.89/17.02 (((subsetE2) =>
% 128.89/17.02 (((notsubsetI) =>
% 128.89/17.02 (((notequalI1) =>
% 128.89/17.02 (((notequalI2) =>
% 128.89/17.02 (((subsetRefl) =>
% 128.89/17.02 (((subsetTrans) =>
% 128.89/17.02 (((setadjoinSub) =>
% 128.89/17.02 (((setadjoinSub2) =>
% 128.89/17.02 (((subset2powerset) =>
% 128.89/17.02 (((setextsub) =>
% 128.89/17.02 (((subsetemptysetimpeq) =>
% 128.89/17.02 (((powersetI1) =>
% 128.89/17.02 (((powersetE1) =>
% 128.89/17.02 (((inPowerset) =>
% 128.89/17.02 (((powersetsubset) =>
% 128.89/17.02 (((sepInPowerset) =>
% 128.89/17.02 (((sepSubset) =>
% 128.89/17.02 (((binunionIL) =>
% 128.89/17.02 (((upairset2IR) =>
% 128.89/17.02 (((binunionIR) =>
% 128.89/17.02 (((binunionEcases) =>
% 128.89/17.02 (((binunionE) =>
% 128.89/17.02 (((binunionLsub) =>
% 128.89/17.02 (((binunionRsub) =>
% 128.89/17.02 (((binintersectI) =>
% 128.89/17.02 ((
% 128.89/17.02 (binintersectSubset5) =>
% 128.89/17.02 ((
% 128.89/17.02 (binintersectEL) =>
% 128.89/17.02 ((
% 128.89/17.02 (binintersectLsub) =>
% 128.89/17.02 ((
% 128.89/17.02 (binintersectSubset2) =>
% 128.89/17.02 ((
% 128.89/17.02 (binintersectSubset3) =>
% 128.89/17.02 ((
% 128.89/17.02 (binintersectER) =>
% 128.89/17.02 ((
% 128.89/17.02 (disjointsetsI1) =>
% 128.89/17.02 ((
% 128.89/17.02 (binintersectRsub) =>
% 128.89/17.02 ((
% 128.89/17.02 (binintersectSubset4) =>
% 128.89/17.02 ((
% 128.89/17.02 (binintersectSubset1) =>
% 128.89/17.02 ((
% 128.89/17.02 (bs114d) =>
% 128.89/17.02 ((
% 128.89/17.02 (setminusI) =>
% 128.89/17.02 ((
% 128.89/17.02 (setminusEL) =>
% 128.89/17.02 ((
% 128.89/17.02 (setminusER) =>
% 128.89/17.02 ((
% 128.89/17.02 (setminusSubset2) =>
% 128.89/17.02 ((
% 128.89/17.02 (setminusERneg) =>
% 128.89/17.02 ((
% 128.89/17.02 (setminusELneg) =>
% 128.89/17.02 ((
% 128.89/17.02 (setminusILneg) =>
% 128.89/17.02 ((
% 128.89/17.02 (setminusIRneg) =>
% 128.89/17.02 ((
% 128.89/17.02 (setminusLsub) =>
% 128.89/17.02 ((
% 128.89/17.02 (setminusSubset1) =>
% 128.89/17.02 ((
% 128.89/17.02 (symdiffE) =>
% 128.89/17.02 ((
% 128.89/17.02 (symdiffI1) =>
% 128.89/17.02 ((
% 128.89/17.02 (symdiffI2) =>
% 128.89/17.02 ((
% 128.89/17.02 (symdiffIneg1) =>
% 128.89/17.02 ((
% 128.89/17.02 (symdiffIneg2) =>
% 128.89/17.02 ((
% 128.89/17.02 (secondinupair) =>
% 128.89/17.02 ((
% 128.89/17.02 (setukpairIL) =>
% 128.89/17.02 ((
% 128.89/17.02 (setukpairIR) =>
% 128.89/17.02 ((
% 128.89/17.02 (kpairiskpair) =>
% 128.89/17.02 ((
% 128.89/17.02 (kpairp) =>
% 128.89/17.02 ((
% 128.89/17.02 (singletonsubset) =>
% 128.89/17.02 ((
% 128.89/17.02 (singletoninpowerset) =>
% 128.89/17.02 ((
% 128.89/17.02 (singletoninpowunion) =>
% 128.89/17.02 ((
% 128.89/17.02 (upairset2E) =>
% 128.89/17.02 ((
% 128.89/17.02 (upairsubunion) =>
% 128.89/17.02 ((
% 128.89/17.02 (upairinpowunion) =>
% 128.89/17.02 ((
% 129.57/17.02 (ubforcartprodlem1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem3) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairin) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempair1) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempair) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionE2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton1) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1E1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1I) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1I2) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonsuniq) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL1) =>
% 129.57/17.02 ((
% 129.57/17.02 (kfstsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (theprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (kfstpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodfstin) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR11) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR12) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR1) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairequniteq) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR) =>
% 129.57/17.02 ((
% 129.57/17.02 (ksndsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (ksndpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairsurjEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodsndin) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairmemEL) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairmemER) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempaircEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodfstpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodsndpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairsurjEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrI) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrSub) =>
% 129.57/17.02 ((
% 129.57/17.02 (setOfPairsIsBReln) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrERa) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrEL1) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrEL2) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrER) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcImageSingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (apProp) =>
% 129.57/17.02 ((
% 129.57/17.02 (app) =>
% 129.57/17.02 ((
% 129.57/17.02 (infuncsetfunc) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2p) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcinfuncset) =>
% 129.57/17.02 ((
% 129.57/17.02 (lamProp) =>
% 129.57/17.02 ((
% 129.57/17.02 (lamp) =>
% 129.57/17.02 ((
% 129.57/17.02 (lam2p) =>
% 129.57/17.02 ((
% 129.57/17.02 (brelnall1) =>
% 129.57/17.02 ((
% 129.57/17.02 (brelnall2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1E2) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp3) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcextLem) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp4) =>
% 129.57/17.02 ((
% 129.57/17.02 (subbreln) =>
% 129.57/17.02 ((
% 129.57/17.02 (eqbreln) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcext) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcext2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2apEq1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2apEq2) =>
% 129.57/17.02 ((
% 129.57/17.02 (beta1) =>
% 129.57/17.02 ((
% 129.57/17.02 (eta1) =>
% 129.57/17.02 ((
% 129.57/17.02 (lam2lamEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (beta2) =>
% 129.57/17.02 ((
% 129.57/17.02 (eta2) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalseProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalseProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ifSingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (ifp) =>
% 129.57/17.02 ((
% 129.57/17.02 (theeq) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrue) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalse) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueorfalse) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (setextT) =>
% 129.57/17.02 ((
% 129.57/17.02 (subsetTI) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetTI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetTE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectTELcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectTERcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT1) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT2) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT3) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementSub1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementSub2) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTnotintersectT) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementImpComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementSubsetComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementInPowersetComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (contraSubsetComplement) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTcontraSubset) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTILcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTIRcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInUnion) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInUnion2) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInIntersectUnions) =>
% 129.57/17.02 ((
% 129.57/17.02 (intersectInPowersetIntersectUnions) =>
% 129.57/17.02 ((
% 129.57/17.02 (inComplementUnionImpNotIn1) =>
% 129.57/17.02 ((
% 129.57/17.02 (inComplementUnionImpInComplement1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTE) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTEcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementUnionInPowersetComplement) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a2) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1a) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1b) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2b2) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2b) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule0) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule1) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule3) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule4) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_1) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_3) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_4) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_5) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1all2) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1SetBreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (choice2fnsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (setOfPairsIsBReln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1all1) =>
% 129.57/17.02 ((
% 129.57/17.02 (subbreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (eqbreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invI) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invE) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compI) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compE) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compEex) =>
% 129.57/17.02 ((
% 129.57/17.02 (!!) @ (
% 129.57/17.02 (('#B') @ (
% 129.57/17.02 !!) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#S') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#S') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 =>))) @
% 129.57/17.02 breln1)))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 !!))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#S') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#S') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 =>))) @
% 129.57/17.02 breln1)))))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#C') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 breln1)))) @
% 129.57/17.02 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl789])).
% 129.57/17.02 thf(zip_derived_cl824, plain,
% 129.57/17.02 (~ (((eqimpsubset1) =>
% 129.57/17.02 (((subsetI2) =>
% 129.57/17.02 (((emptysetsubset) =>
% 129.57/17.02 (((subsetE) =>
% 129.57/17.02 (((subsetE2) =>
% 129.57/17.02 (((notsubsetI) =>
% 129.57/17.02 (((notequalI1) =>
% 129.57/17.02 (((notequalI2) =>
% 129.57/17.02 (((subsetRefl) =>
% 129.57/17.02 (((subsetTrans) =>
% 129.57/17.02 (((setadjoinSub) =>
% 129.57/17.02 (((setadjoinSub2) =>
% 129.57/17.02 (((subset2powerset) =>
% 129.57/17.02 (((setextsub) =>
% 129.57/17.02 (((subsetemptysetimpeq) =>
% 129.57/17.02 (((powersetI1) =>
% 129.57/17.02 (((powersetE1) =>
% 129.57/17.02 (((inPowerset) =>
% 129.57/17.02 (((powersetsubset) =>
% 129.57/17.02 (((sepInPowerset) =>
% 129.57/17.02 (((sepSubset) =>
% 129.57/17.02 (((binunionIL) =>
% 129.57/17.02 (((upairset2IR) =>
% 129.57/17.02 (((binunionIR) =>
% 129.57/17.02 (((binunionEcases) =>
% 129.57/17.02 (((binunionE) =>
% 129.57/17.02 (((binunionLsub) =>
% 129.57/17.02 (((binunionRsub) =>
% 129.57/17.02 (((binintersectI) =>
% 129.57/17.02 (((binintersectSubset5) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectEL) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectLsub) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset2) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset3) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectER) =>
% 129.57/17.02 ((
% 129.57/17.02 (disjointsetsI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectRsub) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset4) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset1) =>
% 129.57/17.02 ((
% 129.57/17.02 (bs114d) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusI) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusEL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusER) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusSubset2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusERneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusELneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusILneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusIRneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusLsub) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusSubset1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffE) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffI2) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffIneg1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffIneg2) =>
% 129.57/17.02 ((
% 129.57/17.02 (secondinupair) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairIL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairIR) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairiskpair) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairp) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonsubset) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletoninpowerset) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletoninpowunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairset2E) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairsubunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairinpowunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem3) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairin) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempair1) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempair) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionE2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton1) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1E1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1I) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1I2) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonsuniq) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL1) =>
% 129.57/17.02 ((
% 129.57/17.02 (kfstsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (theprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (kfstpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodfstin) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR11) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR12) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR1) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairequniteq) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR) =>
% 129.57/17.02 ((
% 129.57/17.02 (ksndsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (ksndpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairsurjEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodsndin) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairmemEL) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairmemER) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempaircEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodfstpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodsndpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairsurjEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrI) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrSub) =>
% 129.57/17.02 ((
% 129.57/17.02 (setOfPairsIsBReln) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrERa) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrEL1) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrEL2) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrER) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcImageSingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (apProp) =>
% 129.57/17.02 ((
% 129.57/17.02 (app) =>
% 129.57/17.02 ((
% 129.57/17.02 (infuncsetfunc) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2p) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcinfuncset) =>
% 129.57/17.02 ((
% 129.57/17.02 (lamProp) =>
% 129.57/17.02 ((
% 129.57/17.02 (lamp) =>
% 129.57/17.02 ((
% 129.57/17.02 (lam2p) =>
% 129.57/17.02 ((
% 129.57/17.02 (brelnall1) =>
% 129.57/17.02 ((
% 129.57/17.02 (brelnall2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1E2) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp3) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcextLem) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp4) =>
% 129.57/17.02 ((
% 129.57/17.02 (subbreln) =>
% 129.57/17.02 ((
% 129.57/17.02 (eqbreln) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcext) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcext2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2apEq1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2apEq2) =>
% 129.57/17.02 ((
% 129.57/17.02 (beta1) =>
% 129.57/17.02 ((
% 129.57/17.02 (eta1) =>
% 129.57/17.02 ((
% 129.57/17.02 (lam2lamEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (beta2) =>
% 129.57/17.02 ((
% 129.57/17.02 (eta2) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalseProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalseProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ifSingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (ifp) =>
% 129.57/17.02 ((
% 129.57/17.02 (theeq) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrue) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalse) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueorfalse) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (setextT) =>
% 129.57/17.02 ((
% 129.57/17.02 (subsetTI) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetTI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetTE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectTELcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectTERcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT1) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT2) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT3) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementSub1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementSub2) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTnotintersectT) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementImpComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementSubsetComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementInPowersetComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (contraSubsetComplement) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTcontraSubset) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTILcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTIRcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInUnion) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInUnion2) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInIntersectUnions) =>
% 129.57/17.02 ((
% 129.57/17.02 (intersectInPowersetIntersectUnions) =>
% 129.57/17.02 ((
% 129.57/17.02 (inComplementUnionImpNotIn1) =>
% 129.57/17.02 ((
% 129.57/17.02 (inComplementUnionImpInComplement1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTE) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTEcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementUnionInPowersetComplement) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a2) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1a) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1b) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2b2) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2b) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule0) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule1) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule3) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule4) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_1) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_3) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_4) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_5) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1all2) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1SetBreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (choice2fnsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (setOfPairsIsBReln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1all1) =>
% 129.57/17.02 ((
% 129.57/17.02 (subbreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (eqbreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invI) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invE) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compI) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compE) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compEex) =>
% 129.57/17.02 ((
% 129.57/17.02 (!!) @ (
% 129.57/17.02 (('#B') @ (
% 129.57/17.02 !!) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#S') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#S') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 =>))) @
% 129.57/17.02 breln1)))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 !!))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#S') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#S') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 =>))) @
% 129.57/17.02 breln1)))))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#C') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 breln1)))) @
% 129.57/17.02 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl807])).
% 129.57/17.02 thf(zip_derived_cl838, plain,
% 129.57/17.02 (~ (((subsetI2) =>
% 129.57/17.02 (((emptysetsubset) =>
% 129.57/17.02 (((subsetE) =>
% 129.57/17.02 (((subsetE2) =>
% 129.57/17.02 (((notsubsetI) =>
% 129.57/17.02 (((notequalI1) =>
% 129.57/17.02 (((notequalI2) =>
% 129.57/17.02 (((subsetRefl) =>
% 129.57/17.02 (((subsetTrans) =>
% 129.57/17.02 (((setadjoinSub) =>
% 129.57/17.02 (((setadjoinSub2) =>
% 129.57/17.02 (((subset2powerset) =>
% 129.57/17.02 (((setextsub) =>
% 129.57/17.02 (((subsetemptysetimpeq) =>
% 129.57/17.02 (((powersetI1) =>
% 129.57/17.02 (((powersetE1) =>
% 129.57/17.02 (((inPowerset) =>
% 129.57/17.02 (((powersetsubset) =>
% 129.57/17.02 (((sepInPowerset) =>
% 129.57/17.02 (((sepSubset) =>
% 129.57/17.02 (((binunionIL) =>
% 129.57/17.02 (((upairset2IR) =>
% 129.57/17.02 (((binunionIR) =>
% 129.57/17.02 (((binunionEcases) =>
% 129.57/17.02 (((binunionE) =>
% 129.57/17.02 (((binunionLsub) =>
% 129.57/17.02 (((binunionRsub) =>
% 129.57/17.02 (((binintersectI) =>
% 129.57/17.02 (((binintersectSubset5) =>
% 129.57/17.02 (((binintersectEL) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectLsub) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset2) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset3) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectER) =>
% 129.57/17.02 ((
% 129.57/17.02 (disjointsetsI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectRsub) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset4) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset1) =>
% 129.57/17.02 ((
% 129.57/17.02 (bs114d) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusI) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusEL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusER) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusSubset2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusERneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusELneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusILneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusIRneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusLsub) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusSubset1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffE) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffI2) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffIneg1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffIneg2) =>
% 129.57/17.02 ((
% 129.57/17.02 (secondinupair) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairIL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairIR) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairiskpair) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairp) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonsubset) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletoninpowerset) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletoninpowunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairset2E) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairsubunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairinpowunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem3) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairin) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempair1) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempair) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionE2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton1) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1E1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1I) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1I2) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonsuniq) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL1) =>
% 129.57/17.02 ((
% 129.57/17.02 (kfstsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (theprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (kfstpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodfstin) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR11) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR12) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR1) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairequniteq) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR) =>
% 129.57/17.02 ((
% 129.57/17.02 (ksndsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (ksndpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairsurjEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodsndin) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairmemEL) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairmemER) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempaircEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodfstpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodsndpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairsurjEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrI) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrSub) =>
% 129.57/17.02 ((
% 129.57/17.02 (setOfPairsIsBReln) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrERa) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrEL1) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrEL2) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrER) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcImageSingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (apProp) =>
% 129.57/17.02 ((
% 129.57/17.02 (app) =>
% 129.57/17.02 ((
% 129.57/17.02 (infuncsetfunc) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2p) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcinfuncset) =>
% 129.57/17.02 ((
% 129.57/17.02 (lamProp) =>
% 129.57/17.02 ((
% 129.57/17.02 (lamp) =>
% 129.57/17.02 ((
% 129.57/17.02 (lam2p) =>
% 129.57/17.02 ((
% 129.57/17.02 (brelnall1) =>
% 129.57/17.02 ((
% 129.57/17.02 (brelnall2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1E2) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp3) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcextLem) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp4) =>
% 129.57/17.02 ((
% 129.57/17.02 (subbreln) =>
% 129.57/17.02 ((
% 129.57/17.02 (eqbreln) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcext) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcext2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2apEq1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2apEq2) =>
% 129.57/17.02 ((
% 129.57/17.02 (beta1) =>
% 129.57/17.02 ((
% 129.57/17.02 (eta1) =>
% 129.57/17.02 ((
% 129.57/17.02 (lam2lamEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (beta2) =>
% 129.57/17.02 ((
% 129.57/17.02 (eta2) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalseProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalseProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ifSingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (ifp) =>
% 129.57/17.02 ((
% 129.57/17.02 (theeq) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrue) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalse) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueorfalse) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (setextT) =>
% 129.57/17.02 ((
% 129.57/17.02 (subsetTI) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetTI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetTE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectTELcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectTERcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT1) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT2) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT3) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementSub1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementSub2) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTnotintersectT) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementImpComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementSubsetComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementInPowersetComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (contraSubsetComplement) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTcontraSubset) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTILcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTIRcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInUnion) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInUnion2) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInIntersectUnions) =>
% 129.57/17.02 ((
% 129.57/17.02 (intersectInPowersetIntersectUnions) =>
% 129.57/17.02 ((
% 129.57/17.02 (inComplementUnionImpNotIn1) =>
% 129.57/17.02 ((
% 129.57/17.02 (inComplementUnionImpInComplement1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTE) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTEcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementUnionInPowersetComplement) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a2) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1a) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1b) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2b2) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2b) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule0) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule1) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule3) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule4) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_1) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_3) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_4) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_5) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1all2) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1SetBreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (choice2fnsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (setOfPairsIsBReln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1all1) =>
% 129.57/17.02 ((
% 129.57/17.02 (subbreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (eqbreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invI) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invE) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compI) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compE) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compEex) =>
% 129.57/17.02 ((
% 129.57/17.02 (!!) @ (
% 129.57/17.02 (('#B') @ (
% 129.57/17.02 !!) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#S') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#S') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 =>))) @
% 129.57/17.02 breln1)))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 !!))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#S') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#S') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 =>))) @
% 129.57/17.02 breln1)))))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#C') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 breln1)))) @
% 129.57/17.02 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl824])).
% 129.57/17.02 thf(zip_derived_cl850, plain,
% 129.57/17.02 (~ (((emptysetsubset) =>
% 129.57/17.02 (((subsetE) =>
% 129.57/17.02 (((subsetE2) =>
% 129.57/17.02 (((notsubsetI) =>
% 129.57/17.02 (((notequalI1) =>
% 129.57/17.02 (((notequalI2) =>
% 129.57/17.02 (((subsetRefl) =>
% 129.57/17.02 (((subsetTrans) =>
% 129.57/17.02 (((setadjoinSub) =>
% 129.57/17.02 (((setadjoinSub2) =>
% 129.57/17.02 (((subset2powerset) =>
% 129.57/17.02 (((setextsub) =>
% 129.57/17.02 (((subsetemptysetimpeq) =>
% 129.57/17.02 (((powersetI1) =>
% 129.57/17.02 (((powersetE1) =>
% 129.57/17.02 (((inPowerset) =>
% 129.57/17.02 (((powersetsubset) =>
% 129.57/17.02 (((sepInPowerset) =>
% 129.57/17.02 (((sepSubset) =>
% 129.57/17.02 (((binunionIL) =>
% 129.57/17.02 (((upairset2IR) =>
% 129.57/17.02 (((binunionIR) =>
% 129.57/17.02 (((binunionEcases) =>
% 129.57/17.02 (((binunionE) =>
% 129.57/17.02 (((binunionLsub) =>
% 129.57/17.02 (((binunionRsub) =>
% 129.57/17.02 (((binintersectI) =>
% 129.57/17.02 (((binintersectSubset5) =>
% 129.57/17.02 (((binintersectEL) =>
% 129.57/17.02 (((binintersectLsub) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset2) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset3) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectER) =>
% 129.57/17.02 ((
% 129.57/17.02 (disjointsetsI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectRsub) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset4) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset1) =>
% 129.57/17.02 ((
% 129.57/17.02 (bs114d) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusI) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusEL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusER) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusSubset2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusERneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusELneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusILneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusIRneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusLsub) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusSubset1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffE) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffI2) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffIneg1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffIneg2) =>
% 129.57/17.02 ((
% 129.57/17.02 (secondinupair) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairIL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairIR) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairiskpair) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairp) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonsubset) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletoninpowerset) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletoninpowunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairset2E) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairsubunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairinpowunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem3) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairin) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempair1) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempair) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionE2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton1) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1E1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1I) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1I2) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonsuniq) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL1) =>
% 129.57/17.02 ((
% 129.57/17.02 (kfstsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (theprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (kfstpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodfstin) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR11) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR12) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR1) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairequniteq) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR) =>
% 129.57/17.02 ((
% 129.57/17.02 (ksndsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (ksndpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairsurjEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodsndin) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairmemEL) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairmemER) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempaircEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodfstpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodsndpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairsurjEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrI) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrSub) =>
% 129.57/17.02 ((
% 129.57/17.02 (setOfPairsIsBReln) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrERa) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrEL1) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrEL2) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrER) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcImageSingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (apProp) =>
% 129.57/17.02 ((
% 129.57/17.02 (app) =>
% 129.57/17.02 ((
% 129.57/17.02 (infuncsetfunc) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2p) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcinfuncset) =>
% 129.57/17.02 ((
% 129.57/17.02 (lamProp) =>
% 129.57/17.02 ((
% 129.57/17.02 (lamp) =>
% 129.57/17.02 ((
% 129.57/17.02 (lam2p) =>
% 129.57/17.02 ((
% 129.57/17.02 (brelnall1) =>
% 129.57/17.02 ((
% 129.57/17.02 (brelnall2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1E2) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp3) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcextLem) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp4) =>
% 129.57/17.02 ((
% 129.57/17.02 (subbreln) =>
% 129.57/17.02 ((
% 129.57/17.02 (eqbreln) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcext) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcext2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2apEq1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2apEq2) =>
% 129.57/17.02 ((
% 129.57/17.02 (beta1) =>
% 129.57/17.02 ((
% 129.57/17.02 (eta1) =>
% 129.57/17.02 ((
% 129.57/17.02 (lam2lamEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (beta2) =>
% 129.57/17.02 ((
% 129.57/17.02 (eta2) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalseProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalseProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ifSingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (ifp) =>
% 129.57/17.02 ((
% 129.57/17.02 (theeq) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrue) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalse) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueorfalse) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (setextT) =>
% 129.57/17.02 ((
% 129.57/17.02 (subsetTI) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetTI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetTE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectTELcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectTERcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT1) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT2) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT3) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementSub1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementSub2) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTnotintersectT) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementImpComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementSubsetComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementInPowersetComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (contraSubsetComplement) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTcontraSubset) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTILcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTIRcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInUnion) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInUnion2) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInIntersectUnions) =>
% 129.57/17.02 ((
% 129.57/17.02 (intersectInPowersetIntersectUnions) =>
% 129.57/17.02 ((
% 129.57/17.02 (inComplementUnionImpNotIn1) =>
% 129.57/17.02 ((
% 129.57/17.02 (inComplementUnionImpInComplement1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTE) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTEcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementUnionInPowersetComplement) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a2) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1a) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1b) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2b2) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2b) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule0) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule1) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule3) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule4) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_1) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_3) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_4) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_5) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1all2) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1SetBreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (choice2fnsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (setOfPairsIsBReln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1all1) =>
% 129.57/17.02 ((
% 129.57/17.02 (subbreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (eqbreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invI) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invE) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compI) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compE) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compEex) =>
% 129.57/17.02 ((
% 129.57/17.02 (!!) @ (
% 129.57/17.02 (('#B') @ (
% 129.57/17.02 !!) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#S') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#S') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 =>))) @
% 129.57/17.02 breln1)))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 !!))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#S') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#S') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 =>))) @
% 129.57/17.02 breln1)))))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#C') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 breln1)))) @
% 129.57/17.02 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl838])).
% 129.57/17.02 thf(zip_derived_cl863, plain,
% 129.57/17.02 (~ (((subsetE) =>
% 129.57/17.02 (((subsetE2) =>
% 129.57/17.02 (((notsubsetI) =>
% 129.57/17.02 (((notequalI1) =>
% 129.57/17.02 (((notequalI2) =>
% 129.57/17.02 (((subsetRefl) =>
% 129.57/17.02 (((subsetTrans) =>
% 129.57/17.02 (((setadjoinSub) =>
% 129.57/17.02 (((setadjoinSub2) =>
% 129.57/17.02 (((subset2powerset) =>
% 129.57/17.02 (((setextsub) =>
% 129.57/17.02 (((subsetemptysetimpeq) =>
% 129.57/17.02 (((powersetI1) =>
% 129.57/17.02 (((powersetE1) =>
% 129.57/17.02 (((inPowerset) =>
% 129.57/17.02 (((powersetsubset) =>
% 129.57/17.02 (((sepInPowerset) =>
% 129.57/17.02 (((sepSubset) =>
% 129.57/17.02 (((binunionIL) =>
% 129.57/17.02 (((upairset2IR) =>
% 129.57/17.02 (((binunionIR) =>
% 129.57/17.02 (((binunionEcases) =>
% 129.57/17.02 (((binunionE) =>
% 129.57/17.02 (((binunionLsub) =>
% 129.57/17.02 (((binunionRsub) =>
% 129.57/17.02 (((binintersectI) =>
% 129.57/17.02 (((binintersectSubset5) =>
% 129.57/17.02 (((binintersectEL) =>
% 129.57/17.02 (((binintersectLsub) =>
% 129.57/17.02 (((binintersectSubset2) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset3) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectER) =>
% 129.57/17.02 ((
% 129.57/17.02 (disjointsetsI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectRsub) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset4) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset1) =>
% 129.57/17.02 ((
% 129.57/17.02 (bs114d) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusI) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusEL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusER) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusSubset2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusERneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusELneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusILneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusIRneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusLsub) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusSubset1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffE) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffI2) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffIneg1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffIneg2) =>
% 129.57/17.02 ((
% 129.57/17.02 (secondinupair) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairIL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairIR) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairiskpair) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairp) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonsubset) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletoninpowerset) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletoninpowunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairset2E) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairsubunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairinpowunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem3) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairin) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempair1) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempair) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionE2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton1) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1E1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1I) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1I2) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonsuniq) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL1) =>
% 129.57/17.02 ((
% 129.57/17.02 (kfstsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (theprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (kfstpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodfstin) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR11) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR12) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR1) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairequniteq) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR) =>
% 129.57/17.02 ((
% 129.57/17.02 (ksndsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (ksndpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairsurjEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodsndin) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairmemEL) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairmemER) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempaircEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodfstpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodsndpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairsurjEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrI) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrSub) =>
% 129.57/17.02 ((
% 129.57/17.02 (setOfPairsIsBReln) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrERa) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrEL1) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrEL2) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrER) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcImageSingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (apProp) =>
% 129.57/17.02 ((
% 129.57/17.02 (app) =>
% 129.57/17.02 ((
% 129.57/17.02 (infuncsetfunc) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2p) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcinfuncset) =>
% 129.57/17.02 ((
% 129.57/17.02 (lamProp) =>
% 129.57/17.02 ((
% 129.57/17.02 (lamp) =>
% 129.57/17.02 ((
% 129.57/17.02 (lam2p) =>
% 129.57/17.02 ((
% 129.57/17.02 (brelnall1) =>
% 129.57/17.02 ((
% 129.57/17.02 (brelnall2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1E2) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp3) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcextLem) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp4) =>
% 129.57/17.02 ((
% 129.57/17.02 (subbreln) =>
% 129.57/17.02 ((
% 129.57/17.02 (eqbreln) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcext) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcext2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2apEq1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2apEq2) =>
% 129.57/17.02 ((
% 129.57/17.02 (beta1) =>
% 129.57/17.02 ((
% 129.57/17.02 (eta1) =>
% 129.57/17.02 ((
% 129.57/17.02 (lam2lamEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (beta2) =>
% 129.57/17.02 ((
% 129.57/17.02 (eta2) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalseProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalseProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ifSingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (ifp) =>
% 129.57/17.02 ((
% 129.57/17.02 (theeq) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrue) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalse) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueorfalse) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (setextT) =>
% 129.57/17.02 ((
% 129.57/17.02 (subsetTI) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetTI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetTE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectTELcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectTERcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT1) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT2) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT3) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementSub1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementSub2) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTnotintersectT) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementImpComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementSubsetComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementInPowersetComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (contraSubsetComplement) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTcontraSubset) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTILcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTIRcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInUnion) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInUnion2) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInIntersectUnions) =>
% 129.57/17.02 ((
% 129.57/17.02 (intersectInPowersetIntersectUnions) =>
% 129.57/17.02 ((
% 129.57/17.02 (inComplementUnionImpNotIn1) =>
% 129.57/17.02 ((
% 129.57/17.02 (inComplementUnionImpInComplement1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTE) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTEcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementUnionInPowersetComplement) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a2) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1a) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1b) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2b2) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2b) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule0) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule1) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule3) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule4) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_1) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_3) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_4) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_5) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1all2) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1SetBreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (choice2fnsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (setOfPairsIsBReln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1all1) =>
% 129.57/17.02 ((
% 129.57/17.02 (subbreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (eqbreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invI) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invE) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compI) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compE) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compEex) =>
% 129.57/17.02 ((
% 129.57/17.02 (!!) @ (
% 129.57/17.02 (('#B') @ (
% 129.57/17.02 !!) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#S') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#S') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 =>))) @
% 129.57/17.02 breln1)))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 !!))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#S') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#S') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 =>))) @
% 129.57/17.02 breln1)))))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#C') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 breln1)))) @
% 129.57/17.02 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl850])).
% 129.57/17.02 thf(zip_derived_cl878, plain,
% 129.57/17.02 (~ (((subsetE2) =>
% 129.57/17.02 (((notsubsetI) =>
% 129.57/17.02 (((notequalI1) =>
% 129.57/17.02 (((notequalI2) =>
% 129.57/17.02 (((subsetRefl) =>
% 129.57/17.02 (((subsetTrans) =>
% 129.57/17.02 (((setadjoinSub) =>
% 129.57/17.02 (((setadjoinSub2) =>
% 129.57/17.02 (((subset2powerset) =>
% 129.57/17.02 (((setextsub) =>
% 129.57/17.02 (((subsetemptysetimpeq) =>
% 129.57/17.02 (((powersetI1) =>
% 129.57/17.02 (((powersetE1) =>
% 129.57/17.02 (((inPowerset) =>
% 129.57/17.02 (((powersetsubset) =>
% 129.57/17.02 (((sepInPowerset) =>
% 129.57/17.02 (((sepSubset) =>
% 129.57/17.02 (((binunionIL) =>
% 129.57/17.02 (((upairset2IR) =>
% 129.57/17.02 (((binunionIR) =>
% 129.57/17.02 (((binunionEcases) =>
% 129.57/17.02 (((binunionE) =>
% 129.57/17.02 (((binunionLsub) =>
% 129.57/17.02 (((binunionRsub) =>
% 129.57/17.02 (((binintersectI) =>
% 129.57/17.02 (((binintersectSubset5) =>
% 129.57/17.02 (((binintersectEL) =>
% 129.57/17.02 (((binintersectLsub) =>
% 129.57/17.02 (((binintersectSubset2) =>
% 129.57/17.02 (((binintersectSubset3) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectER) =>
% 129.57/17.02 ((
% 129.57/17.02 (disjointsetsI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectRsub) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset4) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset1) =>
% 129.57/17.02 ((
% 129.57/17.02 (bs114d) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusI) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusEL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusER) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusSubset2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusERneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusELneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusILneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusIRneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusLsub) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusSubset1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffE) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffI2) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffIneg1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffIneg2) =>
% 129.57/17.02 ((
% 129.57/17.02 (secondinupair) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairIL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairIR) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairiskpair) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairp) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonsubset) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletoninpowerset) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletoninpowunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairset2E) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairsubunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairinpowunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem3) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairin) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempair1) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempair) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionE2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton1) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1E1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1I) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1I2) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonsuniq) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL1) =>
% 129.57/17.02 ((
% 129.57/17.02 (kfstsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (theprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (kfstpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodfstin) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR11) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR12) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR1) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairequniteq) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR) =>
% 129.57/17.02 ((
% 129.57/17.02 (ksndsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (ksndpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairsurjEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodsndin) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairmemEL) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairmemER) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempaircEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodfstpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodsndpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairsurjEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrI) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrSub) =>
% 129.57/17.02 ((
% 129.57/17.02 (setOfPairsIsBReln) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrERa) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrEL1) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrEL2) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrER) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcImageSingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (apProp) =>
% 129.57/17.02 ((
% 129.57/17.02 (app) =>
% 129.57/17.02 ((
% 129.57/17.02 (infuncsetfunc) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2p) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcinfuncset) =>
% 129.57/17.02 ((
% 129.57/17.02 (lamProp) =>
% 129.57/17.02 ((
% 129.57/17.02 (lamp) =>
% 129.57/17.02 ((
% 129.57/17.02 (lam2p) =>
% 129.57/17.02 ((
% 129.57/17.02 (brelnall1) =>
% 129.57/17.02 ((
% 129.57/17.02 (brelnall2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1E2) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp3) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcextLem) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp4) =>
% 129.57/17.02 ((
% 129.57/17.02 (subbreln) =>
% 129.57/17.02 ((
% 129.57/17.02 (eqbreln) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcext) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcext2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2apEq1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2apEq2) =>
% 129.57/17.02 ((
% 129.57/17.02 (beta1) =>
% 129.57/17.02 ((
% 129.57/17.02 (eta1) =>
% 129.57/17.02 ((
% 129.57/17.02 (lam2lamEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (beta2) =>
% 129.57/17.02 ((
% 129.57/17.02 (eta2) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalseProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalseProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ifSingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (ifp) =>
% 129.57/17.02 ((
% 129.57/17.02 (theeq) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrue) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalse) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueorfalse) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (setextT) =>
% 129.57/17.02 ((
% 129.57/17.02 (subsetTI) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetTI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetTE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectTELcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectTERcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT1) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT2) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT3) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementSub1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementSub2) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTnotintersectT) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementImpComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementSubsetComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementInPowersetComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (contraSubsetComplement) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTcontraSubset) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTILcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTIRcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInUnion) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInUnion2) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInIntersectUnions) =>
% 129.57/17.02 ((
% 129.57/17.02 (intersectInPowersetIntersectUnions) =>
% 129.57/17.02 ((
% 129.57/17.02 (inComplementUnionImpNotIn1) =>
% 129.57/17.02 ((
% 129.57/17.02 (inComplementUnionImpInComplement1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTE) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTEcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementUnionInPowersetComplement) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a2) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1a) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1b) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2b2) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2b) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule0) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule1) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule3) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule4) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_1) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_3) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_4) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_5) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1all2) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1SetBreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (choice2fnsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (setOfPairsIsBReln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1all1) =>
% 129.57/17.02 ((
% 129.57/17.02 (subbreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (eqbreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invI) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invE) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compI) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compE) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1compEex) =>
% 129.57/17.02 ((
% 129.57/17.02 (!!) @ (
% 129.57/17.02 (('#B') @ (
% 129.57/17.02 !!) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#S') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#S') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 =>))) @
% 129.57/17.02 breln1)))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 !!))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#S') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#S') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 =>))) @
% 129.57/17.02 breln1)))))) @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#C') @ (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 (
% 129.57/17.02 (
% 129.57/17.02 ('#B') @ (
% 129.57/17.02 '#B') @
% 129.57/17.02 breln1)))) @
% 129.57/17.02 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl863])).
% 129.57/17.02 thf(zip_derived_cl896, plain,
% 129.57/17.02 (~ (((notsubsetI) =>
% 129.57/17.02 (((notequalI1) =>
% 129.57/17.02 (((notequalI2) =>
% 129.57/17.02 (((subsetRefl) =>
% 129.57/17.02 (((subsetTrans) =>
% 129.57/17.02 (((setadjoinSub) =>
% 129.57/17.02 (((setadjoinSub2) =>
% 129.57/17.02 (((subset2powerset) =>
% 129.57/17.02 (((setextsub) =>
% 129.57/17.02 (((subsetemptysetimpeq) =>
% 129.57/17.02 (((powersetI1) =>
% 129.57/17.02 (((powersetE1) =>
% 129.57/17.02 (((inPowerset) =>
% 129.57/17.02 (((powersetsubset) =>
% 129.57/17.02 (((sepInPowerset) =>
% 129.57/17.02 (((sepSubset) =>
% 129.57/17.02 (((binunionIL) =>
% 129.57/17.02 (((upairset2IR) =>
% 129.57/17.02 (((binunionIR) =>
% 129.57/17.02 (((binunionEcases) =>
% 129.57/17.02 (((binunionE) =>
% 129.57/17.02 (((binunionLsub) =>
% 129.57/17.02 (((binunionRsub) =>
% 129.57/17.02 (((binintersectI) =>
% 129.57/17.02 (((binintersectSubset5) =>
% 129.57/17.02 (((binintersectEL) =>
% 129.57/17.02 (((binintersectLsub) =>
% 129.57/17.02 (((binintersectSubset2) =>
% 129.57/17.02 (((binintersectSubset3) =>
% 129.57/17.02 (((binintersectER) =>
% 129.57/17.02 ((
% 129.57/17.02 (disjointsetsI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectRsub) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset4) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectSubset1) =>
% 129.57/17.02 ((
% 129.57/17.02 (bs114d) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusI) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusEL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusER) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusSubset2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusERneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusELneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusILneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusIRneg) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusLsub) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusSubset1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffE) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffI2) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffIneg1) =>
% 129.57/17.02 ((
% 129.57/17.02 (symdiffIneg2) =>
% 129.57/17.02 ((
% 129.57/17.02 (secondinupair) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairIL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairIR) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairiskpair) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairp) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonsubset) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletoninpowerset) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletoninpowunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairset2E) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairsubunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairinpowunion) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ubforcartprodlem3) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairin) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempair1) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempair) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionE2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton1) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setunionsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1E1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1I) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1I2) =>
% 129.57/17.02 ((
% 129.57/17.02 (singletonsuniq) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL1) =>
% 129.57/17.02 ((
% 129.57/17.02 (kfstsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (theprop) =>
% 129.57/17.02 ((
% 129.57/17.02 (kfstpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodfstin) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjL) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR11) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR12) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR1) =>
% 129.57/17.02 ((
% 129.57/17.02 (upairequniteq) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR2) =>
% 129.57/17.02 ((
% 129.57/17.02 (setukpairinjR) =>
% 129.57/17.02 ((
% 129.57/17.02 (ksndsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (ksndpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (kpairsurjEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodsndin) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairmemEL) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairmemER) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodmempaircEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodfstpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodsndpairEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (cartprodpairsurjEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrI) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrSub) =>
% 129.57/17.02 ((
% 129.57/17.02 (setOfPairsIsBReln) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrERa) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrEL1) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrEL2) =>
% 129.57/17.02 ((
% 129.57/17.02 (dpsetconstrER) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcImageSingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (apProp) =>
% 129.57/17.02 ((
% 129.57/17.02 (app) =>
% 129.57/17.02 ((
% 129.57/17.02 (infuncsetfunc) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2p) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcinfuncset) =>
% 129.57/17.02 ((
% 129.57/17.02 (lamProp) =>
% 129.57/17.02 ((
% 129.57/17.02 (lamp) =>
% 129.57/17.02 ((
% 129.57/17.02 (lam2p) =>
% 129.57/17.02 ((
% 129.57/17.02 (brelnall1) =>
% 129.57/17.02 ((
% 129.57/17.02 (brelnall2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ex1E2) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp3) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcextLem) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcGraphProp4) =>
% 129.57/17.02 ((
% 129.57/17.02 (subbreln) =>
% 129.57/17.02 ((
% 129.57/17.02 (eqbreln) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcext) =>
% 129.57/17.02 ((
% 129.57/17.02 (funcext2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2apEq1) =>
% 129.57/17.02 ((
% 129.57/17.02 (ap2apEq2) =>
% 129.57/17.02 ((
% 129.57/17.02 (beta1) =>
% 129.57/17.02 ((
% 129.57/17.02 (eta1) =>
% 129.57/17.02 ((
% 129.57/17.02 (lam2lamEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (beta2) =>
% 129.57/17.02 ((
% 129.57/17.02 (eta2) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalseProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalseProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueProp1) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueProp2) =>
% 129.57/17.02 ((
% 129.57/17.02 (ifSingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (ifp) =>
% 129.57/17.02 ((
% 129.57/17.02 (theeq) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrue) =>
% 129.57/17.02 ((
% 129.57/17.02 (iffalse) =>
% 129.57/17.02 ((
% 129.57/17.02 (iftrueorfalse) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (setminusT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementT_lem) =>
% 129.57/17.02 ((
% 129.57/17.02 (setextT) =>
% 129.57/17.02 ((
% 129.57/17.02 (subsetTI) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetTI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (powersetTE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectTELcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (binintersectTERcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT1) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT2) =>
% 129.57/17.02 ((
% 129.57/17.02 (contrasubsetT3) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementI1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementE1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementSub1) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementSub2) =>
% 129.57/17.02 ((
% 129.57/17.02 (doubleComplementEq) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTnotintersectT) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementImpComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementSubsetComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementInPowersetComplementIntersect) =>
% 129.57/17.02 ((
% 129.57/17.02 (contraSubsetComplement) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementTcontraSubset) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTILcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTIRcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInUnion) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInUnion2) =>
% 129.57/17.02 ((
% 129.57/17.02 (inIntersectImpInIntersectUnions) =>
% 129.57/17.02 ((
% 129.57/17.02 (intersectInPowersetIntersectUnions) =>
% 129.57/17.02 ((
% 129.57/17.02 (inComplementUnionImpNotIn1) =>
% 129.57/17.02 ((
% 129.57/17.02 (inComplementUnionImpInComplement1) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTE) =>
% 129.57/17.02 ((
% 129.57/17.02 (binunionTEcontra) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a1) =>
% 129.57/17.02 ((
% 129.57/17.02 (complementUnionInPowersetComplement) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a2) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1a) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1b) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan1) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2a) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2b2) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2b) =>
% 129.57/17.02 ((
% 129.57/17.02 (demorgan2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule0) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule1) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule3) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz13rule4) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_1) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_2) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_3) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_4) =>
% 129.57/17.02 ((
% 129.57/17.02 (woz1_5) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1all2) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1SetBreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (choice2fnsingleton) =>
% 129.57/17.02 ((
% 129.57/17.02 (setOfPairsIsBReln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1all1) =>
% 129.57/17.02 ((
% 129.57/17.02 (subbreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (eqbreln1) =>
% 129.57/17.02 ((
% 129.57/17.02 (breln1invprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invI) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invE) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compI) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compE) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compEex) =>
% 129.57/17.03 ((
% 129.57/17.03 (!!) @ (
% 129.57/17.03 (('#B') @ (
% 129.57/17.03 !!) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#S') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#S') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 =>))) @
% 129.57/17.03 breln1)))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 !!))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#S') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#S') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 =>))) @
% 129.57/17.03 breln1)))))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#C') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 breln1)))) @
% 129.57/17.03 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl878])).
% 129.57/17.03 thf(zip_derived_cl909, plain,
% 129.57/17.03 (~ (((notequalI1) =>
% 129.57/17.03 (((notequalI2) =>
% 129.57/17.03 (((subsetRefl) =>
% 129.57/17.03 (((subsetTrans) =>
% 129.57/17.03 (((setadjoinSub) =>
% 129.57/17.03 (((setadjoinSub2) =>
% 129.57/17.03 (((subset2powerset) =>
% 129.57/17.03 (((setextsub) =>
% 129.57/17.03 (((subsetemptysetimpeq) =>
% 129.57/17.03 (((powersetI1) =>
% 129.57/17.03 (((powersetE1) =>
% 129.57/17.03 (((inPowerset) =>
% 129.57/17.03 (((powersetsubset) =>
% 129.57/17.03 (((sepInPowerset) =>
% 129.57/17.03 (((sepSubset) =>
% 129.57/17.03 (((binunionIL) =>
% 129.57/17.03 (((upairset2IR) =>
% 129.57/17.03 (((binunionIR) =>
% 129.57/17.03 (((binunionEcases) =>
% 129.57/17.03 (((binunionE) =>
% 129.57/17.03 (((binunionLsub) =>
% 129.57/17.03 (((binunionRsub) =>
% 129.57/17.03 (((binintersectI) =>
% 129.57/17.03 (((binintersectSubset5) =>
% 129.57/17.03 (((binintersectEL) =>
% 129.57/17.03 (((binintersectLsub) =>
% 129.57/17.03 (((binintersectSubset2) =>
% 129.57/17.03 (((binintersectSubset3) =>
% 129.57/17.03 (((binintersectER) =>
% 129.57/17.03 (((disjointsetsI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectRsub) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectSubset4) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectSubset1) =>
% 129.57/17.03 ((
% 129.57/17.03 (bs114d) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusI) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusEL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusER) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusSubset2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusERneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusELneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusILneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusIRneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusLsub) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusSubset1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffE) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffI2) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffIneg1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffIneg2) =>
% 129.57/17.03 ((
% 129.57/17.03 (secondinupair) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairIL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairIR) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairiskpair) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairp) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonsubset) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletoninpowerset) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletoninpowunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairset2E) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairsubunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairinpowunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem3) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairin) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempair1) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempair) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionE2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton1) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1E1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1I) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1I2) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonsuniq) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL1) =>
% 129.57/17.03 ((
% 129.57/17.03 (kfstsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (theprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (kfstpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodfstin) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR11) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR12) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR1) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairequniteq) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR) =>
% 129.57/17.03 ((
% 129.57/17.03 (ksndsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (ksndpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairsurjEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodsndin) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairmemEL) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairmemER) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempaircEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodfstpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodsndpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairsurjEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrI) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrSub) =>
% 129.57/17.03 ((
% 129.57/17.03 (setOfPairsIsBReln) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrERa) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrEL1) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrEL2) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrER) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcImageSingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (apProp) =>
% 129.57/17.03 ((
% 129.57/17.03 (app) =>
% 129.57/17.03 ((
% 129.57/17.03 (infuncsetfunc) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2p) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcinfuncset) =>
% 129.57/17.03 ((
% 129.57/17.03 (lamProp) =>
% 129.57/17.03 ((
% 129.57/17.03 (lamp) =>
% 129.57/17.03 ((
% 129.57/17.03 (lam2p) =>
% 129.57/17.03 ((
% 129.57/17.03 (brelnall1) =>
% 129.57/17.03 ((
% 129.57/17.03 (brelnall2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1E2) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp3) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcextLem) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp4) =>
% 129.57/17.03 ((
% 129.57/17.03 (subbreln) =>
% 129.57/17.03 ((
% 129.57/17.03 (eqbreln) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcext) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcext2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2apEq1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2apEq2) =>
% 129.57/17.03 ((
% 129.57/17.03 (beta1) =>
% 129.57/17.03 ((
% 129.57/17.03 (eta1) =>
% 129.57/17.03 ((
% 129.57/17.03 (lam2lamEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (beta2) =>
% 129.57/17.03 ((
% 129.57/17.03 (eta2) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalseProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalseProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ifSingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (ifp) =>
% 129.57/17.03 ((
% 129.57/17.03 (theeq) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrue) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalse) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueorfalse) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (setextT) =>
% 129.57/17.03 ((
% 129.57/17.03 (subsetTI) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetTI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetTE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectTELcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectTERcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT1) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT2) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT3) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementSub1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementSub2) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTnotintersectT) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementImpComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementSubsetComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementInPowersetComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (contraSubsetComplement) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTcontraSubset) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTILcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTIRcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInUnion) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInUnion2) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInIntersectUnions) =>
% 129.57/17.03 ((
% 129.57/17.03 (intersectInPowersetIntersectUnions) =>
% 129.57/17.03 ((
% 129.57/17.03 (inComplementUnionImpNotIn1) =>
% 129.57/17.03 ((
% 129.57/17.03 (inComplementUnionImpInComplement1) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTE) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTEcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementUnionInPowersetComplement) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a2) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1a) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1b) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2b2) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2b) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule0) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule1) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule3) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule4) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_1) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_3) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_4) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_5) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1all2) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1SetBreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (choice2fnsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (setOfPairsIsBReln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1all1) =>
% 129.57/17.03 ((
% 129.57/17.03 (subbreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (eqbreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invI) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invE) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compI) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compE) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compEex) =>
% 129.57/17.03 ((
% 129.57/17.03 (!!) @ (
% 129.57/17.03 (('#B') @ (
% 129.57/17.03 !!) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#S') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#S') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 =>))) @
% 129.57/17.03 breln1)))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 !!))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#S') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#S') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 =>))) @
% 129.57/17.03 breln1)))))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#C') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 breln1)))) @
% 129.57/17.03 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl896])).
% 129.57/17.03 thf(zip_derived_cl924, plain,
% 129.57/17.03 (~ (((notequalI2) =>
% 129.57/17.03 (((subsetRefl) =>
% 129.57/17.03 (((subsetTrans) =>
% 129.57/17.03 (((setadjoinSub) =>
% 129.57/17.03 (((setadjoinSub2) =>
% 129.57/17.03 (((subset2powerset) =>
% 129.57/17.03 (((setextsub) =>
% 129.57/17.03 (((subsetemptysetimpeq) =>
% 129.57/17.03 (((powersetI1) =>
% 129.57/17.03 (((powersetE1) =>
% 129.57/17.03 (((inPowerset) =>
% 129.57/17.03 (((powersetsubset) =>
% 129.57/17.03 (((sepInPowerset) =>
% 129.57/17.03 (((sepSubset) =>
% 129.57/17.03 (((binunionIL) =>
% 129.57/17.03 (((upairset2IR) =>
% 129.57/17.03 (((binunionIR) =>
% 129.57/17.03 (((binunionEcases) =>
% 129.57/17.03 (((binunionE) =>
% 129.57/17.03 (((binunionLsub) =>
% 129.57/17.03 (((binunionRsub) =>
% 129.57/17.03 (((binintersectI) =>
% 129.57/17.03 (((binintersectSubset5) =>
% 129.57/17.03 (((binintersectEL) =>
% 129.57/17.03 (((binintersectLsub) =>
% 129.57/17.03 (((binintersectSubset2) =>
% 129.57/17.03 (((binintersectSubset3) =>
% 129.57/17.03 (((binintersectER) =>
% 129.57/17.03 (((disjointsetsI1) =>
% 129.57/17.03 (((binintersectRsub) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectSubset4) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectSubset1) =>
% 129.57/17.03 ((
% 129.57/17.03 (bs114d) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusI) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusEL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusER) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusSubset2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusERneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusELneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusILneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusIRneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusLsub) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusSubset1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffE) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffI2) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffIneg1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffIneg2) =>
% 129.57/17.03 ((
% 129.57/17.03 (secondinupair) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairIL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairIR) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairiskpair) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairp) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonsubset) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletoninpowerset) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletoninpowunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairset2E) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairsubunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairinpowunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem3) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairin) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempair1) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempair) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionE2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton1) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1E1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1I) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1I2) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonsuniq) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL1) =>
% 129.57/17.03 ((
% 129.57/17.03 (kfstsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (theprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (kfstpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodfstin) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR11) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR12) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR1) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairequniteq) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR) =>
% 129.57/17.03 ((
% 129.57/17.03 (ksndsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (ksndpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairsurjEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodsndin) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairmemEL) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairmemER) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempaircEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodfstpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodsndpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairsurjEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrI) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrSub) =>
% 129.57/17.03 ((
% 129.57/17.03 (setOfPairsIsBReln) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrERa) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrEL1) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrEL2) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrER) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcImageSingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (apProp) =>
% 129.57/17.03 ((
% 129.57/17.03 (app) =>
% 129.57/17.03 ((
% 129.57/17.03 (infuncsetfunc) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2p) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcinfuncset) =>
% 129.57/17.03 ((
% 129.57/17.03 (lamProp) =>
% 129.57/17.03 ((
% 129.57/17.03 (lamp) =>
% 129.57/17.03 ((
% 129.57/17.03 (lam2p) =>
% 129.57/17.03 ((
% 129.57/17.03 (brelnall1) =>
% 129.57/17.03 ((
% 129.57/17.03 (brelnall2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1E2) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp3) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcextLem) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp4) =>
% 129.57/17.03 ((
% 129.57/17.03 (subbreln) =>
% 129.57/17.03 ((
% 129.57/17.03 (eqbreln) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcext) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcext2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2apEq1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2apEq2) =>
% 129.57/17.03 ((
% 129.57/17.03 (beta1) =>
% 129.57/17.03 ((
% 129.57/17.03 (eta1) =>
% 129.57/17.03 ((
% 129.57/17.03 (lam2lamEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (beta2) =>
% 129.57/17.03 ((
% 129.57/17.03 (eta2) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalseProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalseProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ifSingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (ifp) =>
% 129.57/17.03 ((
% 129.57/17.03 (theeq) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrue) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalse) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueorfalse) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (setextT) =>
% 129.57/17.03 ((
% 129.57/17.03 (subsetTI) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetTI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetTE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectTELcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectTERcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT1) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT2) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT3) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementSub1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementSub2) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTnotintersectT) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementImpComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementSubsetComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementInPowersetComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (contraSubsetComplement) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTcontraSubset) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTILcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTIRcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInUnion) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInUnion2) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInIntersectUnions) =>
% 129.57/17.03 ((
% 129.57/17.03 (intersectInPowersetIntersectUnions) =>
% 129.57/17.03 ((
% 129.57/17.03 (inComplementUnionImpNotIn1) =>
% 129.57/17.03 ((
% 129.57/17.03 (inComplementUnionImpInComplement1) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTE) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTEcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementUnionInPowersetComplement) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a2) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1a) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1b) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2b2) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2b) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule0) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule1) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule3) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule4) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_1) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_3) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_4) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_5) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1all2) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1SetBreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (choice2fnsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (setOfPairsIsBReln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1all1) =>
% 129.57/17.03 ((
% 129.57/17.03 (subbreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (eqbreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invI) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invE) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compI) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compE) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compEex) =>
% 129.57/17.03 ((
% 129.57/17.03 (!!) @ (
% 129.57/17.03 (('#B') @ (
% 129.57/17.03 !!) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#S') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#S') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 =>))) @
% 129.57/17.03 breln1)))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 !!))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#S') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#S') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 =>))) @
% 129.57/17.03 breln1)))))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#C') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 breln1)))) @
% 129.57/17.03 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl909])).
% 129.57/17.03 thf(zip_derived_cl938, plain,
% 129.57/17.03 (~ (((subsetRefl) =>
% 129.57/17.03 (((subsetTrans) =>
% 129.57/17.03 (((setadjoinSub) =>
% 129.57/17.03 (((setadjoinSub2) =>
% 129.57/17.03 (((subset2powerset) =>
% 129.57/17.03 (((setextsub) =>
% 129.57/17.03 (((subsetemptysetimpeq) =>
% 129.57/17.03 (((powersetI1) =>
% 129.57/17.03 (((powersetE1) =>
% 129.57/17.03 (((inPowerset) =>
% 129.57/17.03 (((powersetsubset) =>
% 129.57/17.03 (((sepInPowerset) =>
% 129.57/17.03 (((sepSubset) =>
% 129.57/17.03 (((binunionIL) =>
% 129.57/17.03 (((upairset2IR) =>
% 129.57/17.03 (((binunionIR) =>
% 129.57/17.03 (((binunionEcases) =>
% 129.57/17.03 (((binunionE) =>
% 129.57/17.03 (((binunionLsub) =>
% 129.57/17.03 (((binunionRsub) =>
% 129.57/17.03 (((binintersectI) =>
% 129.57/17.03 (((binintersectSubset5) =>
% 129.57/17.03 (((binintersectEL) =>
% 129.57/17.03 (((binintersectLsub) =>
% 129.57/17.03 (((binintersectSubset2) =>
% 129.57/17.03 (((binintersectSubset3) =>
% 129.57/17.03 (((binintersectER) =>
% 129.57/17.03 (((disjointsetsI1) =>
% 129.57/17.03 (((binintersectRsub) =>
% 129.57/17.03 (((binintersectSubset4) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectSubset1) =>
% 129.57/17.03 ((
% 129.57/17.03 (bs114d) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusI) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusEL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusER) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusSubset2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusERneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusELneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusILneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusIRneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusLsub) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusSubset1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffE) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffI2) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffIneg1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffIneg2) =>
% 129.57/17.03 ((
% 129.57/17.03 (secondinupair) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairIL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairIR) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairiskpair) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairp) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonsubset) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletoninpowerset) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletoninpowunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairset2E) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairsubunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairinpowunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem3) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairin) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempair1) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempair) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionE2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton1) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1E1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1I) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1I2) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonsuniq) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL1) =>
% 129.57/17.03 ((
% 129.57/17.03 (kfstsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (theprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (kfstpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodfstin) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR11) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR12) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR1) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairequniteq) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR) =>
% 129.57/17.03 ((
% 129.57/17.03 (ksndsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (ksndpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairsurjEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodsndin) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairmemEL) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairmemER) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempaircEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodfstpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodsndpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairsurjEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrI) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrSub) =>
% 129.57/17.03 ((
% 129.57/17.03 (setOfPairsIsBReln) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrERa) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrEL1) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrEL2) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrER) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcImageSingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (apProp) =>
% 129.57/17.03 ((
% 129.57/17.03 (app) =>
% 129.57/17.03 ((
% 129.57/17.03 (infuncsetfunc) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2p) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcinfuncset) =>
% 129.57/17.03 ((
% 129.57/17.03 (lamProp) =>
% 129.57/17.03 ((
% 129.57/17.03 (lamp) =>
% 129.57/17.03 ((
% 129.57/17.03 (lam2p) =>
% 129.57/17.03 ((
% 129.57/17.03 (brelnall1) =>
% 129.57/17.03 ((
% 129.57/17.03 (brelnall2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1E2) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp3) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcextLem) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp4) =>
% 129.57/17.03 ((
% 129.57/17.03 (subbreln) =>
% 129.57/17.03 ((
% 129.57/17.03 (eqbreln) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcext) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcext2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2apEq1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2apEq2) =>
% 129.57/17.03 ((
% 129.57/17.03 (beta1) =>
% 129.57/17.03 ((
% 129.57/17.03 (eta1) =>
% 129.57/17.03 ((
% 129.57/17.03 (lam2lamEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (beta2) =>
% 129.57/17.03 ((
% 129.57/17.03 (eta2) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalseProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalseProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ifSingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (ifp) =>
% 129.57/17.03 ((
% 129.57/17.03 (theeq) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrue) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalse) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueorfalse) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (setextT) =>
% 129.57/17.03 ((
% 129.57/17.03 (subsetTI) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetTI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetTE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectTELcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectTERcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT1) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT2) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT3) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementSub1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementSub2) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTnotintersectT) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementImpComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementSubsetComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementInPowersetComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (contraSubsetComplement) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTcontraSubset) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTILcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTIRcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInUnion) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInUnion2) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInIntersectUnions) =>
% 129.57/17.03 ((
% 129.57/17.03 (intersectInPowersetIntersectUnions) =>
% 129.57/17.03 ((
% 129.57/17.03 (inComplementUnionImpNotIn1) =>
% 129.57/17.03 ((
% 129.57/17.03 (inComplementUnionImpInComplement1) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTE) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTEcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementUnionInPowersetComplement) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a2) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1a) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1b) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2b2) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2b) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule0) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule1) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule3) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule4) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_1) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_3) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_4) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_5) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1all2) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1SetBreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (choice2fnsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (setOfPairsIsBReln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1all1) =>
% 129.57/17.03 ((
% 129.57/17.03 (subbreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (eqbreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invI) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invE) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compI) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compE) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compEex) =>
% 129.57/17.03 ((
% 129.57/17.03 (!!) @ (
% 129.57/17.03 (('#B') @ (
% 129.57/17.03 !!) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#S') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#S') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 =>))) @
% 129.57/17.03 breln1)))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 !!))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#S') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#S') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 =>))) @
% 129.57/17.03 breln1)))))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#C') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 breln1)))) @
% 129.57/17.03 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl924])).
% 129.57/17.03 thf(zip_derived_cl952, plain,
% 129.57/17.03 (~ (((subsetTrans) =>
% 129.57/17.03 (((setadjoinSub) =>
% 129.57/17.03 (((setadjoinSub2) =>
% 129.57/17.03 (((subset2powerset) =>
% 129.57/17.03 (((setextsub) =>
% 129.57/17.03 (((subsetemptysetimpeq) =>
% 129.57/17.03 (((powersetI1) =>
% 129.57/17.03 (((powersetE1) =>
% 129.57/17.03 (((inPowerset) =>
% 129.57/17.03 (((powersetsubset) =>
% 129.57/17.03 (((sepInPowerset) =>
% 129.57/17.03 (((sepSubset) =>
% 129.57/17.03 (((binunionIL) =>
% 129.57/17.03 (((upairset2IR) =>
% 129.57/17.03 (((binunionIR) =>
% 129.57/17.03 (((binunionEcases) =>
% 129.57/17.03 (((binunionE) =>
% 129.57/17.03 (((binunionLsub) =>
% 129.57/17.03 (((binunionRsub) =>
% 129.57/17.03 (((binintersectI) =>
% 129.57/17.03 (((binintersectSubset5) =>
% 129.57/17.03 (((binintersectEL) =>
% 129.57/17.03 (((binintersectLsub) =>
% 129.57/17.03 (((binintersectSubset2) =>
% 129.57/17.03 (((binintersectSubset3) =>
% 129.57/17.03 (((binintersectER) =>
% 129.57/17.03 (((disjointsetsI1) =>
% 129.57/17.03 (((binintersectRsub) =>
% 129.57/17.03 (((binintersectSubset4) =>
% 129.57/17.03 (((binintersectSubset1) =>
% 129.57/17.03 ((
% 129.57/17.03 (bs114d) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusI) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusEL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusER) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusSubset2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusERneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusELneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusILneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusIRneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusLsub) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusSubset1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffE) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffI2) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffIneg1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffIneg2) =>
% 129.57/17.03 ((
% 129.57/17.03 (secondinupair) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairIL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairIR) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairiskpair) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairp) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonsubset) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletoninpowerset) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletoninpowunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairset2E) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairsubunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairinpowunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem3) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairin) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempair1) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempair) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionE2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton1) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1E1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1I) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1I2) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonsuniq) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL1) =>
% 129.57/17.03 ((
% 129.57/17.03 (kfstsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (theprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (kfstpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodfstin) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR11) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR12) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR1) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairequniteq) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR) =>
% 129.57/17.03 ((
% 129.57/17.03 (ksndsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (ksndpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairsurjEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodsndin) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairmemEL) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairmemER) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempaircEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodfstpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodsndpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairsurjEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrI) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrSub) =>
% 129.57/17.03 ((
% 129.57/17.03 (setOfPairsIsBReln) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrERa) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrEL1) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrEL2) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrER) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcImageSingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (apProp) =>
% 129.57/17.03 ((
% 129.57/17.03 (app) =>
% 129.57/17.03 ((
% 129.57/17.03 (infuncsetfunc) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2p) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcinfuncset) =>
% 129.57/17.03 ((
% 129.57/17.03 (lamProp) =>
% 129.57/17.03 ((
% 129.57/17.03 (lamp) =>
% 129.57/17.03 ((
% 129.57/17.03 (lam2p) =>
% 129.57/17.03 ((
% 129.57/17.03 (brelnall1) =>
% 129.57/17.03 ((
% 129.57/17.03 (brelnall2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1E2) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp3) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcextLem) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp4) =>
% 129.57/17.03 ((
% 129.57/17.03 (subbreln) =>
% 129.57/17.03 ((
% 129.57/17.03 (eqbreln) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcext) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcext2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2apEq1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2apEq2) =>
% 129.57/17.03 ((
% 129.57/17.03 (beta1) =>
% 129.57/17.03 ((
% 129.57/17.03 (eta1) =>
% 129.57/17.03 ((
% 129.57/17.03 (lam2lamEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (beta2) =>
% 129.57/17.03 ((
% 129.57/17.03 (eta2) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalseProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalseProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ifSingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (ifp) =>
% 129.57/17.03 ((
% 129.57/17.03 (theeq) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrue) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalse) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueorfalse) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (setextT) =>
% 129.57/17.03 ((
% 129.57/17.03 (subsetTI) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetTI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetTE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectTELcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectTERcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT1) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT2) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT3) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementSub1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementSub2) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTnotintersectT) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementImpComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementSubsetComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementInPowersetComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (contraSubsetComplement) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTcontraSubset) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTILcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTIRcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInUnion) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInUnion2) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInIntersectUnions) =>
% 129.57/17.03 ((
% 129.57/17.03 (intersectInPowersetIntersectUnions) =>
% 129.57/17.03 ((
% 129.57/17.03 (inComplementUnionImpNotIn1) =>
% 129.57/17.03 ((
% 129.57/17.03 (inComplementUnionImpInComplement1) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTE) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTEcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementUnionInPowersetComplement) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a2) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1a) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1b) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2b2) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2b) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule0) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule1) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule3) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule4) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_1) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_3) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_4) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_5) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1all2) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1SetBreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (choice2fnsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (setOfPairsIsBReln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1all1) =>
% 129.57/17.03 ((
% 129.57/17.03 (subbreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (eqbreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invI) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invE) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compI) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compE) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compEex) =>
% 129.57/17.03 ((
% 129.57/17.03 (!!) @ (
% 129.57/17.03 (('#B') @ (
% 129.57/17.03 !!) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#S') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#S') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 =>))) @
% 129.57/17.03 breln1)))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 !!))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#S') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#S') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 =>))) @
% 129.57/17.03 breln1)))))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#C') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 breln1)))) @
% 129.57/17.03 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl938])).
% 129.57/17.03 thf(zip_derived_cl967, plain,
% 129.57/17.03 (~ (((setadjoinSub) =>
% 129.57/17.03 (((setadjoinSub2) =>
% 129.57/17.03 (((subset2powerset) =>
% 129.57/17.03 (((setextsub) =>
% 129.57/17.03 (((subsetemptysetimpeq) =>
% 129.57/17.03 (((powersetI1) =>
% 129.57/17.03 (((powersetE1) =>
% 129.57/17.03 (((inPowerset) =>
% 129.57/17.03 (((powersetsubset) =>
% 129.57/17.03 (((sepInPowerset) =>
% 129.57/17.03 (((sepSubset) =>
% 129.57/17.03 (((binunionIL) =>
% 129.57/17.03 (((upairset2IR) =>
% 129.57/17.03 (((binunionIR) =>
% 129.57/17.03 (((binunionEcases) =>
% 129.57/17.03 (((binunionE) =>
% 129.57/17.03 (((binunionLsub) =>
% 129.57/17.03 (((binunionRsub) =>
% 129.57/17.03 (((binintersectI) =>
% 129.57/17.03 (((binintersectSubset5) =>
% 129.57/17.03 (((binintersectEL) =>
% 129.57/17.03 (((binintersectLsub) =>
% 129.57/17.03 (((binintersectSubset2) =>
% 129.57/17.03 (((binintersectSubset3) =>
% 129.57/17.03 (((binintersectER) =>
% 129.57/17.03 (((disjointsetsI1) =>
% 129.57/17.03 (((binintersectRsub) =>
% 129.57/17.03 (((binintersectSubset4) =>
% 129.57/17.03 (((binintersectSubset1) =>
% 129.57/17.03 (((bs114d) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusI) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusEL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusER) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusSubset2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusERneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusELneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusILneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusIRneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusLsub) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusSubset1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffE) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffI2) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffIneg1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffIneg2) =>
% 129.57/17.03 ((
% 129.57/17.03 (secondinupair) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairIL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairIR) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairiskpair) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairp) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonsubset) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletoninpowerset) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletoninpowunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairset2E) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairsubunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairinpowunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem3) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairin) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempair1) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempair) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionE2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton1) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1E1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1I) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1I2) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonsuniq) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL1) =>
% 129.57/17.03 ((
% 129.57/17.03 (kfstsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (theprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (kfstpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodfstin) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR11) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR12) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR1) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairequniteq) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR) =>
% 129.57/17.03 ((
% 129.57/17.03 (ksndsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (ksndpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairsurjEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodsndin) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairmemEL) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairmemER) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempaircEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodfstpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodsndpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairsurjEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrI) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrSub) =>
% 129.57/17.03 ((
% 129.57/17.03 (setOfPairsIsBReln) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrERa) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrEL1) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrEL2) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrER) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcImageSingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (apProp) =>
% 129.57/17.03 ((
% 129.57/17.03 (app) =>
% 129.57/17.03 ((
% 129.57/17.03 (infuncsetfunc) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2p) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcinfuncset) =>
% 129.57/17.03 ((
% 129.57/17.03 (lamProp) =>
% 129.57/17.03 ((
% 129.57/17.03 (lamp) =>
% 129.57/17.03 ((
% 129.57/17.03 (lam2p) =>
% 129.57/17.03 ((
% 129.57/17.03 (brelnall1) =>
% 129.57/17.03 ((
% 129.57/17.03 (brelnall2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1E2) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp3) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcextLem) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp4) =>
% 129.57/17.03 ((
% 129.57/17.03 (subbreln) =>
% 129.57/17.03 ((
% 129.57/17.03 (eqbreln) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcext) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcext2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2apEq1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2apEq2) =>
% 129.57/17.03 ((
% 129.57/17.03 (beta1) =>
% 129.57/17.03 ((
% 129.57/17.03 (eta1) =>
% 129.57/17.03 ((
% 129.57/17.03 (lam2lamEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (beta2) =>
% 129.57/17.03 ((
% 129.57/17.03 (eta2) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalseProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalseProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ifSingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (ifp) =>
% 129.57/17.03 ((
% 129.57/17.03 (theeq) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrue) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalse) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueorfalse) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (setextT) =>
% 129.57/17.03 ((
% 129.57/17.03 (subsetTI) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetTI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetTE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectTELcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectTERcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT1) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT2) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT3) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementSub1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementSub2) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTnotintersectT) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementImpComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementSubsetComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementInPowersetComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (contraSubsetComplement) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTcontraSubset) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTILcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTIRcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInUnion) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInUnion2) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInIntersectUnions) =>
% 129.57/17.03 ((
% 129.57/17.03 (intersectInPowersetIntersectUnions) =>
% 129.57/17.03 ((
% 129.57/17.03 (inComplementUnionImpNotIn1) =>
% 129.57/17.03 ((
% 129.57/17.03 (inComplementUnionImpInComplement1) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTE) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTEcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementUnionInPowersetComplement) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a2) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1a) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1b) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2b2) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2b) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule0) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule1) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule3) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule4) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_1) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_3) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_4) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_5) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1all2) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1SetBreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (choice2fnsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (setOfPairsIsBReln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1all1) =>
% 129.57/17.03 ((
% 129.57/17.03 (subbreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (eqbreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invI) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invE) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compI) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compE) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compEex) =>
% 129.57/17.03 ((
% 129.57/17.03 (!!) @ (
% 129.57/17.03 (('#B') @ (
% 129.57/17.03 !!) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#S') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#S') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 =>))) @
% 129.57/17.03 breln1)))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 !!))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#S') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#S') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 =>))) @
% 129.57/17.03 breln1)))))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#C') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 breln1)))) @
% 129.57/17.03 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl952])).
% 129.57/17.03 thf(zip_derived_cl984, plain,
% 129.57/17.03 (~ (((setadjoinSub2) =>
% 129.57/17.03 (((subset2powerset) =>
% 129.57/17.03 (((setextsub) =>
% 129.57/17.03 (((subsetemptysetimpeq) =>
% 129.57/17.03 (((powersetI1) =>
% 129.57/17.03 (((powersetE1) =>
% 129.57/17.03 (((inPowerset) =>
% 129.57/17.03 (((powersetsubset) =>
% 129.57/17.03 (((sepInPowerset) =>
% 129.57/17.03 (((sepSubset) =>
% 129.57/17.03 (((binunionIL) =>
% 129.57/17.03 (((upairset2IR) =>
% 129.57/17.03 (((binunionIR) =>
% 129.57/17.03 (((binunionEcases) =>
% 129.57/17.03 (((binunionE) =>
% 129.57/17.03 (((binunionLsub) =>
% 129.57/17.03 (((binunionRsub) =>
% 129.57/17.03 (((binintersectI) =>
% 129.57/17.03 (((binintersectSubset5) =>
% 129.57/17.03 (((binintersectEL) =>
% 129.57/17.03 (((binintersectLsub) =>
% 129.57/17.03 (((binintersectSubset2) =>
% 129.57/17.03 (((binintersectSubset3) =>
% 129.57/17.03 (((binintersectER) =>
% 129.57/17.03 (((disjointsetsI1) =>
% 129.57/17.03 (((binintersectRsub) =>
% 129.57/17.03 (((binintersectSubset4) =>
% 129.57/17.03 (((binintersectSubset1) =>
% 129.57/17.03 (((bs114d) =>
% 129.57/17.03 (((setminusI) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusEL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusER) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusSubset2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusERneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusELneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusILneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusIRneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusLsub) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusSubset1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffE) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffI2) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffIneg1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffIneg2) =>
% 129.57/17.03 ((
% 129.57/17.03 (secondinupair) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairIL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairIR) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairiskpair) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairp) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonsubset) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletoninpowerset) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletoninpowunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairset2E) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairsubunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairinpowunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem3) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairin) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempair1) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempair) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionE2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton1) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1E1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1I) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1I2) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonsuniq) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL1) =>
% 129.57/17.03 ((
% 129.57/17.03 (kfstsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (theprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (kfstpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodfstin) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR11) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR12) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR1) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairequniteq) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR) =>
% 129.57/17.03 ((
% 129.57/17.03 (ksndsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (ksndpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairsurjEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodsndin) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairmemEL) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairmemER) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempaircEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodfstpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodsndpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairsurjEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrI) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrSub) =>
% 129.57/17.03 ((
% 129.57/17.03 (setOfPairsIsBReln) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrERa) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrEL1) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrEL2) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrER) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcImageSingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (apProp) =>
% 129.57/17.03 ((
% 129.57/17.03 (app) =>
% 129.57/17.03 ((
% 129.57/17.03 (infuncsetfunc) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2p) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcinfuncset) =>
% 129.57/17.03 ((
% 129.57/17.03 (lamProp) =>
% 129.57/17.03 ((
% 129.57/17.03 (lamp) =>
% 129.57/17.03 ((
% 129.57/17.03 (lam2p) =>
% 129.57/17.03 ((
% 129.57/17.03 (brelnall1) =>
% 129.57/17.03 ((
% 129.57/17.03 (brelnall2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1E2) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp3) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcextLem) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp4) =>
% 129.57/17.03 ((
% 129.57/17.03 (subbreln) =>
% 129.57/17.03 ((
% 129.57/17.03 (eqbreln) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcext) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcext2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2apEq1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2apEq2) =>
% 129.57/17.03 ((
% 129.57/17.03 (beta1) =>
% 129.57/17.03 ((
% 129.57/17.03 (eta1) =>
% 129.57/17.03 ((
% 129.57/17.03 (lam2lamEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (beta2) =>
% 129.57/17.03 ((
% 129.57/17.03 (eta2) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalseProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalseProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ifSingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (ifp) =>
% 129.57/17.03 ((
% 129.57/17.03 (theeq) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrue) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalse) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueorfalse) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (setextT) =>
% 129.57/17.03 ((
% 129.57/17.03 (subsetTI) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetTI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetTE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectTELcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectTERcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT1) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT2) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT3) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementSub1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementSub2) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTnotintersectT) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementImpComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementSubsetComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementInPowersetComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (contraSubsetComplement) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTcontraSubset) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTILcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTIRcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInUnion) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInUnion2) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInIntersectUnions) =>
% 129.57/17.03 ((
% 129.57/17.03 (intersectInPowersetIntersectUnions) =>
% 129.57/17.03 ((
% 129.57/17.03 (inComplementUnionImpNotIn1) =>
% 129.57/17.03 ((
% 129.57/17.03 (inComplementUnionImpInComplement1) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTE) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTEcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementUnionInPowersetComplement) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a2) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1a) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1b) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2b2) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2b) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule0) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule1) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule3) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule4) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_1) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_3) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_4) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_5) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1all2) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1SetBreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (choice2fnsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (setOfPairsIsBReln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1all1) =>
% 129.57/17.03 ((
% 129.57/17.03 (subbreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (eqbreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invI) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invE) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compI) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compE) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compEex) =>
% 129.57/17.03 ((
% 129.57/17.03 (!!) @ (
% 129.57/17.03 (('#B') @ (
% 129.57/17.03 !!) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#S') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#S') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 =>))) @
% 129.57/17.03 breln1)))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 !!))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#S') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#S') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 =>))) @
% 129.57/17.03 breln1)))))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#C') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 breln1)))) @
% 129.57/17.03 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl967])).
% 129.57/17.03 thf(zip_derived_cl1000, plain,
% 129.57/17.03 (~ (((subset2powerset) =>
% 129.57/17.03 (((setextsub) =>
% 129.57/17.03 (((subsetemptysetimpeq) =>
% 129.57/17.03 (((powersetI1) =>
% 129.57/17.03 (((powersetE1) =>
% 129.57/17.03 (((inPowerset) =>
% 129.57/17.03 (((powersetsubset) =>
% 129.57/17.03 (((sepInPowerset) =>
% 129.57/17.03 (((sepSubset) =>
% 129.57/17.03 (((binunionIL) =>
% 129.57/17.03 (((upairset2IR) =>
% 129.57/17.03 (((binunionIR) =>
% 129.57/17.03 (((binunionEcases) =>
% 129.57/17.03 (((binunionE) =>
% 129.57/17.03 (((binunionLsub) =>
% 129.57/17.03 (((binunionRsub) =>
% 129.57/17.03 (((binintersectI) =>
% 129.57/17.03 (((binintersectSubset5) =>
% 129.57/17.03 (((binintersectEL) =>
% 129.57/17.03 (((binintersectLsub) =>
% 129.57/17.03 (((binintersectSubset2) =>
% 129.57/17.03 (((binintersectSubset3) =>
% 129.57/17.03 (((binintersectER) =>
% 129.57/17.03 (((disjointsetsI1) =>
% 129.57/17.03 (((binintersectRsub) =>
% 129.57/17.03 (((binintersectSubset4) =>
% 129.57/17.03 (((binintersectSubset1) =>
% 129.57/17.03 (((bs114d) =>
% 129.57/17.03 (((setminusI) =>
% 129.57/17.03 (((setminusEL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusER) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusSubset2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusERneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusELneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusILneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusIRneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusLsub) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusSubset1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffE) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffI2) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffIneg1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffIneg2) =>
% 129.57/17.03 ((
% 129.57/17.03 (secondinupair) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairIL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairIR) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairiskpair) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairp) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonsubset) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletoninpowerset) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletoninpowunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairset2E) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairsubunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairinpowunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem3) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairin) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempair1) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempair) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionE2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton1) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1E1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1I) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1I2) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonsuniq) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL1) =>
% 129.57/17.03 ((
% 129.57/17.03 (kfstsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (theprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (kfstpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodfstin) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR11) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR12) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR1) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairequniteq) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR) =>
% 129.57/17.03 ((
% 129.57/17.03 (ksndsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (ksndpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairsurjEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodsndin) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairmemEL) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairmemER) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempaircEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodfstpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodsndpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairsurjEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrI) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrSub) =>
% 129.57/17.03 ((
% 129.57/17.03 (setOfPairsIsBReln) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrERa) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrEL1) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrEL2) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrER) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcImageSingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (apProp) =>
% 129.57/17.03 ((
% 129.57/17.03 (app) =>
% 129.57/17.03 ((
% 129.57/17.03 (infuncsetfunc) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2p) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcinfuncset) =>
% 129.57/17.03 ((
% 129.57/17.03 (lamProp) =>
% 129.57/17.03 ((
% 129.57/17.03 (lamp) =>
% 129.57/17.03 ((
% 129.57/17.03 (lam2p) =>
% 129.57/17.03 ((
% 129.57/17.03 (brelnall1) =>
% 129.57/17.03 ((
% 129.57/17.03 (brelnall2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1E2) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp3) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcextLem) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp4) =>
% 129.57/17.03 ((
% 129.57/17.03 (subbreln) =>
% 129.57/17.03 ((
% 129.57/17.03 (eqbreln) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcext) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcext2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2apEq1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2apEq2) =>
% 129.57/17.03 ((
% 129.57/17.03 (beta1) =>
% 129.57/17.03 ((
% 129.57/17.03 (eta1) =>
% 129.57/17.03 ((
% 129.57/17.03 (lam2lamEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (beta2) =>
% 129.57/17.03 ((
% 129.57/17.03 (eta2) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalseProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalseProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ifSingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (ifp) =>
% 129.57/17.03 ((
% 129.57/17.03 (theeq) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrue) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalse) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueorfalse) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (setextT) =>
% 129.57/17.03 ((
% 129.57/17.03 (subsetTI) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetTI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetTE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectTELcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectTERcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT1) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT2) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT3) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementSub1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementSub2) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTnotintersectT) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementImpComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementSubsetComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementInPowersetComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (contraSubsetComplement) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTcontraSubset) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTILcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTIRcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInUnion) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInUnion2) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInIntersectUnions) =>
% 129.57/17.03 ((
% 129.57/17.03 (intersectInPowersetIntersectUnions) =>
% 129.57/17.03 ((
% 129.57/17.03 (inComplementUnionImpNotIn1) =>
% 129.57/17.03 ((
% 129.57/17.03 (inComplementUnionImpInComplement1) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTE) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTEcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementUnionInPowersetComplement) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a2) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1a) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1b) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2b2) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2b) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule0) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule1) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule3) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz13rule4) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_1) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_2) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_3) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_4) =>
% 129.57/17.03 ((
% 129.57/17.03 (woz1_5) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1all2) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1SetBreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (choice2fnsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (setOfPairsIsBReln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1all1) =>
% 129.57/17.03 ((
% 129.57/17.03 (subbreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (eqbreln1) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invI) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1invE) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compI) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compE) =>
% 129.57/17.03 ((
% 129.57/17.03 (breln1compEex) =>
% 129.57/17.03 ((
% 129.57/17.03 (!!) @ (
% 129.57/17.03 (('#B') @ (
% 129.57/17.03 !!) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#S') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#S') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 =>))) @
% 129.57/17.03 breln1)))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 !!))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#S') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#S') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 =>))) @
% 129.57/17.03 breln1)))))) @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#C') @ (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 (
% 129.57/17.03 (
% 129.57/17.03 ('#B') @ (
% 129.57/17.03 '#B') @
% 129.57/17.03 breln1)))) @
% 129.57/17.03 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl984])).
% 129.57/17.03 thf(zip_derived_cl1015, plain,
% 129.57/17.03 (~ (((setextsub) =>
% 129.57/17.03 (((subsetemptysetimpeq) =>
% 129.57/17.03 (((powersetI1) =>
% 129.57/17.03 (((powersetE1) =>
% 129.57/17.03 (((inPowerset) =>
% 129.57/17.03 (((powersetsubset) =>
% 129.57/17.03 (((sepInPowerset) =>
% 129.57/17.03 (((sepSubset) =>
% 129.57/17.03 (((binunionIL) =>
% 129.57/17.03 (((upairset2IR) =>
% 129.57/17.03 (((binunionIR) =>
% 129.57/17.03 (((binunionEcases) =>
% 129.57/17.03 (((binunionE) =>
% 129.57/17.03 (((binunionLsub) =>
% 129.57/17.03 (((binunionRsub) =>
% 129.57/17.03 (((binintersectI) =>
% 129.57/17.03 (((binintersectSubset5) =>
% 129.57/17.03 (((binintersectEL) =>
% 129.57/17.03 (((binintersectLsub) =>
% 129.57/17.03 (((binintersectSubset2) =>
% 129.57/17.03 (((binintersectSubset3) =>
% 129.57/17.03 (((binintersectER) =>
% 129.57/17.03 (((disjointsetsI1) =>
% 129.57/17.03 (((binintersectRsub) =>
% 129.57/17.03 (((binintersectSubset4) =>
% 129.57/17.03 (((binintersectSubset1) =>
% 129.57/17.03 (((bs114d) =>
% 129.57/17.03 (((setminusI) =>
% 129.57/17.03 (((setminusEL) =>
% 129.57/17.03 (((setminusER) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusSubset2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusERneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusELneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusILneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusIRneg) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusLsub) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusSubset1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffE) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffI2) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffIneg1) =>
% 129.57/17.03 ((
% 129.57/17.03 (symdiffIneg2) =>
% 129.57/17.03 ((
% 129.57/17.03 (secondinupair) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairIL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairIR) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairiskpair) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairp) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonsubset) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletoninpowerset) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletoninpowunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairset2E) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairsubunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairinpowunion) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ubforcartprodlem3) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairin) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempair1) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempair) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionE2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton1) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setunionsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1E1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1I) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1I2) =>
% 129.57/17.03 ((
% 129.57/17.03 (singletonsuniq) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL1) =>
% 129.57/17.03 ((
% 129.57/17.03 (kfstsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (theprop) =>
% 129.57/17.03 ((
% 129.57/17.03 (kfstpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodfstin) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjL) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR11) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR12) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR1) =>
% 129.57/17.03 ((
% 129.57/17.03 (upairequniteq) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR2) =>
% 129.57/17.03 ((
% 129.57/17.03 (setukpairinjR) =>
% 129.57/17.03 ((
% 129.57/17.03 (ksndsingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (ksndpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (kpairsurjEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodsndin) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairmemEL) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairmemER) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodmempaircEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodfstpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodsndpairEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (cartprodpairsurjEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrI) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrSub) =>
% 129.57/17.03 ((
% 129.57/17.03 (setOfPairsIsBReln) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrERa) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrEL1) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrEL2) =>
% 129.57/17.03 ((
% 129.57/17.03 (dpsetconstrER) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcImageSingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (apProp) =>
% 129.57/17.03 ((
% 129.57/17.03 (app) =>
% 129.57/17.03 ((
% 129.57/17.03 (infuncsetfunc) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2p) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcinfuncset) =>
% 129.57/17.03 ((
% 129.57/17.03 (lamProp) =>
% 129.57/17.03 ((
% 129.57/17.03 (lamp) =>
% 129.57/17.03 ((
% 129.57/17.03 (lam2p) =>
% 129.57/17.03 ((
% 129.57/17.03 (brelnall1) =>
% 129.57/17.03 ((
% 129.57/17.03 (brelnall2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ex1E2) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp3) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcextLem) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcGraphProp4) =>
% 129.57/17.03 ((
% 129.57/17.03 (subbreln) =>
% 129.57/17.03 ((
% 129.57/17.03 (eqbreln) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcext) =>
% 129.57/17.03 ((
% 129.57/17.03 (funcext2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2apEq1) =>
% 129.57/17.03 ((
% 129.57/17.03 (ap2apEq2) =>
% 129.57/17.03 ((
% 129.57/17.03 (beta1) =>
% 129.57/17.03 ((
% 129.57/17.03 (eta1) =>
% 129.57/17.03 ((
% 129.57/17.03 (lam2lamEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (beta2) =>
% 129.57/17.03 ((
% 129.57/17.03 (eta2) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalseProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalseProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueProp1) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueProp2) =>
% 129.57/17.03 ((
% 129.57/17.03 (ifSingleton) =>
% 129.57/17.03 ((
% 129.57/17.03 (ifp) =>
% 129.57/17.03 ((
% 129.57/17.03 (theeq) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrue) =>
% 129.57/17.03 ((
% 129.57/17.03 (iffalse) =>
% 129.57/17.03 ((
% 129.57/17.03 (iftrueorfalse) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (setminusT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementT_lem) =>
% 129.57/17.03 ((
% 129.57/17.03 (setextT) =>
% 129.57/17.03 ((
% 129.57/17.03 (subsetTI) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetTI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (powersetTE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectTELcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (binintersectTERcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT1) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT2) =>
% 129.57/17.03 ((
% 129.57/17.03 (contrasubsetT3) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementI1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementE1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementSub1) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementSub2) =>
% 129.57/17.03 ((
% 129.57/17.03 (doubleComplementEq) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTnotintersectT) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementImpComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementSubsetComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementInPowersetComplementIntersect) =>
% 129.57/17.03 ((
% 129.57/17.03 (contraSubsetComplement) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementTcontraSubset) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTILcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTIRcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInUnion) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInUnion2) =>
% 129.57/17.03 ((
% 129.57/17.03 (inIntersectImpInIntersectUnions) =>
% 129.57/17.03 ((
% 129.57/17.03 (intersectInPowersetIntersectUnions) =>
% 129.57/17.03 ((
% 129.57/17.03 (inComplementUnionImpNotIn1) =>
% 129.57/17.03 ((
% 129.57/17.03 (inComplementUnionImpInComplement1) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTE) =>
% 129.57/17.03 ((
% 129.57/17.03 (binunionTEcontra) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a1) =>
% 129.57/17.03 ((
% 129.57/17.03 (complementUnionInPowersetComplement) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan2a2) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1a) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1b) =>
% 129.57/17.03 ((
% 129.57/17.03 (demorgan1) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b2) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule0) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_5) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all2) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1SetBreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (choice2fnsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (setOfPairsIsBReln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all1) =>
% 129.57/17.04 ((
% 129.57/17.04 (subbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (eqbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invI) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invE) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compI) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compE) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compEex) =>
% 129.57/17.04 ((
% 129.57/17.04 (!!) @ (
% 129.57/17.04 (('#B') @ (
% 129.57/17.04 !!) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#S') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#S') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 =>))) @
% 129.57/17.04 breln1)))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 !!))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#S') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#S') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 =>))) @
% 129.57/17.04 breln1)))))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#C') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 breln1)))) @
% 129.57/17.04 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1000])).
% 129.57/17.04 thf(zip_derived_cl1027, plain,
% 129.57/17.04 (~ (((subsetemptysetimpeq) =>
% 129.57/17.04 (((powersetI1) =>
% 129.57/17.04 (((powersetE1) =>
% 129.57/17.04 (((inPowerset) =>
% 129.57/17.04 (((powersetsubset) =>
% 129.57/17.04 (((sepInPowerset) =>
% 129.57/17.04 (((sepSubset) =>
% 129.57/17.04 (((binunionIL) =>
% 129.57/17.04 (((upairset2IR) =>
% 129.57/17.04 (((binunionIR) =>
% 129.57/17.04 (((binunionEcases) =>
% 129.57/17.04 (((binunionE) =>
% 129.57/17.04 (((binunionLsub) =>
% 129.57/17.04 (((binunionRsub) =>
% 129.57/17.04 (((binintersectI) =>
% 129.57/17.04 (((binintersectSubset5) =>
% 129.57/17.04 (((binintersectEL) =>
% 129.57/17.04 (((binintersectLsub) =>
% 129.57/17.04 (((binintersectSubset2) =>
% 129.57/17.04 (((binintersectSubset3) =>
% 129.57/17.04 (((binintersectER) =>
% 129.57/17.04 (((disjointsetsI1) =>
% 129.57/17.04 (((binintersectRsub) =>
% 129.57/17.04 (((binintersectSubset4) =>
% 129.57/17.04 (((binintersectSubset1) =>
% 129.57/17.04 (((bs114d) =>
% 129.57/17.04 (((setminusI) =>
% 129.57/17.04 (((setminusEL) =>
% 129.57/17.04 (((setminusER) =>
% 129.57/17.04 (((setminusSubset2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusERneg) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusELneg) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusILneg) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusIRneg) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusLsub) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusSubset1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffE) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffI2) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffIneg1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffIneg2) =>
% 129.57/17.04 ((
% 129.57/17.04 (secondinupair) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairIL) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairIR) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairiskpair) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairp) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonsubset) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletoninpowerset) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletoninpowunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairset2E) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairsubunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairinpowunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem3) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairin) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempair1) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempair) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionE2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton1) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1E1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1I) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1I2) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonsuniq) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL1) =>
% 129.57/17.04 ((
% 129.57/17.04 (kfstsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (theprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (kfstpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodfstin) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR11) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR12) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR1) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairequniteq) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR) =>
% 129.57/17.04 ((
% 129.57/17.04 (ksndsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (ksndpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairsurjEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodsndin) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairmemEL) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairmemER) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempaircEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodfstpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodsndpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairsurjEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrI) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrSub) =>
% 129.57/17.04 ((
% 129.57/17.04 (setOfPairsIsBReln) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrERa) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrEL1) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrEL2) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrER) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcImageSingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (apProp) =>
% 129.57/17.04 ((
% 129.57/17.04 (app) =>
% 129.57/17.04 ((
% 129.57/17.04 (infuncsetfunc) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2p) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcinfuncset) =>
% 129.57/17.04 ((
% 129.57/17.04 (lamProp) =>
% 129.57/17.04 ((
% 129.57/17.04 (lamp) =>
% 129.57/17.04 ((
% 129.57/17.04 (lam2p) =>
% 129.57/17.04 ((
% 129.57/17.04 (brelnall1) =>
% 129.57/17.04 ((
% 129.57/17.04 (brelnall2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1E2) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp3) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcextLem) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp4) =>
% 129.57/17.04 ((
% 129.57/17.04 (subbreln) =>
% 129.57/17.04 ((
% 129.57/17.04 (eqbreln) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcext) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcext2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2apEq1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2apEq2) =>
% 129.57/17.04 ((
% 129.57/17.04 (beta1) =>
% 129.57/17.04 ((
% 129.57/17.04 (eta1) =>
% 129.57/17.04 ((
% 129.57/17.04 (lam2lamEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (beta2) =>
% 129.57/17.04 ((
% 129.57/17.04 (eta2) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalseProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalseProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ifSingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (ifp) =>
% 129.57/17.04 ((
% 129.57/17.04 (theeq) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrue) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalse) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueorfalse) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (setextT) =>
% 129.57/17.04 ((
% 129.57/17.04 (subsetTI) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetTI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetTE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectTELcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectTERcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT1) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT2) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT3) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementSub1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementSub2) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTnotintersectT) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementImpComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementSubsetComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementInPowersetComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (contraSubsetComplement) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTcontraSubset) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTILcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTIRcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInUnion) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInUnion2) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInIntersectUnions) =>
% 129.57/17.04 ((
% 129.57/17.04 (intersectInPowersetIntersectUnions) =>
% 129.57/17.04 ((
% 129.57/17.04 (inComplementUnionImpNotIn1) =>
% 129.57/17.04 ((
% 129.57/17.04 (inComplementUnionImpInComplement1) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTE) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTEcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementUnionInPowersetComplement) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a2) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1a) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1b) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b2) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule0) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_5) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all2) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1SetBreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (choice2fnsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (setOfPairsIsBReln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all1) =>
% 129.57/17.04 ((
% 129.57/17.04 (subbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (eqbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invI) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invE) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compI) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compE) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compEex) =>
% 129.57/17.04 ((
% 129.57/17.04 (!!) @ (
% 129.57/17.04 (('#B') @ (
% 129.57/17.04 !!) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#S') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#S') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 =>))) @
% 129.57/17.04 breln1)))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 !!))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#S') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#S') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 =>))) @
% 129.57/17.04 breln1)))))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#C') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 breln1)))) @
% 129.57/17.04 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1015])).
% 129.57/17.04 thf(zip_derived_cl1039, plain,
% 129.57/17.04 (~ (((powersetI1) =>
% 129.57/17.04 (((powersetE1) =>
% 129.57/17.04 (((inPowerset) =>
% 129.57/17.04 (((powersetsubset) =>
% 129.57/17.04 (((sepInPowerset) =>
% 129.57/17.04 (((sepSubset) =>
% 129.57/17.04 (((binunionIL) =>
% 129.57/17.04 (((upairset2IR) =>
% 129.57/17.04 (((binunionIR) =>
% 129.57/17.04 (((binunionEcases) =>
% 129.57/17.04 (((binunionE) =>
% 129.57/17.04 (((binunionLsub) =>
% 129.57/17.04 (((binunionRsub) =>
% 129.57/17.04 (((binintersectI) =>
% 129.57/17.04 (((binintersectSubset5) =>
% 129.57/17.04 (((binintersectEL) =>
% 129.57/17.04 (((binintersectLsub) =>
% 129.57/17.04 (((binintersectSubset2) =>
% 129.57/17.04 (((binintersectSubset3) =>
% 129.57/17.04 (((binintersectER) =>
% 129.57/17.04 (((disjointsetsI1) =>
% 129.57/17.04 (((binintersectRsub) =>
% 129.57/17.04 (((binintersectSubset4) =>
% 129.57/17.04 (((binintersectSubset1) =>
% 129.57/17.04 (((bs114d) =>
% 129.57/17.04 (((setminusI) =>
% 129.57/17.04 (((setminusEL) =>
% 129.57/17.04 (((setminusER) =>
% 129.57/17.04 (((setminusSubset2) =>
% 129.57/17.04 (((setminusERneg) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusELneg) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusILneg) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusIRneg) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusLsub) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusSubset1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffE) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffI2) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffIneg1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffIneg2) =>
% 129.57/17.04 ((
% 129.57/17.04 (secondinupair) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairIL) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairIR) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairiskpair) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairp) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonsubset) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletoninpowerset) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletoninpowunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairset2E) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairsubunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairinpowunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem3) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairin) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempair1) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempair) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionE2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton1) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1E1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1I) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1I2) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonsuniq) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL1) =>
% 129.57/17.04 ((
% 129.57/17.04 (kfstsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (theprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (kfstpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodfstin) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR11) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR12) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR1) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairequniteq) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR) =>
% 129.57/17.04 ((
% 129.57/17.04 (ksndsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (ksndpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairsurjEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodsndin) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairmemEL) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairmemER) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempaircEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodfstpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodsndpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairsurjEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrI) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrSub) =>
% 129.57/17.04 ((
% 129.57/17.04 (setOfPairsIsBReln) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrERa) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrEL1) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrEL2) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrER) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcImageSingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (apProp) =>
% 129.57/17.04 ((
% 129.57/17.04 (app) =>
% 129.57/17.04 ((
% 129.57/17.04 (infuncsetfunc) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2p) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcinfuncset) =>
% 129.57/17.04 ((
% 129.57/17.04 (lamProp) =>
% 129.57/17.04 ((
% 129.57/17.04 (lamp) =>
% 129.57/17.04 ((
% 129.57/17.04 (lam2p) =>
% 129.57/17.04 ((
% 129.57/17.04 (brelnall1) =>
% 129.57/17.04 ((
% 129.57/17.04 (brelnall2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1E2) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp3) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcextLem) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp4) =>
% 129.57/17.04 ((
% 129.57/17.04 (subbreln) =>
% 129.57/17.04 ((
% 129.57/17.04 (eqbreln) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcext) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcext2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2apEq1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2apEq2) =>
% 129.57/17.04 ((
% 129.57/17.04 (beta1) =>
% 129.57/17.04 ((
% 129.57/17.04 (eta1) =>
% 129.57/17.04 ((
% 129.57/17.04 (lam2lamEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (beta2) =>
% 129.57/17.04 ((
% 129.57/17.04 (eta2) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalseProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalseProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ifSingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (ifp) =>
% 129.57/17.04 ((
% 129.57/17.04 (theeq) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrue) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalse) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueorfalse) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (setextT) =>
% 129.57/17.04 ((
% 129.57/17.04 (subsetTI) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetTI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetTE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectTELcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectTERcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT1) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT2) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT3) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementSub1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementSub2) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTnotintersectT) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementImpComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementSubsetComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementInPowersetComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (contraSubsetComplement) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTcontraSubset) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTILcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTIRcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInUnion) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInUnion2) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInIntersectUnions) =>
% 129.57/17.04 ((
% 129.57/17.04 (intersectInPowersetIntersectUnions) =>
% 129.57/17.04 ((
% 129.57/17.04 (inComplementUnionImpNotIn1) =>
% 129.57/17.04 ((
% 129.57/17.04 (inComplementUnionImpInComplement1) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTE) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTEcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementUnionInPowersetComplement) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a2) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1a) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1b) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b2) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule0) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_5) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all2) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1SetBreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (choice2fnsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (setOfPairsIsBReln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all1) =>
% 129.57/17.04 ((
% 129.57/17.04 (subbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (eqbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invI) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invE) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compI) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compE) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compEex) =>
% 129.57/17.04 ((
% 129.57/17.04 (!!) @ (
% 129.57/17.04 (('#B') @ (
% 129.57/17.04 !!) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#S') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#S') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 =>))) @
% 129.57/17.04 breln1)))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 !!))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#S') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#S') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 =>))) @
% 129.57/17.04 breln1)))))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#C') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 breln1)))) @
% 129.57/17.04 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1027])).
% 129.57/17.04 thf(zip_derived_cl1055, plain,
% 129.57/17.04 (~ (((powersetE1) =>
% 129.57/17.04 (((inPowerset) =>
% 129.57/17.04 (((powersetsubset) =>
% 129.57/17.04 (((sepInPowerset) =>
% 129.57/17.04 (((sepSubset) =>
% 129.57/17.04 (((binunionIL) =>
% 129.57/17.04 (((upairset2IR) =>
% 129.57/17.04 (((binunionIR) =>
% 129.57/17.04 (((binunionEcases) =>
% 129.57/17.04 (((binunionE) =>
% 129.57/17.04 (((binunionLsub) =>
% 129.57/17.04 (((binunionRsub) =>
% 129.57/17.04 (((binintersectI) =>
% 129.57/17.04 (((binintersectSubset5) =>
% 129.57/17.04 (((binintersectEL) =>
% 129.57/17.04 (((binintersectLsub) =>
% 129.57/17.04 (((binintersectSubset2) =>
% 129.57/17.04 (((binintersectSubset3) =>
% 129.57/17.04 (((binintersectER) =>
% 129.57/17.04 (((disjointsetsI1) =>
% 129.57/17.04 (((binintersectRsub) =>
% 129.57/17.04 (((binintersectSubset4) =>
% 129.57/17.04 (((binintersectSubset1) =>
% 129.57/17.04 (((bs114d) =>
% 129.57/17.04 (((setminusI) =>
% 129.57/17.04 (((setminusEL) =>
% 129.57/17.04 (((setminusER) =>
% 129.57/17.04 (((setminusSubset2) =>
% 129.57/17.04 (((setminusERneg) =>
% 129.57/17.04 (((setminusELneg) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusILneg) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusIRneg) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusLsub) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusSubset1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffE) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffI2) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffIneg1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffIneg2) =>
% 129.57/17.04 ((
% 129.57/17.04 (secondinupair) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairIL) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairIR) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairiskpair) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairp) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonsubset) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletoninpowerset) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletoninpowunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairset2E) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairsubunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairinpowunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem3) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairin) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempair1) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempair) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionE2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton1) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1E1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1I) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1I2) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonsuniq) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL1) =>
% 129.57/17.04 ((
% 129.57/17.04 (kfstsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (theprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (kfstpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodfstin) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR11) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR12) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR1) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairequniteq) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR) =>
% 129.57/17.04 ((
% 129.57/17.04 (ksndsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (ksndpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairsurjEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodsndin) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairmemEL) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairmemER) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempaircEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodfstpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodsndpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairsurjEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrI) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrSub) =>
% 129.57/17.04 ((
% 129.57/17.04 (setOfPairsIsBReln) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrERa) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrEL1) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrEL2) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrER) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcImageSingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (apProp) =>
% 129.57/17.04 ((
% 129.57/17.04 (app) =>
% 129.57/17.04 ((
% 129.57/17.04 (infuncsetfunc) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2p) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcinfuncset) =>
% 129.57/17.04 ((
% 129.57/17.04 (lamProp) =>
% 129.57/17.04 ((
% 129.57/17.04 (lamp) =>
% 129.57/17.04 ((
% 129.57/17.04 (lam2p) =>
% 129.57/17.04 ((
% 129.57/17.04 (brelnall1) =>
% 129.57/17.04 ((
% 129.57/17.04 (brelnall2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1E2) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp3) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcextLem) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp4) =>
% 129.57/17.04 ((
% 129.57/17.04 (subbreln) =>
% 129.57/17.04 ((
% 129.57/17.04 (eqbreln) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcext) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcext2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2apEq1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2apEq2) =>
% 129.57/17.04 ((
% 129.57/17.04 (beta1) =>
% 129.57/17.04 ((
% 129.57/17.04 (eta1) =>
% 129.57/17.04 ((
% 129.57/17.04 (lam2lamEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (beta2) =>
% 129.57/17.04 ((
% 129.57/17.04 (eta2) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalseProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalseProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ifSingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (ifp) =>
% 129.57/17.04 ((
% 129.57/17.04 (theeq) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrue) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalse) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueorfalse) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (setextT) =>
% 129.57/17.04 ((
% 129.57/17.04 (subsetTI) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetTI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetTE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectTELcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectTERcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT1) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT2) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT3) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementSub1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementSub2) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTnotintersectT) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementImpComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementSubsetComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementInPowersetComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (contraSubsetComplement) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTcontraSubset) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTILcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTIRcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInUnion) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInUnion2) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInIntersectUnions) =>
% 129.57/17.04 ((
% 129.57/17.04 (intersectInPowersetIntersectUnions) =>
% 129.57/17.04 ((
% 129.57/17.04 (inComplementUnionImpNotIn1) =>
% 129.57/17.04 ((
% 129.57/17.04 (inComplementUnionImpInComplement1) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTE) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTEcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementUnionInPowersetComplement) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a2) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1a) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1b) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b2) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule0) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_5) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all2) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1SetBreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (choice2fnsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (setOfPairsIsBReln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all1) =>
% 129.57/17.04 ((
% 129.57/17.04 (subbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (eqbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invI) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invE) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compI) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compE) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compEex) =>
% 129.57/17.04 ((
% 129.57/17.04 (!!) @ (
% 129.57/17.04 (('#B') @ (
% 129.57/17.04 !!) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#S') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#S') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 =>))) @
% 129.57/17.04 breln1)))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 !!))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#S') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#S') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 =>))) @
% 129.57/17.04 breln1)))))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#C') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 breln1)))) @
% 129.57/17.04 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1039])).
% 129.57/17.04 thf(zip_derived_cl1067, plain,
% 129.57/17.04 (~ (((inPowerset) =>
% 129.57/17.04 (((powersetsubset) =>
% 129.57/17.04 (((sepInPowerset) =>
% 129.57/17.04 (((sepSubset) =>
% 129.57/17.04 (((binunionIL) =>
% 129.57/17.04 (((upairset2IR) =>
% 129.57/17.04 (((binunionIR) =>
% 129.57/17.04 (((binunionEcases) =>
% 129.57/17.04 (((binunionE) =>
% 129.57/17.04 (((binunionLsub) =>
% 129.57/17.04 (((binunionRsub) =>
% 129.57/17.04 (((binintersectI) =>
% 129.57/17.04 (((binintersectSubset5) =>
% 129.57/17.04 (((binintersectEL) =>
% 129.57/17.04 (((binintersectLsub) =>
% 129.57/17.04 (((binintersectSubset2) =>
% 129.57/17.04 (((binintersectSubset3) =>
% 129.57/17.04 (((binintersectER) =>
% 129.57/17.04 (((disjointsetsI1) =>
% 129.57/17.04 (((binintersectRsub) =>
% 129.57/17.04 (((binintersectSubset4) =>
% 129.57/17.04 (((binintersectSubset1) =>
% 129.57/17.04 (((bs114d) =>
% 129.57/17.04 (((setminusI) =>
% 129.57/17.04 (((setminusEL) =>
% 129.57/17.04 (((setminusER) =>
% 129.57/17.04 (((setminusSubset2) =>
% 129.57/17.04 (((setminusERneg) =>
% 129.57/17.04 (((setminusELneg) =>
% 129.57/17.04 (((setminusILneg) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusIRneg) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusLsub) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusSubset1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffE) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffI2) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffIneg1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffIneg2) =>
% 129.57/17.04 ((
% 129.57/17.04 (secondinupair) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairIL) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairIR) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairiskpair) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairp) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonsubset) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletoninpowerset) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletoninpowunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairset2E) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairsubunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairinpowunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem3) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairin) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempair1) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempair) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionE2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton1) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1E1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1I) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1I2) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonsuniq) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL1) =>
% 129.57/17.04 ((
% 129.57/17.04 (kfstsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (theprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (kfstpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodfstin) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR11) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR12) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR1) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairequniteq) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR) =>
% 129.57/17.04 ((
% 129.57/17.04 (ksndsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (ksndpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairsurjEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodsndin) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairmemEL) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairmemER) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempaircEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodfstpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodsndpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairsurjEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrI) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrSub) =>
% 129.57/17.04 ((
% 129.57/17.04 (setOfPairsIsBReln) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrERa) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrEL1) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrEL2) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrER) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcImageSingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (apProp) =>
% 129.57/17.04 ((
% 129.57/17.04 (app) =>
% 129.57/17.04 ((
% 129.57/17.04 (infuncsetfunc) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2p) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcinfuncset) =>
% 129.57/17.04 ((
% 129.57/17.04 (lamProp) =>
% 129.57/17.04 ((
% 129.57/17.04 (lamp) =>
% 129.57/17.04 ((
% 129.57/17.04 (lam2p) =>
% 129.57/17.04 ((
% 129.57/17.04 (brelnall1) =>
% 129.57/17.04 ((
% 129.57/17.04 (brelnall2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1E2) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp3) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcextLem) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp4) =>
% 129.57/17.04 ((
% 129.57/17.04 (subbreln) =>
% 129.57/17.04 ((
% 129.57/17.04 (eqbreln) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcext) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcext2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2apEq1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2apEq2) =>
% 129.57/17.04 ((
% 129.57/17.04 (beta1) =>
% 129.57/17.04 ((
% 129.57/17.04 (eta1) =>
% 129.57/17.04 ((
% 129.57/17.04 (lam2lamEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (beta2) =>
% 129.57/17.04 ((
% 129.57/17.04 (eta2) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalseProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalseProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ifSingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (ifp) =>
% 129.57/17.04 ((
% 129.57/17.04 (theeq) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrue) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalse) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueorfalse) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (setextT) =>
% 129.57/17.04 ((
% 129.57/17.04 (subsetTI) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetTI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetTE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectTELcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectTERcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT1) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT2) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT3) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementSub1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementSub2) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTnotintersectT) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementImpComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementSubsetComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementInPowersetComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (contraSubsetComplement) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTcontraSubset) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTILcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTIRcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInUnion) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInUnion2) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInIntersectUnions) =>
% 129.57/17.04 ((
% 129.57/17.04 (intersectInPowersetIntersectUnions) =>
% 129.57/17.04 ((
% 129.57/17.04 (inComplementUnionImpNotIn1) =>
% 129.57/17.04 ((
% 129.57/17.04 (inComplementUnionImpInComplement1) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTE) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTEcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementUnionInPowersetComplement) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a2) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1a) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1b) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b2) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule0) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_5) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all2) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1SetBreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (choice2fnsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (setOfPairsIsBReln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all1) =>
% 129.57/17.04 ((
% 129.57/17.04 (subbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (eqbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invI) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invE) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compI) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compE) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compEex) =>
% 129.57/17.04 ((
% 129.57/17.04 (!!) @ (
% 129.57/17.04 (('#B') @ (
% 129.57/17.04 !!) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#S') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#S') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 =>))) @
% 129.57/17.04 breln1)))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 !!))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#S') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#S') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 =>))) @
% 129.57/17.04 breln1)))))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#C') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 breln1)))) @
% 129.57/17.04 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1055])).
% 129.57/17.04 thf(zip_derived_cl1074, plain,
% 129.57/17.04 (~ (((powersetsubset) =>
% 129.57/17.04 (((sepInPowerset) =>
% 129.57/17.04 (((sepSubset) =>
% 129.57/17.04 (((binunionIL) =>
% 129.57/17.04 (((upairset2IR) =>
% 129.57/17.04 (((binunionIR) =>
% 129.57/17.04 (((binunionEcases) =>
% 129.57/17.04 (((binunionE) =>
% 129.57/17.04 (((binunionLsub) =>
% 129.57/17.04 (((binunionRsub) =>
% 129.57/17.04 (((binintersectI) =>
% 129.57/17.04 (((binintersectSubset5) =>
% 129.57/17.04 (((binintersectEL) =>
% 129.57/17.04 (((binintersectLsub) =>
% 129.57/17.04 (((binintersectSubset2) =>
% 129.57/17.04 (((binintersectSubset3) =>
% 129.57/17.04 (((binintersectER) =>
% 129.57/17.04 (((disjointsetsI1) =>
% 129.57/17.04 (((binintersectRsub) =>
% 129.57/17.04 (((binintersectSubset4) =>
% 129.57/17.04 (((binintersectSubset1) =>
% 129.57/17.04 (((bs114d) =>
% 129.57/17.04 (((setminusI) =>
% 129.57/17.04 (((setminusEL) =>
% 129.57/17.04 (((setminusER) =>
% 129.57/17.04 (((setminusSubset2) =>
% 129.57/17.04 (((setminusERneg) =>
% 129.57/17.04 (((setminusELneg) =>
% 129.57/17.04 (((setminusILneg) =>
% 129.57/17.04 (((setminusIRneg) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusLsub) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusSubset1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffE) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffI2) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffIneg1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffIneg2) =>
% 129.57/17.04 ((
% 129.57/17.04 (secondinupair) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairIL) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairIR) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairiskpair) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairp) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonsubset) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletoninpowerset) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletoninpowunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairset2E) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairsubunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairinpowunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem3) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairin) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempair1) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempair) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionE2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton1) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1E1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1I) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1I2) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonsuniq) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL1) =>
% 129.57/17.04 ((
% 129.57/17.04 (kfstsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (theprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (kfstpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodfstin) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR11) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR12) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR1) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairequniteq) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR) =>
% 129.57/17.04 ((
% 129.57/17.04 (ksndsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (ksndpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairsurjEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodsndin) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairmemEL) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairmemER) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempaircEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodfstpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodsndpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairsurjEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrI) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrSub) =>
% 129.57/17.04 ((
% 129.57/17.04 (setOfPairsIsBReln) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrERa) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrEL1) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrEL2) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrER) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcImageSingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (apProp) =>
% 129.57/17.04 ((
% 129.57/17.04 (app) =>
% 129.57/17.04 ((
% 129.57/17.04 (infuncsetfunc) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2p) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcinfuncset) =>
% 129.57/17.04 ((
% 129.57/17.04 (lamProp) =>
% 129.57/17.04 ((
% 129.57/17.04 (lamp) =>
% 129.57/17.04 ((
% 129.57/17.04 (lam2p) =>
% 129.57/17.04 ((
% 129.57/17.04 (brelnall1) =>
% 129.57/17.04 ((
% 129.57/17.04 (brelnall2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1E2) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp3) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcextLem) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp4) =>
% 129.57/17.04 ((
% 129.57/17.04 (subbreln) =>
% 129.57/17.04 ((
% 129.57/17.04 (eqbreln) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcext) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcext2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2apEq1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2apEq2) =>
% 129.57/17.04 ((
% 129.57/17.04 (beta1) =>
% 129.57/17.04 ((
% 129.57/17.04 (eta1) =>
% 129.57/17.04 ((
% 129.57/17.04 (lam2lamEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (beta2) =>
% 129.57/17.04 ((
% 129.57/17.04 (eta2) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalseProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalseProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ifSingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (ifp) =>
% 129.57/17.04 ((
% 129.57/17.04 (theeq) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrue) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalse) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueorfalse) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (setextT) =>
% 129.57/17.04 ((
% 129.57/17.04 (subsetTI) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetTI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetTE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectTELcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectTERcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT1) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT2) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT3) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementSub1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementSub2) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTnotintersectT) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementImpComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementSubsetComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementInPowersetComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (contraSubsetComplement) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTcontraSubset) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTILcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTIRcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInUnion) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInUnion2) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInIntersectUnions) =>
% 129.57/17.04 ((
% 129.57/17.04 (intersectInPowersetIntersectUnions) =>
% 129.57/17.04 ((
% 129.57/17.04 (inComplementUnionImpNotIn1) =>
% 129.57/17.04 ((
% 129.57/17.04 (inComplementUnionImpInComplement1) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTE) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTEcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementUnionInPowersetComplement) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a2) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1a) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1b) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b2) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule0) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_5) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all2) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1SetBreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (choice2fnsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (setOfPairsIsBReln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all1) =>
% 129.57/17.04 ((
% 129.57/17.04 (subbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (eqbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invI) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invE) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compI) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compE) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compEex) =>
% 129.57/17.04 ((
% 129.57/17.04 (!!) @ (
% 129.57/17.04 (('#B') @ (
% 129.57/17.04 !!) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#S') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#S') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 =>))) @
% 129.57/17.04 breln1)))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 !!))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#S') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#S') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 =>))) @
% 129.57/17.04 breln1)))))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#C') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 breln1)))) @
% 129.57/17.04 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1067])).
% 129.57/17.04 thf(zip_derived_cl1082, plain,
% 129.57/17.04 (~ (((sepInPowerset) =>
% 129.57/17.04 (((sepSubset) =>
% 129.57/17.04 (((binunionIL) =>
% 129.57/17.04 (((upairset2IR) =>
% 129.57/17.04 (((binunionIR) =>
% 129.57/17.04 (((binunionEcases) =>
% 129.57/17.04 (((binunionE) =>
% 129.57/17.04 (((binunionLsub) =>
% 129.57/17.04 (((binunionRsub) =>
% 129.57/17.04 (((binintersectI) =>
% 129.57/17.04 (((binintersectSubset5) =>
% 129.57/17.04 (((binintersectEL) =>
% 129.57/17.04 (((binintersectLsub) =>
% 129.57/17.04 (((binintersectSubset2) =>
% 129.57/17.04 (((binintersectSubset3) =>
% 129.57/17.04 (((binintersectER) =>
% 129.57/17.04 (((disjointsetsI1) =>
% 129.57/17.04 (((binintersectRsub) =>
% 129.57/17.04 (((binintersectSubset4) =>
% 129.57/17.04 (((binintersectSubset1) =>
% 129.57/17.04 (((bs114d) =>
% 129.57/17.04 (((setminusI) =>
% 129.57/17.04 (((setminusEL) =>
% 129.57/17.04 (((setminusER) =>
% 129.57/17.04 (((setminusSubset2) =>
% 129.57/17.04 (((setminusERneg) =>
% 129.57/17.04 (((setminusELneg) =>
% 129.57/17.04 (((setminusILneg) =>
% 129.57/17.04 (((setminusIRneg) =>
% 129.57/17.04 (((setminusLsub) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusSubset1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffE) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffI2) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffIneg1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffIneg2) =>
% 129.57/17.04 ((
% 129.57/17.04 (secondinupair) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairIL) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairIR) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairiskpair) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairp) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonsubset) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletoninpowerset) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletoninpowunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairset2E) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairsubunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairinpowunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem3) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairin) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempair1) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempair) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionE2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton1) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1E1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1I) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1I2) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonsuniq) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL1) =>
% 129.57/17.04 ((
% 129.57/17.04 (kfstsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (theprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (kfstpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodfstin) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR11) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR12) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR1) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairequniteq) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR) =>
% 129.57/17.04 ((
% 129.57/17.04 (ksndsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (ksndpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairsurjEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodsndin) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairmemEL) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairmemER) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempaircEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodfstpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodsndpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairsurjEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrI) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrSub) =>
% 129.57/17.04 ((
% 129.57/17.04 (setOfPairsIsBReln) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrERa) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrEL1) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrEL2) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrER) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcImageSingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (apProp) =>
% 129.57/17.04 ((
% 129.57/17.04 (app) =>
% 129.57/17.04 ((
% 129.57/17.04 (infuncsetfunc) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2p) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcinfuncset) =>
% 129.57/17.04 ((
% 129.57/17.04 (lamProp) =>
% 129.57/17.04 ((
% 129.57/17.04 (lamp) =>
% 129.57/17.04 ((
% 129.57/17.04 (lam2p) =>
% 129.57/17.04 ((
% 129.57/17.04 (brelnall1) =>
% 129.57/17.04 ((
% 129.57/17.04 (brelnall2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1E2) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp3) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcextLem) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp4) =>
% 129.57/17.04 ((
% 129.57/17.04 (subbreln) =>
% 129.57/17.04 ((
% 129.57/17.04 (eqbreln) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcext) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcext2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2apEq1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2apEq2) =>
% 129.57/17.04 ((
% 129.57/17.04 (beta1) =>
% 129.57/17.04 ((
% 129.57/17.04 (eta1) =>
% 129.57/17.04 ((
% 129.57/17.04 (lam2lamEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (beta2) =>
% 129.57/17.04 ((
% 129.57/17.04 (eta2) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalseProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalseProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ifSingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (ifp) =>
% 129.57/17.04 ((
% 129.57/17.04 (theeq) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrue) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalse) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueorfalse) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (setextT) =>
% 129.57/17.04 ((
% 129.57/17.04 (subsetTI) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetTI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetTE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectTELcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectTERcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT1) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT2) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT3) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementSub1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementSub2) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTnotintersectT) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementImpComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementSubsetComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementInPowersetComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (contraSubsetComplement) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTcontraSubset) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTILcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTIRcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInUnion) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInUnion2) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInIntersectUnions) =>
% 129.57/17.04 ((
% 129.57/17.04 (intersectInPowersetIntersectUnions) =>
% 129.57/17.04 ((
% 129.57/17.04 (inComplementUnionImpNotIn1) =>
% 129.57/17.04 ((
% 129.57/17.04 (inComplementUnionImpInComplement1) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTE) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTEcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementUnionInPowersetComplement) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a2) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1a) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1b) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b2) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule0) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_5) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all2) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1SetBreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (choice2fnsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (setOfPairsIsBReln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all1) =>
% 129.57/17.04 ((
% 129.57/17.04 (subbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (eqbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invI) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invE) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compI) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compE) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compEex) =>
% 129.57/17.04 ((
% 129.57/17.04 (!!) @ (
% 129.57/17.04 (('#B') @ (
% 129.57/17.04 !!) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#S') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#S') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 =>))) @
% 129.57/17.04 breln1)))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 !!))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#S') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#S') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 =>))) @
% 129.57/17.04 breln1)))))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#C') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 breln1)))) @
% 129.57/17.04 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1074])).
% 129.57/17.04 thf(zip_derived_cl1090, plain,
% 129.57/17.04 (~ (((sepSubset) =>
% 129.57/17.04 (((binunionIL) =>
% 129.57/17.04 (((upairset2IR) =>
% 129.57/17.04 (((binunionIR) =>
% 129.57/17.04 (((binunionEcases) =>
% 129.57/17.04 (((binunionE) =>
% 129.57/17.04 (((binunionLsub) =>
% 129.57/17.04 (((binunionRsub) =>
% 129.57/17.04 (((binintersectI) =>
% 129.57/17.04 (((binintersectSubset5) =>
% 129.57/17.04 (((binintersectEL) =>
% 129.57/17.04 (((binintersectLsub) =>
% 129.57/17.04 (((binintersectSubset2) =>
% 129.57/17.04 (((binintersectSubset3) =>
% 129.57/17.04 (((binintersectER) =>
% 129.57/17.04 (((disjointsetsI1) =>
% 129.57/17.04 (((binintersectRsub) =>
% 129.57/17.04 (((binintersectSubset4) =>
% 129.57/17.04 (((binintersectSubset1) =>
% 129.57/17.04 (((bs114d) =>
% 129.57/17.04 (((setminusI) =>
% 129.57/17.04 (((setminusEL) =>
% 129.57/17.04 (((setminusER) =>
% 129.57/17.04 (((setminusSubset2) =>
% 129.57/17.04 (((setminusERneg) =>
% 129.57/17.04 (((setminusELneg) =>
% 129.57/17.04 (((setminusILneg) =>
% 129.57/17.04 (((setminusIRneg) =>
% 129.57/17.04 (((setminusLsub) =>
% 129.57/17.04 (((setminusSubset1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffE) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffI2) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffIneg1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffIneg2) =>
% 129.57/17.04 ((
% 129.57/17.04 (secondinupair) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairIL) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairIR) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairiskpair) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairp) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonsubset) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletoninpowerset) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletoninpowunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairset2E) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairsubunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairinpowunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem3) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairin) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempair1) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempair) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionE2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton1) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1E1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1I) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1I2) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonsuniq) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL1) =>
% 129.57/17.04 ((
% 129.57/17.04 (kfstsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (theprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (kfstpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodfstin) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR11) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR12) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR1) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairequniteq) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR) =>
% 129.57/17.04 ((
% 129.57/17.04 (ksndsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (ksndpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairsurjEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodsndin) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairmemEL) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairmemER) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempaircEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodfstpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodsndpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairsurjEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrI) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrSub) =>
% 129.57/17.04 ((
% 129.57/17.04 (setOfPairsIsBReln) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrERa) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrEL1) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrEL2) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrER) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcImageSingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (apProp) =>
% 129.57/17.04 ((
% 129.57/17.04 (app) =>
% 129.57/17.04 ((
% 129.57/17.04 (infuncsetfunc) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2p) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcinfuncset) =>
% 129.57/17.04 ((
% 129.57/17.04 (lamProp) =>
% 129.57/17.04 ((
% 129.57/17.04 (lamp) =>
% 129.57/17.04 ((
% 129.57/17.04 (lam2p) =>
% 129.57/17.04 ((
% 129.57/17.04 (brelnall1) =>
% 129.57/17.04 ((
% 129.57/17.04 (brelnall2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1E2) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp3) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcextLem) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp4) =>
% 129.57/17.04 ((
% 129.57/17.04 (subbreln) =>
% 129.57/17.04 ((
% 129.57/17.04 (eqbreln) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcext) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcext2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2apEq1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2apEq2) =>
% 129.57/17.04 ((
% 129.57/17.04 (beta1) =>
% 129.57/17.04 ((
% 129.57/17.04 (eta1) =>
% 129.57/17.04 ((
% 129.57/17.04 (lam2lamEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (beta2) =>
% 129.57/17.04 ((
% 129.57/17.04 (eta2) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalseProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalseProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ifSingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (ifp) =>
% 129.57/17.04 ((
% 129.57/17.04 (theeq) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrue) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalse) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueorfalse) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (setextT) =>
% 129.57/17.04 ((
% 129.57/17.04 (subsetTI) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetTI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetTE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectTELcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectTERcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT1) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT2) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT3) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementSub1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementSub2) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTnotintersectT) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementImpComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementSubsetComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementInPowersetComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (contraSubsetComplement) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTcontraSubset) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTILcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTIRcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInUnion) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInUnion2) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInIntersectUnions) =>
% 129.57/17.04 ((
% 129.57/17.04 (intersectInPowersetIntersectUnions) =>
% 129.57/17.04 ((
% 129.57/17.04 (inComplementUnionImpNotIn1) =>
% 129.57/17.04 ((
% 129.57/17.04 (inComplementUnionImpInComplement1) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTE) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTEcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementUnionInPowersetComplement) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a2) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1a) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1b) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b2) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule0) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_5) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all2) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1SetBreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (choice2fnsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (setOfPairsIsBReln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all1) =>
% 129.57/17.04 ((
% 129.57/17.04 (subbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (eqbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invI) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invE) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compI) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compE) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1compEex) =>
% 129.57/17.04 ((
% 129.57/17.04 (!!) @ (
% 129.57/17.04 (('#B') @ (
% 129.57/17.04 !!) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#S') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#S') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 =>))) @
% 129.57/17.04 breln1)))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 !!))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#S') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#S') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 =>))) @
% 129.57/17.04 breln1)))))) @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#C') @ (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 (
% 129.57/17.04 (
% 129.57/17.04 ('#B') @ (
% 129.57/17.04 '#B') @
% 129.57/17.04 breln1)))) @
% 129.57/17.04 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1082])).
% 129.57/17.04 thf(zip_derived_cl1096, plain,
% 129.57/17.04 (~ (((binunionIL) =>
% 129.57/17.04 (((upairset2IR) =>
% 129.57/17.04 (((binunionIR) =>
% 129.57/17.04 (((binunionEcases) =>
% 129.57/17.04 (((binunionE) =>
% 129.57/17.04 (((binunionLsub) =>
% 129.57/17.04 (((binunionRsub) =>
% 129.57/17.04 (((binintersectI) =>
% 129.57/17.04 (((binintersectSubset5) =>
% 129.57/17.04 (((binintersectEL) =>
% 129.57/17.04 (((binintersectLsub) =>
% 129.57/17.04 (((binintersectSubset2) =>
% 129.57/17.04 (((binintersectSubset3) =>
% 129.57/17.04 (((binintersectER) =>
% 129.57/17.04 (((disjointsetsI1) =>
% 129.57/17.04 (((binintersectRsub) =>
% 129.57/17.04 (((binintersectSubset4) =>
% 129.57/17.04 (((binintersectSubset1) =>
% 129.57/17.04 (((bs114d) =>
% 129.57/17.04 (((setminusI) =>
% 129.57/17.04 (((setminusEL) =>
% 129.57/17.04 (((setminusER) =>
% 129.57/17.04 (((setminusSubset2) =>
% 129.57/17.04 (((setminusERneg) =>
% 129.57/17.04 (((setminusELneg) =>
% 129.57/17.04 (((setminusILneg) =>
% 129.57/17.04 (((setminusIRneg) =>
% 129.57/17.04 (((setminusLsub) =>
% 129.57/17.04 (((setminusSubset1) =>
% 129.57/17.04 (((symdiffE) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffI2) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffIneg1) =>
% 129.57/17.04 ((
% 129.57/17.04 (symdiffIneg2) =>
% 129.57/17.04 ((
% 129.57/17.04 (secondinupair) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairIL) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairIR) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairiskpair) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairp) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonsubset) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletoninpowerset) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletoninpowunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairset2E) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairsubunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairinpowunion) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ubforcartprodlem3) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairin) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempair1) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempair) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionE2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton1) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setunionsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1E1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1I) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1I2) =>
% 129.57/17.04 ((
% 129.57/17.04 (singletonsuniq) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL1) =>
% 129.57/17.04 ((
% 129.57/17.04 (kfstsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (theprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (kfstpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodfstin) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjL) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR11) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR12) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR1) =>
% 129.57/17.04 ((
% 129.57/17.04 (upairequniteq) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR2) =>
% 129.57/17.04 ((
% 129.57/17.04 (setukpairinjR) =>
% 129.57/17.04 ((
% 129.57/17.04 (ksndsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (ksndpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (kpairsurjEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodsndin) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairmemEL) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairmemER) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodmempaircEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodfstpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodsndpairEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (cartprodpairsurjEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrI) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrSub) =>
% 129.57/17.04 ((
% 129.57/17.04 (setOfPairsIsBReln) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrERa) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrEL1) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrEL2) =>
% 129.57/17.04 ((
% 129.57/17.04 (dpsetconstrER) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcImageSingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (apProp) =>
% 129.57/17.04 ((
% 129.57/17.04 (app) =>
% 129.57/17.04 ((
% 129.57/17.04 (infuncsetfunc) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2p) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcinfuncset) =>
% 129.57/17.04 ((
% 129.57/17.04 (lamProp) =>
% 129.57/17.04 ((
% 129.57/17.04 (lamp) =>
% 129.57/17.04 ((
% 129.57/17.04 (lam2p) =>
% 129.57/17.04 ((
% 129.57/17.04 (brelnall1) =>
% 129.57/17.04 ((
% 129.57/17.04 (brelnall2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ex1E2) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp3) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcextLem) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcGraphProp4) =>
% 129.57/17.04 ((
% 129.57/17.04 (subbreln) =>
% 129.57/17.04 ((
% 129.57/17.04 (eqbreln) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcext) =>
% 129.57/17.04 ((
% 129.57/17.04 (funcext2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2apEq1) =>
% 129.57/17.04 ((
% 129.57/17.04 (ap2apEq2) =>
% 129.57/17.04 ((
% 129.57/17.04 (beta1) =>
% 129.57/17.04 ((
% 129.57/17.04 (eta1) =>
% 129.57/17.04 ((
% 129.57/17.04 (lam2lamEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (beta2) =>
% 129.57/17.04 ((
% 129.57/17.04 (eta2) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalseProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalseProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueProp1) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueProp2) =>
% 129.57/17.04 ((
% 129.57/17.04 (ifSingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (ifp) =>
% 129.57/17.04 ((
% 129.57/17.04 (theeq) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrue) =>
% 129.57/17.04 ((
% 129.57/17.04 (iffalse) =>
% 129.57/17.04 ((
% 129.57/17.04 (iftrueorfalse) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (setminusT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementT_lem) =>
% 129.57/17.04 ((
% 129.57/17.04 (setextT) =>
% 129.57/17.04 ((
% 129.57/17.04 (subsetTI) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetTI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (powersetTE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectTELcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (binintersectTERcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT1) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT2) =>
% 129.57/17.04 ((
% 129.57/17.04 (contrasubsetT3) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementI1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementE1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementSub1) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementSub2) =>
% 129.57/17.04 ((
% 129.57/17.04 (doubleComplementEq) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTnotintersectT) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementImpComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementSubsetComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementInPowersetComplementIntersect) =>
% 129.57/17.04 ((
% 129.57/17.04 (contraSubsetComplement) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementTcontraSubset) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTILcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTIRcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInUnion) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInUnion2) =>
% 129.57/17.04 ((
% 129.57/17.04 (inIntersectImpInIntersectUnions) =>
% 129.57/17.04 ((
% 129.57/17.04 (intersectInPowersetIntersectUnions) =>
% 129.57/17.04 ((
% 129.57/17.04 (inComplementUnionImpNotIn1) =>
% 129.57/17.04 ((
% 129.57/17.04 (inComplementUnionImpInComplement1) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTE) =>
% 129.57/17.04 ((
% 129.57/17.04 (binunionTEcontra) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a1) =>
% 129.57/17.04 ((
% 129.57/17.04 (complementUnionInPowersetComplement) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a2) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1a) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1b) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan1) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2a) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b2) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2b) =>
% 129.57/17.04 ((
% 129.57/17.04 (demorgan2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule0) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz13rule4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_1) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_2) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_3) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_4) =>
% 129.57/17.04 ((
% 129.57/17.04 (woz1_5) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all2) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1SetBreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (choice2fnsingleton) =>
% 129.57/17.04 ((
% 129.57/17.04 (setOfPairsIsBReln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1all1) =>
% 129.57/17.04 ((
% 129.57/17.04 (subbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (eqbreln1) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invprop) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invI) =>
% 129.57/17.04 ((
% 129.57/17.04 (breln1invE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compI) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compEex) =>
% 129.57/17.05 ((
% 129.57/17.05 (!!) @ (
% 129.57/17.05 (('#B') @ (
% 129.57/17.05 !!) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 !!))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#C') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1090])).
% 129.57/17.05 thf(zip_derived_cl1102, plain,
% 129.57/17.05 (~ (((upairset2IR) =>
% 129.57/17.05 (((binunionIR) =>
% 129.57/17.05 (((binunionEcases) =>
% 129.57/17.05 (((binunionE) =>
% 129.57/17.05 (((binunionLsub) =>
% 129.57/17.05 (((binunionRsub) =>
% 129.57/17.05 (((binintersectI) =>
% 129.57/17.05 (((binintersectSubset5) =>
% 129.57/17.05 (((binintersectEL) =>
% 129.57/17.05 (((binintersectLsub) =>
% 129.57/17.05 (((binintersectSubset2) =>
% 129.57/17.05 (((binintersectSubset3) =>
% 129.57/17.05 (((binintersectER) =>
% 129.57/17.05 (((disjointsetsI1) =>
% 129.57/17.05 (((binintersectRsub) =>
% 129.57/17.05 (((binintersectSubset4) =>
% 129.57/17.05 (((binintersectSubset1) =>
% 129.57/17.05 (((bs114d) =>
% 129.57/17.05 (((setminusI) =>
% 129.57/17.05 (((setminusEL) =>
% 129.57/17.05 (((setminusER) =>
% 129.57/17.05 (((setminusSubset2) =>
% 129.57/17.05 (((setminusERneg) =>
% 129.57/17.05 (((setminusELneg) =>
% 129.57/17.05 (((setminusILneg) =>
% 129.57/17.05 (((setminusIRneg) =>
% 129.57/17.05 (((setminusLsub) =>
% 129.57/17.05 (((setminusSubset1) =>
% 129.57/17.05 (((symdiffE) =>
% 129.57/17.05 (((symdiffI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (symdiffI2) =>
% 129.57/17.05 ((
% 129.57/17.05 (symdiffIneg1) =>
% 129.57/17.05 ((
% 129.57/17.05 (symdiffIneg2) =>
% 129.57/17.05 ((
% 129.57/17.05 (secondinupair) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairIL) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairIR) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairiskpair) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairp) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsubset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowerset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairset2E) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairsubunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairinpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem3) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair1) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionE2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton1) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I2) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsuniq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (theprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstin) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR11) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR12) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR1) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairequniteq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemEL) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemER) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempaircEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrI) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrSub) =>
% 129.57/17.05 ((
% 129.57/17.05 (setOfPairsIsBReln) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrERa) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrER) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcImageSingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (apProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (app) =>
% 129.57/17.05 ((
% 129.57/17.05 (infuncsetfunc) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcinfuncset) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lam2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall1) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E2) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp3) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcextLem) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp4) =>
% 129.57/17.05 ((
% 129.57/17.05 (subbreln) =>
% 129.57/17.05 ((
% 129.57/17.05 (eqbreln) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcext) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcext2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2apEq1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2apEq2) =>
% 129.57/17.05 ((
% 129.57/17.05 (beta1) =>
% 129.57/17.05 ((
% 129.57/17.05 (eta1) =>
% 129.57/17.05 ((
% 129.57/17.05 (lam2lamEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (beta2) =>
% 129.57/17.05 ((
% 129.57/17.05 (eta2) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalseProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalseProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ifSingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (ifp) =>
% 129.57/17.05 ((
% 129.57/17.05 (theeq) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrue) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalse) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueorfalse) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (setminusT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (setextT) =>
% 129.57/17.05 ((
% 129.57/17.05 (subsetTI) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetTI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetTE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectTELcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectTERcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT1) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT2) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT3) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementSub1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementSub2) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTnotintersectT) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementImpComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementSubsetComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementInPowersetComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (contraSubsetComplement) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTcontraSubset) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTILcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTIRcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInUnion) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInUnion2) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInIntersectUnions) =>
% 129.57/17.05 ((
% 129.57/17.05 (intersectInPowersetIntersectUnions) =>
% 129.57/17.05 ((
% 129.57/17.05 (inComplementUnionImpNotIn1) =>
% 129.57/17.05 ((
% 129.57/17.05 (inComplementUnionImpInComplement1) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTE) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTEcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementUnionInPowersetComplement) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a2) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1a) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1b) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2b2) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2b) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule0) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule1) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule3) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule4) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_1) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_3) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_4) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_5) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1all2) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1SetBreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (choice2fnsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (setOfPairsIsBReln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1all1) =>
% 129.57/17.05 ((
% 129.57/17.05 (subbreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (eqbreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invI) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compI) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compEex) =>
% 129.57/17.05 ((
% 129.57/17.05 (!!) @ (
% 129.57/17.05 (('#B') @ (
% 129.57/17.05 !!) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 !!))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#C') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1096])).
% 129.57/17.05 thf(zip_derived_cl1109, plain,
% 129.57/17.05 (~ (((binunionIR) =>
% 129.57/17.05 (((binunionEcases) =>
% 129.57/17.05 (((binunionE) =>
% 129.57/17.05 (((binunionLsub) =>
% 129.57/17.05 (((binunionRsub) =>
% 129.57/17.05 (((binintersectI) =>
% 129.57/17.05 (((binintersectSubset5) =>
% 129.57/17.05 (((binintersectEL) =>
% 129.57/17.05 (((binintersectLsub) =>
% 129.57/17.05 (((binintersectSubset2) =>
% 129.57/17.05 (((binintersectSubset3) =>
% 129.57/17.05 (((binintersectER) =>
% 129.57/17.05 (((disjointsetsI1) =>
% 129.57/17.05 (((binintersectRsub) =>
% 129.57/17.05 (((binintersectSubset4) =>
% 129.57/17.05 (((binintersectSubset1) =>
% 129.57/17.05 (((bs114d) =>
% 129.57/17.05 (((setminusI) =>
% 129.57/17.05 (((setminusEL) =>
% 129.57/17.05 (((setminusER) =>
% 129.57/17.05 (((setminusSubset2) =>
% 129.57/17.05 (((setminusERneg) =>
% 129.57/17.05 (((setminusELneg) =>
% 129.57/17.05 (((setminusILneg) =>
% 129.57/17.05 (((setminusIRneg) =>
% 129.57/17.05 (((setminusLsub) =>
% 129.57/17.05 (((setminusSubset1) =>
% 129.57/17.05 (((symdiffE) =>
% 129.57/17.05 (((symdiffI1) =>
% 129.57/17.05 (((symdiffI2) =>
% 129.57/17.05 ((
% 129.57/17.05 (symdiffIneg1) =>
% 129.57/17.05 ((
% 129.57/17.05 (symdiffIneg2) =>
% 129.57/17.05 ((
% 129.57/17.05 (secondinupair) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairIL) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairIR) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairiskpair) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairp) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsubset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowerset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairset2E) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairsubunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairinpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem3) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair1) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionE2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton1) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I2) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsuniq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (theprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstin) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR11) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR12) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR1) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairequniteq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemEL) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemER) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempaircEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrI) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrSub) =>
% 129.57/17.05 ((
% 129.57/17.05 (setOfPairsIsBReln) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrERa) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrER) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcImageSingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (apProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (app) =>
% 129.57/17.05 ((
% 129.57/17.05 (infuncsetfunc) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcinfuncset) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lam2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall1) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E2) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp3) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcextLem) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp4) =>
% 129.57/17.05 ((
% 129.57/17.05 (subbreln) =>
% 129.57/17.05 ((
% 129.57/17.05 (eqbreln) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcext) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcext2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2apEq1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2apEq2) =>
% 129.57/17.05 ((
% 129.57/17.05 (beta1) =>
% 129.57/17.05 ((
% 129.57/17.05 (eta1) =>
% 129.57/17.05 ((
% 129.57/17.05 (lam2lamEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (beta2) =>
% 129.57/17.05 ((
% 129.57/17.05 (eta2) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalseProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalseProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ifSingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (ifp) =>
% 129.57/17.05 ((
% 129.57/17.05 (theeq) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrue) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalse) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueorfalse) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (setminusT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (setextT) =>
% 129.57/17.05 ((
% 129.57/17.05 (subsetTI) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetTI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetTE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectTELcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectTERcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT1) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT2) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT3) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementSub1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementSub2) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTnotintersectT) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementImpComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementSubsetComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementInPowersetComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (contraSubsetComplement) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTcontraSubset) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTILcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTIRcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInUnion) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInUnion2) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInIntersectUnions) =>
% 129.57/17.05 ((
% 129.57/17.05 (intersectInPowersetIntersectUnions) =>
% 129.57/17.05 ((
% 129.57/17.05 (inComplementUnionImpNotIn1) =>
% 129.57/17.05 ((
% 129.57/17.05 (inComplementUnionImpInComplement1) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTE) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTEcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementUnionInPowersetComplement) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a2) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1a) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1b) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2b2) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2b) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule0) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule1) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule3) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule4) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_1) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_3) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_4) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_5) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1all2) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1SetBreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (choice2fnsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (setOfPairsIsBReln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1all1) =>
% 129.57/17.05 ((
% 129.57/17.05 (subbreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (eqbreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invI) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compI) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compEex) =>
% 129.57/17.05 ((
% 129.57/17.05 (!!) @ (
% 129.57/17.05 (('#B') @ (
% 129.57/17.05 !!) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 !!))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#C') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1102])).
% 129.57/17.05 thf(zip_derived_cl1115, plain,
% 129.57/17.05 (~ (((binunionEcases) =>
% 129.57/17.05 (((binunionE) =>
% 129.57/17.05 (((binunionLsub) =>
% 129.57/17.05 (((binunionRsub) =>
% 129.57/17.05 (((binintersectI) =>
% 129.57/17.05 (((binintersectSubset5) =>
% 129.57/17.05 (((binintersectEL) =>
% 129.57/17.05 (((binintersectLsub) =>
% 129.57/17.05 (((binintersectSubset2) =>
% 129.57/17.05 (((binintersectSubset3) =>
% 129.57/17.05 (((binintersectER) =>
% 129.57/17.05 (((disjointsetsI1) =>
% 129.57/17.05 (((binintersectRsub) =>
% 129.57/17.05 (((binintersectSubset4) =>
% 129.57/17.05 (((binintersectSubset1) =>
% 129.57/17.05 (((bs114d) =>
% 129.57/17.05 (((setminusI) =>
% 129.57/17.05 (((setminusEL) =>
% 129.57/17.05 (((setminusER) =>
% 129.57/17.05 (((setminusSubset2) =>
% 129.57/17.05 (((setminusERneg) =>
% 129.57/17.05 (((setminusELneg) =>
% 129.57/17.05 (((setminusILneg) =>
% 129.57/17.05 (((setminusIRneg) =>
% 129.57/17.05 (((setminusLsub) =>
% 129.57/17.05 (((setminusSubset1) =>
% 129.57/17.05 (((symdiffE) =>
% 129.57/17.05 (((symdiffI1) =>
% 129.57/17.05 (((symdiffI2) =>
% 129.57/17.05 (((symdiffIneg1) =>
% 129.57/17.05 ((
% 129.57/17.05 (symdiffIneg2) =>
% 129.57/17.05 ((
% 129.57/17.05 (secondinupair) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairIL) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairIR) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairiskpair) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairp) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsubset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowerset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairset2E) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairsubunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairinpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem3) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair1) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionE2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton1) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I2) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsuniq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (theprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstin) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR11) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR12) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR1) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairequniteq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemEL) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemER) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempaircEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrI) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrSub) =>
% 129.57/17.05 ((
% 129.57/17.05 (setOfPairsIsBReln) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrERa) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrER) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcImageSingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (apProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (app) =>
% 129.57/17.05 ((
% 129.57/17.05 (infuncsetfunc) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcinfuncset) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lam2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall1) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E2) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp3) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcextLem) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp4) =>
% 129.57/17.05 ((
% 129.57/17.05 (subbreln) =>
% 129.57/17.05 ((
% 129.57/17.05 (eqbreln) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcext) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcext2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2apEq1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2apEq2) =>
% 129.57/17.05 ((
% 129.57/17.05 (beta1) =>
% 129.57/17.05 ((
% 129.57/17.05 (eta1) =>
% 129.57/17.05 ((
% 129.57/17.05 (lam2lamEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (beta2) =>
% 129.57/17.05 ((
% 129.57/17.05 (eta2) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalseProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalseProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ifSingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (ifp) =>
% 129.57/17.05 ((
% 129.57/17.05 (theeq) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrue) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalse) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueorfalse) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (setminusT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (setextT) =>
% 129.57/17.05 ((
% 129.57/17.05 (subsetTI) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetTI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetTE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectTELcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectTERcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT1) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT2) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT3) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementSub1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementSub2) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTnotintersectT) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementImpComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementSubsetComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementInPowersetComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (contraSubsetComplement) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTcontraSubset) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTILcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTIRcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInUnion) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInUnion2) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInIntersectUnions) =>
% 129.57/17.05 ((
% 129.57/17.05 (intersectInPowersetIntersectUnions) =>
% 129.57/17.05 ((
% 129.57/17.05 (inComplementUnionImpNotIn1) =>
% 129.57/17.05 ((
% 129.57/17.05 (inComplementUnionImpInComplement1) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTE) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTEcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementUnionInPowersetComplement) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a2) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1a) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1b) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2b2) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2b) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule0) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule1) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule3) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule4) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_1) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_3) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_4) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_5) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1all2) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1SetBreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (choice2fnsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (setOfPairsIsBReln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1all1) =>
% 129.57/17.05 ((
% 129.57/17.05 (subbreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (eqbreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invI) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compI) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compEex) =>
% 129.57/17.05 ((
% 129.57/17.05 (!!) @ (
% 129.57/17.05 (('#B') @ (
% 129.57/17.05 !!) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 !!))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#C') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1109])).
% 129.57/17.05 thf(zip_derived_cl1121, plain,
% 129.57/17.05 (~ (((binunionE) =>
% 129.57/17.05 (((binunionLsub) =>
% 129.57/17.05 (((binunionRsub) =>
% 129.57/17.05 (((binintersectI) =>
% 129.57/17.05 (((binintersectSubset5) =>
% 129.57/17.05 (((binintersectEL) =>
% 129.57/17.05 (((binintersectLsub) =>
% 129.57/17.05 (((binintersectSubset2) =>
% 129.57/17.05 (((binintersectSubset3) =>
% 129.57/17.05 (((binintersectER) =>
% 129.57/17.05 (((disjointsetsI1) =>
% 129.57/17.05 (((binintersectRsub) =>
% 129.57/17.05 (((binintersectSubset4) =>
% 129.57/17.05 (((binintersectSubset1) =>
% 129.57/17.05 (((bs114d) =>
% 129.57/17.05 (((setminusI) =>
% 129.57/17.05 (((setminusEL) =>
% 129.57/17.05 (((setminusER) =>
% 129.57/17.05 (((setminusSubset2) =>
% 129.57/17.05 (((setminusERneg) =>
% 129.57/17.05 (((setminusELneg) =>
% 129.57/17.05 (((setminusILneg) =>
% 129.57/17.05 (((setminusIRneg) =>
% 129.57/17.05 (((setminusLsub) =>
% 129.57/17.05 (((setminusSubset1) =>
% 129.57/17.05 (((symdiffE) =>
% 129.57/17.05 (((symdiffI1) =>
% 129.57/17.05 (((symdiffI2) =>
% 129.57/17.05 (((symdiffIneg1) =>
% 129.57/17.05 (((symdiffIneg2) =>
% 129.57/17.05 ((
% 129.57/17.05 (secondinupair) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairIL) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairIR) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairiskpair) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairp) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsubset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowerset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairset2E) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairsubunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairinpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem3) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair1) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionE2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton1) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I2) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsuniq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (theprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstin) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR11) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR12) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR1) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairequniteq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemEL) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemER) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempaircEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrI) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrSub) =>
% 129.57/17.05 ((
% 129.57/17.05 (setOfPairsIsBReln) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrERa) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrER) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcImageSingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (apProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (app) =>
% 129.57/17.05 ((
% 129.57/17.05 (infuncsetfunc) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcinfuncset) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lam2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall1) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E2) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp3) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcextLem) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp4) =>
% 129.57/17.05 ((
% 129.57/17.05 (subbreln) =>
% 129.57/17.05 ((
% 129.57/17.05 (eqbreln) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcext) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcext2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2apEq1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2apEq2) =>
% 129.57/17.05 ((
% 129.57/17.05 (beta1) =>
% 129.57/17.05 ((
% 129.57/17.05 (eta1) =>
% 129.57/17.05 ((
% 129.57/17.05 (lam2lamEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (beta2) =>
% 129.57/17.05 ((
% 129.57/17.05 (eta2) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalseProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalseProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ifSingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (ifp) =>
% 129.57/17.05 ((
% 129.57/17.05 (theeq) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrue) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalse) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueorfalse) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (setminusT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (setextT) =>
% 129.57/17.05 ((
% 129.57/17.05 (subsetTI) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetTI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetTE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectTELcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectTERcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT1) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT2) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT3) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementSub1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementSub2) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTnotintersectT) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementImpComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementSubsetComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementInPowersetComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (contraSubsetComplement) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTcontraSubset) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTILcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTIRcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInUnion) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInUnion2) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInIntersectUnions) =>
% 129.57/17.05 ((
% 129.57/17.05 (intersectInPowersetIntersectUnions) =>
% 129.57/17.05 ((
% 129.57/17.05 (inComplementUnionImpNotIn1) =>
% 129.57/17.05 ((
% 129.57/17.05 (inComplementUnionImpInComplement1) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTE) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTEcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementUnionInPowersetComplement) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a2) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1a) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1b) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2b2) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2b) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule0) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule1) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule3) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule4) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_1) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_3) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_4) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_5) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1all2) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1SetBreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (choice2fnsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (setOfPairsIsBReln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1all1) =>
% 129.57/17.05 ((
% 129.57/17.05 (subbreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (eqbreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invI) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compI) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compEex) =>
% 129.57/17.05 ((
% 129.57/17.05 (!!) @ (
% 129.57/17.05 (('#B') @ (
% 129.57/17.05 !!) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 !!))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#C') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1115])).
% 129.57/17.05 thf(zip_derived_cl1128, plain,
% 129.57/17.05 (~ (((binunionLsub) =>
% 129.57/17.05 (((binunionRsub) =>
% 129.57/17.05 (((binintersectI) =>
% 129.57/17.05 (((binintersectSubset5) =>
% 129.57/17.05 (((binintersectEL) =>
% 129.57/17.05 (((binintersectLsub) =>
% 129.57/17.05 (((binintersectSubset2) =>
% 129.57/17.05 (((binintersectSubset3) =>
% 129.57/17.05 (((binintersectER) =>
% 129.57/17.05 (((disjointsetsI1) =>
% 129.57/17.05 (((binintersectRsub) =>
% 129.57/17.05 (((binintersectSubset4) =>
% 129.57/17.05 (((binintersectSubset1) =>
% 129.57/17.05 (((bs114d) =>
% 129.57/17.05 (((setminusI) =>
% 129.57/17.05 (((setminusEL) =>
% 129.57/17.05 (((setminusER) =>
% 129.57/17.05 (((setminusSubset2) =>
% 129.57/17.05 (((setminusERneg) =>
% 129.57/17.05 (((setminusELneg) =>
% 129.57/17.05 (((setminusILneg) =>
% 129.57/17.05 (((setminusIRneg) =>
% 129.57/17.05 (((setminusLsub) =>
% 129.57/17.05 (((setminusSubset1) =>
% 129.57/17.05 (((symdiffE) =>
% 129.57/17.05 (((symdiffI1) =>
% 129.57/17.05 (((symdiffI2) =>
% 129.57/17.05 (((symdiffIneg1) =>
% 129.57/17.05 (((symdiffIneg2) =>
% 129.57/17.05 (((secondinupair) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairIL) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairIR) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairiskpair) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairp) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsubset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowerset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairset2E) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairsubunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairinpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem3) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair1) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionE2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton1) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I2) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsuniq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (theprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstin) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR11) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR12) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR1) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairequniteq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemEL) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemER) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempaircEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrI) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrSub) =>
% 129.57/17.05 ((
% 129.57/17.05 (setOfPairsIsBReln) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrERa) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrER) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcImageSingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (apProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (app) =>
% 129.57/17.05 ((
% 129.57/17.05 (infuncsetfunc) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcinfuncset) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lam2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall1) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E2) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp3) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcextLem) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp4) =>
% 129.57/17.05 ((
% 129.57/17.05 (subbreln) =>
% 129.57/17.05 ((
% 129.57/17.05 (eqbreln) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcext) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcext2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2apEq1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2apEq2) =>
% 129.57/17.05 ((
% 129.57/17.05 (beta1) =>
% 129.57/17.05 ((
% 129.57/17.05 (eta1) =>
% 129.57/17.05 ((
% 129.57/17.05 (lam2lamEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (beta2) =>
% 129.57/17.05 ((
% 129.57/17.05 (eta2) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalseProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalseProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ifSingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (ifp) =>
% 129.57/17.05 ((
% 129.57/17.05 (theeq) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrue) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalse) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueorfalse) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (setminusT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (setextT) =>
% 129.57/17.05 ((
% 129.57/17.05 (subsetTI) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetTI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetTE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectTELcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectTERcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT1) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT2) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT3) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementSub1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementSub2) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTnotintersectT) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementImpComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementSubsetComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementInPowersetComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (contraSubsetComplement) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTcontraSubset) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTILcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTIRcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInUnion) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInUnion2) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInIntersectUnions) =>
% 129.57/17.05 ((
% 129.57/17.05 (intersectInPowersetIntersectUnions) =>
% 129.57/17.05 ((
% 129.57/17.05 (inComplementUnionImpNotIn1) =>
% 129.57/17.05 ((
% 129.57/17.05 (inComplementUnionImpInComplement1) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTE) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTEcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementUnionInPowersetComplement) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a2) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1a) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1b) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2b2) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2b) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule0) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule1) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule3) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule4) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_1) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_3) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_4) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_5) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1all2) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1SetBreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (choice2fnsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (setOfPairsIsBReln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1all1) =>
% 129.57/17.05 ((
% 129.57/17.05 (subbreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (eqbreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invI) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compI) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compEex) =>
% 129.57/17.05 ((
% 129.57/17.05 (!!) @ (
% 129.57/17.05 (('#B') @ (
% 129.57/17.05 !!) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 !!))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#C') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1121])).
% 129.57/17.05 thf(zip_derived_cl1135, plain,
% 129.57/17.05 (~ (((binunionRsub) =>
% 129.57/17.05 (((binintersectI) =>
% 129.57/17.05 (((binintersectSubset5) =>
% 129.57/17.05 (((binintersectEL) =>
% 129.57/17.05 (((binintersectLsub) =>
% 129.57/17.05 (((binintersectSubset2) =>
% 129.57/17.05 (((binintersectSubset3) =>
% 129.57/17.05 (((binintersectER) =>
% 129.57/17.05 (((disjointsetsI1) =>
% 129.57/17.05 (((binintersectRsub) =>
% 129.57/17.05 (((binintersectSubset4) =>
% 129.57/17.05 (((binintersectSubset1) =>
% 129.57/17.05 (((bs114d) =>
% 129.57/17.05 (((setminusI) =>
% 129.57/17.05 (((setminusEL) =>
% 129.57/17.05 (((setminusER) =>
% 129.57/17.05 (((setminusSubset2) =>
% 129.57/17.05 (((setminusERneg) =>
% 129.57/17.05 (((setminusELneg) =>
% 129.57/17.05 (((setminusILneg) =>
% 129.57/17.05 (((setminusIRneg) =>
% 129.57/17.05 (((setminusLsub) =>
% 129.57/17.05 (((setminusSubset1) =>
% 129.57/17.05 (((symdiffE) =>
% 129.57/17.05 (((symdiffI1) =>
% 129.57/17.05 (((symdiffI2) =>
% 129.57/17.05 (((symdiffIneg1) =>
% 129.57/17.05 (((symdiffIneg2) =>
% 129.57/17.05 (((secondinupair) =>
% 129.57/17.05 (((setukpairIL) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairIR) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairiskpair) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairp) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsubset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowerset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairset2E) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairsubunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairinpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem3) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair1) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionE2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton1) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I2) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsuniq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (theprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstin) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR11) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR12) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR1) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairequniteq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemEL) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemER) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempaircEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrI) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrSub) =>
% 129.57/17.05 ((
% 129.57/17.05 (setOfPairsIsBReln) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrERa) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrER) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcImageSingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (apProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (app) =>
% 129.57/17.05 ((
% 129.57/17.05 (infuncsetfunc) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcinfuncset) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lam2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall1) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E2) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp3) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcextLem) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp4) =>
% 129.57/17.05 ((
% 129.57/17.05 (subbreln) =>
% 129.57/17.05 ((
% 129.57/17.05 (eqbreln) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcext) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcext2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2apEq1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2apEq2) =>
% 129.57/17.05 ((
% 129.57/17.05 (beta1) =>
% 129.57/17.05 ((
% 129.57/17.05 (eta1) =>
% 129.57/17.05 ((
% 129.57/17.05 (lam2lamEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (beta2) =>
% 129.57/17.05 ((
% 129.57/17.05 (eta2) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalseProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalseProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ifSingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (ifp) =>
% 129.57/17.05 ((
% 129.57/17.05 (theeq) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrue) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalse) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueorfalse) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (setminusT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (setextT) =>
% 129.57/17.05 ((
% 129.57/17.05 (subsetTI) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetTI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetTE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectTELcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectTERcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT1) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT2) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT3) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementSub1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementSub2) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTnotintersectT) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementImpComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementSubsetComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementInPowersetComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (contraSubsetComplement) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTcontraSubset) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTILcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTIRcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInUnion) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInUnion2) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInIntersectUnions) =>
% 129.57/17.05 ((
% 129.57/17.05 (intersectInPowersetIntersectUnions) =>
% 129.57/17.05 ((
% 129.57/17.05 (inComplementUnionImpNotIn1) =>
% 129.57/17.05 ((
% 129.57/17.05 (inComplementUnionImpInComplement1) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTE) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTEcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementUnionInPowersetComplement) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a2) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1a) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1b) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2b2) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2b) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule0) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule1) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule3) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule4) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_1) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_3) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_4) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_5) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1all2) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1SetBreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (choice2fnsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (setOfPairsIsBReln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1all1) =>
% 129.57/17.05 ((
% 129.57/17.05 (subbreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (eqbreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invI) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compI) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compEex) =>
% 129.57/17.05 ((
% 129.57/17.05 (!!) @ (
% 129.57/17.05 (('#B') @ (
% 129.57/17.05 !!) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 !!))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#C') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1128])).
% 129.57/17.05 thf(zip_derived_cl1142, plain,
% 129.57/17.05 (~ (((binintersectI) =>
% 129.57/17.05 (((binintersectSubset5) =>
% 129.57/17.05 (((binintersectEL) =>
% 129.57/17.05 (((binintersectLsub) =>
% 129.57/17.05 (((binintersectSubset2) =>
% 129.57/17.05 (((binintersectSubset3) =>
% 129.57/17.05 (((binintersectER) =>
% 129.57/17.05 (((disjointsetsI1) =>
% 129.57/17.05 (((binintersectRsub) =>
% 129.57/17.05 (((binintersectSubset4) =>
% 129.57/17.05 (((binintersectSubset1) =>
% 129.57/17.05 (((bs114d) =>
% 129.57/17.05 (((setminusI) =>
% 129.57/17.05 (((setminusEL) =>
% 129.57/17.05 (((setminusER) =>
% 129.57/17.05 (((setminusSubset2) =>
% 129.57/17.05 (((setminusERneg) =>
% 129.57/17.05 (((setminusELneg) =>
% 129.57/17.05 (((setminusILneg) =>
% 129.57/17.05 (((setminusIRneg) =>
% 129.57/17.05 (((setminusLsub) =>
% 129.57/17.05 (((setminusSubset1) =>
% 129.57/17.05 (((symdiffE) =>
% 129.57/17.05 (((symdiffI1) =>
% 129.57/17.05 (((symdiffI2) =>
% 129.57/17.05 (((symdiffIneg1) =>
% 129.57/17.05 (((symdiffIneg2) =>
% 129.57/17.05 (((secondinupair) =>
% 129.57/17.05 (((setukpairIL) =>
% 129.57/17.05 (((setukpairIR) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairiskpair) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairp) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsubset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowerset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairset2E) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairsubunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairinpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem3) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair1) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionE2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton1) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I2) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsuniq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (theprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstin) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR11) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR12) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR1) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairequniteq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemEL) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemER) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempaircEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrI) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrSub) =>
% 129.57/17.05 ((
% 129.57/17.05 (setOfPairsIsBReln) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrERa) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrER) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcImageSingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (apProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (app) =>
% 129.57/17.05 ((
% 129.57/17.05 (infuncsetfunc) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcinfuncset) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lam2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall1) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E2) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp3) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcextLem) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp4) =>
% 129.57/17.05 ((
% 129.57/17.05 (subbreln) =>
% 129.57/17.05 ((
% 129.57/17.05 (eqbreln) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcext) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcext2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2apEq1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2apEq2) =>
% 129.57/17.05 ((
% 129.57/17.05 (beta1) =>
% 129.57/17.05 ((
% 129.57/17.05 (eta1) =>
% 129.57/17.05 ((
% 129.57/17.05 (lam2lamEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (beta2) =>
% 129.57/17.05 ((
% 129.57/17.05 (eta2) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalseProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalseProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ifSingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (ifp) =>
% 129.57/17.05 ((
% 129.57/17.05 (theeq) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrue) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalse) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueorfalse) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (setminusT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (setextT) =>
% 129.57/17.05 ((
% 129.57/17.05 (subsetTI) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetTI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetTE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectTELcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectTERcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT1) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT2) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT3) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementSub1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementSub2) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTnotintersectT) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementImpComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementSubsetComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementInPowersetComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (contraSubsetComplement) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTcontraSubset) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTILcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTIRcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInUnion) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInUnion2) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInIntersectUnions) =>
% 129.57/17.05 ((
% 129.57/17.05 (intersectInPowersetIntersectUnions) =>
% 129.57/17.05 ((
% 129.57/17.05 (inComplementUnionImpNotIn1) =>
% 129.57/17.05 ((
% 129.57/17.05 (inComplementUnionImpInComplement1) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTE) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTEcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementUnionInPowersetComplement) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a2) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1a) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1b) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2b2) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2b) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule0) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule1) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule3) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule4) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_1) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_3) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_4) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_5) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1all2) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1SetBreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (choice2fnsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (setOfPairsIsBReln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1all1) =>
% 129.57/17.05 ((
% 129.57/17.05 (subbreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (eqbreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invI) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compI) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compEex) =>
% 129.57/17.05 ((
% 129.57/17.05 (!!) @ (
% 129.57/17.05 (('#B') @ (
% 129.57/17.05 !!) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 !!))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#C') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1135])).
% 129.57/17.05 thf(zip_derived_cl1150, plain,
% 129.57/17.05 (~ (((binintersectSubset5) =>
% 129.57/17.05 (((binintersectEL) =>
% 129.57/17.05 (((binintersectLsub) =>
% 129.57/17.05 (((binintersectSubset2) =>
% 129.57/17.05 (((binintersectSubset3) =>
% 129.57/17.05 (((binintersectER) =>
% 129.57/17.05 (((disjointsetsI1) =>
% 129.57/17.05 (((binintersectRsub) =>
% 129.57/17.05 (((binintersectSubset4) =>
% 129.57/17.05 (((binintersectSubset1) =>
% 129.57/17.05 (((bs114d) =>
% 129.57/17.05 (((setminusI) =>
% 129.57/17.05 (((setminusEL) =>
% 129.57/17.05 (((setminusER) =>
% 129.57/17.05 (((setminusSubset2) =>
% 129.57/17.05 (((setminusERneg) =>
% 129.57/17.05 (((setminusELneg) =>
% 129.57/17.05 (((setminusILneg) =>
% 129.57/17.05 (((setminusIRneg) =>
% 129.57/17.05 (((setminusLsub) =>
% 129.57/17.05 (((setminusSubset1) =>
% 129.57/17.05 (((symdiffE) =>
% 129.57/17.05 (((symdiffI1) =>
% 129.57/17.05 (((symdiffI2) =>
% 129.57/17.05 (((symdiffIneg1) =>
% 129.57/17.05 (((symdiffIneg2) =>
% 129.57/17.05 (((secondinupair) =>
% 129.57/17.05 (((setukpairIL) =>
% 129.57/17.05 (((setukpairIR) =>
% 129.57/17.05 (((kpairiskpair) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairp) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsubset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowerset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairset2E) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairsubunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairinpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem3) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair1) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionE2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton1) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I2) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsuniq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (theprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstin) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR11) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR12) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR1) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairequniteq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemEL) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemER) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempaircEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrI) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrSub) =>
% 129.57/17.05 ((
% 129.57/17.05 (setOfPairsIsBReln) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrERa) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrER) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcImageSingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (apProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (app) =>
% 129.57/17.05 ((
% 129.57/17.05 (infuncsetfunc) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcinfuncset) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lam2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall1) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E2) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp3) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcextLem) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp4) =>
% 129.57/17.05 ((
% 129.57/17.05 (subbreln) =>
% 129.57/17.05 ((
% 129.57/17.05 (eqbreln) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcext) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcext2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2apEq1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2apEq2) =>
% 129.57/17.05 ((
% 129.57/17.05 (beta1) =>
% 129.57/17.05 ((
% 129.57/17.05 (eta1) =>
% 129.57/17.05 ((
% 129.57/17.05 (lam2lamEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (beta2) =>
% 129.57/17.05 ((
% 129.57/17.05 (eta2) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalseProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalseProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueProp1) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueProp2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ifSingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (ifp) =>
% 129.57/17.05 ((
% 129.57/17.05 (theeq) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrue) =>
% 129.57/17.05 ((
% 129.57/17.05 (iffalse) =>
% 129.57/17.05 ((
% 129.57/17.05 (iftrueorfalse) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (setminusT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementT_lem) =>
% 129.57/17.05 ((
% 129.57/17.05 (setextT) =>
% 129.57/17.05 ((
% 129.57/17.05 (subsetTI) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetTI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (powersetTE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectTELcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (binintersectTERcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT1) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT2) =>
% 129.57/17.05 ((
% 129.57/17.05 (contrasubsetT3) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementI1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementE1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementSub1) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementSub2) =>
% 129.57/17.05 ((
% 129.57/17.05 (doubleComplementEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTnotintersectT) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementImpComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementSubsetComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementInPowersetComplementIntersect) =>
% 129.57/17.05 ((
% 129.57/17.05 (contraSubsetComplement) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementTcontraSubset) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTILcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTIRcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInUnion) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInUnion2) =>
% 129.57/17.05 ((
% 129.57/17.05 (inIntersectImpInIntersectUnions) =>
% 129.57/17.05 ((
% 129.57/17.05 (intersectInPowersetIntersectUnions) =>
% 129.57/17.05 ((
% 129.57/17.05 (inComplementUnionImpNotIn1) =>
% 129.57/17.05 ((
% 129.57/17.05 (inComplementUnionImpInComplement1) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTE) =>
% 129.57/17.05 ((
% 129.57/17.05 (binunionTEcontra) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a1) =>
% 129.57/17.05 ((
% 129.57/17.05 (complementUnionInPowersetComplement) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a2) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1a) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1b) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan1) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2a) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2b2) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2b) =>
% 129.57/17.05 ((
% 129.57/17.05 (demorgan2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule0) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule1) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule3) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz13rule4) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_1) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_2) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_3) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_4) =>
% 129.57/17.05 ((
% 129.57/17.05 (woz1_5) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1all2) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1SetBreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (choice2fnsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (setOfPairsIsBReln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1all1) =>
% 129.57/17.05 ((
% 129.57/17.05 (subbreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (eqbreln1) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invI) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1invE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compI) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compE) =>
% 129.57/17.05 ((
% 129.57/17.05 (breln1compEex) =>
% 129.57/17.05 ((
% 129.57/17.05 (!!) @ (
% 129.57/17.05 (('#B') @ (
% 129.57/17.05 !!) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 !!))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#S') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#S') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 =>))) @
% 129.57/17.05 breln1)))))) @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#C') @ (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 (
% 129.57/17.05 (
% 129.57/17.05 ('#B') @ (
% 129.57/17.05 '#B') @
% 129.57/17.05 breln1)))) @
% 129.57/17.05 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1142])).
% 129.57/17.05 thf(zip_derived_cl1158, plain,
% 129.57/17.05 (~ (((binintersectEL) =>
% 129.57/17.05 (((binintersectLsub) =>
% 129.57/17.05 (((binintersectSubset2) =>
% 129.57/17.05 (((binintersectSubset3) =>
% 129.57/17.05 (((binintersectER) =>
% 129.57/17.05 (((disjointsetsI1) =>
% 129.57/17.05 (((binintersectRsub) =>
% 129.57/17.05 (((binintersectSubset4) =>
% 129.57/17.05 (((binintersectSubset1) =>
% 129.57/17.05 (((bs114d) =>
% 129.57/17.05 (((setminusI) =>
% 129.57/17.05 (((setminusEL) =>
% 129.57/17.05 (((setminusER) =>
% 129.57/17.05 (((setminusSubset2) =>
% 129.57/17.05 (((setminusERneg) =>
% 129.57/17.05 (((setminusELneg) =>
% 129.57/17.05 (((setminusILneg) =>
% 129.57/17.05 (((setminusIRneg) =>
% 129.57/17.05 (((setminusLsub) =>
% 129.57/17.05 (((setminusSubset1) =>
% 129.57/17.05 (((symdiffE) =>
% 129.57/17.05 (((symdiffI1) =>
% 129.57/17.05 (((symdiffI2) =>
% 129.57/17.05 (((symdiffIneg1) =>
% 129.57/17.05 (((symdiffIneg2) =>
% 129.57/17.05 (((secondinupair) =>
% 129.57/17.05 (((setukpairIL) =>
% 129.57/17.05 (((setukpairIR) =>
% 129.57/17.05 (((kpairiskpair) =>
% 129.57/17.05 (((kpairp) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsubset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowerset) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletoninpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairset2E) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairsubunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairinpowunion) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ubforcartprodlem3) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair1) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempair) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionE2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton1) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setunionsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E1) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1I2) =>
% 129.57/17.05 ((
% 129.57/17.05 (singletonsuniq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (theprop) =>
% 129.57/17.05 ((
% 129.57/17.05 (kfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstin) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjL) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR11) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR12) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR1) =>
% 129.57/17.05 ((
% 129.57/17.05 (upairequniteq) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR2) =>
% 129.57/17.05 ((
% 129.57/17.05 (setukpairinjR) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndsingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (ksndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (kpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndin) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemEL) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairmemER) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodmempaircEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodfstpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodsndpairEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (cartprodpairsurjEq) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrI) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrSub) =>
% 129.57/17.05 ((
% 129.57/17.05 (setOfPairsIsBReln) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrERa) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL1) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrEL2) =>
% 129.57/17.05 ((
% 129.57/17.05 (dpsetconstrER) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcImageSingleton) =>
% 129.57/17.05 ((
% 129.57/17.05 (apProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (app) =>
% 129.57/17.05 ((
% 129.57/17.05 (infuncsetfunc) =>
% 129.57/17.05 ((
% 129.57/17.05 (ap2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcinfuncset) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamProp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lamp) =>
% 129.57/17.05 ((
% 129.57/17.05 (lam2p) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall1) =>
% 129.57/17.05 ((
% 129.57/17.05 (brelnall2) =>
% 129.57/17.05 ((
% 129.57/17.05 (ex1E2) =>
% 129.57/17.05 ((
% 129.57/17.05 (funcGraphProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp3) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcextLem) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp4) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq2) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (lam2lamEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifp) =>
% 129.57/17.06 ((
% 129.57/17.06 (theeq) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrue) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueorfalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setminusT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setextT) =>
% 129.57/17.06 ((
% 129.57/17.06 (subsetTI) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTELcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTERcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT1) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT2) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT3) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub2) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTnotintersectT) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementImpComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementSubsetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementInPowersetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (contraSubsetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTcontraSubset) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTILcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTIRcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion2) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (intersectInPowersetIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpNotIn1) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpInComplement1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTE) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTEcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementUnionInPowersetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule0) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_5) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all2) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1SetBreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (choice2fnsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all1) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compEex) =>
% 129.57/17.06 ((
% 129.57/17.06 (!!) @ (
% 129.57/17.06 (('#B') @ (
% 129.57/17.06 !!) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 !!))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#C') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1150])).
% 129.57/17.06 thf(zip_derived_cl1166, plain,
% 129.57/17.06 (~ (((binintersectLsub) =>
% 129.57/17.06 (((binintersectSubset2) =>
% 129.57/17.06 (((binintersectSubset3) =>
% 129.57/17.06 (((binintersectER) =>
% 129.57/17.06 (((disjointsetsI1) =>
% 129.57/17.06 (((binintersectRsub) =>
% 129.57/17.06 (((binintersectSubset4) =>
% 129.57/17.06 (((binintersectSubset1) =>
% 129.57/17.06 (((bs114d) =>
% 129.57/17.06 (((setminusI) =>
% 129.57/17.06 (((setminusEL) =>
% 129.57/17.06 (((setminusER) =>
% 129.57/17.06 (((setminusSubset2) =>
% 129.57/17.06 (((setminusERneg) =>
% 129.57/17.06 (((setminusELneg) =>
% 129.57/17.06 (((setminusILneg) =>
% 129.57/17.06 (((setminusIRneg) =>
% 129.57/17.06 (((setminusLsub) =>
% 129.57/17.06 (((setminusSubset1) =>
% 129.57/17.06 (((symdiffE) =>
% 129.57/17.06 (((symdiffI1) =>
% 129.57/17.06 (((symdiffI2) =>
% 129.57/17.06 (((symdiffIneg1) =>
% 129.57/17.06 (((symdiffIneg2) =>
% 129.57/17.06 (((secondinupair) =>
% 129.57/17.06 (((setukpairIL) =>
% 129.57/17.06 (((setukpairIR) =>
% 129.57/17.06 (((kpairiskpair) =>
% 129.57/17.06 (((kpairp) =>
% 129.57/17.06 (((singletonsubset) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletoninpowerset) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletoninpowunion) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairset2E) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairsubunion) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairinpowunion) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem3) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair1) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionE2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton1) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1E1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I2) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonsuniq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (theprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstin) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR11) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR12) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR1) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairequniteq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (kpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemEL) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemER) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempaircEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrI) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrSub) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrERa) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrER) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcImageSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (apProp) =>
% 129.57/17.06 ((
% 129.57/17.06 (app) =>
% 129.57/17.06 ((
% 129.57/17.06 (infuncsetfunc) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2p) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcinfuncset) =>
% 129.57/17.06 ((
% 129.57/17.06 (lamProp) =>
% 129.57/17.06 ((
% 129.57/17.06 (lamp) =>
% 129.57/17.06 ((
% 129.57/17.06 (lam2p) =>
% 129.57/17.06 ((
% 129.57/17.06 (brelnall1) =>
% 129.57/17.06 ((
% 129.57/17.06 (brelnall2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1E2) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp3) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcextLem) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp4) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq2) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (lam2lamEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifp) =>
% 129.57/17.06 ((
% 129.57/17.06 (theeq) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrue) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueorfalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setminusT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setextT) =>
% 129.57/17.06 ((
% 129.57/17.06 (subsetTI) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTELcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTERcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT1) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT2) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT3) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub2) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTnotintersectT) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementImpComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementSubsetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementInPowersetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (contraSubsetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTcontraSubset) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTILcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTIRcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion2) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (intersectInPowersetIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpNotIn1) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpInComplement1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTE) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTEcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementUnionInPowersetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule0) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_5) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all2) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1SetBreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (choice2fnsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all1) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compEex) =>
% 129.57/17.06 ((
% 129.57/17.06 (!!) @ (
% 129.57/17.06 (('#B') @ (
% 129.57/17.06 !!) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 !!))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#C') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1158])).
% 129.57/17.06 thf(zip_derived_cl1174, plain,
% 129.57/17.06 (~ (((binintersectSubset2) =>
% 129.57/17.06 (((binintersectSubset3) =>
% 129.57/17.06 (((binintersectER) =>
% 129.57/17.06 (((disjointsetsI1) =>
% 129.57/17.06 (((binintersectRsub) =>
% 129.57/17.06 (((binintersectSubset4) =>
% 129.57/17.06 (((binintersectSubset1) =>
% 129.57/17.06 (((bs114d) =>
% 129.57/17.06 (((setminusI) =>
% 129.57/17.06 (((setminusEL) =>
% 129.57/17.06 (((setminusER) =>
% 129.57/17.06 (((setminusSubset2) =>
% 129.57/17.06 (((setminusERneg) =>
% 129.57/17.06 (((setminusELneg) =>
% 129.57/17.06 (((setminusILneg) =>
% 129.57/17.06 (((setminusIRneg) =>
% 129.57/17.06 (((setminusLsub) =>
% 129.57/17.06 (((setminusSubset1) =>
% 129.57/17.06 (((symdiffE) =>
% 129.57/17.06 (((symdiffI1) =>
% 129.57/17.06 (((symdiffI2) =>
% 129.57/17.06 (((symdiffIneg1) =>
% 129.57/17.06 (((symdiffIneg2) =>
% 129.57/17.06 (((secondinupair) =>
% 129.57/17.06 (((setukpairIL) =>
% 129.57/17.06 (((setukpairIR) =>
% 129.57/17.06 (((kpairiskpair) =>
% 129.57/17.06 (((kpairp) =>
% 129.57/17.06 (((singletonsubset) =>
% 129.57/17.06 (((singletoninpowerset) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletoninpowunion) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairset2E) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairsubunion) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairinpowunion) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem3) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair1) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionE2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton1) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1E1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I2) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonsuniq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (theprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstin) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR11) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR12) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR1) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairequniteq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (kpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemEL) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemER) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempaircEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrI) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrSub) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrERa) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrER) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcImageSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (apProp) =>
% 129.57/17.06 ((
% 129.57/17.06 (app) =>
% 129.57/17.06 ((
% 129.57/17.06 (infuncsetfunc) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2p) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcinfuncset) =>
% 129.57/17.06 ((
% 129.57/17.06 (lamProp) =>
% 129.57/17.06 ((
% 129.57/17.06 (lamp) =>
% 129.57/17.06 ((
% 129.57/17.06 (lam2p) =>
% 129.57/17.06 ((
% 129.57/17.06 (brelnall1) =>
% 129.57/17.06 ((
% 129.57/17.06 (brelnall2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1E2) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp3) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcextLem) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp4) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq2) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (lam2lamEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifp) =>
% 129.57/17.06 ((
% 129.57/17.06 (theeq) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrue) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueorfalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setminusT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setextT) =>
% 129.57/17.06 ((
% 129.57/17.06 (subsetTI) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTELcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTERcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT1) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT2) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT3) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub2) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTnotintersectT) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementImpComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementSubsetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementInPowersetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (contraSubsetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTcontraSubset) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTILcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTIRcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion2) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (intersectInPowersetIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpNotIn1) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpInComplement1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTE) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTEcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementUnionInPowersetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule0) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_5) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all2) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1SetBreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (choice2fnsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all1) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compEex) =>
% 129.57/17.06 ((
% 129.57/17.06 (!!) @ (
% 129.57/17.06 (('#B') @ (
% 129.57/17.06 !!) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 !!))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#C') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1166])).
% 129.57/17.06 thf(zip_derived_cl1183, plain,
% 129.57/17.06 (~ (((binintersectSubset3) =>
% 129.57/17.06 (((binintersectER) =>
% 129.57/17.06 (((disjointsetsI1) =>
% 129.57/17.06 (((binintersectRsub) =>
% 129.57/17.06 (((binintersectSubset4) =>
% 129.57/17.06 (((binintersectSubset1) =>
% 129.57/17.06 (((bs114d) =>
% 129.57/17.06 (((setminusI) =>
% 129.57/17.06 (((setminusEL) =>
% 129.57/17.06 (((setminusER) =>
% 129.57/17.06 (((setminusSubset2) =>
% 129.57/17.06 (((setminusERneg) =>
% 129.57/17.06 (((setminusELneg) =>
% 129.57/17.06 (((setminusILneg) =>
% 129.57/17.06 (((setminusIRneg) =>
% 129.57/17.06 (((setminusLsub) =>
% 129.57/17.06 (((setminusSubset1) =>
% 129.57/17.06 (((symdiffE) =>
% 129.57/17.06 (((symdiffI1) =>
% 129.57/17.06 (((symdiffI2) =>
% 129.57/17.06 (((symdiffIneg1) =>
% 129.57/17.06 (((symdiffIneg2) =>
% 129.57/17.06 (((secondinupair) =>
% 129.57/17.06 (((setukpairIL) =>
% 129.57/17.06 (((setukpairIR) =>
% 129.57/17.06 (((kpairiskpair) =>
% 129.57/17.06 (((kpairp) =>
% 129.57/17.06 (((singletonsubset) =>
% 129.57/17.06 (((singletoninpowerset) =>
% 129.57/17.06 (((singletoninpowunion) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairset2E) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairsubunion) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairinpowunion) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem3) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair1) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionE2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton1) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1E1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I2) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonsuniq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (theprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstin) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR11) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR12) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR1) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairequniteq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (kpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemEL) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemER) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempaircEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrI) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrSub) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrERa) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrER) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcImageSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (apProp) =>
% 129.57/17.06 ((
% 129.57/17.06 (app) =>
% 129.57/17.06 ((
% 129.57/17.06 (infuncsetfunc) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2p) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcinfuncset) =>
% 129.57/17.06 ((
% 129.57/17.06 (lamProp) =>
% 129.57/17.06 ((
% 129.57/17.06 (lamp) =>
% 129.57/17.06 ((
% 129.57/17.06 (lam2p) =>
% 129.57/17.06 ((
% 129.57/17.06 (brelnall1) =>
% 129.57/17.06 ((
% 129.57/17.06 (brelnall2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1E2) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp3) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcextLem) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp4) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq2) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (lam2lamEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifp) =>
% 129.57/17.06 ((
% 129.57/17.06 (theeq) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrue) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueorfalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setminusT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setextT) =>
% 129.57/17.06 ((
% 129.57/17.06 (subsetTI) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTELcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTERcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT1) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT2) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT3) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub2) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTnotintersectT) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementImpComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementSubsetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementInPowersetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (contraSubsetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTcontraSubset) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTILcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTIRcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion2) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (intersectInPowersetIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpNotIn1) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpInComplement1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTE) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTEcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementUnionInPowersetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule0) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_5) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all2) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1SetBreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (choice2fnsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all1) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compEex) =>
% 129.57/17.06 ((
% 129.57/17.06 (!!) @ (
% 129.57/17.06 (('#B') @ (
% 129.57/17.06 !!) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 !!))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#C') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1174])).
% 129.57/17.06 thf(zip_derived_cl1193, plain,
% 129.57/17.06 (~ (((binintersectER) =>
% 129.57/17.06 (((disjointsetsI1) =>
% 129.57/17.06 (((binintersectRsub) =>
% 129.57/17.06 (((binintersectSubset4) =>
% 129.57/17.06 (((binintersectSubset1) =>
% 129.57/17.06 (((bs114d) =>
% 129.57/17.06 (((setminusI) =>
% 129.57/17.06 (((setminusEL) =>
% 129.57/17.06 (((setminusER) =>
% 129.57/17.06 (((setminusSubset2) =>
% 129.57/17.06 (((setminusERneg) =>
% 129.57/17.06 (((setminusELneg) =>
% 129.57/17.06 (((setminusILneg) =>
% 129.57/17.06 (((setminusIRneg) =>
% 129.57/17.06 (((setminusLsub) =>
% 129.57/17.06 (((setminusSubset1) =>
% 129.57/17.06 (((symdiffE) =>
% 129.57/17.06 (((symdiffI1) =>
% 129.57/17.06 (((symdiffI2) =>
% 129.57/17.06 (((symdiffIneg1) =>
% 129.57/17.06 (((symdiffIneg2) =>
% 129.57/17.06 (((secondinupair) =>
% 129.57/17.06 (((setukpairIL) =>
% 129.57/17.06 (((setukpairIR) =>
% 129.57/17.06 (((kpairiskpair) =>
% 129.57/17.06 (((kpairp) =>
% 129.57/17.06 (((singletonsubset) =>
% 129.57/17.06 (((singletoninpowerset) =>
% 129.57/17.06 (((singletoninpowunion) =>
% 129.57/17.06 (((upairset2E) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairsubunion) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairinpowunion) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem3) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair1) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionE2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton1) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1E1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I2) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonsuniq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (theprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstin) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR11) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR12) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR1) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairequniteq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (kpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemEL) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemER) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempaircEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrI) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrSub) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrERa) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrER) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcImageSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (apProp) =>
% 129.57/17.06 ((
% 129.57/17.06 (app) =>
% 129.57/17.06 ((
% 129.57/17.06 (infuncsetfunc) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2p) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcinfuncset) =>
% 129.57/17.06 ((
% 129.57/17.06 (lamProp) =>
% 129.57/17.06 ((
% 129.57/17.06 (lamp) =>
% 129.57/17.06 ((
% 129.57/17.06 (lam2p) =>
% 129.57/17.06 ((
% 129.57/17.06 (brelnall1) =>
% 129.57/17.06 ((
% 129.57/17.06 (brelnall2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1E2) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp3) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcextLem) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp4) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq2) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (lam2lamEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifp) =>
% 129.57/17.06 ((
% 129.57/17.06 (theeq) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrue) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueorfalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setminusT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setextT) =>
% 129.57/17.06 ((
% 129.57/17.06 (subsetTI) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTELcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTERcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT1) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT2) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT3) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub2) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTnotintersectT) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementImpComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementSubsetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementInPowersetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (contraSubsetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTcontraSubset) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTILcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTIRcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion2) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (intersectInPowersetIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpNotIn1) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpInComplement1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTE) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTEcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementUnionInPowersetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule0) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_5) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all2) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1SetBreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (choice2fnsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all1) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compEex) =>
% 129.57/17.06 ((
% 129.57/17.06 (!!) @ (
% 129.57/17.06 (('#B') @ (
% 129.57/17.06 !!) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 !!))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#C') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1183])).
% 129.57/17.06 thf(zip_derived_cl1206, plain,
% 129.57/17.06 (~ (((disjointsetsI1) =>
% 129.57/17.06 (((binintersectRsub) =>
% 129.57/17.06 (((binintersectSubset4) =>
% 129.57/17.06 (((binintersectSubset1) =>
% 129.57/17.06 (((bs114d) =>
% 129.57/17.06 (((setminusI) =>
% 129.57/17.06 (((setminusEL) =>
% 129.57/17.06 (((setminusER) =>
% 129.57/17.06 (((setminusSubset2) =>
% 129.57/17.06 (((setminusERneg) =>
% 129.57/17.06 (((setminusELneg) =>
% 129.57/17.06 (((setminusILneg) =>
% 129.57/17.06 (((setminusIRneg) =>
% 129.57/17.06 (((setminusLsub) =>
% 129.57/17.06 (((setminusSubset1) =>
% 129.57/17.06 (((symdiffE) =>
% 129.57/17.06 (((symdiffI1) =>
% 129.57/17.06 (((symdiffI2) =>
% 129.57/17.06 (((symdiffIneg1) =>
% 129.57/17.06 (((symdiffIneg2) =>
% 129.57/17.06 (((secondinupair) =>
% 129.57/17.06 (((setukpairIL) =>
% 129.57/17.06 (((setukpairIR) =>
% 129.57/17.06 (((kpairiskpair) =>
% 129.57/17.06 (((kpairp) =>
% 129.57/17.06 (((singletonsubset) =>
% 129.57/17.06 (((singletoninpowerset) =>
% 129.57/17.06 (((singletoninpowunion) =>
% 129.57/17.06 (((upairset2E) =>
% 129.57/17.06 (((upairsubunion) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairinpowunion) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem3) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair1) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionE2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton1) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1E1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I2) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonsuniq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (theprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstin) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR11) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR12) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR1) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairequniteq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (kpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemEL) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemER) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempaircEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrI) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrSub) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrERa) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrER) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcImageSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (apProp) =>
% 129.57/17.06 ((
% 129.57/17.06 (app) =>
% 129.57/17.06 ((
% 129.57/17.06 (infuncsetfunc) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2p) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcinfuncset) =>
% 129.57/17.06 ((
% 129.57/17.06 (lamProp) =>
% 129.57/17.06 ((
% 129.57/17.06 (lamp) =>
% 129.57/17.06 ((
% 129.57/17.06 (lam2p) =>
% 129.57/17.06 ((
% 129.57/17.06 (brelnall1) =>
% 129.57/17.06 ((
% 129.57/17.06 (brelnall2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1E2) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp3) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcextLem) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp4) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq2) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (lam2lamEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifp) =>
% 129.57/17.06 ((
% 129.57/17.06 (theeq) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrue) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueorfalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setminusT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setextT) =>
% 129.57/17.06 ((
% 129.57/17.06 (subsetTI) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTELcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTERcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT1) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT2) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT3) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub2) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTnotintersectT) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementImpComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementSubsetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementInPowersetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (contraSubsetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTcontraSubset) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTILcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTIRcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion2) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (intersectInPowersetIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpNotIn1) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpInComplement1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTE) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTEcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementUnionInPowersetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule0) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_5) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all2) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1SetBreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (choice2fnsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all1) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compEex) =>
% 129.57/17.06 ((
% 129.57/17.06 (!!) @ (
% 129.57/17.06 (('#B') @ (
% 129.57/17.06 !!) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 !!))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#C') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1193])).
% 129.57/17.06 thf(zip_derived_cl1216, plain,
% 129.57/17.06 (~ (((binintersectRsub) =>
% 129.57/17.06 (((binintersectSubset4) =>
% 129.57/17.06 (((binintersectSubset1) =>
% 129.57/17.06 (((bs114d) =>
% 129.57/17.06 (((setminusI) =>
% 129.57/17.06 (((setminusEL) =>
% 129.57/17.06 (((setminusER) =>
% 129.57/17.06 (((setminusSubset2) =>
% 129.57/17.06 (((setminusERneg) =>
% 129.57/17.06 (((setminusELneg) =>
% 129.57/17.06 (((setminusILneg) =>
% 129.57/17.06 (((setminusIRneg) =>
% 129.57/17.06 (((setminusLsub) =>
% 129.57/17.06 (((setminusSubset1) =>
% 129.57/17.06 (((symdiffE) =>
% 129.57/17.06 (((symdiffI1) =>
% 129.57/17.06 (((symdiffI2) =>
% 129.57/17.06 (((symdiffIneg1) =>
% 129.57/17.06 (((symdiffIneg2) =>
% 129.57/17.06 (((secondinupair) =>
% 129.57/17.06 (((setukpairIL) =>
% 129.57/17.06 (((setukpairIR) =>
% 129.57/17.06 (((kpairiskpair) =>
% 129.57/17.06 (((kpairp) =>
% 129.57/17.06 (((singletonsubset) =>
% 129.57/17.06 (((singletoninpowerset) =>
% 129.57/17.06 (((singletoninpowunion) =>
% 129.57/17.06 (((upairset2E) =>
% 129.57/17.06 (((upairsubunion) =>
% 129.57/17.06 (((upairinpowunion) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem3) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair1) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionE2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton1) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1E1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I2) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonsuniq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (theprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstin) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR11) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR12) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR1) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairequniteq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (kpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemEL) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemER) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempaircEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrI) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrSub) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrERa) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrER) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcImageSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (apProp) =>
% 129.57/17.06 ((
% 129.57/17.06 (app) =>
% 129.57/17.06 ((
% 129.57/17.06 (infuncsetfunc) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2p) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcinfuncset) =>
% 129.57/17.06 ((
% 129.57/17.06 (lamProp) =>
% 129.57/17.06 ((
% 129.57/17.06 (lamp) =>
% 129.57/17.06 ((
% 129.57/17.06 (lam2p) =>
% 129.57/17.06 ((
% 129.57/17.06 (brelnall1) =>
% 129.57/17.06 ((
% 129.57/17.06 (brelnall2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1E2) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp3) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcextLem) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp4) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq2) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (lam2lamEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifp) =>
% 129.57/17.06 ((
% 129.57/17.06 (theeq) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrue) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueorfalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setminusT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setextT) =>
% 129.57/17.06 ((
% 129.57/17.06 (subsetTI) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTELcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTERcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT1) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT2) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT3) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub2) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTnotintersectT) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementImpComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementSubsetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementInPowersetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (contraSubsetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTcontraSubset) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTILcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTIRcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion2) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (intersectInPowersetIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpNotIn1) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpInComplement1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTE) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTEcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementUnionInPowersetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule0) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_5) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all2) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1SetBreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (choice2fnsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all1) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compEex) =>
% 129.57/17.06 ((
% 129.57/17.06 (!!) @ (
% 129.57/17.06 (('#B') @ (
% 129.57/17.06 !!) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 !!))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#C') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1206])).
% 129.57/17.06 thf(zip_derived_cl1223, plain,
% 129.57/17.06 (~ (((binintersectSubset4) =>
% 129.57/17.06 (((binintersectSubset1) =>
% 129.57/17.06 (((bs114d) =>
% 129.57/17.06 (((setminusI) =>
% 129.57/17.06 (((setminusEL) =>
% 129.57/17.06 (((setminusER) =>
% 129.57/17.06 (((setminusSubset2) =>
% 129.57/17.06 (((setminusERneg) =>
% 129.57/17.06 (((setminusELneg) =>
% 129.57/17.06 (((setminusILneg) =>
% 129.57/17.06 (((setminusIRneg) =>
% 129.57/17.06 (((setminusLsub) =>
% 129.57/17.06 (((setminusSubset1) =>
% 129.57/17.06 (((symdiffE) =>
% 129.57/17.06 (((symdiffI1) =>
% 129.57/17.06 (((symdiffI2) =>
% 129.57/17.06 (((symdiffIneg1) =>
% 129.57/17.06 (((symdiffIneg2) =>
% 129.57/17.06 (((secondinupair) =>
% 129.57/17.06 (((setukpairIL) =>
% 129.57/17.06 (((setukpairIR) =>
% 129.57/17.06 (((kpairiskpair) =>
% 129.57/17.06 (((kpairp) =>
% 129.57/17.06 (((singletonsubset) =>
% 129.57/17.06 (((singletoninpowerset) =>
% 129.57/17.06 (((singletoninpowunion) =>
% 129.57/17.06 (((upairset2E) =>
% 129.57/17.06 (((upairsubunion) =>
% 129.57/17.06 (((upairinpowunion) =>
% 129.57/17.06 (((ubforcartprodlem1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem3) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair1) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionE2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton1) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1E1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I2) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonsuniq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (theprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstin) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR11) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR12) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR1) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairequniteq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (kpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemEL) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemER) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempaircEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrI) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrSub) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrERa) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrER) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcImageSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (apProp) =>
% 129.57/17.06 ((
% 129.57/17.06 (app) =>
% 129.57/17.06 ((
% 129.57/17.06 (infuncsetfunc) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2p) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcinfuncset) =>
% 129.57/17.06 ((
% 129.57/17.06 (lamProp) =>
% 129.57/17.06 ((
% 129.57/17.06 (lamp) =>
% 129.57/17.06 ((
% 129.57/17.06 (lam2p) =>
% 129.57/17.06 ((
% 129.57/17.06 (brelnall1) =>
% 129.57/17.06 ((
% 129.57/17.06 (brelnall2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1E2) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp3) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcextLem) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp4) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq2) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (lam2lamEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifp) =>
% 129.57/17.06 ((
% 129.57/17.06 (theeq) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrue) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueorfalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setminusT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setextT) =>
% 129.57/17.06 ((
% 129.57/17.06 (subsetTI) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTELcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTERcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT1) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT2) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT3) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub2) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTnotintersectT) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementImpComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementSubsetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementInPowersetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (contraSubsetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTcontraSubset) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTILcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTIRcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion2) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (intersectInPowersetIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpNotIn1) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpInComplement1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTE) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTEcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementUnionInPowersetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule0) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_5) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all2) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1SetBreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (choice2fnsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all1) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compEex) =>
% 129.57/17.06 ((
% 129.57/17.06 (!!) @ (
% 129.57/17.06 (('#B') @ (
% 129.57/17.06 !!) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 !!))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#C') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1216])).
% 129.57/17.06 thf(zip_derived_cl1231, plain,
% 129.57/17.06 (~ (((binintersectSubset1) =>
% 129.57/17.06 (((bs114d) =>
% 129.57/17.06 (((setminusI) =>
% 129.57/17.06 (((setminusEL) =>
% 129.57/17.06 (((setminusER) =>
% 129.57/17.06 (((setminusSubset2) =>
% 129.57/17.06 (((setminusERneg) =>
% 129.57/17.06 (((setminusELneg) =>
% 129.57/17.06 (((setminusILneg) =>
% 129.57/17.06 (((setminusIRneg) =>
% 129.57/17.06 (((setminusLsub) =>
% 129.57/17.06 (((setminusSubset1) =>
% 129.57/17.06 (((symdiffE) =>
% 129.57/17.06 (((symdiffI1) =>
% 129.57/17.06 (((symdiffI2) =>
% 129.57/17.06 (((symdiffIneg1) =>
% 129.57/17.06 (((symdiffIneg2) =>
% 129.57/17.06 (((secondinupair) =>
% 129.57/17.06 (((setukpairIL) =>
% 129.57/17.06 (((setukpairIR) =>
% 129.57/17.06 (((kpairiskpair) =>
% 129.57/17.06 (((kpairp) =>
% 129.57/17.06 (((singletonsubset) =>
% 129.57/17.06 (((singletoninpowerset) =>
% 129.57/17.06 (((singletoninpowunion) =>
% 129.57/17.06 (((upairset2E) =>
% 129.57/17.06 (((upairsubunion) =>
% 129.57/17.06 (((upairinpowunion) =>
% 129.57/17.06 (((ubforcartprodlem1) =>
% 129.57/17.06 (((ubforcartprodlem2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ubforcartprodlem3) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair1) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionE2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton1) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1E1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I2) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonsuniq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (theprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstin) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR11) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR12) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR1) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairequniteq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (kpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemEL) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemER) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempaircEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrI) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrSub) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrERa) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrER) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcImageSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (apProp) =>
% 129.57/17.06 ((
% 129.57/17.06 (app) =>
% 129.57/17.06 ((
% 129.57/17.06 (infuncsetfunc) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2p) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcinfuncset) =>
% 129.57/17.06 ((
% 129.57/17.06 (lamProp) =>
% 129.57/17.06 ((
% 129.57/17.06 (lamp) =>
% 129.57/17.06 ((
% 129.57/17.06 (lam2p) =>
% 129.57/17.06 ((
% 129.57/17.06 (brelnall1) =>
% 129.57/17.06 ((
% 129.57/17.06 (brelnall2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1E2) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp3) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcextLem) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcGraphProp4) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcext2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ap2apEq2) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta1) =>
% 129.57/17.06 ((
% 129.57/17.06 (lam2lamEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (beta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (eta2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalseProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp1) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueProp2) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ifp) =>
% 129.57/17.06 ((
% 129.57/17.06 (theeq) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrue) =>
% 129.57/17.06 ((
% 129.57/17.06 (iffalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (iftrueorfalse) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setminusT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementT_lem) =>
% 129.57/17.06 ((
% 129.57/17.06 (setextT) =>
% 129.57/17.06 ((
% 129.57/17.06 (subsetTI) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (powersetTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTELcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binintersectTERcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT1) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT2) =>
% 129.57/17.06 ((
% 129.57/17.06 (contrasubsetT3) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementI1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementE1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub1) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementSub2) =>
% 129.57/17.06 ((
% 129.57/17.06 (doubleComplementEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTnotintersectT) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementImpComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementSubsetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementInPowersetComplementIntersect) =>
% 129.57/17.06 ((
% 129.57/17.06 (contraSubsetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementTcontraSubset) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTILcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTIRcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInUnion2) =>
% 129.57/17.06 ((
% 129.57/17.06 (inIntersectImpInIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (intersectInPowersetIntersectUnions) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpNotIn1) =>
% 129.57/17.06 ((
% 129.57/17.06 (inComplementUnionImpInComplement1) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTE) =>
% 129.57/17.06 ((
% 129.57/17.06 (binunionTEcontra) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a1) =>
% 129.57/17.06 ((
% 129.57/17.06 (complementUnionInPowersetComplement) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan1) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2a) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b2) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2b) =>
% 129.57/17.06 ((
% 129.57/17.06 (demorgan2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule0) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz13rule4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_1) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_2) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_3) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_4) =>
% 129.57/17.06 ((
% 129.57/17.06 (woz1_5) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all2) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1SetBreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (choice2fnsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1all1) =>
% 129.57/17.06 ((
% 129.57/17.06 (subbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (eqbreln1) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1invE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compI) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compE) =>
% 129.57/17.06 ((
% 129.57/17.06 (breln1compEex) =>
% 129.57/17.06 ((
% 129.57/17.06 (!!) @ (
% 129.57/17.06 (('#B') @ (
% 129.57/17.06 !!) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 !!))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#S') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#S') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 =>))) @
% 129.57/17.06 breln1)))))) @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#C') @ (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 (
% 129.57/17.06 (
% 129.57/17.06 ('#B') @ (
% 129.57/17.06 '#B') @
% 129.57/17.06 breln1)))) @
% 129.57/17.06 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1223])).
% 129.57/17.06 thf(zip_derived_cl1239, plain,
% 129.57/17.06 (~ (((bs114d) =>
% 129.57/17.06 (((setminusI) =>
% 129.57/17.06 (((setminusEL) =>
% 129.57/17.06 (((setminusER) =>
% 129.57/17.06 (((setminusSubset2) =>
% 129.57/17.06 (((setminusERneg) =>
% 129.57/17.06 (((setminusELneg) =>
% 129.57/17.06 (((setminusILneg) =>
% 129.57/17.06 (((setminusIRneg) =>
% 129.57/17.06 (((setminusLsub) =>
% 129.57/17.06 (((setminusSubset1) =>
% 129.57/17.06 (((symdiffE) =>
% 129.57/17.06 (((symdiffI1) =>
% 129.57/17.06 (((symdiffI2) =>
% 129.57/17.06 (((symdiffIneg1) =>
% 129.57/17.06 (((symdiffIneg2) =>
% 129.57/17.06 (((secondinupair) =>
% 129.57/17.06 (((setukpairIL) =>
% 129.57/17.06 (((setukpairIR) =>
% 129.57/17.06 (((kpairiskpair) =>
% 129.57/17.06 (((kpairp) =>
% 129.57/17.06 (((singletonsubset) =>
% 129.57/17.06 (((singletoninpowerset) =>
% 129.57/17.06 (((singletoninpowunion) =>
% 129.57/17.06 (((upairset2E) =>
% 129.57/17.06 (((upairsubunion) =>
% 129.57/17.06 (((upairinpowunion) =>
% 129.57/17.06 (((ubforcartprodlem1) =>
% 129.57/17.06 (((ubforcartprodlem2) =>
% 129.57/17.06 (((ubforcartprodlem3) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair1) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempair) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionE2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton1) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setunionsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1E1) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I) =>
% 129.57/17.06 ((
% 129.57/17.06 (ex1I2) =>
% 129.57/17.06 ((
% 129.57/17.06 (singletonsuniq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (theprop) =>
% 129.57/17.06 ((
% 129.57/17.06 (kfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstin) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjL) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR11) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR12) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR1) =>
% 129.57/17.06 ((
% 129.57/17.06 (upairequniteq) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR2) =>
% 129.57/17.06 ((
% 129.57/17.06 (setukpairinjR) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndsingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (ksndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (kpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndin) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemEL) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairmemER) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodmempaircEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodfstpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodsndpairEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (cartprodpairsurjEq) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrI) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrSub) =>
% 129.57/17.06 ((
% 129.57/17.06 (setOfPairsIsBReln) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrERa) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL1) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrEL2) =>
% 129.57/17.06 ((
% 129.57/17.06 (dpsetconstrER) =>
% 129.57/17.06 ((
% 129.57/17.06 (funcImageSingleton) =>
% 129.57/17.06 ((
% 129.57/17.06 (apProp) =>
% 129.57/17.06 ((
% 129.57/17.07 (app) =>
% 129.57/17.07 ((
% 129.57/17.07 (infuncsetfunc) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcinfuncset) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall1) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp3) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcextLem) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp4) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq2) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2lamEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifp) =>
% 129.57/17.07 ((
% 129.57/17.07 (theeq) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrue) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueorfalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setminusT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setextT) =>
% 129.57/17.07 ((
% 129.57/17.07 (subsetTI) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTELcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTERcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT1) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT2) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT3) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub2) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTnotintersectT) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementImpComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementSubsetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementInPowersetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (contraSubsetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTcontraSubset) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTILcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTIRcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion2) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (intersectInPowersetIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpNotIn1) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpInComplement1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTE) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTEcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementUnionInPowersetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule0) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_5) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all2) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1SetBreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (choice2fnsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all1) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compEex) =>
% 129.57/17.07 ((
% 129.57/17.07 (!!) @ (
% 129.57/17.07 (('#B') @ (
% 129.57/17.07 !!) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 !!))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#C') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1231])).
% 129.57/17.07 thf(zip_derived_cl1247, plain,
% 129.57/17.07 (~ (((setminusI) =>
% 129.57/17.07 (((setminusEL) =>
% 129.57/17.07 (((setminusER) =>
% 129.57/17.07 (((setminusSubset2) =>
% 129.57/17.07 (((setminusERneg) =>
% 129.57/17.07 (((setminusELneg) =>
% 129.57/17.07 (((setminusILneg) =>
% 129.57/17.07 (((setminusIRneg) =>
% 129.57/17.07 (((setminusLsub) =>
% 129.57/17.07 (((setminusSubset1) =>
% 129.57/17.07 (((symdiffE) =>
% 129.57/17.07 (((symdiffI1) =>
% 129.57/17.07 (((symdiffI2) =>
% 129.57/17.07 (((symdiffIneg1) =>
% 129.57/17.07 (((symdiffIneg2) =>
% 129.57/17.07 (((secondinupair) =>
% 129.57/17.07 (((setukpairIL) =>
% 129.57/17.07 (((setukpairIR) =>
% 129.57/17.07 (((kpairiskpair) =>
% 129.57/17.07 (((kpairp) =>
% 129.57/17.07 (((singletonsubset) =>
% 129.57/17.07 (((singletoninpowerset) =>
% 129.57/17.07 (((singletoninpowunion) =>
% 129.57/17.07 (((upairset2E) =>
% 129.57/17.07 (((upairsubunion) =>
% 129.57/17.07 (((upairinpowunion) =>
% 129.57/17.07 (((ubforcartprodlem1) =>
% 129.57/17.07 (((ubforcartprodlem2) =>
% 129.57/17.07 (((ubforcartprodlem3) =>
% 129.57/17.07 (((cartprodpairin) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodmempair1) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodmempair) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionE2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionsingleton1) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionsingleton2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (singletonprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I2) =>
% 129.57/17.07 ((
% 129.57/17.07 (singletonsuniq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (theprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstin) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR11) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR12) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR1) =>
% 129.57/17.07 ((
% 129.57/17.07 (upairequniteq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (kpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndin) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemEL) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemER) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodmempaircEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrI) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrSub) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrERa) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrER) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcImageSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (apProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (app) =>
% 129.57/17.07 ((
% 129.57/17.07 (infuncsetfunc) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcinfuncset) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall1) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp3) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcextLem) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp4) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq2) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2lamEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifp) =>
% 129.57/17.07 ((
% 129.57/17.07 (theeq) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrue) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueorfalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setminusT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setextT) =>
% 129.57/17.07 ((
% 129.57/17.07 (subsetTI) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTELcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTERcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT1) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT2) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT3) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub2) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTnotintersectT) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementImpComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementSubsetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementInPowersetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (contraSubsetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTcontraSubset) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTILcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTIRcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion2) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (intersectInPowersetIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpNotIn1) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpInComplement1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTE) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTEcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementUnionInPowersetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule0) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_5) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all2) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1SetBreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (choice2fnsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all1) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compEex) =>
% 129.57/17.07 ((
% 129.57/17.07 (!!) @ (
% 129.57/17.07 (('#B') @ (
% 129.57/17.07 !!) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 !!))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#C') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1239])).
% 129.57/17.07 thf(zip_derived_cl1255, plain,
% 129.57/17.07 (~ (((setminusEL) =>
% 129.57/17.07 (((setminusER) =>
% 129.57/17.07 (((setminusSubset2) =>
% 129.57/17.07 (((setminusERneg) =>
% 129.57/17.07 (((setminusELneg) =>
% 129.57/17.07 (((setminusILneg) =>
% 129.57/17.07 (((setminusIRneg) =>
% 129.57/17.07 (((setminusLsub) =>
% 129.57/17.07 (((setminusSubset1) =>
% 129.57/17.07 (((symdiffE) =>
% 129.57/17.07 (((symdiffI1) =>
% 129.57/17.07 (((symdiffI2) =>
% 129.57/17.07 (((symdiffIneg1) =>
% 129.57/17.07 (((symdiffIneg2) =>
% 129.57/17.07 (((secondinupair) =>
% 129.57/17.07 (((setukpairIL) =>
% 129.57/17.07 (((setukpairIR) =>
% 129.57/17.07 (((kpairiskpair) =>
% 129.57/17.07 (((kpairp) =>
% 129.57/17.07 (((singletonsubset) =>
% 129.57/17.07 (((singletoninpowerset) =>
% 129.57/17.07 (((singletoninpowunion) =>
% 129.57/17.07 (((upairset2E) =>
% 129.57/17.07 (((upairsubunion) =>
% 129.57/17.07 (((upairinpowunion) =>
% 129.57/17.07 (((ubforcartprodlem1) =>
% 129.57/17.07 (((ubforcartprodlem2) =>
% 129.57/17.07 (((ubforcartprodlem3) =>
% 129.57/17.07 (((cartprodpairin) =>
% 129.57/17.07 (((cartprodmempair1) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodmempair) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionE2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionsingleton1) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionsingleton2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (singletonprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I2) =>
% 129.57/17.07 ((
% 129.57/17.07 (singletonsuniq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (theprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstin) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR11) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR12) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR1) =>
% 129.57/17.07 ((
% 129.57/17.07 (upairequniteq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (kpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndin) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemEL) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemER) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodmempaircEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrI) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrSub) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrERa) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrER) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcImageSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (apProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (app) =>
% 129.57/17.07 ((
% 129.57/17.07 (infuncsetfunc) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcinfuncset) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall1) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp3) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcextLem) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp4) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq2) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2lamEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifp) =>
% 129.57/17.07 ((
% 129.57/17.07 (theeq) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrue) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueorfalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setminusT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setextT) =>
% 129.57/17.07 ((
% 129.57/17.07 (subsetTI) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTELcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTERcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT1) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT2) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT3) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub2) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTnotintersectT) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementImpComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementSubsetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementInPowersetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (contraSubsetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTcontraSubset) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTILcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTIRcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion2) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (intersectInPowersetIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpNotIn1) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpInComplement1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTE) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTEcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementUnionInPowersetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule0) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_5) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all2) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1SetBreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (choice2fnsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all1) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compEex) =>
% 129.57/17.07 ((
% 129.57/17.07 (!!) @ (
% 129.57/17.07 (('#B') @ (
% 129.57/17.07 !!) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 !!))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#C') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1247])).
% 129.57/17.07 thf(zip_derived_cl1264, plain,
% 129.57/17.07 (~ (((setminusER) =>
% 129.57/17.07 (((setminusSubset2) =>
% 129.57/17.07 (((setminusERneg) =>
% 129.57/17.07 (((setminusELneg) =>
% 129.57/17.07 (((setminusILneg) =>
% 129.57/17.07 (((setminusIRneg) =>
% 129.57/17.07 (((setminusLsub) =>
% 129.57/17.07 (((setminusSubset1) =>
% 129.57/17.07 (((symdiffE) =>
% 129.57/17.07 (((symdiffI1) =>
% 129.57/17.07 (((symdiffI2) =>
% 129.57/17.07 (((symdiffIneg1) =>
% 129.57/17.07 (((symdiffIneg2) =>
% 129.57/17.07 (((secondinupair) =>
% 129.57/17.07 (((setukpairIL) =>
% 129.57/17.07 (((setukpairIR) =>
% 129.57/17.07 (((kpairiskpair) =>
% 129.57/17.07 (((kpairp) =>
% 129.57/17.07 (((singletonsubset) =>
% 129.57/17.07 (((singletoninpowerset) =>
% 129.57/17.07 (((singletoninpowunion) =>
% 129.57/17.07 (((upairset2E) =>
% 129.57/17.07 (((upairsubunion) =>
% 129.57/17.07 (((upairinpowunion) =>
% 129.57/17.07 (((ubforcartprodlem1) =>
% 129.57/17.07 (((ubforcartprodlem2) =>
% 129.57/17.07 (((ubforcartprodlem3) =>
% 129.57/17.07 (((cartprodpairin) =>
% 129.57/17.07 (((cartprodmempair1) =>
% 129.57/17.07 (((cartprodmempair) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionE2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionsingleton1) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionsingleton2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (singletonprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I2) =>
% 129.57/17.07 ((
% 129.57/17.07 (singletonsuniq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (theprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstin) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR11) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR12) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR1) =>
% 129.57/17.07 ((
% 129.57/17.07 (upairequniteq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (kpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndin) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemEL) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemER) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodmempaircEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrI) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrSub) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrERa) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrER) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcImageSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (apProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (app) =>
% 129.57/17.07 ((
% 129.57/17.07 (infuncsetfunc) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcinfuncset) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall1) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp3) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcextLem) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp4) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq2) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2lamEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifp) =>
% 129.57/17.07 ((
% 129.57/17.07 (theeq) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrue) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueorfalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setminusT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setextT) =>
% 129.57/17.07 ((
% 129.57/17.07 (subsetTI) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTELcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTERcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT1) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT2) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT3) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub2) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTnotintersectT) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementImpComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementSubsetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementInPowersetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (contraSubsetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTcontraSubset) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTILcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTIRcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion2) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (intersectInPowersetIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpNotIn1) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpInComplement1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTE) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTEcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementUnionInPowersetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule0) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_5) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all2) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1SetBreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (choice2fnsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all1) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compEex) =>
% 129.57/17.07 ((
% 129.57/17.07 (!!) @ (
% 129.57/17.07 (('#B') @ (
% 129.57/17.07 !!) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 !!))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#C') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1255])).
% 129.57/17.07 thf(zip_derived_cl1272, plain,
% 129.57/17.07 (~ (((setminusSubset2) =>
% 129.57/17.07 (((setminusERneg) =>
% 129.57/17.07 (((setminusELneg) =>
% 129.57/17.07 (((setminusILneg) =>
% 129.57/17.07 (((setminusIRneg) =>
% 129.57/17.07 (((setminusLsub) =>
% 129.57/17.07 (((setminusSubset1) =>
% 129.57/17.07 (((symdiffE) =>
% 129.57/17.07 (((symdiffI1) =>
% 129.57/17.07 (((symdiffI2) =>
% 129.57/17.07 (((symdiffIneg1) =>
% 129.57/17.07 (((symdiffIneg2) =>
% 129.57/17.07 (((secondinupair) =>
% 129.57/17.07 (((setukpairIL) =>
% 129.57/17.07 (((setukpairIR) =>
% 129.57/17.07 (((kpairiskpair) =>
% 129.57/17.07 (((kpairp) =>
% 129.57/17.07 (((singletonsubset) =>
% 129.57/17.07 (((singletoninpowerset) =>
% 129.57/17.07 (((singletoninpowunion) =>
% 129.57/17.07 (((upairset2E) =>
% 129.57/17.07 (((upairsubunion) =>
% 129.57/17.07 (((upairinpowunion) =>
% 129.57/17.07 (((ubforcartprodlem1) =>
% 129.57/17.07 (((ubforcartprodlem2) =>
% 129.57/17.07 (((ubforcartprodlem3) =>
% 129.57/17.07 (((cartprodpairin) =>
% 129.57/17.07 (((cartprodmempair1) =>
% 129.57/17.07 (((cartprodmempair) =>
% 129.57/17.07 (((setunionE2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionsingleton1) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionsingleton2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (singletonprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I2) =>
% 129.57/17.07 ((
% 129.57/17.07 (singletonsuniq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (theprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstin) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR11) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR12) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR1) =>
% 129.57/17.07 ((
% 129.57/17.07 (upairequniteq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (kpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndin) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemEL) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemER) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodmempaircEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrI) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrSub) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrERa) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrER) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcImageSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (apProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (app) =>
% 129.57/17.07 ((
% 129.57/17.07 (infuncsetfunc) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcinfuncset) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall1) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp3) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcextLem) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp4) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq2) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2lamEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifp) =>
% 129.57/17.07 ((
% 129.57/17.07 (theeq) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrue) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueorfalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setminusT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setextT) =>
% 129.57/17.07 ((
% 129.57/17.07 (subsetTI) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTELcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTERcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT1) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT2) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT3) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub2) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTnotintersectT) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementImpComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementSubsetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementInPowersetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (contraSubsetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTcontraSubset) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTILcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTIRcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion2) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (intersectInPowersetIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpNotIn1) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpInComplement1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTE) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTEcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementUnionInPowersetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule0) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_5) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all2) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1SetBreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (choice2fnsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all1) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compEex) =>
% 129.57/17.07 ((
% 129.57/17.07 (!!) @ (
% 129.57/17.07 (('#B') @ (
% 129.57/17.07 !!) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 !!))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#C') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1264])).
% 129.57/17.07 thf(zip_derived_cl1280, plain,
% 129.57/17.07 (~ (((setminusERneg) =>
% 129.57/17.07 (((setminusELneg) =>
% 129.57/17.07 (((setminusILneg) =>
% 129.57/17.07 (((setminusIRneg) =>
% 129.57/17.07 (((setminusLsub) =>
% 129.57/17.07 (((setminusSubset1) =>
% 129.57/17.07 (((symdiffE) =>
% 129.57/17.07 (((symdiffI1) =>
% 129.57/17.07 (((symdiffI2) =>
% 129.57/17.07 (((symdiffIneg1) =>
% 129.57/17.07 (((symdiffIneg2) =>
% 129.57/17.07 (((secondinupair) =>
% 129.57/17.07 (((setukpairIL) =>
% 129.57/17.07 (((setukpairIR) =>
% 129.57/17.07 (((kpairiskpair) =>
% 129.57/17.07 (((kpairp) =>
% 129.57/17.07 (((singletonsubset) =>
% 129.57/17.07 (((singletoninpowerset) =>
% 129.57/17.07 (((singletoninpowunion) =>
% 129.57/17.07 (((upairset2E) =>
% 129.57/17.07 (((upairsubunion) =>
% 129.57/17.07 (((upairinpowunion) =>
% 129.57/17.07 (((ubforcartprodlem1) =>
% 129.57/17.07 (((ubforcartprodlem2) =>
% 129.57/17.07 (((ubforcartprodlem3) =>
% 129.57/17.07 (((cartprodpairin) =>
% 129.57/17.07 (((cartprodmempair1) =>
% 129.57/17.07 (((cartprodmempair) =>
% 129.57/17.07 (((setunionE2) =>
% 129.57/17.07 (((setunionsingleton1) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionsingleton2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (singletonprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I2) =>
% 129.57/17.07 ((
% 129.57/17.07 (singletonsuniq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (theprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstin) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR11) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR12) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR1) =>
% 129.57/17.07 ((
% 129.57/17.07 (upairequniteq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (kpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndin) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemEL) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemER) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodmempaircEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrI) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrSub) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrERa) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrER) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcImageSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (apProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (app) =>
% 129.57/17.07 ((
% 129.57/17.07 (infuncsetfunc) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcinfuncset) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall1) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp3) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcextLem) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp4) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq2) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2lamEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifp) =>
% 129.57/17.07 ((
% 129.57/17.07 (theeq) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrue) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueorfalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setminusT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setextT) =>
% 129.57/17.07 ((
% 129.57/17.07 (subsetTI) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTELcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTERcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT1) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT2) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT3) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub2) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTnotintersectT) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementImpComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementSubsetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementInPowersetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (contraSubsetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTcontraSubset) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTILcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTIRcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion2) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (intersectInPowersetIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpNotIn1) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpInComplement1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTE) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTEcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementUnionInPowersetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule0) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_5) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all2) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1SetBreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (choice2fnsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all1) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compEex) =>
% 129.57/17.07 ((
% 129.57/17.07 (!!) @ (
% 129.57/17.07 (('#B') @ (
% 129.57/17.07 !!) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 !!))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#C') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1272])).
% 129.57/17.07 thf(zip_derived_cl1288, plain,
% 129.57/17.07 (~ (((setminusELneg) =>
% 129.57/17.07 (((setminusILneg) =>
% 129.57/17.07 (((setminusIRneg) =>
% 129.57/17.07 (((setminusLsub) =>
% 129.57/17.07 (((setminusSubset1) =>
% 129.57/17.07 (((symdiffE) =>
% 129.57/17.07 (((symdiffI1) =>
% 129.57/17.07 (((symdiffI2) =>
% 129.57/17.07 (((symdiffIneg1) =>
% 129.57/17.07 (((symdiffIneg2) =>
% 129.57/17.07 (((secondinupair) =>
% 129.57/17.07 (((setukpairIL) =>
% 129.57/17.07 (((setukpairIR) =>
% 129.57/17.07 (((kpairiskpair) =>
% 129.57/17.07 (((kpairp) =>
% 129.57/17.07 (((singletonsubset) =>
% 129.57/17.07 (((singletoninpowerset) =>
% 129.57/17.07 (((singletoninpowunion) =>
% 129.57/17.07 (((upairset2E) =>
% 129.57/17.07 (((upairsubunion) =>
% 129.57/17.07 (((upairinpowunion) =>
% 129.57/17.07 (((ubforcartprodlem1) =>
% 129.57/17.07 (((ubforcartprodlem2) =>
% 129.57/17.07 (((ubforcartprodlem3) =>
% 129.57/17.07 (((cartprodpairin) =>
% 129.57/17.07 (((cartprodmempair1) =>
% 129.57/17.07 (((cartprodmempair) =>
% 129.57/17.07 (((setunionE2) =>
% 129.57/17.07 (((setunionsingleton1) =>
% 129.57/17.07 (((setunionsingleton2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setunionsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (singletonprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I2) =>
% 129.57/17.07 ((
% 129.57/17.07 (singletonsuniq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (theprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstin) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR11) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR12) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR1) =>
% 129.57/17.07 ((
% 129.57/17.07 (upairequniteq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (kpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndin) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemEL) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemER) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodmempaircEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrI) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrSub) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrERa) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrER) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcImageSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (apProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (app) =>
% 129.57/17.07 ((
% 129.57/17.07 (infuncsetfunc) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcinfuncset) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall1) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp3) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcextLem) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp4) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq2) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2lamEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifp) =>
% 129.57/17.07 ((
% 129.57/17.07 (theeq) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrue) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueorfalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setminusT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setextT) =>
% 129.57/17.07 ((
% 129.57/17.07 (subsetTI) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTELcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTERcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT1) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT2) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT3) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub2) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTnotintersectT) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementImpComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementSubsetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementInPowersetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (contraSubsetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTcontraSubset) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTILcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTIRcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion2) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (intersectInPowersetIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpNotIn1) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpInComplement1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTE) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTEcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementUnionInPowersetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule0) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_5) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all2) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1SetBreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (choice2fnsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all1) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compEex) =>
% 129.57/17.07 ((
% 129.57/17.07 (!!) @ (
% 129.57/17.07 (('#B') @ (
% 129.57/17.07 !!) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 !!))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#C') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1280])).
% 129.57/17.07 thf(zip_derived_cl1296, plain,
% 129.57/17.07 (~ (((setminusILneg) =>
% 129.57/17.07 (((setminusIRneg) =>
% 129.57/17.07 (((setminusLsub) =>
% 129.57/17.07 (((setminusSubset1) =>
% 129.57/17.07 (((symdiffE) =>
% 129.57/17.07 (((symdiffI1) =>
% 129.57/17.07 (((symdiffI2) =>
% 129.57/17.07 (((symdiffIneg1) =>
% 129.57/17.07 (((symdiffIneg2) =>
% 129.57/17.07 (((secondinupair) =>
% 129.57/17.07 (((setukpairIL) =>
% 129.57/17.07 (((setukpairIR) =>
% 129.57/17.07 (((kpairiskpair) =>
% 129.57/17.07 (((kpairp) =>
% 129.57/17.07 (((singletonsubset) =>
% 129.57/17.07 (((singletoninpowerset) =>
% 129.57/17.07 (((singletoninpowunion) =>
% 129.57/17.07 (((upairset2E) =>
% 129.57/17.07 (((upairsubunion) =>
% 129.57/17.07 (((upairinpowunion) =>
% 129.57/17.07 (((ubforcartprodlem1) =>
% 129.57/17.07 (((ubforcartprodlem2) =>
% 129.57/17.07 (((ubforcartprodlem3) =>
% 129.57/17.07 (((cartprodpairin) =>
% 129.57/17.07 (((cartprodmempair1) =>
% 129.57/17.07 (((cartprodmempair) =>
% 129.57/17.07 (((setunionE2) =>
% 129.57/17.07 (((setunionsingleton1) =>
% 129.57/17.07 (((setunionsingleton2) =>
% 129.57/17.07 (((setunionsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (singletonprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I2) =>
% 129.57/17.07 ((
% 129.57/17.07 (singletonsuniq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (theprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstin) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR11) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR12) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR1) =>
% 129.57/17.07 ((
% 129.57/17.07 (upairequniteq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (kpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndin) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemEL) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemER) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodmempaircEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrI) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrSub) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrERa) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrER) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcImageSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (apProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (app) =>
% 129.57/17.07 ((
% 129.57/17.07 (infuncsetfunc) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcinfuncset) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall1) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp3) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcextLem) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp4) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq2) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2lamEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifp) =>
% 129.57/17.07 ((
% 129.57/17.07 (theeq) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrue) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueorfalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setminusT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setextT) =>
% 129.57/17.07 ((
% 129.57/17.07 (subsetTI) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTELcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTERcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT1) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT2) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT3) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub2) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTnotintersectT) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementImpComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementSubsetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementInPowersetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (contraSubsetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTcontraSubset) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTILcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTIRcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion2) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (intersectInPowersetIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpNotIn1) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpInComplement1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTE) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTEcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementUnionInPowersetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule0) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_5) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all2) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1SetBreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (choice2fnsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all1) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compEex) =>
% 129.57/17.07 ((
% 129.57/17.07 (!!) @ (
% 129.57/17.07 (('#B') @ (
% 129.57/17.07 !!) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 !!))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#C') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1288])).
% 129.57/17.07 thf(zip_derived_cl1305, plain,
% 129.57/17.07 (~ (((setminusIRneg) =>
% 129.57/17.07 (((setminusLsub) =>
% 129.57/17.07 (((setminusSubset1) =>
% 129.57/17.07 (((symdiffE) =>
% 129.57/17.07 (((symdiffI1) =>
% 129.57/17.07 (((symdiffI2) =>
% 129.57/17.07 (((symdiffIneg1) =>
% 129.57/17.07 (((symdiffIneg2) =>
% 129.57/17.07 (((secondinupair) =>
% 129.57/17.07 (((setukpairIL) =>
% 129.57/17.07 (((setukpairIR) =>
% 129.57/17.07 (((kpairiskpair) =>
% 129.57/17.07 (((kpairp) =>
% 129.57/17.07 (((singletonsubset) =>
% 129.57/17.07 (((singletoninpowerset) =>
% 129.57/17.07 (((singletoninpowunion) =>
% 129.57/17.07 (((upairset2E) =>
% 129.57/17.07 (((upairsubunion) =>
% 129.57/17.07 (((upairinpowunion) =>
% 129.57/17.07 (((ubforcartprodlem1) =>
% 129.57/17.07 (((ubforcartprodlem2) =>
% 129.57/17.07 (((ubforcartprodlem3) =>
% 129.57/17.07 (((cartprodpairin) =>
% 129.57/17.07 (((cartprodmempair1) =>
% 129.57/17.07 (((cartprodmempair) =>
% 129.57/17.07 (((setunionE2) =>
% 129.57/17.07 (((setunionsingleton1) =>
% 129.57/17.07 (((setunionsingleton2) =>
% 129.57/17.07 (((setunionsingleton) =>
% 129.57/17.07 (((singletonprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I2) =>
% 129.57/17.07 ((
% 129.57/17.07 (singletonsuniq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (theprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstin) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR11) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR12) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR1) =>
% 129.57/17.07 ((
% 129.57/17.07 (upairequniteq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (kpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndin) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemEL) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemER) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodmempaircEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrI) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrSub) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrERa) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrER) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcImageSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (apProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (app) =>
% 129.57/17.07 ((
% 129.57/17.07 (infuncsetfunc) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcinfuncset) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall1) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp3) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcextLem) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp4) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq2) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2lamEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifp) =>
% 129.57/17.07 ((
% 129.57/17.07 (theeq) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrue) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueorfalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setminusT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setextT) =>
% 129.57/17.07 ((
% 129.57/17.07 (subsetTI) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTELcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTERcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT1) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT2) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT3) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub2) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTnotintersectT) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementImpComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementSubsetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementInPowersetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (contraSubsetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTcontraSubset) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTILcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTIRcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion2) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (intersectInPowersetIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpNotIn1) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpInComplement1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTE) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTEcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementUnionInPowersetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan1) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2a) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b2) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2b) =>
% 129.57/17.07 ((
% 129.57/17.07 (demorgan2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule0) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz13rule4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_1) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_2) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_3) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_4) =>
% 129.57/17.07 ((
% 129.57/17.07 (woz1_5) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all2) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1SetBreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (choice2fnsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1all1) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln1) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1invE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compI) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compE) =>
% 129.57/17.07 ((
% 129.57/17.07 (breln1compEex) =>
% 129.57/17.07 ((
% 129.57/17.07 (!!) @ (
% 129.57/17.07 (('#B') @ (
% 129.57/17.07 !!) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 !!))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#S') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#S') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 =>))) @
% 129.57/17.07 breln1)))))) @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#C') @ (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 (
% 129.57/17.07 (
% 129.57/17.07 ('#B') @ (
% 129.57/17.07 '#B') @
% 129.57/17.07 breln1)))) @
% 129.57/17.07 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1296])).
% 129.57/17.07 thf(zip_derived_cl1313, plain,
% 129.57/17.07 (~ (((setminusLsub) =>
% 129.57/17.07 (((setminusSubset1) =>
% 129.57/17.07 (((symdiffE) =>
% 129.57/17.07 (((symdiffI1) =>
% 129.57/17.07 (((symdiffI2) =>
% 129.57/17.07 (((symdiffIneg1) =>
% 129.57/17.07 (((symdiffIneg2) =>
% 129.57/17.07 (((secondinupair) =>
% 129.57/17.07 (((setukpairIL) =>
% 129.57/17.07 (((setukpairIR) =>
% 129.57/17.07 (((kpairiskpair) =>
% 129.57/17.07 (((kpairp) =>
% 129.57/17.07 (((singletonsubset) =>
% 129.57/17.07 (((singletoninpowerset) =>
% 129.57/17.07 (((singletoninpowunion) =>
% 129.57/17.07 (((upairset2E) =>
% 129.57/17.07 (((upairsubunion) =>
% 129.57/17.07 (((upairinpowunion) =>
% 129.57/17.07 (((ubforcartprodlem1) =>
% 129.57/17.07 (((ubforcartprodlem2) =>
% 129.57/17.07 (((ubforcartprodlem3) =>
% 129.57/17.07 (((cartprodpairin) =>
% 129.57/17.07 (((cartprodmempair1) =>
% 129.57/17.07 (((cartprodmempair) =>
% 129.57/17.07 (((setunionE2) =>
% 129.57/17.07 (((setunionsingleton1) =>
% 129.57/17.07 (((setunionsingleton2) =>
% 129.57/17.07 (((setunionsingleton) =>
% 129.57/17.07 (((singletonprop) =>
% 129.57/17.07 (((ex1E1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1I2) =>
% 129.57/17.07 ((
% 129.57/17.07 (singletonsuniq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (theprop) =>
% 129.57/17.07 ((
% 129.57/17.07 (kfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstin) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjL) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR11) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR12) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR1) =>
% 129.57/17.07 ((
% 129.57/17.07 (upairequniteq) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR2) =>
% 129.57/17.07 ((
% 129.57/17.07 (setukpairinjR) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndsingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ksndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (kpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndin) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemEL) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairmemER) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodmempaircEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodfstpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodsndpairEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (cartprodpairsurjEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrI) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrSub) =>
% 129.57/17.07 ((
% 129.57/17.07 (setOfPairsIsBReln) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrERa) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL1) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrEL2) =>
% 129.57/17.07 ((
% 129.57/17.07 (dpsetconstrER) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcImageSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (apProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (app) =>
% 129.57/17.07 ((
% 129.57/17.07 (infuncsetfunc) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcinfuncset) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamProp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lamp) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2p) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall1) =>
% 129.57/17.07 ((
% 129.57/17.07 (brelnall2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ex1E2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp3) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcextLem) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcGraphProp4) =>
% 129.57/17.07 ((
% 129.57/17.07 (subbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (eqbreln) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext) =>
% 129.57/17.07 ((
% 129.57/17.07 (funcext2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq1) =>
% 129.57/17.07 ((
% 129.57/17.07 (ap2apEq2) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta1) =>
% 129.57/17.07 ((
% 129.57/17.07 (lam2lamEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (beta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (eta2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalseProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp1) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueProp2) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifSingleton) =>
% 129.57/17.07 ((
% 129.57/17.07 (ifp) =>
% 129.57/17.07 ((
% 129.57/17.07 (theeq) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrue) =>
% 129.57/17.07 ((
% 129.57/17.07 (iffalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (iftrueorfalse) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setminusT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementT_lem) =>
% 129.57/17.07 ((
% 129.57/17.07 (setextT) =>
% 129.57/17.07 ((
% 129.57/17.07 (subsetTI) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (powersetTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTELcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binintersectTERcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT1) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT2) =>
% 129.57/17.07 ((
% 129.57/17.07 (contrasubsetT3) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementI1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementE1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub1) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementSub2) =>
% 129.57/17.07 ((
% 129.57/17.07 (doubleComplementEq) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTnotintersectT) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementImpComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementSubsetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementInPowersetComplementIntersect) =>
% 129.57/17.07 ((
% 129.57/17.07 (contraSubsetComplement) =>
% 129.57/17.07 ((
% 129.57/17.07 (complementTcontraSubset) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTILcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (binunionTIRcontra) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInUnion2) =>
% 129.57/17.07 ((
% 129.57/17.07 (inIntersectImpInIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (intersectInPowersetIntersectUnions) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpNotIn1) =>
% 129.57/17.07 ((
% 129.57/17.07 (inComplementUnionImpInComplement1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTE) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTEcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementUnionInPowersetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule0) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_5) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all2) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1SetBreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (choice2fnsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all1) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compEex) =>
% 129.57/17.08 ((
% 129.57/17.08 (!!) @ (
% 129.57/17.08 (('#B') @ (
% 129.57/17.08 !!) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 !!))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#C') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1305])).
% 129.57/17.08 thf(zip_derived_cl1321, plain,
% 129.57/17.08 (~ (((setminusSubset1) =>
% 129.57/17.08 (((symdiffE) =>
% 129.57/17.08 (((symdiffI1) =>
% 129.57/17.08 (((symdiffI2) =>
% 129.57/17.08 (((symdiffIneg1) =>
% 129.57/17.08 (((symdiffIneg2) =>
% 129.57/17.08 (((secondinupair) =>
% 129.57/17.08 (((setukpairIL) =>
% 129.57/17.08 (((setukpairIR) =>
% 129.57/17.08 (((kpairiskpair) =>
% 129.57/17.08 (((kpairp) =>
% 129.57/17.08 (((singletonsubset) =>
% 129.57/17.08 (((singletoninpowerset) =>
% 129.57/17.08 (((singletoninpowunion) =>
% 129.57/17.08 (((upairset2E) =>
% 129.57/17.08 (((upairsubunion) =>
% 129.57/17.08 (((upairinpowunion) =>
% 129.57/17.08 (((ubforcartprodlem1) =>
% 129.57/17.08 (((ubforcartprodlem2) =>
% 129.57/17.08 (((ubforcartprodlem3) =>
% 129.57/17.08 (((cartprodpairin) =>
% 129.57/17.08 (((cartprodmempair1) =>
% 129.57/17.08 (((cartprodmempair) =>
% 129.57/17.08 (((setunionE2) =>
% 129.57/17.08 (((setunionsingleton1) =>
% 129.57/17.08 (((setunionsingleton2) =>
% 129.57/17.08 (((setunionsingleton) =>
% 129.57/17.08 (((singletonprop) =>
% 129.57/17.08 (((ex1E1) =>
% 129.57/17.08 (((ex1I) =>
% 129.57/17.08 ((
% 129.57/17.08 (ex1I2) =>
% 129.57/17.08 ((
% 129.57/17.08 (singletonsuniq) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL1) =>
% 129.57/17.08 ((
% 129.57/17.08 (kfstsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (theprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (kfstpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodfstin) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR11) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR12) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR1) =>
% 129.57/17.08 ((
% 129.57/17.08 (upairequniteq) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (kpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndin) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemEL) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemER) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodmempaircEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodfstpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrI) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrSub) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrERa) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL1) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrER) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcImageSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (apProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (app) =>
% 129.57/17.08 ((
% 129.57/17.08 (infuncsetfunc) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcinfuncset) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall1) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ex1E2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp3) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcextLem) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp4) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq1) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq2) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2lamEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifp) =>
% 129.57/17.08 ((
% 129.57/17.08 (theeq) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrue) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueorfalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setminusT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setextT) =>
% 129.57/17.08 ((
% 129.57/17.08 (subsetTI) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTELcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTERcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT1) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT2) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT3) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub2) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTnotintersectT) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementImpComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementSubsetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementInPowersetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (contraSubsetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTcontraSubset) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTILcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTIRcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion2) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (intersectInPowersetIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpNotIn1) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpInComplement1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTE) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTEcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementUnionInPowersetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule0) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_5) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all2) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1SetBreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (choice2fnsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all1) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compEex) =>
% 129.57/17.08 ((
% 129.57/17.08 (!!) @ (
% 129.57/17.08 (('#B') @ (
% 129.57/17.08 !!) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 !!))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#C') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1313])).
% 129.57/17.08 thf(zip_derived_cl1329, plain,
% 129.57/17.08 (~ (((symdiffE) =>
% 129.57/17.08 (((symdiffI1) =>
% 129.57/17.08 (((symdiffI2) =>
% 129.57/17.08 (((symdiffIneg1) =>
% 129.57/17.08 (((symdiffIneg2) =>
% 129.57/17.08 (((secondinupair) =>
% 129.57/17.08 (((setukpairIL) =>
% 129.57/17.08 (((setukpairIR) =>
% 129.57/17.08 (((kpairiskpair) =>
% 129.57/17.08 (((kpairp) =>
% 129.57/17.08 (((singletonsubset) =>
% 129.57/17.08 (((singletoninpowerset) =>
% 129.57/17.08 (((singletoninpowunion) =>
% 129.57/17.08 (((upairset2E) =>
% 129.57/17.08 (((upairsubunion) =>
% 129.57/17.08 (((upairinpowunion) =>
% 129.57/17.08 (((ubforcartprodlem1) =>
% 129.57/17.08 (((ubforcartprodlem2) =>
% 129.57/17.08 (((ubforcartprodlem3) =>
% 129.57/17.08 (((cartprodpairin) =>
% 129.57/17.08 (((cartprodmempair1) =>
% 129.57/17.08 (((cartprodmempair) =>
% 129.57/17.08 (((setunionE2) =>
% 129.57/17.08 (((setunionsingleton1) =>
% 129.57/17.08 (((setunionsingleton2) =>
% 129.57/17.08 (((setunionsingleton) =>
% 129.57/17.08 (((singletonprop) =>
% 129.57/17.08 (((ex1E1) =>
% 129.57/17.08 (((ex1I) =>
% 129.57/17.08 (((ex1I2) =>
% 129.57/17.08 ((
% 129.57/17.08 (singletonsuniq) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL1) =>
% 129.57/17.08 ((
% 129.57/17.08 (kfstsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (theprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (kfstpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodfstin) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR11) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR12) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR1) =>
% 129.57/17.08 ((
% 129.57/17.08 (upairequniteq) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (kpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndin) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemEL) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemER) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodmempaircEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodfstpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrI) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrSub) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrERa) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL1) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrER) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcImageSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (apProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (app) =>
% 129.57/17.08 ((
% 129.57/17.08 (infuncsetfunc) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcinfuncset) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall1) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ex1E2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp3) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcextLem) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp4) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq1) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq2) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2lamEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifp) =>
% 129.57/17.08 ((
% 129.57/17.08 (theeq) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrue) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueorfalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setminusT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setextT) =>
% 129.57/17.08 ((
% 129.57/17.08 (subsetTI) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTELcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTERcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT1) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT2) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT3) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub2) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTnotintersectT) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementImpComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementSubsetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementInPowersetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (contraSubsetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTcontraSubset) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTILcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTIRcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion2) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (intersectInPowersetIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpNotIn1) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpInComplement1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTE) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTEcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementUnionInPowersetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule0) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_5) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all2) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1SetBreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (choice2fnsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all1) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compEex) =>
% 129.57/17.08 ((
% 129.57/17.08 (!!) @ (
% 129.57/17.08 (('#B') @ (
% 129.57/17.08 !!) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 !!))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#C') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1321])).
% 129.57/17.08 thf(zip_derived_cl1338, plain,
% 129.57/17.08 (~ (((symdiffI1) =>
% 129.57/17.08 (((symdiffI2) =>
% 129.57/17.08 (((symdiffIneg1) =>
% 129.57/17.08 (((symdiffIneg2) =>
% 129.57/17.08 (((secondinupair) =>
% 129.57/17.08 (((setukpairIL) =>
% 129.57/17.08 (((setukpairIR) =>
% 129.57/17.08 (((kpairiskpair) =>
% 129.57/17.08 (((kpairp) =>
% 129.57/17.08 (((singletonsubset) =>
% 129.57/17.08 (((singletoninpowerset) =>
% 129.57/17.08 (((singletoninpowunion) =>
% 129.57/17.08 (((upairset2E) =>
% 129.57/17.08 (((upairsubunion) =>
% 129.57/17.08 (((upairinpowunion) =>
% 129.57/17.08 (((ubforcartprodlem1) =>
% 129.57/17.08 (((ubforcartprodlem2) =>
% 129.57/17.08 (((ubforcartprodlem3) =>
% 129.57/17.08 (((cartprodpairin) =>
% 129.57/17.08 (((cartprodmempair1) =>
% 129.57/17.08 (((cartprodmempair) =>
% 129.57/17.08 (((setunionE2) =>
% 129.57/17.08 (((setunionsingleton1) =>
% 129.57/17.08 (((setunionsingleton2) =>
% 129.57/17.08 (((setunionsingleton) =>
% 129.57/17.08 (((singletonprop) =>
% 129.57/17.08 (((ex1E1) =>
% 129.57/17.08 (((ex1I) =>
% 129.57/17.08 (((ex1I2) =>
% 129.57/17.08 (((singletonsuniq) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL1) =>
% 129.57/17.08 ((
% 129.57/17.08 (kfstsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (theprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (kfstpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodfstin) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR11) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR12) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR1) =>
% 129.57/17.08 ((
% 129.57/17.08 (upairequniteq) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (kpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndin) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemEL) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemER) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodmempaircEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodfstpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrI) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrSub) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrERa) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL1) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrER) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcImageSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (apProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (app) =>
% 129.57/17.08 ((
% 129.57/17.08 (infuncsetfunc) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcinfuncset) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall1) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ex1E2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp3) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcextLem) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp4) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq1) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq2) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2lamEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifp) =>
% 129.57/17.08 ((
% 129.57/17.08 (theeq) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrue) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueorfalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setminusT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setextT) =>
% 129.57/17.08 ((
% 129.57/17.08 (subsetTI) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTELcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTERcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT1) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT2) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT3) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub2) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTnotintersectT) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementImpComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementSubsetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementInPowersetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (contraSubsetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTcontraSubset) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTILcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTIRcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion2) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (intersectInPowersetIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpNotIn1) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpInComplement1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTE) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTEcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementUnionInPowersetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule0) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_5) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all2) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1SetBreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (choice2fnsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all1) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compEex) =>
% 129.57/17.08 ((
% 129.57/17.08 (!!) @ (
% 129.57/17.08 (('#B') @ (
% 129.57/17.08 !!) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 !!))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#C') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1329])).
% 129.57/17.08 thf(zip_derived_cl1347, plain,
% 129.57/17.08 (~ (((symdiffI2) =>
% 129.57/17.08 (((symdiffIneg1) =>
% 129.57/17.08 (((symdiffIneg2) =>
% 129.57/17.08 (((secondinupair) =>
% 129.57/17.08 (((setukpairIL) =>
% 129.57/17.08 (((setukpairIR) =>
% 129.57/17.08 (((kpairiskpair) =>
% 129.57/17.08 (((kpairp) =>
% 129.57/17.08 (((singletonsubset) =>
% 129.57/17.08 (((singletoninpowerset) =>
% 129.57/17.08 (((singletoninpowunion) =>
% 129.57/17.08 (((upairset2E) =>
% 129.57/17.08 (((upairsubunion) =>
% 129.57/17.08 (((upairinpowunion) =>
% 129.57/17.08 (((ubforcartprodlem1) =>
% 129.57/17.08 (((ubforcartprodlem2) =>
% 129.57/17.08 (((ubforcartprodlem3) =>
% 129.57/17.08 (((cartprodpairin) =>
% 129.57/17.08 (((cartprodmempair1) =>
% 129.57/17.08 (((cartprodmempair) =>
% 129.57/17.08 (((setunionE2) =>
% 129.57/17.08 (((setunionsingleton1) =>
% 129.57/17.08 (((setunionsingleton2) =>
% 129.57/17.08 (((setunionsingleton) =>
% 129.57/17.08 (((singletonprop) =>
% 129.57/17.08 (((ex1E1) =>
% 129.57/17.08 (((ex1I) =>
% 129.57/17.08 (((ex1I2) =>
% 129.57/17.08 (((singletonsuniq) =>
% 129.57/17.08 (((setukpairinjL1) =>
% 129.57/17.08 ((
% 129.57/17.08 (kfstsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (theprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (kfstpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodfstin) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR11) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR12) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR1) =>
% 129.57/17.08 ((
% 129.57/17.08 (upairequniteq) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (kpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndin) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemEL) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemER) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodmempaircEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodfstpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrI) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrSub) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrERa) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL1) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrER) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcImageSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (apProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (app) =>
% 129.57/17.08 ((
% 129.57/17.08 (infuncsetfunc) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcinfuncset) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall1) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ex1E2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp3) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcextLem) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp4) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq1) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq2) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2lamEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifp) =>
% 129.57/17.08 ((
% 129.57/17.08 (theeq) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrue) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueorfalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setminusT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setextT) =>
% 129.57/17.08 ((
% 129.57/17.08 (subsetTI) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTELcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTERcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT1) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT2) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT3) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub2) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTnotintersectT) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementImpComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementSubsetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementInPowersetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (contraSubsetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTcontraSubset) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTILcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTIRcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion2) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (intersectInPowersetIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpNotIn1) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpInComplement1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTE) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTEcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementUnionInPowersetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule0) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_5) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all2) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1SetBreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (choice2fnsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all1) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compEex) =>
% 129.57/17.08 ((
% 129.57/17.08 (!!) @ (
% 129.57/17.08 (('#B') @ (
% 129.57/17.08 !!) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 !!))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#C') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1338])).
% 129.57/17.08 thf(zip_derived_cl1354, plain,
% 129.57/17.08 (~ (((symdiffIneg1) =>
% 129.57/17.08 (((symdiffIneg2) =>
% 129.57/17.08 (((secondinupair) =>
% 129.57/17.08 (((setukpairIL) =>
% 129.57/17.08 (((setukpairIR) =>
% 129.57/17.08 (((kpairiskpair) =>
% 129.57/17.08 (((kpairp) =>
% 129.57/17.08 (((singletonsubset) =>
% 129.57/17.08 (((singletoninpowerset) =>
% 129.57/17.08 (((singletoninpowunion) =>
% 129.57/17.08 (((upairset2E) =>
% 129.57/17.08 (((upairsubunion) =>
% 129.57/17.08 (((upairinpowunion) =>
% 129.57/17.08 (((ubforcartprodlem1) =>
% 129.57/17.08 (((ubforcartprodlem2) =>
% 129.57/17.08 (((ubforcartprodlem3) =>
% 129.57/17.08 (((cartprodpairin) =>
% 129.57/17.08 (((cartprodmempair1) =>
% 129.57/17.08 (((cartprodmempair) =>
% 129.57/17.08 (((setunionE2) =>
% 129.57/17.08 (((setunionsingleton1) =>
% 129.57/17.08 (((setunionsingleton2) =>
% 129.57/17.08 (((setunionsingleton) =>
% 129.57/17.08 (((singletonprop) =>
% 129.57/17.08 (((ex1E1) =>
% 129.57/17.08 (((ex1I) =>
% 129.57/17.08 (((ex1I2) =>
% 129.57/17.08 (((singletonsuniq) =>
% 129.57/17.08 (((setukpairinjL1) =>
% 129.57/17.08 (((kfstsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (theprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (kfstpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodfstin) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR11) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR12) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR1) =>
% 129.57/17.08 ((
% 129.57/17.08 (upairequniteq) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (kpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndin) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemEL) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemER) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodmempaircEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodfstpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrI) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrSub) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrERa) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL1) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrER) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcImageSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (apProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (app) =>
% 129.57/17.08 ((
% 129.57/17.08 (infuncsetfunc) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcinfuncset) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall1) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ex1E2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp3) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcextLem) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp4) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq1) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq2) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2lamEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifp) =>
% 129.57/17.08 ((
% 129.57/17.08 (theeq) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrue) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueorfalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setminusT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setextT) =>
% 129.57/17.08 ((
% 129.57/17.08 (subsetTI) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTELcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTERcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT1) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT2) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT3) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub2) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTnotintersectT) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementImpComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementSubsetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementInPowersetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (contraSubsetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTcontraSubset) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTILcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTIRcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion2) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (intersectInPowersetIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpNotIn1) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpInComplement1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTE) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTEcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementUnionInPowersetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule0) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_5) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all2) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1SetBreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (choice2fnsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all1) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compEex) =>
% 129.57/17.08 ((
% 129.57/17.08 (!!) @ (
% 129.57/17.08 (('#B') @ (
% 129.57/17.08 !!) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 !!))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#C') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1347])).
% 129.57/17.08 thf(zip_derived_cl1361, plain,
% 129.57/17.08 (~ (((symdiffIneg2) =>
% 129.57/17.08 (((secondinupair) =>
% 129.57/17.08 (((setukpairIL) =>
% 129.57/17.08 (((setukpairIR) =>
% 129.57/17.08 (((kpairiskpair) =>
% 129.57/17.08 (((kpairp) =>
% 129.57/17.08 (((singletonsubset) =>
% 129.57/17.08 (((singletoninpowerset) =>
% 129.57/17.08 (((singletoninpowunion) =>
% 129.57/17.08 (((upairset2E) =>
% 129.57/17.08 (((upairsubunion) =>
% 129.57/17.08 (((upairinpowunion) =>
% 129.57/17.08 (((ubforcartprodlem1) =>
% 129.57/17.08 (((ubforcartprodlem2) =>
% 129.57/17.08 (((ubforcartprodlem3) =>
% 129.57/17.08 (((cartprodpairin) =>
% 129.57/17.08 (((cartprodmempair1) =>
% 129.57/17.08 (((cartprodmempair) =>
% 129.57/17.08 (((setunionE2) =>
% 129.57/17.08 (((setunionsingleton1) =>
% 129.57/17.08 (((setunionsingleton2) =>
% 129.57/17.08 (((setunionsingleton) =>
% 129.57/17.08 (((singletonprop) =>
% 129.57/17.08 (((ex1E1) =>
% 129.57/17.08 (((ex1I) =>
% 129.57/17.08 (((ex1I2) =>
% 129.57/17.08 (((singletonsuniq) =>
% 129.57/17.08 (((setukpairinjL1) =>
% 129.57/17.08 (((kfstsingleton) =>
% 129.57/17.08 (((theprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (kfstpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodfstin) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR11) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR12) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR1) =>
% 129.57/17.08 ((
% 129.57/17.08 (upairequniteq) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (kpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndin) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemEL) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemER) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodmempaircEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodfstpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrI) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrSub) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrERa) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL1) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrER) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcImageSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (apProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (app) =>
% 129.57/17.08 ((
% 129.57/17.08 (infuncsetfunc) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcinfuncset) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall1) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ex1E2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp3) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcextLem) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp4) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq1) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq2) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2lamEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifp) =>
% 129.57/17.08 ((
% 129.57/17.08 (theeq) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrue) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueorfalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setminusT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setextT) =>
% 129.57/17.08 ((
% 129.57/17.08 (subsetTI) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTELcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTERcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT1) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT2) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT3) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub2) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTnotintersectT) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementImpComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementSubsetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementInPowersetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (contraSubsetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTcontraSubset) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTILcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTIRcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion2) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (intersectInPowersetIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpNotIn1) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpInComplement1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTE) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTEcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementUnionInPowersetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule0) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_5) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all2) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1SetBreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (choice2fnsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all1) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compEex) =>
% 129.57/17.08 ((
% 129.57/17.08 (!!) @ (
% 129.57/17.08 (('#B') @ (
% 129.57/17.08 !!) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 !!))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#C') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1354])).
% 129.57/17.08 thf(zip_derived_cl1369, plain,
% 129.57/17.08 (~ (((secondinupair) =>
% 129.57/17.08 (((setukpairIL) =>
% 129.57/17.08 (((setukpairIR) =>
% 129.57/17.08 (((kpairiskpair) =>
% 129.57/17.08 (((kpairp) =>
% 129.57/17.08 (((singletonsubset) =>
% 129.57/17.08 (((singletoninpowerset) =>
% 129.57/17.08 (((singletoninpowunion) =>
% 129.57/17.08 (((upairset2E) =>
% 129.57/17.08 (((upairsubunion) =>
% 129.57/17.08 (((upairinpowunion) =>
% 129.57/17.08 (((ubforcartprodlem1) =>
% 129.57/17.08 (((ubforcartprodlem2) =>
% 129.57/17.08 (((ubforcartprodlem3) =>
% 129.57/17.08 (((cartprodpairin) =>
% 129.57/17.08 (((cartprodmempair1) =>
% 129.57/17.08 (((cartprodmempair) =>
% 129.57/17.08 (((setunionE2) =>
% 129.57/17.08 (((setunionsingleton1) =>
% 129.57/17.08 (((setunionsingleton2) =>
% 129.57/17.08 (((setunionsingleton) =>
% 129.57/17.08 (((singletonprop) =>
% 129.57/17.08 (((ex1E1) =>
% 129.57/17.08 (((ex1I) =>
% 129.57/17.08 (((ex1I2) =>
% 129.57/17.08 (((singletonsuniq) =>
% 129.57/17.08 (((setukpairinjL1) =>
% 129.57/17.08 (((kfstsingleton) =>
% 129.57/17.08 (((theprop) =>
% 129.57/17.08 (((kfstpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodfstin) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR11) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR12) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR1) =>
% 129.57/17.08 ((
% 129.57/17.08 (upairequniteq) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (kpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndin) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemEL) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemER) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodmempaircEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodfstpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrI) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrSub) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrERa) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL1) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrER) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcImageSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (apProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (app) =>
% 129.57/17.08 ((
% 129.57/17.08 (infuncsetfunc) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcinfuncset) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall1) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ex1E2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp3) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcextLem) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp4) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq1) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq2) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2lamEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifp) =>
% 129.57/17.08 ((
% 129.57/17.08 (theeq) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrue) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueorfalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setminusT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setextT) =>
% 129.57/17.08 ((
% 129.57/17.08 (subsetTI) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTELcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTERcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT1) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT2) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT3) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub2) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTnotintersectT) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementImpComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementSubsetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementInPowersetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (contraSubsetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTcontraSubset) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTILcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTIRcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion2) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (intersectInPowersetIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpNotIn1) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpInComplement1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTE) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTEcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementUnionInPowersetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule0) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_5) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all2) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1SetBreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (choice2fnsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all1) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compEex) =>
% 129.57/17.08 ((
% 129.57/17.08 (!!) @ (
% 129.57/17.08 (('#B') @ (
% 129.57/17.08 !!) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 !!))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#C') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])).
% 129.57/17.08 thf(zip_derived_cl1377, plain,
% 129.57/17.08 (~ (((setukpairIL) =>
% 129.57/17.08 (((setukpairIR) =>
% 129.57/17.08 (((kpairiskpair) =>
% 129.57/17.08 (((kpairp) =>
% 129.57/17.08 (((singletonsubset) =>
% 129.57/17.08 (((singletoninpowerset) =>
% 129.57/17.08 (((singletoninpowunion) =>
% 129.57/17.08 (((upairset2E) =>
% 129.57/17.08 (((upairsubunion) =>
% 129.57/17.08 (((upairinpowunion) =>
% 129.57/17.08 (((ubforcartprodlem1) =>
% 129.57/17.08 (((ubforcartprodlem2) =>
% 129.57/17.08 (((ubforcartprodlem3) =>
% 129.57/17.08 (((cartprodpairin) =>
% 129.57/17.08 (((cartprodmempair1) =>
% 129.57/17.08 (((cartprodmempair) =>
% 129.57/17.08 (((setunionE2) =>
% 129.57/17.08 (((setunionsingleton1) =>
% 129.57/17.08 (((setunionsingleton2) =>
% 129.57/17.08 (((setunionsingleton) =>
% 129.57/17.08 (((singletonprop) =>
% 129.57/17.08 (((ex1E1) =>
% 129.57/17.08 (((ex1I) =>
% 129.57/17.08 (((ex1I2) =>
% 129.57/17.08 (((singletonsuniq) =>
% 129.57/17.08 (((setukpairinjL1) =>
% 129.57/17.08 (((kfstsingleton) =>
% 129.57/17.08 (((theprop) =>
% 129.57/17.08 (((kfstpairEq) =>
% 129.57/17.08 (((cartprodfstin) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR11) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR12) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR1) =>
% 129.57/17.08 ((
% 129.57/17.08 (upairequniteq) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (kpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndin) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemEL) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemER) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodmempaircEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodfstpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrI) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrSub) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrERa) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL1) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrER) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcImageSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (apProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (app) =>
% 129.57/17.08 ((
% 129.57/17.08 (infuncsetfunc) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcinfuncset) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall1) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ex1E2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp3) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcextLem) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp4) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq1) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq2) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2lamEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifp) =>
% 129.57/17.08 ((
% 129.57/17.08 (theeq) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrue) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueorfalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setminusT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setextT) =>
% 129.57/17.08 ((
% 129.57/17.08 (subsetTI) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTELcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTERcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT1) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT2) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT3) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub2) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTnotintersectT) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementImpComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementSubsetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementInPowersetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (contraSubsetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTcontraSubset) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTILcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTIRcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion2) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (intersectInPowersetIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpNotIn1) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpInComplement1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTE) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTEcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementUnionInPowersetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule0) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_5) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all2) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1SetBreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (choice2fnsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all1) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compEex) =>
% 129.57/17.08 ((
% 129.57/17.08 (!!) @ (
% 129.57/17.08 (('#B') @ (
% 129.57/17.08 !!) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 !!))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#C') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1369])).
% 129.57/17.08 thf(zip_derived_cl1386, plain,
% 129.57/17.08 (~ (((setukpairIR) =>
% 129.57/17.08 (((kpairiskpair) =>
% 129.57/17.08 (((kpairp) =>
% 129.57/17.08 (((singletonsubset) =>
% 129.57/17.08 (((singletoninpowerset) =>
% 129.57/17.08 (((singletoninpowunion) =>
% 129.57/17.08 (((upairset2E) =>
% 129.57/17.08 (((upairsubunion) =>
% 129.57/17.08 (((upairinpowunion) =>
% 129.57/17.08 (((ubforcartprodlem1) =>
% 129.57/17.08 (((ubforcartprodlem2) =>
% 129.57/17.08 (((ubforcartprodlem3) =>
% 129.57/17.08 (((cartprodpairin) =>
% 129.57/17.08 (((cartprodmempair1) =>
% 129.57/17.08 (((cartprodmempair) =>
% 129.57/17.08 (((setunionE2) =>
% 129.57/17.08 (((setunionsingleton1) =>
% 129.57/17.08 (((setunionsingleton2) =>
% 129.57/17.08 (((setunionsingleton) =>
% 129.57/17.08 (((singletonprop) =>
% 129.57/17.08 (((ex1E1) =>
% 129.57/17.08 (((ex1I) =>
% 129.57/17.08 (((ex1I2) =>
% 129.57/17.08 (((singletonsuniq) =>
% 129.57/17.08 (((setukpairinjL1) =>
% 129.57/17.08 (((kfstsingleton) =>
% 129.57/17.08 (((theprop) =>
% 129.57/17.08 (((kfstpairEq) =>
% 129.57/17.08 (((cartprodfstin) =>
% 129.57/17.08 (((setukpairinjL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjL) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR11) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR12) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR1) =>
% 129.57/17.08 ((
% 129.57/17.08 (upairequniteq) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (kpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndin) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemEL) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemER) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodmempaircEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodfstpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrI) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrSub) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrERa) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL1) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrER) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcImageSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (apProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (app) =>
% 129.57/17.08 ((
% 129.57/17.08 (infuncsetfunc) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcinfuncset) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall1) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ex1E2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp3) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcextLem) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp4) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq1) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq2) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2lamEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifp) =>
% 129.57/17.08 ((
% 129.57/17.08 (theeq) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrue) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueorfalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setminusT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setextT) =>
% 129.57/17.08 ((
% 129.57/17.08 (subsetTI) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTELcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTERcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT1) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT2) =>
% 129.57/17.08 ((
% 129.57/17.08 (contrasubsetT3) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub1) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementSub2) =>
% 129.57/17.08 ((
% 129.57/17.08 (doubleComplementEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTnotintersectT) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementImpComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementSubsetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementInPowersetComplementIntersect) =>
% 129.57/17.08 ((
% 129.57/17.08 (contraSubsetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTcontraSubset) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTILcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTIRcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInUnion2) =>
% 129.57/17.08 ((
% 129.57/17.08 (inIntersectImpInIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (intersectInPowersetIntersectUnions) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpNotIn1) =>
% 129.57/17.08 ((
% 129.57/17.08 (inComplementUnionImpInComplement1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTE) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionTEcontra) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementUnionInPowersetComplement) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan1) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2a) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b2) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2b) =>
% 129.57/17.08 ((
% 129.57/17.08 (demorgan2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule0) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz13rule4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_1) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_2) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_3) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_4) =>
% 129.57/17.08 ((
% 129.57/17.08 (woz1_5) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all2) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1SetBreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (choice2fnsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1all1) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln1) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1invE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compprop) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compI) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compE) =>
% 129.57/17.08 ((
% 129.57/17.08 (breln1compEex) =>
% 129.57/17.08 ((
% 129.57/17.08 (!!) @ (
% 129.57/17.08 (('#B') @ (
% 129.57/17.08 !!) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 !!))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#S') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#S') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 =>))) @
% 129.57/17.08 breln1)))))) @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#C') @ (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 (
% 129.57/17.08 (
% 129.57/17.08 ('#B') @ (
% 129.57/17.08 '#B') @
% 129.57/17.08 breln1)))) @
% 129.57/17.08 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1377])).
% 129.57/17.08 thf(zip_derived_cl1396, plain,
% 129.57/17.08 (~ (((kpairiskpair) =>
% 129.57/17.08 (((kpairp) =>
% 129.57/17.08 (((singletonsubset) =>
% 129.57/17.08 (((singletoninpowerset) =>
% 129.57/17.08 (((singletoninpowunion) =>
% 129.57/17.08 (((upairset2E) =>
% 129.57/17.08 (((upairsubunion) =>
% 129.57/17.08 (((upairinpowunion) =>
% 129.57/17.08 (((ubforcartprodlem1) =>
% 129.57/17.08 (((ubforcartprodlem2) =>
% 129.57/17.08 (((ubforcartprodlem3) =>
% 129.57/17.08 (((cartprodpairin) =>
% 129.57/17.08 (((cartprodmempair1) =>
% 129.57/17.08 (((cartprodmempair) =>
% 129.57/17.08 (((setunionE2) =>
% 129.57/17.08 (((setunionsingleton1) =>
% 129.57/17.08 (((setunionsingleton2) =>
% 129.57/17.08 (((setunionsingleton) =>
% 129.57/17.08 (((singletonprop) =>
% 129.57/17.08 (((ex1E1) =>
% 129.57/17.08 (((ex1I) =>
% 129.57/17.08 (((ex1I2) =>
% 129.57/17.08 (((singletonsuniq) =>
% 129.57/17.08 (((setukpairinjL1) =>
% 129.57/17.08 (((kfstsingleton) =>
% 129.57/17.08 (((theprop) =>
% 129.57/17.08 (((kfstpairEq) =>
% 129.57/17.08 (((cartprodfstin) =>
% 129.57/17.08 (((setukpairinjL2) =>
% 129.57/17.08 (((setukpairinjL) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR11) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR12) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR1) =>
% 129.57/17.08 ((
% 129.57/17.08 (upairequniteq) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR2) =>
% 129.57/17.08 ((
% 129.57/17.08 (setukpairinjR) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndsingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ksndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (kpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndin) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemEL) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairmemER) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodmempaircEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodfstpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodsndpairEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (cartprodpairsurjEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrI) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrSub) =>
% 129.57/17.08 ((
% 129.57/17.08 (setOfPairsIsBReln) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrERa) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL1) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrEL2) =>
% 129.57/17.08 ((
% 129.57/17.08 (dpsetconstrER) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcImageSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (apProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (app) =>
% 129.57/17.08 ((
% 129.57/17.08 (infuncsetfunc) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcinfuncset) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamProp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lamp) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2p) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall1) =>
% 129.57/17.08 ((
% 129.57/17.08 (brelnall2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ex1E2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp3) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcextLem) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcGraphProp4) =>
% 129.57/17.08 ((
% 129.57/17.08 (subbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (eqbreln) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext) =>
% 129.57/17.08 ((
% 129.57/17.08 (funcext2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq1) =>
% 129.57/17.08 ((
% 129.57/17.08 (ap2apEq2) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta1) =>
% 129.57/17.08 ((
% 129.57/17.08 (lam2lamEq) =>
% 129.57/17.08 ((
% 129.57/17.08 (beta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (eta2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalseProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp1) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueProp2) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifSingleton) =>
% 129.57/17.08 ((
% 129.57/17.08 (ifp) =>
% 129.57/17.08 ((
% 129.57/17.08 (theeq) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrue) =>
% 129.57/17.08 ((
% 129.57/17.08 (iffalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (iftrueorfalse) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (binunionT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setminusT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementT_lem) =>
% 129.57/17.08 ((
% 129.57/17.08 (setextT) =>
% 129.57/17.08 ((
% 129.57/17.08 (subsetTI) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (powersetTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTI1) =>
% 129.57/17.08 ((
% 129.57/17.08 (complementTE1) =>
% 129.57/17.08 ((
% 129.57/17.08 (binintersectTELcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTERcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT1) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT2) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT3) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub2) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTnotintersectT) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementImpComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementSubsetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementInPowersetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (contraSubsetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTcontraSubset) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTILcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTIRcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion2) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (intersectInPowersetIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpNotIn1) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpInComplement1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTE) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTEcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementUnionInPowersetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule0) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_5) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all2) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1SetBreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (choice2fnsingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all1) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compEex) =>
% 129.57/17.09 ((
% 129.57/17.09 (!!) @ (
% 129.57/17.09 (('#B') @ (
% 129.57/17.09 !!) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 !!))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#C') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1386])).
% 129.57/17.09 thf(zip_derived_cl1407, plain,
% 129.57/17.09 (~ (((kpairp) =>
% 129.57/17.09 (((singletonsubset) =>
% 129.57/17.09 (((singletoninpowerset) =>
% 129.57/17.09 (((singletoninpowunion) =>
% 129.57/17.09 (((upairset2E) =>
% 129.57/17.09 (((upairsubunion) =>
% 129.57/17.09 (((upairinpowunion) =>
% 129.57/17.09 (((ubforcartprodlem1) =>
% 129.57/17.09 (((ubforcartprodlem2) =>
% 129.57/17.09 (((ubforcartprodlem3) =>
% 129.57/17.09 (((cartprodpairin) =>
% 129.57/17.09 (((cartprodmempair1) =>
% 129.57/17.09 (((cartprodmempair) =>
% 129.57/17.09 (((setunionE2) =>
% 129.57/17.09 (((setunionsingleton1) =>
% 129.57/17.09 (((setunionsingleton2) =>
% 129.57/17.09 (((setunionsingleton) =>
% 129.57/17.09 (((singletonprop) =>
% 129.57/17.09 (((ex1E1) =>
% 129.57/17.09 (((ex1I) =>
% 129.57/17.09 (((ex1I2) =>
% 129.57/17.09 (((singletonsuniq) =>
% 129.57/17.09 (((setukpairinjL1) =>
% 129.57/17.09 (((kfstsingleton) =>
% 129.57/17.09 (((theprop) =>
% 129.57/17.09 (((kfstpairEq) =>
% 129.57/17.09 (((cartprodfstin) =>
% 129.57/17.09 (((setukpairinjL2) =>
% 129.57/17.09 (((setukpairinjL) =>
% 129.57/17.09 (((setukpairinjR11) =>
% 129.57/17.09 ((
% 129.57/17.09 (setukpairinjR12) =>
% 129.57/17.09 ((
% 129.57/17.09 (setukpairinjR1) =>
% 129.57/17.09 ((
% 129.57/17.09 (upairequniteq) =>
% 129.57/17.09 ((
% 129.57/17.09 (setukpairinjR2) =>
% 129.57/17.09 ((
% 129.57/17.09 (setukpairinjR) =>
% 129.57/17.09 ((
% 129.57/17.09 (ksndsingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (ksndpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (kpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndin) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemEL) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemER) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodmempaircEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodfstpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrI) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrSub) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrERa) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL1) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL2) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrER) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcImageSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (apProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (app) =>
% 129.57/17.09 ((
% 129.57/17.09 (infuncsetfunc) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcinfuncset) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall1) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ex1E2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp3) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcextLem) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp4) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq1) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq2) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2lamEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifp) =>
% 129.57/17.09 ((
% 129.57/17.09 (theeq) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrue) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueorfalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setminusT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setextT) =>
% 129.57/17.09 ((
% 129.57/17.09 (subsetTI) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTELcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTERcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT1) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT2) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT3) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub2) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTnotintersectT) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementImpComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementSubsetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementInPowersetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (contraSubsetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTcontraSubset) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTILcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTIRcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion2) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (intersectInPowersetIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpNotIn1) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpInComplement1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTE) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTEcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementUnionInPowersetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule0) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_5) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all2) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1SetBreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (choice2fnsingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all1) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compEex) =>
% 129.57/17.09 ((
% 129.57/17.09 (!!) @ (
% 129.57/17.09 (('#B') @ (
% 129.57/17.09 !!) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 !!))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#C') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1396])).
% 129.57/17.09 thf(zip_derived_cl1420, plain,
% 129.57/17.09 (~ (((singletonsubset) =>
% 129.57/17.09 (((singletoninpowerset) =>
% 129.57/17.09 (((singletoninpowunion) =>
% 129.57/17.09 (((upairset2E) =>
% 129.57/17.09 (((upairsubunion) =>
% 129.57/17.09 (((upairinpowunion) =>
% 129.57/17.09 (((ubforcartprodlem1) =>
% 129.57/17.09 (((ubforcartprodlem2) =>
% 129.57/17.09 (((ubforcartprodlem3) =>
% 129.57/17.09 (((cartprodpairin) =>
% 129.57/17.09 (((cartprodmempair1) =>
% 129.57/17.09 (((cartprodmempair) =>
% 129.57/17.09 (((setunionE2) =>
% 129.57/17.09 (((setunionsingleton1) =>
% 129.57/17.09 (((setunionsingleton2) =>
% 129.57/17.09 (((setunionsingleton) =>
% 129.57/17.09 (((singletonprop) =>
% 129.57/17.09 (((ex1E1) =>
% 129.57/17.09 (((ex1I) =>
% 129.57/17.09 (((ex1I2) =>
% 129.57/17.09 (((singletonsuniq) =>
% 129.57/17.09 (((setukpairinjL1) =>
% 129.57/17.09 (((kfstsingleton) =>
% 129.57/17.09 (((theprop) =>
% 129.57/17.09 (((kfstpairEq) =>
% 129.57/17.09 (((cartprodfstin) =>
% 129.57/17.09 (((setukpairinjL2) =>
% 129.57/17.09 (((setukpairinjL) =>
% 129.57/17.09 (((setukpairinjR11) =>
% 129.57/17.09 (((setukpairinjR12) =>
% 129.57/17.09 ((
% 129.57/17.09 (setukpairinjR1) =>
% 129.57/17.09 ((
% 129.57/17.09 (upairequniteq) =>
% 129.57/17.09 ((
% 129.57/17.09 (setukpairinjR2) =>
% 129.57/17.09 ((
% 129.57/17.09 (setukpairinjR) =>
% 129.57/17.09 ((
% 129.57/17.09 (ksndsingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (ksndpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (kpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndin) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemEL) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemER) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodmempaircEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodfstpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrI) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrSub) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrERa) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL1) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL2) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrER) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcImageSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (apProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (app) =>
% 129.57/17.09 ((
% 129.57/17.09 (infuncsetfunc) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcinfuncset) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall1) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ex1E2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp3) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcextLem) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp4) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq1) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq2) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2lamEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifp) =>
% 129.57/17.09 ((
% 129.57/17.09 (theeq) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrue) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueorfalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setminusT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setextT) =>
% 129.57/17.09 ((
% 129.57/17.09 (subsetTI) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTELcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTERcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT1) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT2) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT3) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub2) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTnotintersectT) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementImpComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementSubsetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementInPowersetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (contraSubsetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTcontraSubset) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTILcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTIRcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion2) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (intersectInPowersetIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpNotIn1) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpInComplement1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTE) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTEcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementUnionInPowersetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule0) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_5) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all2) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1SetBreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (choice2fnsingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all1) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compEex) =>
% 129.57/17.09 ((
% 129.57/17.09 (!!) @ (
% 129.57/17.09 (('#B') @ (
% 129.57/17.09 !!) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 !!))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#C') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1407])).
% 129.57/17.09 thf(zip_derived_cl1433, plain,
% 129.57/17.09 (~ (((singletoninpowerset) =>
% 129.57/17.09 (((singletoninpowunion) =>
% 129.57/17.09 (((upairset2E) =>
% 129.57/17.09 (((upairsubunion) =>
% 129.57/17.09 (((upairinpowunion) =>
% 129.57/17.09 (((ubforcartprodlem1) =>
% 129.57/17.09 (((ubforcartprodlem2) =>
% 129.57/17.09 (((ubforcartprodlem3) =>
% 129.57/17.09 (((cartprodpairin) =>
% 129.57/17.09 (((cartprodmempair1) =>
% 129.57/17.09 (((cartprodmempair) =>
% 129.57/17.09 (((setunionE2) =>
% 129.57/17.09 (((setunionsingleton1) =>
% 129.57/17.09 (((setunionsingleton2) =>
% 129.57/17.09 (((setunionsingleton) =>
% 129.57/17.09 (((singletonprop) =>
% 129.57/17.09 (((ex1E1) =>
% 129.57/17.09 (((ex1I) =>
% 129.57/17.09 (((ex1I2) =>
% 129.57/17.09 (((singletonsuniq) =>
% 129.57/17.09 (((setukpairinjL1) =>
% 129.57/17.09 (((kfstsingleton) =>
% 129.57/17.09 (((theprop) =>
% 129.57/17.09 (((kfstpairEq) =>
% 129.57/17.09 (((cartprodfstin) =>
% 129.57/17.09 (((setukpairinjL2) =>
% 129.57/17.09 (((setukpairinjL) =>
% 129.57/17.09 (((setukpairinjR11) =>
% 129.57/17.09 (((setukpairinjR12) =>
% 129.57/17.09 (((setukpairinjR1) =>
% 129.57/17.09 ((
% 129.57/17.09 (upairequniteq) =>
% 129.57/17.09 ((
% 129.57/17.09 (setukpairinjR2) =>
% 129.57/17.09 ((
% 129.57/17.09 (setukpairinjR) =>
% 129.57/17.09 ((
% 129.57/17.09 (ksndsingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (ksndpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (kpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndin) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemEL) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemER) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodmempaircEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodfstpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrI) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrSub) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrERa) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL1) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL2) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrER) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcImageSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (apProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (app) =>
% 129.57/17.09 ((
% 129.57/17.09 (infuncsetfunc) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcinfuncset) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall1) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ex1E2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp3) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcextLem) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp4) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq1) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq2) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2lamEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifp) =>
% 129.57/17.09 ((
% 129.57/17.09 (theeq) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrue) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueorfalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setminusT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setextT) =>
% 129.57/17.09 ((
% 129.57/17.09 (subsetTI) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTELcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTERcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT1) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT2) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT3) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub2) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTnotintersectT) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementImpComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementSubsetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementInPowersetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (contraSubsetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTcontraSubset) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTILcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTIRcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion2) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (intersectInPowersetIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpNotIn1) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpInComplement1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTE) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTEcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementUnionInPowersetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule0) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_5) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all2) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1SetBreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (choice2fnsingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all1) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compEex) =>
% 129.57/17.09 ((
% 129.57/17.09 (!!) @ (
% 129.57/17.09 (('#B') @ (
% 129.57/17.09 !!) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 !!))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#C') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1420])).
% 129.57/17.09 thf(zip_derived_cl1444, plain,
% 129.57/17.09 (~ (((singletoninpowunion) =>
% 129.57/17.09 (((upairset2E) =>
% 129.57/17.09 (((upairsubunion) =>
% 129.57/17.09 (((upairinpowunion) =>
% 129.57/17.09 (((ubforcartprodlem1) =>
% 129.57/17.09 (((ubforcartprodlem2) =>
% 129.57/17.09 (((ubforcartprodlem3) =>
% 129.57/17.09 (((cartprodpairin) =>
% 129.57/17.09 (((cartprodmempair1) =>
% 129.57/17.09 (((cartprodmempair) =>
% 129.57/17.09 (((setunionE2) =>
% 129.57/17.09 (((setunionsingleton1) =>
% 129.57/17.09 (((setunionsingleton2) =>
% 129.57/17.09 (((setunionsingleton) =>
% 129.57/17.09 (((singletonprop) =>
% 129.57/17.09 (((ex1E1) =>
% 129.57/17.09 (((ex1I) =>
% 129.57/17.09 (((ex1I2) =>
% 129.57/17.09 (((singletonsuniq) =>
% 129.57/17.09 (((setukpairinjL1) =>
% 129.57/17.09 (((kfstsingleton) =>
% 129.57/17.09 (((theprop) =>
% 129.57/17.09 (((kfstpairEq) =>
% 129.57/17.09 (((cartprodfstin) =>
% 129.57/17.09 (((setukpairinjL2) =>
% 129.57/17.09 (((setukpairinjL) =>
% 129.57/17.09 (((setukpairinjR11) =>
% 129.57/17.09 (((setukpairinjR12) =>
% 129.57/17.09 (((setukpairinjR1) =>
% 129.57/17.09 (((upairequniteq) =>
% 129.57/17.09 ((
% 129.57/17.09 (setukpairinjR2) =>
% 129.57/17.09 ((
% 129.57/17.09 (setukpairinjR) =>
% 129.57/17.09 ((
% 129.57/17.09 (ksndsingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (ksndpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (kpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndin) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemEL) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemER) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodmempaircEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodfstpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrI) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrSub) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrERa) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL1) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL2) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrER) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcImageSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (apProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (app) =>
% 129.57/17.09 ((
% 129.57/17.09 (infuncsetfunc) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcinfuncset) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall1) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ex1E2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp3) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcextLem) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp4) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq1) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq2) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2lamEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifp) =>
% 129.57/17.09 ((
% 129.57/17.09 (theeq) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrue) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueorfalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setminusT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setextT) =>
% 129.57/17.09 ((
% 129.57/17.09 (subsetTI) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTELcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTERcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT1) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT2) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT3) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub2) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTnotintersectT) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementImpComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementSubsetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementInPowersetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (contraSubsetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTcontraSubset) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTILcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTIRcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion2) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (intersectInPowersetIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpNotIn1) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpInComplement1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTE) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTEcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementUnionInPowersetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule0) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_5) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all2) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1SetBreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (choice2fnsingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all1) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compEex) =>
% 129.57/17.09 ((
% 129.57/17.09 (!!) @ (
% 129.57/17.09 (('#B') @ (
% 129.57/17.09 !!) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 !!))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#C') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1433])).
% 129.57/17.09 thf(zip_derived_cl1452, plain,
% 129.57/17.09 (~ (((upairset2E) =>
% 129.57/17.09 (((upairsubunion) =>
% 129.57/17.09 (((upairinpowunion) =>
% 129.57/17.09 (((ubforcartprodlem1) =>
% 129.57/17.09 (((ubforcartprodlem2) =>
% 129.57/17.09 (((ubforcartprodlem3) =>
% 129.57/17.09 (((cartprodpairin) =>
% 129.57/17.09 (((cartprodmempair1) =>
% 129.57/17.09 (((cartprodmempair) =>
% 129.57/17.09 (((setunionE2) =>
% 129.57/17.09 (((setunionsingleton1) =>
% 129.57/17.09 (((setunionsingleton2) =>
% 129.57/17.09 (((setunionsingleton) =>
% 129.57/17.09 (((singletonprop) =>
% 129.57/17.09 (((ex1E1) =>
% 129.57/17.09 (((ex1I) =>
% 129.57/17.09 (((ex1I2) =>
% 129.57/17.09 (((singletonsuniq) =>
% 129.57/17.09 (((setukpairinjL1) =>
% 129.57/17.09 (((kfstsingleton) =>
% 129.57/17.09 (((theprop) =>
% 129.57/17.09 (((kfstpairEq) =>
% 129.57/17.09 (((cartprodfstin) =>
% 129.57/17.09 (((setukpairinjL2) =>
% 129.57/17.09 (((setukpairinjL) =>
% 129.57/17.09 (((setukpairinjR11) =>
% 129.57/17.09 (((setukpairinjR12) =>
% 129.57/17.09 (((setukpairinjR1) =>
% 129.57/17.09 (((upairequniteq) =>
% 129.57/17.09 (((setukpairinjR2) =>
% 129.57/17.09 ((
% 129.57/17.09 (setukpairinjR) =>
% 129.57/17.09 ((
% 129.57/17.09 (ksndsingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (ksndpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (kpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndin) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemEL) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemER) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodmempaircEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodfstpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrI) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrSub) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrERa) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL1) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL2) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrER) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcImageSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (apProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (app) =>
% 129.57/17.09 ((
% 129.57/17.09 (infuncsetfunc) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcinfuncset) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall1) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ex1E2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp3) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcextLem) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp4) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq1) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq2) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2lamEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifp) =>
% 129.57/17.09 ((
% 129.57/17.09 (theeq) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrue) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueorfalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setminusT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setextT) =>
% 129.57/17.09 ((
% 129.57/17.09 (subsetTI) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTELcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTERcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT1) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT2) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT3) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub2) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTnotintersectT) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementImpComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementSubsetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementInPowersetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (contraSubsetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTcontraSubset) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTILcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTIRcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion2) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (intersectInPowersetIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpNotIn1) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpInComplement1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTE) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTEcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementUnionInPowersetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule0) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_5) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all2) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1SetBreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (choice2fnsingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all1) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compEex) =>
% 129.57/17.09 ((
% 129.57/17.09 (!!) @ (
% 129.57/17.09 (('#B') @ (
% 129.57/17.09 !!) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 !!))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#C') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1444])).
% 129.57/17.09 thf(zip_derived_cl1459, plain,
% 129.57/17.09 (~ (((upairsubunion) =>
% 129.57/17.09 (((upairinpowunion) =>
% 129.57/17.09 (((ubforcartprodlem1) =>
% 129.57/17.09 (((ubforcartprodlem2) =>
% 129.57/17.09 (((ubforcartprodlem3) =>
% 129.57/17.09 (((cartprodpairin) =>
% 129.57/17.09 (((cartprodmempair1) =>
% 129.57/17.09 (((cartprodmempair) =>
% 129.57/17.09 (((setunionE2) =>
% 129.57/17.09 (((setunionsingleton1) =>
% 129.57/17.09 (((setunionsingleton2) =>
% 129.57/17.09 (((setunionsingleton) =>
% 129.57/17.09 (((singletonprop) =>
% 129.57/17.09 (((ex1E1) =>
% 129.57/17.09 (((ex1I) =>
% 129.57/17.09 (((ex1I2) =>
% 129.57/17.09 (((singletonsuniq) =>
% 129.57/17.09 (((setukpairinjL1) =>
% 129.57/17.09 (((kfstsingleton) =>
% 129.57/17.09 (((theprop) =>
% 129.57/17.09 (((kfstpairEq) =>
% 129.57/17.09 (((cartprodfstin) =>
% 129.57/17.09 (((setukpairinjL2) =>
% 129.57/17.09 (((setukpairinjL) =>
% 129.57/17.09 (((setukpairinjR11) =>
% 129.57/17.09 (((setukpairinjR12) =>
% 129.57/17.09 (((setukpairinjR1) =>
% 129.57/17.09 (((upairequniteq) =>
% 129.57/17.09 (((setukpairinjR2) =>
% 129.57/17.09 (((setukpairinjR) =>
% 129.57/17.09 ((
% 129.57/17.09 (ksndsingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (ksndpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (kpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndin) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemEL) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemER) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodmempaircEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodfstpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrI) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrSub) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrERa) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL1) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL2) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrER) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcImageSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (apProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (app) =>
% 129.57/17.09 ((
% 129.57/17.09 (infuncsetfunc) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcinfuncset) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall1) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ex1E2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp3) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcextLem) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp4) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq1) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq2) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2lamEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifp) =>
% 129.57/17.09 ((
% 129.57/17.09 (theeq) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrue) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueorfalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setminusT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setextT) =>
% 129.57/17.09 ((
% 129.57/17.09 (subsetTI) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTELcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTERcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT1) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT2) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT3) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub2) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTnotintersectT) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementImpComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementSubsetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementInPowersetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (contraSubsetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTcontraSubset) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTILcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTIRcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion2) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (intersectInPowersetIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpNotIn1) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpInComplement1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTE) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTEcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementUnionInPowersetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule0) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_5) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all2) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1SetBreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (choice2fnsingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all1) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compEex) =>
% 129.57/17.09 ((
% 129.57/17.09 (!!) @ (
% 129.57/17.09 (('#B') @ (
% 129.57/17.09 !!) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 !!))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#C') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1452])).
% 129.57/17.09 thf(zip_derived_cl1466, plain,
% 129.57/17.09 (~ (((upairinpowunion) =>
% 129.57/17.09 (((ubforcartprodlem1) =>
% 129.57/17.09 (((ubforcartprodlem2) =>
% 129.57/17.09 (((ubforcartprodlem3) =>
% 129.57/17.09 (((cartprodpairin) =>
% 129.57/17.09 (((cartprodmempair1) =>
% 129.57/17.09 (((cartprodmempair) =>
% 129.57/17.09 (((setunionE2) =>
% 129.57/17.09 (((setunionsingleton1) =>
% 129.57/17.09 (((setunionsingleton2) =>
% 129.57/17.09 (((setunionsingleton) =>
% 129.57/17.09 (((singletonprop) =>
% 129.57/17.09 (((ex1E1) =>
% 129.57/17.09 (((ex1I) =>
% 129.57/17.09 (((ex1I2) =>
% 129.57/17.09 (((singletonsuniq) =>
% 129.57/17.09 (((setukpairinjL1) =>
% 129.57/17.09 (((kfstsingleton) =>
% 129.57/17.09 (((theprop) =>
% 129.57/17.09 (((kfstpairEq) =>
% 129.57/17.09 (((cartprodfstin) =>
% 129.57/17.09 (((setukpairinjL2) =>
% 129.57/17.09 (((setukpairinjL) =>
% 129.57/17.09 (((setukpairinjR11) =>
% 129.57/17.09 (((setukpairinjR12) =>
% 129.57/17.09 (((setukpairinjR1) =>
% 129.57/17.09 (((upairequniteq) =>
% 129.57/17.09 (((setukpairinjR2) =>
% 129.57/17.09 (((setukpairinjR) =>
% 129.57/17.09 (((ksndsingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (ksndpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (kpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndin) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemEL) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemER) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodmempaircEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodfstpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrI) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrSub) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrERa) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL1) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL2) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrER) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcImageSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (apProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (app) =>
% 129.57/17.09 ((
% 129.57/17.09 (infuncsetfunc) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcinfuncset) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall1) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ex1E2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp3) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcextLem) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp4) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq1) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq2) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2lamEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifp) =>
% 129.57/17.09 ((
% 129.57/17.09 (theeq) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrue) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueorfalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setminusT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setextT) =>
% 129.57/17.09 ((
% 129.57/17.09 (subsetTI) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTELcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTERcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT1) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT2) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT3) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub2) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTnotintersectT) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementImpComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementSubsetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementInPowersetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (contraSubsetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTcontraSubset) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTILcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTIRcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion2) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (intersectInPowersetIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpNotIn1) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpInComplement1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTE) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTEcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementUnionInPowersetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule0) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_5) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all2) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1SetBreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (choice2fnsingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all1) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compEex) =>
% 129.57/17.09 ((
% 129.57/17.09 (!!) @ (
% 129.57/17.09 (('#B') @ (
% 129.57/17.09 !!) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 !!))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#C') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1459])).
% 129.57/17.09 thf(zip_derived_cl1473, plain,
% 129.57/17.09 (~ (((ubforcartprodlem1) =>
% 129.57/17.09 (((ubforcartprodlem2) =>
% 129.57/17.09 (((ubforcartprodlem3) =>
% 129.57/17.09 (((cartprodpairin) =>
% 129.57/17.09 (((cartprodmempair1) =>
% 129.57/17.09 (((cartprodmempair) =>
% 129.57/17.09 (((setunionE2) =>
% 129.57/17.09 (((setunionsingleton1) =>
% 129.57/17.09 (((setunionsingleton2) =>
% 129.57/17.09 (((setunionsingleton) =>
% 129.57/17.09 (((singletonprop) =>
% 129.57/17.09 (((ex1E1) =>
% 129.57/17.09 (((ex1I) =>
% 129.57/17.09 (((ex1I2) =>
% 129.57/17.09 (((singletonsuniq) =>
% 129.57/17.09 (((setukpairinjL1) =>
% 129.57/17.09 (((kfstsingleton) =>
% 129.57/17.09 (((theprop) =>
% 129.57/17.09 (((kfstpairEq) =>
% 129.57/17.09 (((cartprodfstin) =>
% 129.57/17.09 (((setukpairinjL2) =>
% 129.57/17.09 (((setukpairinjL) =>
% 129.57/17.09 (((setukpairinjR11) =>
% 129.57/17.09 (((setukpairinjR12) =>
% 129.57/17.09 (((setukpairinjR1) =>
% 129.57/17.09 (((upairequniteq) =>
% 129.57/17.09 (((setukpairinjR2) =>
% 129.57/17.09 (((setukpairinjR) =>
% 129.57/17.09 (((ksndsingleton) =>
% 129.57/17.09 (((ksndpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (kpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndin) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemEL) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemER) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodmempaircEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodfstpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrI) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrSub) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrERa) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL1) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL2) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrER) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcImageSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (apProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (app) =>
% 129.57/17.09 ((
% 129.57/17.09 (infuncsetfunc) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcinfuncset) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall1) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ex1E2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp3) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcextLem) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp4) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq1) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq2) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2lamEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifp) =>
% 129.57/17.09 ((
% 129.57/17.09 (theeq) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrue) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueorfalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setminusT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setextT) =>
% 129.57/17.09 ((
% 129.57/17.09 (subsetTI) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTELcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTERcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT1) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT2) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT3) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub2) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTnotintersectT) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementImpComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementSubsetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementInPowersetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (contraSubsetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTcontraSubset) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTILcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTIRcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion2) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (intersectInPowersetIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpNotIn1) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpInComplement1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTE) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTEcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementUnionInPowersetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule0) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_5) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all2) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1SetBreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (choice2fnsingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1all1) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln1) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1invE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compprop) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compI) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compE) =>
% 129.57/17.09 ((
% 129.57/17.09 (breln1compEex) =>
% 129.57/17.09 ((
% 129.57/17.09 (!!) @ (
% 129.57/17.09 (('#B') @ (
% 129.57/17.09 !!) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 !!))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#S') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#S') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 =>))) @
% 129.57/17.09 breln1)))))) @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#C') @ (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 (
% 129.57/17.09 (
% 129.57/17.09 ('#B') @ (
% 129.57/17.09 '#B') @
% 129.57/17.09 breln1)))) @
% 129.57/17.09 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 129.57/17.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1466])).
% 129.57/17.09 thf(zip_derived_cl1480, plain,
% 129.57/17.09 (~ (((ubforcartprodlem2) =>
% 129.57/17.09 (((ubforcartprodlem3) =>
% 129.57/17.09 (((cartprodpairin) =>
% 129.57/17.09 (((cartprodmempair1) =>
% 129.57/17.09 (((cartprodmempair) =>
% 129.57/17.09 (((setunionE2) =>
% 129.57/17.09 (((setunionsingleton1) =>
% 129.57/17.09 (((setunionsingleton2) =>
% 129.57/17.09 (((setunionsingleton) =>
% 129.57/17.09 (((singletonprop) =>
% 129.57/17.09 (((ex1E1) =>
% 129.57/17.09 (((ex1I) =>
% 129.57/17.09 (((ex1I2) =>
% 129.57/17.09 (((singletonsuniq) =>
% 129.57/17.09 (((setukpairinjL1) =>
% 129.57/17.09 (((kfstsingleton) =>
% 129.57/17.09 (((theprop) =>
% 129.57/17.09 (((kfstpairEq) =>
% 129.57/17.09 (((cartprodfstin) =>
% 129.57/17.09 (((setukpairinjL2) =>
% 129.57/17.09 (((setukpairinjL) =>
% 129.57/17.09 (((setukpairinjR11) =>
% 129.57/17.09 (((setukpairinjR12) =>
% 129.57/17.09 (((setukpairinjR1) =>
% 129.57/17.09 (((upairequniteq) =>
% 129.57/17.09 (((setukpairinjR2) =>
% 129.57/17.09 (((setukpairinjR) =>
% 129.57/17.09 (((ksndsingleton) =>
% 129.57/17.09 (((ksndpairEq) =>
% 129.57/17.09 (((kpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndin) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemEL) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairmemER) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodmempaircEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodfstpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodsndpairEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (cartprodpairsurjEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrI) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrSub) =>
% 129.57/17.09 ((
% 129.57/17.09 (setOfPairsIsBReln) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrERa) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL1) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrEL2) =>
% 129.57/17.09 ((
% 129.57/17.09 (dpsetconstrER) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcImageSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (apProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (app) =>
% 129.57/17.09 ((
% 129.57/17.09 (infuncsetfunc) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcinfuncset) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamProp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lamp) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2p) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall1) =>
% 129.57/17.09 ((
% 129.57/17.09 (brelnall2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ex1E2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp3) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcextLem) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcGraphProp4) =>
% 129.57/17.09 ((
% 129.57/17.09 (subbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (eqbreln) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext) =>
% 129.57/17.09 ((
% 129.57/17.09 (funcext2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq1) =>
% 129.57/17.09 ((
% 129.57/17.09 (ap2apEq2) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta1) =>
% 129.57/17.09 ((
% 129.57/17.09 (lam2lamEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (beta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (eta2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalseProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp1) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueProp2) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifSingleton) =>
% 129.57/17.09 ((
% 129.57/17.09 (ifp) =>
% 129.57/17.09 ((
% 129.57/17.09 (theeq) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrue) =>
% 129.57/17.09 ((
% 129.57/17.09 (iffalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (iftrueorfalse) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setminusT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementT_lem) =>
% 129.57/17.09 ((
% 129.57/17.09 (setextT) =>
% 129.57/17.09 ((
% 129.57/17.09 (subsetTI) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (powersetTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTELcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binintersectTERcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT1) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT2) =>
% 129.57/17.09 ((
% 129.57/17.09 (contrasubsetT3) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementI1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementE1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub1) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementSub2) =>
% 129.57/17.09 ((
% 129.57/17.09 (doubleComplementEq) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTnotintersectT) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementImpComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementSubsetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementInPowersetComplementIntersect) =>
% 129.57/17.09 ((
% 129.57/17.09 (contraSubsetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementTcontraSubset) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTILcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTIRcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInUnion2) =>
% 129.57/17.09 ((
% 129.57/17.09 (inIntersectImpInIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (intersectInPowersetIntersectUnions) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpNotIn1) =>
% 129.57/17.09 ((
% 129.57/17.09 (inComplementUnionImpInComplement1) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTE) =>
% 129.57/17.09 ((
% 129.57/17.09 (binunionTEcontra) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a1) =>
% 129.57/17.09 ((
% 129.57/17.09 (complementUnionInPowersetComplement) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan1) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2a) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b2) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2b) =>
% 129.57/17.09 ((
% 129.57/17.09 (demorgan2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule0) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz13rule4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_1) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_2) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_3) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_4) =>
% 129.57/17.09 ((
% 129.57/17.09 (woz1_5) =>
% 130.11/17.09 ((
% 130.11/17.09 (breln1all2) =>
% 130.11/17.09 ((
% 130.11/17.09 (breln1SetBreln1) =>
% 130.11/17.09 ((
% 130.11/17.09 (choice2fnsingleton) =>
% 130.11/17.09 ((
% 130.11/17.09 (setOfPairsIsBReln1) =>
% 130.11/17.09 ((
% 130.11/17.09 (breln1all1) =>
% 130.11/17.09 ((
% 130.11/17.09 (subbreln1) =>
% 130.11/17.09 ((
% 130.11/17.09 (eqbreln1) =>
% 130.11/17.09 ((
% 130.11/17.09 (breln1invprop) =>
% 130.11/17.09 ((
% 130.11/17.09 (breln1invI) =>
% 130.11/17.09 ((
% 130.11/17.09 (breln1invE) =>
% 130.11/17.09 ((
% 130.11/17.09 (breln1compprop) =>
% 130.11/17.09 ((
% 130.11/17.09 (breln1compI) =>
% 130.11/17.09 ((
% 130.11/17.09 (breln1compE) =>
% 130.11/17.09 ((
% 130.11/17.09 (breln1compEex) =>
% 130.11/17.09 ((
% 130.11/17.09 (!!) @ (
% 130.11/17.09 (('#B') @ (
% 130.11/17.09 !!) @
% 130.11/17.09 (
% 130.11/17.09 (
% 130.11/17.09 ('#S') @ (
% 130.11/17.09 (
% 130.11/17.09 ('#B') @ (
% 130.11/17.09 '#S') @
% 130.11/17.09 (
% 130.11/17.09 (
% 130.11/17.09 ('#B') @ (
% 130.11/17.09 (
% 130.11/17.09 ('#B') @ (
% 130.11/17.09 =>))) @
% 130.11/17.09 breln1)))) @
% 130.11/17.09 (
% 130.11/17.09 (
% 130.11/17.09 ('#B') @ (
% 130.11/17.09 (
% 130.11/17.09 ('#B') @ (
% 130.11/17.09 !!))) @
% 130.11/17.09 (
% 130.11/17.09 (
% 130.11/17.09 ('#S') @ (
% 130.11/17.09 (
% 130.11/17.09 ('#B') @ (
% 130.11/17.09 '#B') @
% 130.11/17.09 (
% 130.11/17.09 (
% 130.11/17.09 ('#B') @ (
% 130.11/17.09 '#S') @
% 130.11/17.09 (
% 130.11/17.09 (
% 130.11/17.09 ('#B') @ (
% 130.11/17.09 (
% 130.11/17.09 ('#B') @ (
% 130.11/17.09 =>))) @
% 130.11/17.09 breln1)))))) @
% 130.11/17.09 (
% 130.11/17.09 (
% 130.11/17.09 ('#C') @ (
% 130.11/17.09 (
% 130.11/17.09 ('#B') @ (
% 130.11/17.09 '#B') @
% 130.11/17.09 (
% 130.11/17.09 (
% 130.11/17.09 ('#B') @ (
% 130.11/17.09 '#B') @
% 130.11/17.09 breln1)))) @
% 130.11/17.09 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1473])).
% 130.11/17.09 thf(zip_derived_cl1488, plain,
% 130.11/17.09 (~ (((ubforcartprodlem3) =>
% 130.11/17.09 (((cartprodpairin) =>
% 130.11/17.09 (((cartprodmempair1) =>
% 130.11/17.09 (((cartprodmempair) =>
% 130.11/17.09 (((setunionE2) =>
% 130.11/17.09 (((setunionsingleton1) =>
% 130.11/17.09 (((setunionsingleton2) =>
% 130.11/17.09 (((setunionsingleton) =>
% 130.11/17.09 (((singletonprop) =>
% 130.11/17.09 (((ex1E1) =>
% 130.11/17.09 (((ex1I) =>
% 130.11/17.09 (((ex1I2) =>
% 130.11/17.09 (((singletonsuniq) =>
% 130.11/17.09 (((setukpairinjL1) =>
% 130.11/17.09 (((kfstsingleton) =>
% 130.11/17.09 (((theprop) =>
% 130.11/17.09 (((kfstpairEq) =>
% 130.11/17.09 (((cartprodfstin) =>
% 130.11/17.09 (((setukpairinjL2) =>
% 130.11/17.09 (((setukpairinjL) =>
% 130.11/17.09 (((setukpairinjR11) =>
% 130.11/17.09 (((setukpairinjR12) =>
% 130.11/17.09 (((setukpairinjR1) =>
% 130.11/17.09 (((upairequniteq) =>
% 130.11/17.09 (((setukpairinjR2) =>
% 130.11/17.09 (((setukpairinjR) =>
% 130.11/17.09 (((ksndsingleton) =>
% 130.11/17.09 (((ksndpairEq) =>
% 130.11/17.09 (((kpairsurjEq) =>
% 130.11/17.09 (((cartprodsndin) =>
% 130.11/17.09 ((
% 130.11/17.09 (cartprodpairmemEL) =>
% 130.11/17.09 ((
% 130.11/17.09 (cartprodpairmemER) =>
% 130.11/17.09 ((
% 130.11/17.09 (cartprodmempaircEq) =>
% 130.11/17.09 ((
% 130.11/17.09 (cartprodfstpairEq) =>
% 130.11/17.09 ((
% 130.11/17.09 (cartprodsndpairEq) =>
% 130.11/17.09 ((
% 130.11/17.09 (cartprodpairsurjEq) =>
% 130.11/17.09 ((
% 130.11/17.09 (dpsetconstrI) =>
% 130.11/17.09 ((
% 130.11/17.09 (dpsetconstrSub) =>
% 130.11/17.09 ((
% 130.11/17.09 (setOfPairsIsBReln) =>
% 130.11/17.09 ((
% 130.11/17.09 (dpsetconstrERa) =>
% 130.11/17.09 ((
% 130.11/17.09 (dpsetconstrEL1) =>
% 130.11/17.09 ((
% 130.11/17.09 (dpsetconstrEL2) =>
% 130.11/17.09 ((
% 130.11/17.09 (dpsetconstrER) =>
% 130.11/17.09 ((
% 130.11/17.09 (funcImageSingleton) =>
% 130.11/17.09 ((
% 130.11/17.09 (apProp) =>
% 130.11/17.09 ((
% 130.11/17.09 (app) =>
% 130.11/17.09 ((
% 130.11/17.09 (infuncsetfunc) =>
% 130.11/17.09 ((
% 130.11/17.09 (ap2p) =>
% 130.11/17.09 ((
% 130.11/17.09 (funcinfuncset) =>
% 130.11/17.09 ((
% 130.11/17.09 (lamProp) =>
% 130.11/17.09 ((
% 130.11/17.09 (lamp) =>
% 130.11/17.09 ((
% 130.11/17.09 (lam2p) =>
% 130.11/17.09 ((
% 130.11/17.09 (brelnall1) =>
% 130.11/17.09 ((
% 130.11/17.09 (brelnall2) =>
% 130.11/17.09 ((
% 130.11/17.09 (ex1E2) =>
% 130.11/17.09 ((
% 130.11/17.09 (funcGraphProp1) =>
% 130.11/17.09 ((
% 130.11/17.09 (funcGraphProp3) =>
% 130.11/17.09 ((
% 130.11/17.09 (funcGraphProp2) =>
% 130.11/17.09 ((
% 130.11/17.09 (funcextLem) =>
% 130.11/17.09 ((
% 130.11/17.09 (funcGraphProp4) =>
% 130.11/17.09 ((
% 130.11/17.09 (subbreln) =>
% 130.11/17.09 ((
% 130.11/17.09 (eqbreln) =>
% 130.11/17.09 ((
% 130.11/17.09 (funcext) =>
% 130.11/17.09 ((
% 130.11/17.09 (funcext2) =>
% 130.11/17.09 ((
% 130.11/17.09 (ap2apEq1) =>
% 130.11/17.09 ((
% 130.11/17.09 (ap2apEq2) =>
% 130.11/17.09 ((
% 130.11/17.09 (beta1) =>
% 130.11/17.09 ((
% 130.11/17.09 (eta1) =>
% 130.11/17.09 ((
% 130.11/17.09 (lam2lamEq) =>
% 130.11/17.09 ((
% 130.11/17.09 (beta2) =>
% 130.11/17.09 ((
% 130.11/17.09 (eta2) =>
% 130.11/17.09 ((
% 130.11/17.09 (iffalseProp1) =>
% 130.11/17.09 ((
% 130.11/17.09 (iffalseProp2) =>
% 130.11/17.09 ((
% 130.11/17.09 (iftrueProp1) =>
% 130.11/17.09 ((
% 130.11/17.09 (iftrueProp2) =>
% 130.11/17.09 ((
% 130.11/17.09 (ifSingleton) =>
% 130.11/17.09 ((
% 130.11/17.09 (ifp) =>
% 130.11/17.09 ((
% 130.11/17.09 (theeq) =>
% 130.11/17.09 ((
% 130.11/17.09 (iftrue) =>
% 130.11/17.09 ((
% 130.11/17.09 (iffalse) =>
% 130.11/17.09 ((
% 130.11/17.09 (iftrueorfalse) =>
% 130.11/17.09 ((
% 130.11/17.09 (binintersectT_lem) =>
% 130.11/17.09 ((
% 130.11/17.09 (binunionT_lem) =>
% 130.11/17.09 ((
% 130.11/17.09 (powersetT_lem) =>
% 130.11/17.09 ((
% 130.11/17.09 (setminusT_lem) =>
% 130.11/17.09 ((
% 130.11/17.09 (complementT_lem) =>
% 130.11/17.09 ((
% 130.11/17.09 (setextT) =>
% 130.11/17.09 ((
% 130.11/17.09 (subsetTI) =>
% 130.11/17.09 ((
% 130.11/17.09 (powersetTI1) =>
% 130.11/17.09 ((
% 130.11/17.09 (powersetTE1) =>
% 130.11/17.09 ((
% 130.11/17.09 (complementTI1) =>
% 130.11/17.09 ((
% 130.11/17.09 (complementTE1) =>
% 130.11/17.09 ((
% 130.11/17.09 (binintersectTELcontra) =>
% 130.11/17.09 ((
% 130.11/17.09 (binintersectTERcontra) =>
% 130.11/17.09 ((
% 130.11/17.09 (contrasubsetT) =>
% 130.11/17.09 ((
% 130.11/17.09 (contrasubsetT1) =>
% 130.11/17.09 ((
% 130.11/17.09 (contrasubsetT2) =>
% 130.11/17.09 ((
% 130.11/17.09 (contrasubsetT3) =>
% 130.11/17.09 ((
% 130.11/17.09 (doubleComplementI1) =>
% 130.11/17.09 ((
% 130.11/17.09 (doubleComplementE1) =>
% 130.11/17.09 ((
% 130.11/17.09 (doubleComplementSub1) =>
% 130.11/17.09 ((
% 130.11/17.09 (doubleComplementSub2) =>
% 130.11/17.09 ((
% 130.11/17.09 (doubleComplementEq) =>
% 130.11/17.09 ((
% 130.11/17.09 (complementTnotintersectT) =>
% 130.11/17.09 ((
% 130.11/17.09 (complementImpComplementIntersect) =>
% 130.11/17.09 ((
% 130.11/17.09 (complementSubsetComplementIntersect) =>
% 130.11/17.09 ((
% 130.11/17.09 (complementInPowersetComplementIntersect) =>
% 130.11/17.09 ((
% 130.11/17.09 (contraSubsetComplement) =>
% 130.11/17.09 ((
% 130.11/17.09 (complementTcontraSubset) =>
% 130.11/17.09 ((
% 130.11/17.09 (binunionTILcontra) =>
% 130.11/17.09 ((
% 130.11/17.09 (binunionTIRcontra) =>
% 130.11/17.09 ((
% 130.11/17.09 (inIntersectImpInUnion) =>
% 130.11/17.09 ((
% 130.11/17.09 (inIntersectImpInUnion2) =>
% 130.11/17.09 ((
% 130.11/17.09 (inIntersectImpInIntersectUnions) =>
% 130.11/17.09 ((
% 130.11/17.09 (intersectInPowersetIntersectUnions) =>
% 130.11/17.09 ((
% 130.11/17.09 (inComplementUnionImpNotIn1) =>
% 130.11/17.09 ((
% 130.11/17.09 (inComplementUnionImpInComplement1) =>
% 130.11/17.09 ((
% 130.11/17.09 (binunionTE) =>
% 130.11/17.09 ((
% 130.11/17.09 (binunionTEcontra) =>
% 130.11/17.09 ((
% 130.11/17.09 (demorgan2a1) =>
% 130.11/17.09 ((
% 130.11/17.09 (complementUnionInPowersetComplement) =>
% 130.11/17.09 ((
% 130.11/17.09 (demorgan2a2) =>
% 130.11/17.09 ((
% 130.11/17.09 (demorgan1a) =>
% 130.11/17.09 ((
% 130.11/17.09 (demorgan1b) =>
% 130.11/17.09 ((
% 130.11/17.09 (demorgan1) =>
% 130.11/17.09 ((
% 130.11/17.09 (demorgan2a) =>
% 130.11/17.09 ((
% 130.11/17.09 (demorgan2b2) =>
% 130.11/17.09 ((
% 130.11/17.09 (demorgan2b) =>
% 130.11/17.09 ((
% 130.11/17.09 (demorgan2) =>
% 130.11/17.09 ((
% 130.11/17.09 (woz13rule0) =>
% 130.11/17.09 ((
% 130.11/17.09 (woz13rule1) =>
% 130.11/17.09 ((
% 130.11/17.09 (woz13rule2) =>
% 130.11/17.09 ((
% 130.11/17.09 (woz13rule3) =>
% 130.11/17.09 ((
% 130.11/17.09 (woz13rule4) =>
% 130.11/17.09 ((
% 130.11/17.09 (woz1_1) =>
% 130.11/17.09 ((
% 130.11/17.09 (woz1_2) =>
% 130.11/17.09 ((
% 130.11/17.09 (woz1_3) =>
% 130.11/17.09 ((
% 130.11/17.09 (woz1_4) =>
% 130.11/17.09 ((
% 130.11/17.09 (woz1_5) =>
% 130.11/17.09 ((
% 130.11/17.09 (breln1all2) =>
% 130.11/17.09 ((
% 130.11/17.09 (breln1SetBreln1) =>
% 130.11/17.09 ((
% 130.11/17.09 (choice2fnsingleton) =>
% 130.11/17.09 ((
% 130.11/17.09 (setOfPairsIsBReln1) =>
% 130.11/17.09 ((
% 130.11/17.09 (breln1all1) =>
% 130.11/17.09 ((
% 130.11/17.09 (subbreln1) =>
% 130.11/17.09 ((
% 130.11/17.09 (eqbreln1) =>
% 130.11/17.09 ((
% 130.11/17.09 (breln1invprop) =>
% 130.11/17.09 ((
% 130.11/17.09 (breln1invI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compEex) =>
% 130.11/17.10 ((
% 130.11/17.10 (!!) @ (
% 130.11/17.10 (('#B') @ (
% 130.11/17.10 !!) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 !!))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#C') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1480])).
% 130.11/17.10 thf(zip_derived_cl1496, plain,
% 130.11/17.10 (~ (((cartprodpairin) =>
% 130.11/17.10 (((cartprodmempair1) =>
% 130.11/17.10 (((cartprodmempair) =>
% 130.11/17.10 (((setunionE2) =>
% 130.11/17.10 (((setunionsingleton1) =>
% 130.11/17.10 (((setunionsingleton2) =>
% 130.11/17.10 (((setunionsingleton) =>
% 130.11/17.10 (((singletonprop) =>
% 130.11/17.10 (((ex1E1) =>
% 130.11/17.10 (((ex1I) =>
% 130.11/17.10 (((ex1I2) =>
% 130.11/17.10 (((singletonsuniq) =>
% 130.11/17.10 (((setukpairinjL1) =>
% 130.11/17.10 (((kfstsingleton) =>
% 130.11/17.10 (((theprop) =>
% 130.11/17.10 (((kfstpairEq) =>
% 130.11/17.10 (((cartprodfstin) =>
% 130.11/17.10 (((setukpairinjL2) =>
% 130.11/17.10 (((setukpairinjL) =>
% 130.11/17.10 (((setukpairinjR11) =>
% 130.11/17.10 (((setukpairinjR12) =>
% 130.11/17.10 (((setukpairinjR1) =>
% 130.11/17.10 (((upairequniteq) =>
% 130.11/17.10 (((setukpairinjR2) =>
% 130.11/17.10 (((setukpairinjR) =>
% 130.11/17.10 (((ksndsingleton) =>
% 130.11/17.10 (((ksndpairEq) =>
% 130.11/17.10 (((kpairsurjEq) =>
% 130.11/17.10 (((cartprodsndin) =>
% 130.11/17.10 (((cartprodpairmemEL) =>
% 130.11/17.10 ((
% 130.11/17.10 (cartprodpairmemER) =>
% 130.11/17.10 ((
% 130.11/17.10 (cartprodmempaircEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (cartprodfstpairEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (cartprodsndpairEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (cartprodpairsurjEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrI) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrSub) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrERa) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL1) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL2) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrER) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcImageSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (apProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (app) =>
% 130.11/17.10 ((
% 130.11/17.10 (infuncsetfunc) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcinfuncset) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall1) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ex1E2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp3) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcextLem) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp4) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq1) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq2) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2lamEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifp) =>
% 130.11/17.10 ((
% 130.11/17.10 (theeq) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrue) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueorfalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setminusT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setextT) =>
% 130.11/17.10 ((
% 130.11/17.10 (subsetTI) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTELcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTERcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT1) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT2) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT3) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub2) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTnotintersectT) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementImpComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementSubsetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementInPowersetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (contraSubsetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTcontraSubset) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTILcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTIRcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion2) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (intersectInPowersetIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpNotIn1) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpInComplement1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTE) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTEcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementUnionInPowersetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule0) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_5) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all2) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1SetBreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (choice2fnsingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all1) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compEex) =>
% 130.11/17.10 ((
% 130.11/17.10 (!!) @ (
% 130.11/17.10 (('#B') @ (
% 130.11/17.10 !!) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 !!))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#C') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1488])).
% 130.11/17.10 thf(zip_derived_cl1505, plain,
% 130.11/17.10 (~ (((cartprodmempair1) =>
% 130.11/17.10 (((cartprodmempair) =>
% 130.11/17.10 (((setunionE2) =>
% 130.11/17.10 (((setunionsingleton1) =>
% 130.11/17.10 (((setunionsingleton2) =>
% 130.11/17.10 (((setunionsingleton) =>
% 130.11/17.10 (((singletonprop) =>
% 130.11/17.10 (((ex1E1) =>
% 130.11/17.10 (((ex1I) =>
% 130.11/17.10 (((ex1I2) =>
% 130.11/17.10 (((singletonsuniq) =>
% 130.11/17.10 (((setukpairinjL1) =>
% 130.11/17.10 (((kfstsingleton) =>
% 130.11/17.10 (((theprop) =>
% 130.11/17.10 (((kfstpairEq) =>
% 130.11/17.10 (((cartprodfstin) =>
% 130.11/17.10 (((setukpairinjL2) =>
% 130.11/17.10 (((setukpairinjL) =>
% 130.11/17.10 (((setukpairinjR11) =>
% 130.11/17.10 (((setukpairinjR12) =>
% 130.11/17.10 (((setukpairinjR1) =>
% 130.11/17.10 (((upairequniteq) =>
% 130.11/17.10 (((setukpairinjR2) =>
% 130.11/17.10 (((setukpairinjR) =>
% 130.11/17.10 (((ksndsingleton) =>
% 130.11/17.10 (((ksndpairEq) =>
% 130.11/17.10 (((kpairsurjEq) =>
% 130.11/17.10 (((cartprodsndin) =>
% 130.11/17.10 (((cartprodpairmemEL) =>
% 130.11/17.10 (((cartprodpairmemER) =>
% 130.11/17.10 ((
% 130.11/17.10 (cartprodmempaircEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (cartprodfstpairEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (cartprodsndpairEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (cartprodpairsurjEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrI) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrSub) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrERa) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL1) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL2) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrER) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcImageSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (apProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (app) =>
% 130.11/17.10 ((
% 130.11/17.10 (infuncsetfunc) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcinfuncset) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall1) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ex1E2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp3) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcextLem) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp4) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq1) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq2) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2lamEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifp) =>
% 130.11/17.10 ((
% 130.11/17.10 (theeq) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrue) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueorfalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setminusT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setextT) =>
% 130.11/17.10 ((
% 130.11/17.10 (subsetTI) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTELcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTERcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT1) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT2) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT3) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub2) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTnotintersectT) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementImpComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementSubsetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementInPowersetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (contraSubsetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTcontraSubset) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTILcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTIRcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion2) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (intersectInPowersetIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpNotIn1) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpInComplement1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTE) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTEcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementUnionInPowersetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule0) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_5) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all2) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1SetBreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (choice2fnsingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all1) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compEex) =>
% 130.11/17.10 ((
% 130.11/17.10 (!!) @ (
% 130.11/17.10 (('#B') @ (
% 130.11/17.10 !!) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 !!))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#C') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1496])).
% 130.11/17.10 thf(zip_derived_cl1515, plain,
% 130.11/17.10 (~ (((cartprodmempair) =>
% 130.11/17.10 (((setunionE2) =>
% 130.11/17.10 (((setunionsingleton1) =>
% 130.11/17.10 (((setunionsingleton2) =>
% 130.11/17.10 (((setunionsingleton) =>
% 130.11/17.10 (((singletonprop) =>
% 130.11/17.10 (((ex1E1) =>
% 130.11/17.10 (((ex1I) =>
% 130.11/17.10 (((ex1I2) =>
% 130.11/17.10 (((singletonsuniq) =>
% 130.11/17.10 (((setukpairinjL1) =>
% 130.11/17.10 (((kfstsingleton) =>
% 130.11/17.10 (((theprop) =>
% 130.11/17.10 (((kfstpairEq) =>
% 130.11/17.10 (((cartprodfstin) =>
% 130.11/17.10 (((setukpairinjL2) =>
% 130.11/17.10 (((setukpairinjL) =>
% 130.11/17.10 (((setukpairinjR11) =>
% 130.11/17.10 (((setukpairinjR12) =>
% 130.11/17.10 (((setukpairinjR1) =>
% 130.11/17.10 (((upairequniteq) =>
% 130.11/17.10 (((setukpairinjR2) =>
% 130.11/17.10 (((setukpairinjR) =>
% 130.11/17.10 (((ksndsingleton) =>
% 130.11/17.10 (((ksndpairEq) =>
% 130.11/17.10 (((kpairsurjEq) =>
% 130.11/17.10 (((cartprodsndin) =>
% 130.11/17.10 (((cartprodpairmemEL) =>
% 130.11/17.10 (((cartprodpairmemER) =>
% 130.11/17.10 (((cartprodmempaircEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (cartprodfstpairEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (cartprodsndpairEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (cartprodpairsurjEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrI) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrSub) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrERa) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL1) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL2) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrER) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcImageSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (apProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (app) =>
% 130.11/17.10 ((
% 130.11/17.10 (infuncsetfunc) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcinfuncset) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall1) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ex1E2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp3) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcextLem) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp4) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq1) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq2) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2lamEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifp) =>
% 130.11/17.10 ((
% 130.11/17.10 (theeq) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrue) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueorfalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setminusT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setextT) =>
% 130.11/17.10 ((
% 130.11/17.10 (subsetTI) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTELcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTERcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT1) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT2) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT3) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub2) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTnotintersectT) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementImpComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementSubsetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementInPowersetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (contraSubsetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTcontraSubset) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTILcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTIRcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion2) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (intersectInPowersetIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpNotIn1) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpInComplement1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTE) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTEcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementUnionInPowersetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule0) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_5) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all2) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1SetBreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (choice2fnsingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all1) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compEex) =>
% 130.11/17.10 ((
% 130.11/17.10 (!!) @ (
% 130.11/17.10 (('#B') @ (
% 130.11/17.10 !!) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 !!))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#C') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1505])).
% 130.11/17.10 thf(zip_derived_cl1525, plain,
% 130.11/17.10 (~ (((setunionE2) =>
% 130.11/17.10 (((setunionsingleton1) =>
% 130.11/17.10 (((setunionsingleton2) =>
% 130.11/17.10 (((setunionsingleton) =>
% 130.11/17.10 (((singletonprop) =>
% 130.11/17.10 (((ex1E1) =>
% 130.11/17.10 (((ex1I) =>
% 130.11/17.10 (((ex1I2) =>
% 130.11/17.10 (((singletonsuniq) =>
% 130.11/17.10 (((setukpairinjL1) =>
% 130.11/17.10 (((kfstsingleton) =>
% 130.11/17.10 (((theprop) =>
% 130.11/17.10 (((kfstpairEq) =>
% 130.11/17.10 (((cartprodfstin) =>
% 130.11/17.10 (((setukpairinjL2) =>
% 130.11/17.10 (((setukpairinjL) =>
% 130.11/17.10 (((setukpairinjR11) =>
% 130.11/17.10 (((setukpairinjR12) =>
% 130.11/17.10 (((setukpairinjR1) =>
% 130.11/17.10 (((upairequniteq) =>
% 130.11/17.10 (((setukpairinjR2) =>
% 130.11/17.10 (((setukpairinjR) =>
% 130.11/17.10 (((ksndsingleton) =>
% 130.11/17.10 (((ksndpairEq) =>
% 130.11/17.10 (((kpairsurjEq) =>
% 130.11/17.10 (((cartprodsndin) =>
% 130.11/17.10 (((cartprodpairmemEL) =>
% 130.11/17.10 (((cartprodpairmemER) =>
% 130.11/17.10 (((cartprodmempaircEq) =>
% 130.11/17.10 (((cartprodfstpairEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (cartprodsndpairEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (cartprodpairsurjEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrI) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrSub) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrERa) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL1) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL2) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrER) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcImageSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (apProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (app) =>
% 130.11/17.10 ((
% 130.11/17.10 (infuncsetfunc) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcinfuncset) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall1) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ex1E2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp3) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcextLem) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp4) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq1) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq2) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2lamEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifp) =>
% 130.11/17.10 ((
% 130.11/17.10 (theeq) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrue) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueorfalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setminusT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setextT) =>
% 130.11/17.10 ((
% 130.11/17.10 (subsetTI) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTELcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTERcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT1) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT2) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT3) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub2) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTnotintersectT) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementImpComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementSubsetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementInPowersetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (contraSubsetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTcontraSubset) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTILcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTIRcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion2) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (intersectInPowersetIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpNotIn1) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpInComplement1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTE) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTEcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementUnionInPowersetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule0) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_5) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all2) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1SetBreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (choice2fnsingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all1) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compEex) =>
% 130.11/17.10 ((
% 130.11/17.10 (!!) @ (
% 130.11/17.10 (('#B') @ (
% 130.11/17.10 !!) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 !!))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#C') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1515])).
% 130.11/17.10 thf(zip_derived_cl1535, plain,
% 130.11/17.10 (~ (((setunionsingleton1) =>
% 130.11/17.10 (((setunionsingleton2) =>
% 130.11/17.10 (((setunionsingleton) =>
% 130.11/17.10 (((singletonprop) =>
% 130.11/17.10 (((ex1E1) =>
% 130.11/17.10 (((ex1I) =>
% 130.11/17.10 (((ex1I2) =>
% 130.11/17.10 (((singletonsuniq) =>
% 130.11/17.10 (((setukpairinjL1) =>
% 130.11/17.10 (((kfstsingleton) =>
% 130.11/17.10 (((theprop) =>
% 130.11/17.10 (((kfstpairEq) =>
% 130.11/17.10 (((cartprodfstin) =>
% 130.11/17.10 (((setukpairinjL2) =>
% 130.11/17.10 (((setukpairinjL) =>
% 130.11/17.10 (((setukpairinjR11) =>
% 130.11/17.10 (((setukpairinjR12) =>
% 130.11/17.10 (((setukpairinjR1) =>
% 130.11/17.10 (((upairequniteq) =>
% 130.11/17.10 (((setukpairinjR2) =>
% 130.11/17.10 (((setukpairinjR) =>
% 130.11/17.10 (((ksndsingleton) =>
% 130.11/17.10 (((ksndpairEq) =>
% 130.11/17.10 (((kpairsurjEq) =>
% 130.11/17.10 (((cartprodsndin) =>
% 130.11/17.10 (((cartprodpairmemEL) =>
% 130.11/17.10 (((cartprodpairmemER) =>
% 130.11/17.10 (((cartprodmempaircEq) =>
% 130.11/17.10 (((cartprodfstpairEq) =>
% 130.11/17.10 (((cartprodsndpairEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (cartprodpairsurjEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrI) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrSub) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrERa) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL1) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL2) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrER) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcImageSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (apProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (app) =>
% 130.11/17.10 ((
% 130.11/17.10 (infuncsetfunc) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcinfuncset) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall1) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ex1E2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp3) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcextLem) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp4) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq1) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq2) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2lamEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifp) =>
% 130.11/17.10 ((
% 130.11/17.10 (theeq) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrue) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueorfalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setminusT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setextT) =>
% 130.11/17.10 ((
% 130.11/17.10 (subsetTI) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTELcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTERcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT1) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT2) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT3) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub2) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTnotintersectT) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementImpComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementSubsetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementInPowersetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (contraSubsetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTcontraSubset) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTILcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTIRcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion2) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (intersectInPowersetIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpNotIn1) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpInComplement1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTE) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTEcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementUnionInPowersetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule0) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_5) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all2) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1SetBreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (choice2fnsingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all1) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compEex) =>
% 130.11/17.10 ((
% 130.11/17.10 (!!) @ (
% 130.11/17.10 (('#B') @ (
% 130.11/17.10 !!) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 !!))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#C') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1525])).
% 130.11/17.10 thf(zip_derived_cl1545, plain,
% 130.11/17.10 (~ (((setunionsingleton2) =>
% 130.11/17.10 (((setunionsingleton) =>
% 130.11/17.10 (((singletonprop) =>
% 130.11/17.10 (((ex1E1) =>
% 130.11/17.10 (((ex1I) =>
% 130.11/17.10 (((ex1I2) =>
% 130.11/17.10 (((singletonsuniq) =>
% 130.11/17.10 (((setukpairinjL1) =>
% 130.11/17.10 (((kfstsingleton) =>
% 130.11/17.10 (((theprop) =>
% 130.11/17.10 (((kfstpairEq) =>
% 130.11/17.10 (((cartprodfstin) =>
% 130.11/17.10 (((setukpairinjL2) =>
% 130.11/17.10 (((setukpairinjL) =>
% 130.11/17.10 (((setukpairinjR11) =>
% 130.11/17.10 (((setukpairinjR12) =>
% 130.11/17.10 (((setukpairinjR1) =>
% 130.11/17.10 (((upairequniteq) =>
% 130.11/17.10 (((setukpairinjR2) =>
% 130.11/17.10 (((setukpairinjR) =>
% 130.11/17.10 (((ksndsingleton) =>
% 130.11/17.10 (((ksndpairEq) =>
% 130.11/17.10 (((kpairsurjEq) =>
% 130.11/17.10 (((cartprodsndin) =>
% 130.11/17.10 (((cartprodpairmemEL) =>
% 130.11/17.10 (((cartprodpairmemER) =>
% 130.11/17.10 (((cartprodmempaircEq) =>
% 130.11/17.10 (((cartprodfstpairEq) =>
% 130.11/17.10 (((cartprodsndpairEq) =>
% 130.11/17.10 (((cartprodpairsurjEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrI) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrSub) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrERa) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL1) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL2) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrER) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcImageSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (apProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (app) =>
% 130.11/17.10 ((
% 130.11/17.10 (infuncsetfunc) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcinfuncset) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall1) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ex1E2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp3) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcextLem) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp4) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq1) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq2) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2lamEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifp) =>
% 130.11/17.10 ((
% 130.11/17.10 (theeq) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrue) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueorfalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setminusT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setextT) =>
% 130.11/17.10 ((
% 130.11/17.10 (subsetTI) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTELcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTERcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT1) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT2) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT3) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub2) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTnotintersectT) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementImpComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementSubsetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementInPowersetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (contraSubsetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTcontraSubset) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTILcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTIRcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion2) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (intersectInPowersetIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpNotIn1) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpInComplement1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTE) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTEcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementUnionInPowersetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule0) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_5) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all2) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1SetBreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (choice2fnsingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all1) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compEex) =>
% 130.11/17.10 ((
% 130.11/17.10 (!!) @ (
% 130.11/17.10 (('#B') @ (
% 130.11/17.10 !!) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 !!))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#C') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1535])).
% 130.11/17.10 thf(zip_derived_cl1555, plain,
% 130.11/17.10 (~ (((setunionsingleton) =>
% 130.11/17.10 (((singletonprop) =>
% 130.11/17.10 (((ex1E1) =>
% 130.11/17.10 (((ex1I) =>
% 130.11/17.10 (((ex1I2) =>
% 130.11/17.10 (((singletonsuniq) =>
% 130.11/17.10 (((setukpairinjL1) =>
% 130.11/17.10 (((kfstsingleton) =>
% 130.11/17.10 (((theprop) =>
% 130.11/17.10 (((kfstpairEq) =>
% 130.11/17.10 (((cartprodfstin) =>
% 130.11/17.10 (((setukpairinjL2) =>
% 130.11/17.10 (((setukpairinjL) =>
% 130.11/17.10 (((setukpairinjR11) =>
% 130.11/17.10 (((setukpairinjR12) =>
% 130.11/17.10 (((setukpairinjR1) =>
% 130.11/17.10 (((upairequniteq) =>
% 130.11/17.10 (((setukpairinjR2) =>
% 130.11/17.10 (((setukpairinjR) =>
% 130.11/17.10 (((ksndsingleton) =>
% 130.11/17.10 (((ksndpairEq) =>
% 130.11/17.10 (((kpairsurjEq) =>
% 130.11/17.10 (((cartprodsndin) =>
% 130.11/17.10 (((cartprodpairmemEL) =>
% 130.11/17.10 (((cartprodpairmemER) =>
% 130.11/17.10 (((cartprodmempaircEq) =>
% 130.11/17.10 (((cartprodfstpairEq) =>
% 130.11/17.10 (((cartprodsndpairEq) =>
% 130.11/17.10 (((cartprodpairsurjEq) =>
% 130.11/17.10 (((dpsetconstrI) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrSub) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrERa) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL1) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL2) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrER) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcImageSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (apProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (app) =>
% 130.11/17.10 ((
% 130.11/17.10 (infuncsetfunc) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcinfuncset) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall1) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ex1E2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp3) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcextLem) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp4) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq1) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq2) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2lamEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifp) =>
% 130.11/17.10 ((
% 130.11/17.10 (theeq) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrue) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueorfalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setminusT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setextT) =>
% 130.11/17.10 ((
% 130.11/17.10 (subsetTI) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTELcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTERcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT1) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT2) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT3) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub2) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTnotintersectT) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementImpComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementSubsetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementInPowersetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (contraSubsetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTcontraSubset) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTILcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTIRcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion2) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (intersectInPowersetIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpNotIn1) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpInComplement1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTE) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTEcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementUnionInPowersetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule0) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_5) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all2) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1SetBreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (choice2fnsingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all1) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compEex) =>
% 130.11/17.10 ((
% 130.11/17.10 (!!) @ (
% 130.11/17.10 (('#B') @ (
% 130.11/17.10 !!) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 !!))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#C') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1545])).
% 130.11/17.10 thf(zip_derived_cl1565, plain,
% 130.11/17.10 (~ (((singletonprop) =>
% 130.11/17.10 (((ex1E1) =>
% 130.11/17.10 (((ex1I) =>
% 130.11/17.10 (((ex1I2) =>
% 130.11/17.10 (((singletonsuniq) =>
% 130.11/17.10 (((setukpairinjL1) =>
% 130.11/17.10 (((kfstsingleton) =>
% 130.11/17.10 (((theprop) =>
% 130.11/17.10 (((kfstpairEq) =>
% 130.11/17.10 (((cartprodfstin) =>
% 130.11/17.10 (((setukpairinjL2) =>
% 130.11/17.10 (((setukpairinjL) =>
% 130.11/17.10 (((setukpairinjR11) =>
% 130.11/17.10 (((setukpairinjR12) =>
% 130.11/17.10 (((setukpairinjR1) =>
% 130.11/17.10 (((upairequniteq) =>
% 130.11/17.10 (((setukpairinjR2) =>
% 130.11/17.10 (((setukpairinjR) =>
% 130.11/17.10 (((ksndsingleton) =>
% 130.11/17.10 (((ksndpairEq) =>
% 130.11/17.10 (((kpairsurjEq) =>
% 130.11/17.10 (((cartprodsndin) =>
% 130.11/17.10 (((cartprodpairmemEL) =>
% 130.11/17.10 (((cartprodpairmemER) =>
% 130.11/17.10 (((cartprodmempaircEq) =>
% 130.11/17.10 (((cartprodfstpairEq) =>
% 130.11/17.10 (((cartprodsndpairEq) =>
% 130.11/17.10 (((cartprodpairsurjEq) =>
% 130.11/17.10 (((dpsetconstrI) =>
% 130.11/17.10 (((dpsetconstrSub) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrERa) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL1) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL2) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrER) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcImageSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (apProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (app) =>
% 130.11/17.10 ((
% 130.11/17.10 (infuncsetfunc) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcinfuncset) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall1) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ex1E2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp3) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcextLem) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp4) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq1) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq2) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2lamEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifp) =>
% 130.11/17.10 ((
% 130.11/17.10 (theeq) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrue) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueorfalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setminusT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setextT) =>
% 130.11/17.10 ((
% 130.11/17.10 (subsetTI) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTELcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTERcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT1) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT2) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT3) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub2) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTnotintersectT) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementImpComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementSubsetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementInPowersetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (contraSubsetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTcontraSubset) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTILcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTIRcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion2) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (intersectInPowersetIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpNotIn1) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpInComplement1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTE) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTEcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementUnionInPowersetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule0) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_5) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all2) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1SetBreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (choice2fnsingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all1) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compEex) =>
% 130.11/17.10 ((
% 130.11/17.10 (!!) @ (
% 130.11/17.10 (('#B') @ (
% 130.11/17.10 !!) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 !!))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#C') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1555])).
% 130.11/17.10 thf(zip_derived_cl1574, plain,
% 130.11/17.10 (~ (((ex1E1) =>
% 130.11/17.10 (((ex1I) =>
% 130.11/17.10 (((ex1I2) =>
% 130.11/17.10 (((singletonsuniq) =>
% 130.11/17.10 (((setukpairinjL1) =>
% 130.11/17.10 (((kfstsingleton) =>
% 130.11/17.10 (((theprop) =>
% 130.11/17.10 (((kfstpairEq) =>
% 130.11/17.10 (((cartprodfstin) =>
% 130.11/17.10 (((setukpairinjL2) =>
% 130.11/17.10 (((setukpairinjL) =>
% 130.11/17.10 (((setukpairinjR11) =>
% 130.11/17.10 (((setukpairinjR12) =>
% 130.11/17.10 (((setukpairinjR1) =>
% 130.11/17.10 (((upairequniteq) =>
% 130.11/17.10 (((setukpairinjR2) =>
% 130.11/17.10 (((setukpairinjR) =>
% 130.11/17.10 (((ksndsingleton) =>
% 130.11/17.10 (((ksndpairEq) =>
% 130.11/17.10 (((kpairsurjEq) =>
% 130.11/17.10 (((cartprodsndin) =>
% 130.11/17.10 (((cartprodpairmemEL) =>
% 130.11/17.10 (((cartprodpairmemER) =>
% 130.11/17.10 (((cartprodmempaircEq) =>
% 130.11/17.10 (((cartprodfstpairEq) =>
% 130.11/17.10 (((cartprodsndpairEq) =>
% 130.11/17.10 (((cartprodpairsurjEq) =>
% 130.11/17.10 (((dpsetconstrI) =>
% 130.11/17.10 (((dpsetconstrSub) =>
% 130.11/17.10 (((setOfPairsIsBReln) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrERa) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL1) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL2) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrER) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcImageSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (apProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (app) =>
% 130.11/17.10 ((
% 130.11/17.10 (infuncsetfunc) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcinfuncset) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall1) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ex1E2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp3) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcextLem) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp4) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq1) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq2) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2lamEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifp) =>
% 130.11/17.10 ((
% 130.11/17.10 (theeq) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrue) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueorfalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setminusT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setextT) =>
% 130.11/17.10 ((
% 130.11/17.10 (subsetTI) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTELcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTERcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT1) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT2) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT3) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub2) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTnotintersectT) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementImpComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementSubsetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementInPowersetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (contraSubsetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTcontraSubset) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTILcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTIRcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion2) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (intersectInPowersetIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpNotIn1) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpInComplement1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTE) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTEcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementUnionInPowersetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule0) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_5) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all2) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1SetBreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (choice2fnsingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all1) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compEex) =>
% 130.11/17.10 ((
% 130.11/17.10 (!!) @ (
% 130.11/17.10 (('#B') @ (
% 130.11/17.10 !!) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 !!))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#C') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1565])).
% 130.11/17.10 thf(zip_derived_cl1582, plain,
% 130.11/17.10 (~ (((ex1I) =>
% 130.11/17.10 (((ex1I2) =>
% 130.11/17.10 (((singletonsuniq) =>
% 130.11/17.10 (((setukpairinjL1) =>
% 130.11/17.10 (((kfstsingleton) =>
% 130.11/17.10 (((theprop) =>
% 130.11/17.10 (((kfstpairEq) =>
% 130.11/17.10 (((cartprodfstin) =>
% 130.11/17.10 (((setukpairinjL2) =>
% 130.11/17.10 (((setukpairinjL) =>
% 130.11/17.10 (((setukpairinjR11) =>
% 130.11/17.10 (((setukpairinjR12) =>
% 130.11/17.10 (((setukpairinjR1) =>
% 130.11/17.10 (((upairequniteq) =>
% 130.11/17.10 (((setukpairinjR2) =>
% 130.11/17.10 (((setukpairinjR) =>
% 130.11/17.10 (((ksndsingleton) =>
% 130.11/17.10 (((ksndpairEq) =>
% 130.11/17.10 (((kpairsurjEq) =>
% 130.11/17.10 (((cartprodsndin) =>
% 130.11/17.10 (((cartprodpairmemEL) =>
% 130.11/17.10 (((cartprodpairmemER) =>
% 130.11/17.10 (((cartprodmempaircEq) =>
% 130.11/17.10 (((cartprodfstpairEq) =>
% 130.11/17.10 (((cartprodsndpairEq) =>
% 130.11/17.10 (((cartprodpairsurjEq) =>
% 130.11/17.10 (((dpsetconstrI) =>
% 130.11/17.10 (((dpsetconstrSub) =>
% 130.11/17.10 (((setOfPairsIsBReln) =>
% 130.11/17.10 (((dpsetconstrERa) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL1) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL2) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrER) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcImageSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (apProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (app) =>
% 130.11/17.10 ((
% 130.11/17.10 (infuncsetfunc) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcinfuncset) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall1) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ex1E2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp3) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcextLem) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp4) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq1) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq2) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2lamEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifp) =>
% 130.11/17.10 ((
% 130.11/17.10 (theeq) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrue) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueorfalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setminusT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setextT) =>
% 130.11/17.10 ((
% 130.11/17.10 (subsetTI) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTELcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTERcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT1) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT2) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT3) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub2) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTnotintersectT) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementImpComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementSubsetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementInPowersetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (contraSubsetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTcontraSubset) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTILcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTIRcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion2) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (intersectInPowersetIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpNotIn1) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpInComplement1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTE) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTEcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementUnionInPowersetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule0) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_5) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all2) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1SetBreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (choice2fnsingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all1) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compEex) =>
% 130.11/17.10 ((
% 130.11/17.10 (!!) @ (
% 130.11/17.10 (('#B') @ (
% 130.11/17.10 !!) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 !!))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#S') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 =>))) @
% 130.11/17.10 breln1)))))) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#C') @ (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#B') @ (
% 130.11/17.10 '#B') @
% 130.11/17.10 breln1)))) @
% 130.11/17.10 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1574])).
% 130.11/17.10 thf(zip_derived_cl1591, plain,
% 130.11/17.10 (~ (((ex1I2) =>
% 130.11/17.10 (((singletonsuniq) =>
% 130.11/17.10 (((setukpairinjL1) =>
% 130.11/17.10 (((kfstsingleton) =>
% 130.11/17.10 (((theprop) =>
% 130.11/17.10 (((kfstpairEq) =>
% 130.11/17.10 (((cartprodfstin) =>
% 130.11/17.10 (((setukpairinjL2) =>
% 130.11/17.10 (((setukpairinjL) =>
% 130.11/17.10 (((setukpairinjR11) =>
% 130.11/17.10 (((setukpairinjR12) =>
% 130.11/17.10 (((setukpairinjR1) =>
% 130.11/17.10 (((upairequniteq) =>
% 130.11/17.10 (((setukpairinjR2) =>
% 130.11/17.10 (((setukpairinjR) =>
% 130.11/17.10 (((ksndsingleton) =>
% 130.11/17.10 (((ksndpairEq) =>
% 130.11/17.10 (((kpairsurjEq) =>
% 130.11/17.10 (((cartprodsndin) =>
% 130.11/17.10 (((cartprodpairmemEL) =>
% 130.11/17.10 (((cartprodpairmemER) =>
% 130.11/17.10 (((cartprodmempaircEq) =>
% 130.11/17.10 (((cartprodfstpairEq) =>
% 130.11/17.10 (((cartprodsndpairEq) =>
% 130.11/17.10 (((cartprodpairsurjEq) =>
% 130.11/17.10 (((dpsetconstrI) =>
% 130.11/17.10 (((dpsetconstrSub) =>
% 130.11/17.10 (((setOfPairsIsBReln) =>
% 130.11/17.10 (((dpsetconstrERa) =>
% 130.11/17.10 (((dpsetconstrEL1) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrEL2) =>
% 130.11/17.10 ((
% 130.11/17.10 (dpsetconstrER) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcImageSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (apProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (app) =>
% 130.11/17.10 ((
% 130.11/17.10 (infuncsetfunc) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcinfuncset) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamProp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lamp) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2p) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall1) =>
% 130.11/17.10 ((
% 130.11/17.10 (brelnall2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ex1E2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp3) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcextLem) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcGraphProp4) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext) =>
% 130.11/17.10 ((
% 130.11/17.10 (funcext2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq1) =>
% 130.11/17.10 ((
% 130.11/17.10 (ap2apEq2) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta1) =>
% 130.11/17.10 ((
% 130.11/17.10 (lam2lamEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (beta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (eta2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalseProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp1) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueProp2) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifSingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (ifp) =>
% 130.11/17.10 ((
% 130.11/17.10 (theeq) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrue) =>
% 130.11/17.10 ((
% 130.11/17.10 (iffalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (iftrueorfalse) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setminusT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementT_lem) =>
% 130.11/17.10 ((
% 130.11/17.10 (setextT) =>
% 130.11/17.10 ((
% 130.11/17.10 (subsetTI) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (powersetTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTELcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binintersectTERcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT1) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT2) =>
% 130.11/17.10 ((
% 130.11/17.10 (contrasubsetT3) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementI1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementE1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub1) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementSub2) =>
% 130.11/17.10 ((
% 130.11/17.10 (doubleComplementEq) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTnotintersectT) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementImpComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementSubsetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementInPowersetComplementIntersect) =>
% 130.11/17.10 ((
% 130.11/17.10 (contraSubsetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementTcontraSubset) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTILcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTIRcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInUnion2) =>
% 130.11/17.10 ((
% 130.11/17.10 (inIntersectImpInIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (intersectInPowersetIntersectUnions) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpNotIn1) =>
% 130.11/17.10 ((
% 130.11/17.10 (inComplementUnionImpInComplement1) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTE) =>
% 130.11/17.10 ((
% 130.11/17.10 (binunionTEcontra) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a1) =>
% 130.11/17.10 ((
% 130.11/17.10 (complementUnionInPowersetComplement) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan1) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2a) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b2) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2b) =>
% 130.11/17.10 ((
% 130.11/17.10 (demorgan2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule0) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz13rule4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_1) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_2) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_3) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_4) =>
% 130.11/17.10 ((
% 130.11/17.10 (woz1_5) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all2) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1SetBreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (choice2fnsingleton) =>
% 130.11/17.10 ((
% 130.11/17.10 (setOfPairsIsBReln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1all1) =>
% 130.11/17.10 ((
% 130.11/17.10 (subbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (eqbreln1) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1invE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compprop) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compI) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compE) =>
% 130.11/17.10 ((
% 130.11/17.10 (breln1compEex) =>
% 130.11/17.10 ((
% 130.11/17.10 (!!) @ (
% 130.11/17.10 (('#B') @ (
% 130.11/17.10 !!) @
% 130.11/17.10 (
% 130.11/17.10 (
% 130.11/17.10 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 !!))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#C') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1582])).
% 130.11/17.11 thf(zip_derived_cl1599, plain,
% 130.11/17.11 (~ (((singletonsuniq) =>
% 130.11/17.11 (((setukpairinjL1) =>
% 130.11/17.11 (((kfstsingleton) =>
% 130.11/17.11 (((theprop) =>
% 130.11/17.11 (((kfstpairEq) =>
% 130.11/17.11 (((cartprodfstin) =>
% 130.11/17.11 (((setukpairinjL2) =>
% 130.11/17.11 (((setukpairinjL) =>
% 130.11/17.11 (((setukpairinjR11) =>
% 130.11/17.11 (((setukpairinjR12) =>
% 130.11/17.11 (((setukpairinjR1) =>
% 130.11/17.11 (((upairequniteq) =>
% 130.11/17.11 (((setukpairinjR2) =>
% 130.11/17.11 (((setukpairinjR) =>
% 130.11/17.11 (((ksndsingleton) =>
% 130.11/17.11 (((ksndpairEq) =>
% 130.11/17.11 (((kpairsurjEq) =>
% 130.11/17.11 (((cartprodsndin) =>
% 130.11/17.11 (((cartprodpairmemEL) =>
% 130.11/17.11 (((cartprodpairmemER) =>
% 130.11/17.11 (((cartprodmempaircEq) =>
% 130.11/17.11 (((cartprodfstpairEq) =>
% 130.11/17.11 (((cartprodsndpairEq) =>
% 130.11/17.11 (((cartprodpairsurjEq) =>
% 130.11/17.11 (((dpsetconstrI) =>
% 130.11/17.11 (((dpsetconstrSub) =>
% 130.11/17.11 (((setOfPairsIsBReln) =>
% 130.11/17.11 (((dpsetconstrERa) =>
% 130.11/17.11 (((dpsetconstrEL1) =>
% 130.11/17.11 (((dpsetconstrEL2) =>
% 130.11/17.11 ((
% 130.11/17.11 (dpsetconstrER) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcImageSingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (apProp) =>
% 130.11/17.11 ((
% 130.11/17.11 (app) =>
% 130.11/17.11 ((
% 130.11/17.11 (infuncsetfunc) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcinfuncset) =>
% 130.11/17.11 ((
% 130.11/17.11 (lamProp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lamp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall1) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ex1E2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp3) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcextLem) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp4) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq1) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq2) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2lamEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifSingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifp) =>
% 130.11/17.11 ((
% 130.11/17.11 (theeq) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrue) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueorfalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setminusT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setextT) =>
% 130.11/17.11 ((
% 130.11/17.11 (subsetTI) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTELcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTERcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT1) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT2) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT3) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub2) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTnotintersectT) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementImpComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementSubsetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementInPowersetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (contraSubsetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTcontraSubset) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTILcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTIRcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion2) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (intersectInPowersetIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpNotIn1) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpInComplement1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTE) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTEcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementUnionInPowersetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule0) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_5) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all2) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1SetBreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (choice2fnsingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (setOfPairsIsBReln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all1) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compEex) =>
% 130.11/17.11 ((
% 130.11/17.11 (!!) @ (
% 130.11/17.11 (('#B') @ (
% 130.11/17.11 !!) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 !!))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#C') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1591])).
% 130.11/17.11 thf(zip_derived_cl1607, plain,
% 130.11/17.11 (~ (((setukpairinjL1) =>
% 130.11/17.11 (((kfstsingleton) =>
% 130.11/17.11 (((theprop) =>
% 130.11/17.11 (((kfstpairEq) =>
% 130.11/17.11 (((cartprodfstin) =>
% 130.11/17.11 (((setukpairinjL2) =>
% 130.11/17.11 (((setukpairinjL) =>
% 130.11/17.11 (((setukpairinjR11) =>
% 130.11/17.11 (((setukpairinjR12) =>
% 130.11/17.11 (((setukpairinjR1) =>
% 130.11/17.11 (((upairequniteq) =>
% 130.11/17.11 (((setukpairinjR2) =>
% 130.11/17.11 (((setukpairinjR) =>
% 130.11/17.11 (((ksndsingleton) =>
% 130.11/17.11 (((ksndpairEq) =>
% 130.11/17.11 (((kpairsurjEq) =>
% 130.11/17.11 (((cartprodsndin) =>
% 130.11/17.11 (((cartprodpairmemEL) =>
% 130.11/17.11 (((cartprodpairmemER) =>
% 130.11/17.11 (((cartprodmempaircEq) =>
% 130.11/17.11 (((cartprodfstpairEq) =>
% 130.11/17.11 (((cartprodsndpairEq) =>
% 130.11/17.11 (((cartprodpairsurjEq) =>
% 130.11/17.11 (((dpsetconstrI) =>
% 130.11/17.11 (((dpsetconstrSub) =>
% 130.11/17.11 (((setOfPairsIsBReln) =>
% 130.11/17.11 (((dpsetconstrERa) =>
% 130.11/17.11 (((dpsetconstrEL1) =>
% 130.11/17.11 (((dpsetconstrEL2) =>
% 130.11/17.11 (((dpsetconstrER) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcImageSingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (apProp) =>
% 130.11/17.11 ((
% 130.11/17.11 (app) =>
% 130.11/17.11 ((
% 130.11/17.11 (infuncsetfunc) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcinfuncset) =>
% 130.11/17.11 ((
% 130.11/17.11 (lamProp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lamp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall1) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ex1E2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp3) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcextLem) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp4) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq1) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq2) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2lamEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifSingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifp) =>
% 130.11/17.11 ((
% 130.11/17.11 (theeq) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrue) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueorfalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setminusT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setextT) =>
% 130.11/17.11 ((
% 130.11/17.11 (subsetTI) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTELcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTERcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT1) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT2) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT3) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub2) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTnotintersectT) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementImpComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementSubsetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementInPowersetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (contraSubsetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTcontraSubset) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTILcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTIRcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion2) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (intersectInPowersetIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpNotIn1) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpInComplement1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTE) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTEcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementUnionInPowersetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule0) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_5) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all2) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1SetBreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (choice2fnsingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (setOfPairsIsBReln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all1) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compEex) =>
% 130.11/17.11 ((
% 130.11/17.11 (!!) @ (
% 130.11/17.11 (('#B') @ (
% 130.11/17.11 !!) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 !!))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#C') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1599])).
% 130.11/17.11 thf(zip_derived_cl1615, plain,
% 130.11/17.11 (~ (((kfstsingleton) =>
% 130.11/17.11 (((theprop) =>
% 130.11/17.11 (((kfstpairEq) =>
% 130.11/17.11 (((cartprodfstin) =>
% 130.11/17.11 (((setukpairinjL2) =>
% 130.11/17.11 (((setukpairinjL) =>
% 130.11/17.11 (((setukpairinjR11) =>
% 130.11/17.11 (((setukpairinjR12) =>
% 130.11/17.11 (((setukpairinjR1) =>
% 130.11/17.11 (((upairequniteq) =>
% 130.11/17.11 (((setukpairinjR2) =>
% 130.11/17.11 (((setukpairinjR) =>
% 130.11/17.11 (((ksndsingleton) =>
% 130.11/17.11 (((ksndpairEq) =>
% 130.11/17.11 (((kpairsurjEq) =>
% 130.11/17.11 (((cartprodsndin) =>
% 130.11/17.11 (((cartprodpairmemEL) =>
% 130.11/17.11 (((cartprodpairmemER) =>
% 130.11/17.11 (((cartprodmempaircEq) =>
% 130.11/17.11 (((cartprodfstpairEq) =>
% 130.11/17.11 (((cartprodsndpairEq) =>
% 130.11/17.11 (((cartprodpairsurjEq) =>
% 130.11/17.11 (((dpsetconstrI) =>
% 130.11/17.11 (((dpsetconstrSub) =>
% 130.11/17.11 (((setOfPairsIsBReln) =>
% 130.11/17.11 (((dpsetconstrERa) =>
% 130.11/17.11 (((dpsetconstrEL1) =>
% 130.11/17.11 (((dpsetconstrEL2) =>
% 130.11/17.11 (((dpsetconstrER) =>
% 130.11/17.11 (((funcImageSingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (apProp) =>
% 130.11/17.11 ((
% 130.11/17.11 (app) =>
% 130.11/17.11 ((
% 130.11/17.11 (infuncsetfunc) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcinfuncset) =>
% 130.11/17.11 ((
% 130.11/17.11 (lamProp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lamp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall1) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ex1E2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp3) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcextLem) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp4) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq1) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq2) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2lamEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifSingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifp) =>
% 130.11/17.11 ((
% 130.11/17.11 (theeq) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrue) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueorfalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setminusT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setextT) =>
% 130.11/17.11 ((
% 130.11/17.11 (subsetTI) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTELcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTERcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT1) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT2) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT3) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub2) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTnotintersectT) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementImpComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementSubsetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementInPowersetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (contraSubsetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTcontraSubset) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTILcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTIRcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion2) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (intersectInPowersetIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpNotIn1) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpInComplement1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTE) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTEcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementUnionInPowersetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule0) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_5) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all2) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1SetBreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (choice2fnsingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (setOfPairsIsBReln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all1) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compEex) =>
% 130.11/17.11 ((
% 130.11/17.11 (!!) @ (
% 130.11/17.11 (('#B') @ (
% 130.11/17.11 !!) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 !!))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#C') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1607])).
% 130.11/17.11 thf(zip_derived_cl1625, plain,
% 130.11/17.11 (~ (((theprop) =>
% 130.11/17.11 (((kfstpairEq) =>
% 130.11/17.11 (((cartprodfstin) =>
% 130.11/17.11 (((setukpairinjL2) =>
% 130.11/17.11 (((setukpairinjL) =>
% 130.11/17.11 (((setukpairinjR11) =>
% 130.11/17.11 (((setukpairinjR12) =>
% 130.11/17.11 (((setukpairinjR1) =>
% 130.11/17.11 (((upairequniteq) =>
% 130.11/17.11 (((setukpairinjR2) =>
% 130.11/17.11 (((setukpairinjR) =>
% 130.11/17.11 (((ksndsingleton) =>
% 130.11/17.11 (((ksndpairEq) =>
% 130.11/17.11 (((kpairsurjEq) =>
% 130.11/17.11 (((cartprodsndin) =>
% 130.11/17.11 (((cartprodpairmemEL) =>
% 130.11/17.11 (((cartprodpairmemER) =>
% 130.11/17.11 (((cartprodmempaircEq) =>
% 130.11/17.11 (((cartprodfstpairEq) =>
% 130.11/17.11 (((cartprodsndpairEq) =>
% 130.11/17.11 (((cartprodpairsurjEq) =>
% 130.11/17.11 (((dpsetconstrI) =>
% 130.11/17.11 (((dpsetconstrSub) =>
% 130.11/17.11 (((setOfPairsIsBReln) =>
% 130.11/17.11 (((dpsetconstrERa) =>
% 130.11/17.11 (((dpsetconstrEL1) =>
% 130.11/17.11 (((dpsetconstrEL2) =>
% 130.11/17.11 (((dpsetconstrER) =>
% 130.11/17.11 (((funcImageSingleton) =>
% 130.11/17.11 (((apProp) =>
% 130.11/17.11 ((
% 130.11/17.11 (app) =>
% 130.11/17.11 ((
% 130.11/17.11 (infuncsetfunc) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcinfuncset) =>
% 130.11/17.11 ((
% 130.11/17.11 (lamProp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lamp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall1) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ex1E2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp3) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcextLem) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp4) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq1) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq2) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2lamEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifSingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifp) =>
% 130.11/17.11 ((
% 130.11/17.11 (theeq) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrue) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueorfalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setminusT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setextT) =>
% 130.11/17.11 ((
% 130.11/17.11 (subsetTI) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTELcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTERcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT1) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT2) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT3) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub2) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTnotintersectT) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementImpComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementSubsetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementInPowersetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (contraSubsetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTcontraSubset) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTILcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTIRcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion2) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (intersectInPowersetIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpNotIn1) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpInComplement1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTE) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTEcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementUnionInPowersetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule0) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_5) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all2) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1SetBreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (choice2fnsingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (setOfPairsIsBReln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all1) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compEex) =>
% 130.11/17.11 ((
% 130.11/17.11 (!!) @ (
% 130.11/17.11 (('#B') @ (
% 130.11/17.11 !!) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 !!))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#C') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1615])).
% 130.11/17.11 thf(zip_derived_cl1637, plain,
% 130.11/17.11 (~ (((kfstpairEq) =>
% 130.11/17.11 (((cartprodfstin) =>
% 130.11/17.11 (((setukpairinjL2) =>
% 130.11/17.11 (((setukpairinjL) =>
% 130.11/17.11 (((setukpairinjR11) =>
% 130.11/17.11 (((setukpairinjR12) =>
% 130.11/17.11 (((setukpairinjR1) =>
% 130.11/17.11 (((upairequniteq) =>
% 130.11/17.11 (((setukpairinjR2) =>
% 130.11/17.11 (((setukpairinjR) =>
% 130.11/17.11 (((ksndsingleton) =>
% 130.11/17.11 (((ksndpairEq) =>
% 130.11/17.11 (((kpairsurjEq) =>
% 130.11/17.11 (((cartprodsndin) =>
% 130.11/17.11 (((cartprodpairmemEL) =>
% 130.11/17.11 (((cartprodpairmemER) =>
% 130.11/17.11 (((cartprodmempaircEq) =>
% 130.11/17.11 (((cartprodfstpairEq) =>
% 130.11/17.11 (((cartprodsndpairEq) =>
% 130.11/17.11 (((cartprodpairsurjEq) =>
% 130.11/17.11 (((dpsetconstrI) =>
% 130.11/17.11 (((dpsetconstrSub) =>
% 130.11/17.11 (((setOfPairsIsBReln) =>
% 130.11/17.11 (((dpsetconstrERa) =>
% 130.11/17.11 (((dpsetconstrEL1) =>
% 130.11/17.11 (((dpsetconstrEL2) =>
% 130.11/17.11 (((dpsetconstrER) =>
% 130.11/17.11 (((funcImageSingleton) =>
% 130.11/17.11 (((apProp) =>
% 130.11/17.11 (((app) =>
% 130.11/17.11 ((
% 130.11/17.11 (infuncsetfunc) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcinfuncset) =>
% 130.11/17.11 ((
% 130.11/17.11 (lamProp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lamp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall1) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ex1E2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp3) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcextLem) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp4) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq1) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq2) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2lamEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifSingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifp) =>
% 130.11/17.11 ((
% 130.11/17.11 (theeq) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrue) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueorfalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setminusT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setextT) =>
% 130.11/17.11 ((
% 130.11/17.11 (subsetTI) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTELcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTERcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT1) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT2) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT3) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub2) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTnotintersectT) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementImpComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementSubsetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementInPowersetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (contraSubsetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTcontraSubset) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTILcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTIRcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion2) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (intersectInPowersetIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpNotIn1) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpInComplement1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTE) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTEcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementUnionInPowersetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule0) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_5) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all2) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1SetBreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (choice2fnsingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (setOfPairsIsBReln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all1) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compEex) =>
% 130.11/17.11 ((
% 130.11/17.11 (!!) @ (
% 130.11/17.11 (('#B') @ (
% 130.11/17.11 !!) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 !!))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#C') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1625])).
% 130.11/17.11 thf(zip_derived_cl1649, plain,
% 130.11/17.11 (~ (((cartprodfstin) =>
% 130.11/17.11 (((setukpairinjL2) =>
% 130.11/17.11 (((setukpairinjL) =>
% 130.11/17.11 (((setukpairinjR11) =>
% 130.11/17.11 (((setukpairinjR12) =>
% 130.11/17.11 (((setukpairinjR1) =>
% 130.11/17.11 (((upairequniteq) =>
% 130.11/17.11 (((setukpairinjR2) =>
% 130.11/17.11 (((setukpairinjR) =>
% 130.11/17.11 (((ksndsingleton) =>
% 130.11/17.11 (((ksndpairEq) =>
% 130.11/17.11 (((kpairsurjEq) =>
% 130.11/17.11 (((cartprodsndin) =>
% 130.11/17.11 (((cartprodpairmemEL) =>
% 130.11/17.11 (((cartprodpairmemER) =>
% 130.11/17.11 (((cartprodmempaircEq) =>
% 130.11/17.11 (((cartprodfstpairEq) =>
% 130.11/17.11 (((cartprodsndpairEq) =>
% 130.11/17.11 (((cartprodpairsurjEq) =>
% 130.11/17.11 (((dpsetconstrI) =>
% 130.11/17.11 (((dpsetconstrSub) =>
% 130.11/17.11 (((setOfPairsIsBReln) =>
% 130.11/17.11 (((dpsetconstrERa) =>
% 130.11/17.11 (((dpsetconstrEL1) =>
% 130.11/17.11 (((dpsetconstrEL2) =>
% 130.11/17.11 (((dpsetconstrER) =>
% 130.11/17.11 (((funcImageSingleton) =>
% 130.11/17.11 (((apProp) =>
% 130.11/17.11 (((app) =>
% 130.11/17.11 (((infuncsetfunc) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcinfuncset) =>
% 130.11/17.11 ((
% 130.11/17.11 (lamProp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lamp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall1) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ex1E2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp3) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcextLem) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp4) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq1) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq2) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2lamEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifSingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifp) =>
% 130.11/17.11 ((
% 130.11/17.11 (theeq) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrue) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueorfalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setminusT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setextT) =>
% 130.11/17.11 ((
% 130.11/17.11 (subsetTI) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTELcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTERcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT1) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT2) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT3) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub2) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTnotintersectT) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementImpComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementSubsetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementInPowersetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (contraSubsetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTcontraSubset) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTILcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTIRcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion2) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (intersectInPowersetIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpNotIn1) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpInComplement1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTE) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTEcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementUnionInPowersetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule0) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_5) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all2) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1SetBreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (choice2fnsingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (setOfPairsIsBReln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all1) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compEex) =>
% 130.11/17.11 ((
% 130.11/17.11 (!!) @ (
% 130.11/17.11 (('#B') @ (
% 130.11/17.11 !!) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 !!))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#C') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1637])).
% 130.11/17.11 thf(zip_derived_cl1664, plain,
% 130.11/17.11 (~ (((setukpairinjL2) =>
% 130.11/17.11 (((setukpairinjL) =>
% 130.11/17.11 (((setukpairinjR11) =>
% 130.11/17.11 (((setukpairinjR12) =>
% 130.11/17.11 (((setukpairinjR1) =>
% 130.11/17.11 (((upairequniteq) =>
% 130.11/17.11 (((setukpairinjR2) =>
% 130.11/17.11 (((setukpairinjR) =>
% 130.11/17.11 (((ksndsingleton) =>
% 130.11/17.11 (((ksndpairEq) =>
% 130.11/17.11 (((kpairsurjEq) =>
% 130.11/17.11 (((cartprodsndin) =>
% 130.11/17.11 (((cartprodpairmemEL) =>
% 130.11/17.11 (((cartprodpairmemER) =>
% 130.11/17.11 (((cartprodmempaircEq) =>
% 130.11/17.11 (((cartprodfstpairEq) =>
% 130.11/17.11 (((cartprodsndpairEq) =>
% 130.11/17.11 (((cartprodpairsurjEq) =>
% 130.11/17.11 (((dpsetconstrI) =>
% 130.11/17.11 (((dpsetconstrSub) =>
% 130.11/17.11 (((setOfPairsIsBReln) =>
% 130.11/17.11 (((dpsetconstrERa) =>
% 130.11/17.11 (((dpsetconstrEL1) =>
% 130.11/17.11 (((dpsetconstrEL2) =>
% 130.11/17.11 (((dpsetconstrER) =>
% 130.11/17.11 (((funcImageSingleton) =>
% 130.11/17.11 (((apProp) =>
% 130.11/17.11 (((app) =>
% 130.11/17.11 (((infuncsetfunc) =>
% 130.11/17.11 (((ap2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcinfuncset) =>
% 130.11/17.11 ((
% 130.11/17.11 (lamProp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lamp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall1) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ex1E2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp3) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcextLem) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp4) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq1) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq2) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2lamEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifSingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifp) =>
% 130.11/17.11 ((
% 130.11/17.11 (theeq) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrue) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueorfalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setminusT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setextT) =>
% 130.11/17.11 ((
% 130.11/17.11 (subsetTI) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTELcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTERcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT1) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT2) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT3) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub2) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTnotintersectT) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementImpComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementSubsetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementInPowersetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (contraSubsetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTcontraSubset) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTILcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTIRcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion2) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (intersectInPowersetIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpNotIn1) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpInComplement1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTE) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTEcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementUnionInPowersetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule0) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_5) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all2) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1SetBreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (choice2fnsingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (setOfPairsIsBReln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all1) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compEex) =>
% 130.11/17.11 ((
% 130.11/17.11 (!!) @ (
% 130.11/17.11 (('#B') @ (
% 130.11/17.11 !!) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 !!))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#C') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1649])).
% 130.11/17.11 thf(zip_derived_cl1678, plain,
% 130.11/17.11 (~ (((setukpairinjL) =>
% 130.11/17.11 (((setukpairinjR11) =>
% 130.11/17.11 (((setukpairinjR12) =>
% 130.11/17.11 (((setukpairinjR1) =>
% 130.11/17.11 (((upairequniteq) =>
% 130.11/17.11 (((setukpairinjR2) =>
% 130.11/17.11 (((setukpairinjR) =>
% 130.11/17.11 (((ksndsingleton) =>
% 130.11/17.11 (((ksndpairEq) =>
% 130.11/17.11 (((kpairsurjEq) =>
% 130.11/17.11 (((cartprodsndin) =>
% 130.11/17.11 (((cartprodpairmemEL) =>
% 130.11/17.11 (((cartprodpairmemER) =>
% 130.11/17.11 (((cartprodmempaircEq) =>
% 130.11/17.11 (((cartprodfstpairEq) =>
% 130.11/17.11 (((cartprodsndpairEq) =>
% 130.11/17.11 (((cartprodpairsurjEq) =>
% 130.11/17.11 (((dpsetconstrI) =>
% 130.11/17.11 (((dpsetconstrSub) =>
% 130.11/17.11 (((setOfPairsIsBReln) =>
% 130.11/17.11 (((dpsetconstrERa) =>
% 130.11/17.11 (((dpsetconstrEL1) =>
% 130.11/17.11 (((dpsetconstrEL2) =>
% 130.11/17.11 (((dpsetconstrER) =>
% 130.11/17.11 (((funcImageSingleton) =>
% 130.11/17.11 (((apProp) =>
% 130.11/17.11 (((app) =>
% 130.11/17.11 (((infuncsetfunc) =>
% 130.11/17.11 (((ap2p) =>
% 130.11/17.11 (((funcinfuncset) =>
% 130.11/17.11 ((
% 130.11/17.11 (lamProp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lamp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall1) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ex1E2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp3) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcextLem) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp4) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq1) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq2) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2lamEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifSingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifp) =>
% 130.11/17.11 ((
% 130.11/17.11 (theeq) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrue) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueorfalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setminusT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setextT) =>
% 130.11/17.11 ((
% 130.11/17.11 (subsetTI) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTELcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTERcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT1) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT2) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT3) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub2) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTnotintersectT) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementImpComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementSubsetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementInPowersetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (contraSubsetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTcontraSubset) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTILcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTIRcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion2) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (intersectInPowersetIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpNotIn1) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpInComplement1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTE) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTEcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementUnionInPowersetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule0) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_5) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all2) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1SetBreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (choice2fnsingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (setOfPairsIsBReln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all1) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compEex) =>
% 130.11/17.11 ((
% 130.11/17.11 (!!) @ (
% 130.11/17.11 (('#B') @ (
% 130.11/17.11 !!) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 !!))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#C') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1664])).
% 130.11/17.11 thf(zip_derived_cl1695, plain,
% 130.11/17.11 (~ (((setukpairinjR11) =>
% 130.11/17.11 (((setukpairinjR12) =>
% 130.11/17.11 (((setukpairinjR1) =>
% 130.11/17.11 (((upairequniteq) =>
% 130.11/17.11 (((setukpairinjR2) =>
% 130.11/17.11 (((setukpairinjR) =>
% 130.11/17.11 (((ksndsingleton) =>
% 130.11/17.11 (((ksndpairEq) =>
% 130.11/17.11 (((kpairsurjEq) =>
% 130.11/17.11 (((cartprodsndin) =>
% 130.11/17.11 (((cartprodpairmemEL) =>
% 130.11/17.11 (((cartprodpairmemER) =>
% 130.11/17.11 (((cartprodmempaircEq) =>
% 130.11/17.11 (((cartprodfstpairEq) =>
% 130.11/17.11 (((cartprodsndpairEq) =>
% 130.11/17.11 (((cartprodpairsurjEq) =>
% 130.11/17.11 (((dpsetconstrI) =>
% 130.11/17.11 (((dpsetconstrSub) =>
% 130.11/17.11 (((setOfPairsIsBReln) =>
% 130.11/17.11 (((dpsetconstrERa) =>
% 130.11/17.11 (((dpsetconstrEL1) =>
% 130.11/17.11 (((dpsetconstrEL2) =>
% 130.11/17.11 (((dpsetconstrER) =>
% 130.11/17.11 (((funcImageSingleton) =>
% 130.11/17.11 (((apProp) =>
% 130.11/17.11 (((app) =>
% 130.11/17.11 (((infuncsetfunc) =>
% 130.11/17.11 (((ap2p) =>
% 130.11/17.11 (((funcinfuncset) =>
% 130.11/17.11 (((lamProp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lamp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall1) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ex1E2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp3) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcextLem) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp4) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq1) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq2) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2lamEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifSingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifp) =>
% 130.11/17.11 ((
% 130.11/17.11 (theeq) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrue) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueorfalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setminusT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setextT) =>
% 130.11/17.11 ((
% 130.11/17.11 (subsetTI) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTELcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTERcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT1) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT2) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT3) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub2) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTnotintersectT) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementImpComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementSubsetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementInPowersetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (contraSubsetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTcontraSubset) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTILcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTIRcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion2) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (intersectInPowersetIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpNotIn1) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpInComplement1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTE) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTEcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementUnionInPowersetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule0) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_5) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all2) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1SetBreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (choice2fnsingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (setOfPairsIsBReln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all1) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compEex) =>
% 130.11/17.11 ((
% 130.11/17.11 (!!) @ (
% 130.11/17.11 (('#B') @ (
% 130.11/17.11 !!) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 !!))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#C') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1678])).
% 130.11/17.11 thf(zip_derived_cl1711, plain,
% 130.11/17.11 (~ (((setukpairinjR12) =>
% 130.11/17.11 (((setukpairinjR1) =>
% 130.11/17.11 (((upairequniteq) =>
% 130.11/17.11 (((setukpairinjR2) =>
% 130.11/17.11 (((setukpairinjR) =>
% 130.11/17.11 (((ksndsingleton) =>
% 130.11/17.11 (((ksndpairEq) =>
% 130.11/17.11 (((kpairsurjEq) =>
% 130.11/17.11 (((cartprodsndin) =>
% 130.11/17.11 (((cartprodpairmemEL) =>
% 130.11/17.11 (((cartprodpairmemER) =>
% 130.11/17.11 (((cartprodmempaircEq) =>
% 130.11/17.11 (((cartprodfstpairEq) =>
% 130.11/17.11 (((cartprodsndpairEq) =>
% 130.11/17.11 (((cartprodpairsurjEq) =>
% 130.11/17.11 (((dpsetconstrI) =>
% 130.11/17.11 (((dpsetconstrSub) =>
% 130.11/17.11 (((setOfPairsIsBReln) =>
% 130.11/17.11 (((dpsetconstrERa) =>
% 130.11/17.11 (((dpsetconstrEL1) =>
% 130.11/17.11 (((dpsetconstrEL2) =>
% 130.11/17.11 (((dpsetconstrER) =>
% 130.11/17.11 (((funcImageSingleton) =>
% 130.11/17.11 (((apProp) =>
% 130.11/17.11 (((app) =>
% 130.11/17.11 (((infuncsetfunc) =>
% 130.11/17.11 (((ap2p) =>
% 130.11/17.11 (((funcinfuncset) =>
% 130.11/17.11 (((lamProp) =>
% 130.11/17.11 (((lamp) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall1) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ex1E2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp3) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcextLem) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp4) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq1) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq2) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2lamEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifSingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifp) =>
% 130.11/17.11 ((
% 130.11/17.11 (theeq) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrue) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueorfalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setminusT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setextT) =>
% 130.11/17.11 ((
% 130.11/17.11 (subsetTI) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTELcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTERcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT1) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT2) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT3) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub2) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTnotintersectT) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementImpComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementSubsetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementInPowersetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (contraSubsetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTcontraSubset) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTILcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTIRcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion2) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (intersectInPowersetIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpNotIn1) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpInComplement1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTE) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTEcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementUnionInPowersetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule0) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_5) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all2) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1SetBreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (choice2fnsingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (setOfPairsIsBReln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all1) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compEex) =>
% 130.11/17.11 ((
% 130.11/17.11 (!!) @ (
% 130.11/17.11 (('#B') @ (
% 130.11/17.11 !!) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 !!))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#C') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1695])).
% 130.11/17.11 thf(zip_derived_cl1725, plain,
% 130.11/17.11 (~ (((setukpairinjR1) =>
% 130.11/17.11 (((upairequniteq) =>
% 130.11/17.11 (((setukpairinjR2) =>
% 130.11/17.11 (((setukpairinjR) =>
% 130.11/17.11 (((ksndsingleton) =>
% 130.11/17.11 (((ksndpairEq) =>
% 130.11/17.11 (((kpairsurjEq) =>
% 130.11/17.11 (((cartprodsndin) =>
% 130.11/17.11 (((cartprodpairmemEL) =>
% 130.11/17.11 (((cartprodpairmemER) =>
% 130.11/17.11 (((cartprodmempaircEq) =>
% 130.11/17.11 (((cartprodfstpairEq) =>
% 130.11/17.11 (((cartprodsndpairEq) =>
% 130.11/17.11 (((cartprodpairsurjEq) =>
% 130.11/17.11 (((dpsetconstrI) =>
% 130.11/17.11 (((dpsetconstrSub) =>
% 130.11/17.11 (((setOfPairsIsBReln) =>
% 130.11/17.11 (((dpsetconstrERa) =>
% 130.11/17.11 (((dpsetconstrEL1) =>
% 130.11/17.11 (((dpsetconstrEL2) =>
% 130.11/17.11 (((dpsetconstrER) =>
% 130.11/17.11 (((funcImageSingleton) =>
% 130.11/17.11 (((apProp) =>
% 130.11/17.11 (((app) =>
% 130.11/17.11 (((infuncsetfunc) =>
% 130.11/17.11 (((ap2p) =>
% 130.11/17.11 (((funcinfuncset) =>
% 130.11/17.11 (((lamProp) =>
% 130.11/17.11 (((lamp) =>
% 130.11/17.11 (((lam2p) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall1) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ex1E2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp3) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcextLem) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp4) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq1) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq2) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2lamEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifSingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifp) =>
% 130.11/17.11 ((
% 130.11/17.11 (theeq) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrue) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueorfalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setminusT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setextT) =>
% 130.11/17.11 ((
% 130.11/17.11 (subsetTI) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTELcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTERcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT1) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT2) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT3) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub2) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTnotintersectT) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementImpComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementSubsetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementInPowersetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (contraSubsetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTcontraSubset) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTILcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTIRcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion2) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (intersectInPowersetIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpNotIn1) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpInComplement1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTE) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTEcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementUnionInPowersetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule0) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_5) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all2) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1SetBreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (choice2fnsingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (setOfPairsIsBReln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all1) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compEex) =>
% 130.11/17.11 ((
% 130.11/17.11 (!!) @ (
% 130.11/17.11 (('#B') @ (
% 130.11/17.11 !!) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 !!))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#S') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#S') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 =>))) @
% 130.11/17.11 breln1)))))) @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#C') @ (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 (
% 130.11/17.11 (
% 130.11/17.11 ('#B') @ (
% 130.11/17.11 '#B') @
% 130.11/17.11 breln1)))) @
% 130.11/17.11 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1711])).
% 130.11/17.11 thf(zip_derived_cl1738, plain,
% 130.11/17.11 (~ (((upairequniteq) =>
% 130.11/17.11 (((setukpairinjR2) =>
% 130.11/17.11 (((setukpairinjR) =>
% 130.11/17.11 (((ksndsingleton) =>
% 130.11/17.11 (((ksndpairEq) =>
% 130.11/17.11 (((kpairsurjEq) =>
% 130.11/17.11 (((cartprodsndin) =>
% 130.11/17.11 (((cartprodpairmemEL) =>
% 130.11/17.11 (((cartprodpairmemER) =>
% 130.11/17.11 (((cartprodmempaircEq) =>
% 130.11/17.11 (((cartprodfstpairEq) =>
% 130.11/17.11 (((cartprodsndpairEq) =>
% 130.11/17.11 (((cartprodpairsurjEq) =>
% 130.11/17.11 (((dpsetconstrI) =>
% 130.11/17.11 (((dpsetconstrSub) =>
% 130.11/17.11 (((setOfPairsIsBReln) =>
% 130.11/17.11 (((dpsetconstrERa) =>
% 130.11/17.11 (((dpsetconstrEL1) =>
% 130.11/17.11 (((dpsetconstrEL2) =>
% 130.11/17.11 (((dpsetconstrER) =>
% 130.11/17.11 (((funcImageSingleton) =>
% 130.11/17.11 (((apProp) =>
% 130.11/17.11 (((app) =>
% 130.11/17.11 (((infuncsetfunc) =>
% 130.11/17.11 (((ap2p) =>
% 130.11/17.11 (((funcinfuncset) =>
% 130.11/17.11 (((lamProp) =>
% 130.11/17.11 (((lamp) =>
% 130.11/17.11 (((lam2p) =>
% 130.11/17.11 (((brelnall1) =>
% 130.11/17.11 ((
% 130.11/17.11 (brelnall2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ex1E2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp3) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcextLem) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcGraphProp4) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext) =>
% 130.11/17.11 ((
% 130.11/17.11 (funcext2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq1) =>
% 130.11/17.11 ((
% 130.11/17.11 (ap2apEq2) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta1) =>
% 130.11/17.11 ((
% 130.11/17.11 (lam2lamEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (beta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (eta2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalseProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp1) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueProp2) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifSingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (ifp) =>
% 130.11/17.11 ((
% 130.11/17.11 (theeq) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrue) =>
% 130.11/17.11 ((
% 130.11/17.11 (iffalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (iftrueorfalse) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setminusT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementT_lem) =>
% 130.11/17.11 ((
% 130.11/17.11 (setextT) =>
% 130.11/17.11 ((
% 130.11/17.11 (subsetTI) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (powersetTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTELcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binintersectTERcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT1) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT2) =>
% 130.11/17.11 ((
% 130.11/17.11 (contrasubsetT3) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementI1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementE1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub1) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementSub2) =>
% 130.11/17.11 ((
% 130.11/17.11 (doubleComplementEq) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTnotintersectT) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementImpComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementSubsetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementInPowersetComplementIntersect) =>
% 130.11/17.11 ((
% 130.11/17.11 (contraSubsetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementTcontraSubset) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTILcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTIRcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInUnion2) =>
% 130.11/17.11 ((
% 130.11/17.11 (inIntersectImpInIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (intersectInPowersetIntersectUnions) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpNotIn1) =>
% 130.11/17.11 ((
% 130.11/17.11 (inComplementUnionImpInComplement1) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTE) =>
% 130.11/17.11 ((
% 130.11/17.11 (binunionTEcontra) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a1) =>
% 130.11/17.11 ((
% 130.11/17.11 (complementUnionInPowersetComplement) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan1) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2a) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b2) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2b) =>
% 130.11/17.11 ((
% 130.11/17.11 (demorgan2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule0) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz13rule4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_1) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_2) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_3) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_4) =>
% 130.11/17.11 ((
% 130.11/17.11 (woz1_5) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all2) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1SetBreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (choice2fnsingleton) =>
% 130.11/17.11 ((
% 130.11/17.11 (setOfPairsIsBReln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1all1) =>
% 130.11/17.11 ((
% 130.11/17.11 (subbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (eqbreln1) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1invE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compprop) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compI) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compE) =>
% 130.11/17.11 ((
% 130.11/17.11 (breln1compEex) =>
% 130.11/17.11 ((
% 130.11/17.11 (!!) @ (
% 130.11/17.12 (('#B') @ (
% 130.11/17.12 !!) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 !!))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#C') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1725])).
% 130.11/17.12 thf(zip_derived_cl1749, plain,
% 130.11/17.12 (~ (((setukpairinjR2) =>
% 130.11/17.12 (((setukpairinjR) =>
% 130.11/17.12 (((ksndsingleton) =>
% 130.11/17.12 (((ksndpairEq) =>
% 130.11/17.12 (((kpairsurjEq) =>
% 130.11/17.12 (((cartprodsndin) =>
% 130.11/17.12 (((cartprodpairmemEL) =>
% 130.11/17.12 (((cartprodpairmemER) =>
% 130.11/17.12 (((cartprodmempaircEq) =>
% 130.11/17.12 (((cartprodfstpairEq) =>
% 130.11/17.12 (((cartprodsndpairEq) =>
% 130.11/17.12 (((cartprodpairsurjEq) =>
% 130.11/17.12 (((dpsetconstrI) =>
% 130.11/17.12 (((dpsetconstrSub) =>
% 130.11/17.12 (((setOfPairsIsBReln) =>
% 130.11/17.12 (((dpsetconstrERa) =>
% 130.11/17.12 (((dpsetconstrEL1) =>
% 130.11/17.12 (((dpsetconstrEL2) =>
% 130.11/17.12 (((dpsetconstrER) =>
% 130.11/17.12 (((funcImageSingleton) =>
% 130.11/17.12 (((apProp) =>
% 130.11/17.12 (((app) =>
% 130.11/17.12 (((infuncsetfunc) =>
% 130.11/17.12 (((ap2p) =>
% 130.11/17.12 (((funcinfuncset) =>
% 130.11/17.12 (((lamProp) =>
% 130.11/17.12 (((lamp) =>
% 130.11/17.12 (((lam2p) =>
% 130.11/17.12 (((brelnall1) =>
% 130.11/17.12 (((brelnall2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ex1E2) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcGraphProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcGraphProp3) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcGraphProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcextLem) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcGraphProp4) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq1) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq2) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (lam2lamEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifSingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifp) =>
% 130.11/17.12 ((
% 130.11/17.12 (theeq) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrue) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueorfalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setminusT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setextT) =>
% 130.11/17.12 ((
% 130.11/17.12 (subsetTI) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTELcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTERcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT1) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT2) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT3) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub2) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTnotintersectT) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementImpComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementSubsetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementInPowersetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (contraSubsetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTcontraSubset) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTILcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTIRcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion2) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (intersectInPowersetIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpNotIn1) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpInComplement1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTE) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTEcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementUnionInPowersetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule0) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_5) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all2) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1SetBreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (choice2fnsingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (setOfPairsIsBReln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all1) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compEex) =>
% 130.11/17.12 ((
% 130.11/17.12 (!!) @ (
% 130.11/17.12 (('#B') @ (
% 130.11/17.12 !!) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 !!))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#C') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1738])).
% 130.11/17.12 thf(zip_derived_cl1760, plain,
% 130.11/17.12 (~ (((setukpairinjR) =>
% 130.11/17.12 (((ksndsingleton) =>
% 130.11/17.12 (((ksndpairEq) =>
% 130.11/17.12 (((kpairsurjEq) =>
% 130.11/17.12 (((cartprodsndin) =>
% 130.11/17.12 (((cartprodpairmemEL) =>
% 130.11/17.12 (((cartprodpairmemER) =>
% 130.11/17.12 (((cartprodmempaircEq) =>
% 130.11/17.12 (((cartprodfstpairEq) =>
% 130.11/17.12 (((cartprodsndpairEq) =>
% 130.11/17.12 (((cartprodpairsurjEq) =>
% 130.11/17.12 (((dpsetconstrI) =>
% 130.11/17.12 (((dpsetconstrSub) =>
% 130.11/17.12 (((setOfPairsIsBReln) =>
% 130.11/17.12 (((dpsetconstrERa) =>
% 130.11/17.12 (((dpsetconstrEL1) =>
% 130.11/17.12 (((dpsetconstrEL2) =>
% 130.11/17.12 (((dpsetconstrER) =>
% 130.11/17.12 (((funcImageSingleton) =>
% 130.11/17.12 (((apProp) =>
% 130.11/17.12 (((app) =>
% 130.11/17.12 (((infuncsetfunc) =>
% 130.11/17.12 (((ap2p) =>
% 130.11/17.12 (((funcinfuncset) =>
% 130.11/17.12 (((lamProp) =>
% 130.11/17.12 (((lamp) =>
% 130.11/17.12 (((lam2p) =>
% 130.11/17.12 (((brelnall1) =>
% 130.11/17.12 (((brelnall2) =>
% 130.11/17.12 (((ex1E2) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcGraphProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcGraphProp3) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcGraphProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcextLem) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcGraphProp4) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq1) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq2) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (lam2lamEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifSingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifp) =>
% 130.11/17.12 ((
% 130.11/17.12 (theeq) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrue) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueorfalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setminusT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setextT) =>
% 130.11/17.12 ((
% 130.11/17.12 (subsetTI) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTELcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTERcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT1) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT2) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT3) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub2) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTnotintersectT) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementImpComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementSubsetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementInPowersetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (contraSubsetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTcontraSubset) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTILcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTIRcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion2) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (intersectInPowersetIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpNotIn1) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpInComplement1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTE) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTEcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementUnionInPowersetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule0) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_5) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all2) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1SetBreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (choice2fnsingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (setOfPairsIsBReln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all1) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compEex) =>
% 130.11/17.12 ((
% 130.11/17.12 (!!) @ (
% 130.11/17.12 (('#B') @ (
% 130.11/17.12 !!) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 !!))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#C') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1749])).
% 130.11/17.12 thf(zip_derived_cl1770, plain,
% 130.11/17.12 (~ (((ksndsingleton) =>
% 130.11/17.12 (((ksndpairEq) =>
% 130.11/17.12 (((kpairsurjEq) =>
% 130.11/17.12 (((cartprodsndin) =>
% 130.11/17.12 (((cartprodpairmemEL) =>
% 130.11/17.12 (((cartprodpairmemER) =>
% 130.11/17.12 (((cartprodmempaircEq) =>
% 130.11/17.12 (((cartprodfstpairEq) =>
% 130.11/17.12 (((cartprodsndpairEq) =>
% 130.11/17.12 (((cartprodpairsurjEq) =>
% 130.11/17.12 (((dpsetconstrI) =>
% 130.11/17.12 (((dpsetconstrSub) =>
% 130.11/17.12 (((setOfPairsIsBReln) =>
% 130.11/17.12 (((dpsetconstrERa) =>
% 130.11/17.12 (((dpsetconstrEL1) =>
% 130.11/17.12 (((dpsetconstrEL2) =>
% 130.11/17.12 (((dpsetconstrER) =>
% 130.11/17.12 (((funcImageSingleton) =>
% 130.11/17.12 (((apProp) =>
% 130.11/17.12 (((app) =>
% 130.11/17.12 (((infuncsetfunc) =>
% 130.11/17.12 (((ap2p) =>
% 130.11/17.12 (((funcinfuncset) =>
% 130.11/17.12 (((lamProp) =>
% 130.11/17.12 (((lamp) =>
% 130.11/17.12 (((lam2p) =>
% 130.11/17.12 (((brelnall1) =>
% 130.11/17.12 (((brelnall2) =>
% 130.11/17.12 (((ex1E2) =>
% 130.11/17.12 (((funcGraphProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcGraphProp3) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcGraphProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcextLem) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcGraphProp4) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq1) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq2) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (lam2lamEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifSingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifp) =>
% 130.11/17.12 ((
% 130.11/17.12 (theeq) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrue) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueorfalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setminusT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setextT) =>
% 130.11/17.12 ((
% 130.11/17.12 (subsetTI) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTELcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTERcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT1) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT2) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT3) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub2) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTnotintersectT) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementImpComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementSubsetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementInPowersetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (contraSubsetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTcontraSubset) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTILcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTIRcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion2) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (intersectInPowersetIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpNotIn1) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpInComplement1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTE) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTEcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementUnionInPowersetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule0) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_5) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all2) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1SetBreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (choice2fnsingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (setOfPairsIsBReln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all1) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compEex) =>
% 130.11/17.12 ((
% 130.11/17.12 (!!) @ (
% 130.11/17.12 (('#B') @ (
% 130.11/17.12 !!) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 !!))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#C') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1760])).
% 130.11/17.12 thf(zip_derived_cl1779, plain,
% 130.11/17.12 (~ (((ksndpairEq) =>
% 130.11/17.12 (((kpairsurjEq) =>
% 130.11/17.12 (((cartprodsndin) =>
% 130.11/17.12 (((cartprodpairmemEL) =>
% 130.11/17.12 (((cartprodpairmemER) =>
% 130.11/17.12 (((cartprodmempaircEq) =>
% 130.11/17.12 (((cartprodfstpairEq) =>
% 130.11/17.12 (((cartprodsndpairEq) =>
% 130.11/17.12 (((cartprodpairsurjEq) =>
% 130.11/17.12 (((dpsetconstrI) =>
% 130.11/17.12 (((dpsetconstrSub) =>
% 130.11/17.12 (((setOfPairsIsBReln) =>
% 130.11/17.12 (((dpsetconstrERa) =>
% 130.11/17.12 (((dpsetconstrEL1) =>
% 130.11/17.12 (((dpsetconstrEL2) =>
% 130.11/17.12 (((dpsetconstrER) =>
% 130.11/17.12 (((funcImageSingleton) =>
% 130.11/17.12 (((apProp) =>
% 130.11/17.12 (((app) =>
% 130.11/17.12 (((infuncsetfunc) =>
% 130.11/17.12 (((ap2p) =>
% 130.11/17.12 (((funcinfuncset) =>
% 130.11/17.12 (((lamProp) =>
% 130.11/17.12 (((lamp) =>
% 130.11/17.12 (((lam2p) =>
% 130.11/17.12 (((brelnall1) =>
% 130.11/17.12 (((brelnall2) =>
% 130.11/17.12 (((ex1E2) =>
% 130.11/17.12 (((funcGraphProp1) =>
% 130.11/17.12 (((funcGraphProp3) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcGraphProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcextLem) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcGraphProp4) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq1) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq2) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (lam2lamEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifSingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifp) =>
% 130.11/17.12 ((
% 130.11/17.12 (theeq) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrue) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueorfalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setminusT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setextT) =>
% 130.11/17.12 ((
% 130.11/17.12 (subsetTI) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTELcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTERcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT1) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT2) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT3) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub2) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTnotintersectT) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementImpComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementSubsetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementInPowersetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (contraSubsetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTcontraSubset) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTILcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTIRcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion2) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (intersectInPowersetIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpNotIn1) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpInComplement1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTE) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTEcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementUnionInPowersetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule0) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_5) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all2) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1SetBreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (choice2fnsingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (setOfPairsIsBReln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all1) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compEex) =>
% 130.11/17.12 ((
% 130.11/17.12 (!!) @ (
% 130.11/17.12 (('#B') @ (
% 130.11/17.12 !!) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 !!))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#C') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1770])).
% 130.11/17.12 thf(zip_derived_cl1787, plain,
% 130.11/17.12 (~ (((kpairsurjEq) =>
% 130.11/17.12 (((cartprodsndin) =>
% 130.11/17.12 (((cartprodpairmemEL) =>
% 130.11/17.12 (((cartprodpairmemER) =>
% 130.11/17.12 (((cartprodmempaircEq) =>
% 130.11/17.12 (((cartprodfstpairEq) =>
% 130.11/17.12 (((cartprodsndpairEq) =>
% 130.11/17.12 (((cartprodpairsurjEq) =>
% 130.11/17.12 (((dpsetconstrI) =>
% 130.11/17.12 (((dpsetconstrSub) =>
% 130.11/17.12 (((setOfPairsIsBReln) =>
% 130.11/17.12 (((dpsetconstrERa) =>
% 130.11/17.12 (((dpsetconstrEL1) =>
% 130.11/17.12 (((dpsetconstrEL2) =>
% 130.11/17.12 (((dpsetconstrER) =>
% 130.11/17.12 (((funcImageSingleton) =>
% 130.11/17.12 (((apProp) =>
% 130.11/17.12 (((app) =>
% 130.11/17.12 (((infuncsetfunc) =>
% 130.11/17.12 (((ap2p) =>
% 130.11/17.12 (((funcinfuncset) =>
% 130.11/17.12 (((lamProp) =>
% 130.11/17.12 (((lamp) =>
% 130.11/17.12 (((lam2p) =>
% 130.11/17.12 (((brelnall1) =>
% 130.11/17.12 (((brelnall2) =>
% 130.11/17.12 (((ex1E2) =>
% 130.11/17.12 (((funcGraphProp1) =>
% 130.11/17.12 (((funcGraphProp3) =>
% 130.11/17.12 (((funcGraphProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcextLem) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcGraphProp4) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq1) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq2) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (lam2lamEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifSingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifp) =>
% 130.11/17.12 ((
% 130.11/17.12 (theeq) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrue) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueorfalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setminusT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setextT) =>
% 130.11/17.12 ((
% 130.11/17.12 (subsetTI) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTELcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTERcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT1) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT2) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT3) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub2) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTnotintersectT) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementImpComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementSubsetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementInPowersetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (contraSubsetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTcontraSubset) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTILcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTIRcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion2) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (intersectInPowersetIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpNotIn1) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpInComplement1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTE) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTEcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementUnionInPowersetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule0) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_5) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all2) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1SetBreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (choice2fnsingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (setOfPairsIsBReln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all1) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compEex) =>
% 130.11/17.12 ((
% 130.11/17.12 (!!) @ (
% 130.11/17.12 (('#B') @ (
% 130.11/17.12 !!) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 !!))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#C') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1779])).
% 130.11/17.12 thf(zip_derived_cl1796, plain,
% 130.11/17.12 (~ (((cartprodsndin) =>
% 130.11/17.12 (((cartprodpairmemEL) =>
% 130.11/17.12 (((cartprodpairmemER) =>
% 130.11/17.12 (((cartprodmempaircEq) =>
% 130.11/17.12 (((cartprodfstpairEq) =>
% 130.11/17.12 (((cartprodsndpairEq) =>
% 130.11/17.12 (((cartprodpairsurjEq) =>
% 130.11/17.12 (((dpsetconstrI) =>
% 130.11/17.12 (((dpsetconstrSub) =>
% 130.11/17.12 (((setOfPairsIsBReln) =>
% 130.11/17.12 (((dpsetconstrERa) =>
% 130.11/17.12 (((dpsetconstrEL1) =>
% 130.11/17.12 (((dpsetconstrEL2) =>
% 130.11/17.12 (((dpsetconstrER) =>
% 130.11/17.12 (((funcImageSingleton) =>
% 130.11/17.12 (((apProp) =>
% 130.11/17.12 (((app) =>
% 130.11/17.12 (((infuncsetfunc) =>
% 130.11/17.12 (((ap2p) =>
% 130.11/17.12 (((funcinfuncset) =>
% 130.11/17.12 (((lamProp) =>
% 130.11/17.12 (((lamp) =>
% 130.11/17.12 (((lam2p) =>
% 130.11/17.12 (((brelnall1) =>
% 130.11/17.12 (((brelnall2) =>
% 130.11/17.12 (((ex1E2) =>
% 130.11/17.12 (((funcGraphProp1) =>
% 130.11/17.12 (((funcGraphProp3) =>
% 130.11/17.12 (((funcGraphProp2) =>
% 130.11/17.12 (((funcextLem) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcGraphProp4) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq1) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq2) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (lam2lamEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifSingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifp) =>
% 130.11/17.12 ((
% 130.11/17.12 (theeq) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrue) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueorfalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setminusT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setextT) =>
% 130.11/17.12 ((
% 130.11/17.12 (subsetTI) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTELcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTERcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT1) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT2) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT3) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub2) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTnotintersectT) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementImpComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementSubsetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementInPowersetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (contraSubsetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTcontraSubset) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTILcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTIRcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion2) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (intersectInPowersetIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpNotIn1) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpInComplement1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTE) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTEcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementUnionInPowersetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule0) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_5) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all2) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1SetBreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (choice2fnsingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (setOfPairsIsBReln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all1) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compEex) =>
% 130.11/17.12 ((
% 130.11/17.12 (!!) @ (
% 130.11/17.12 (('#B') @ (
% 130.11/17.12 !!) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 !!))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#C') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1787])).
% 130.11/17.12 thf(zip_derived_cl1807, plain,
% 130.11/17.12 (~ (((cartprodpairmemEL) =>
% 130.11/17.12 (((cartprodpairmemER) =>
% 130.11/17.12 (((cartprodmempaircEq) =>
% 130.11/17.12 (((cartprodfstpairEq) =>
% 130.11/17.12 (((cartprodsndpairEq) =>
% 130.11/17.12 (((cartprodpairsurjEq) =>
% 130.11/17.12 (((dpsetconstrI) =>
% 130.11/17.12 (((dpsetconstrSub) =>
% 130.11/17.12 (((setOfPairsIsBReln) =>
% 130.11/17.12 (((dpsetconstrERa) =>
% 130.11/17.12 (((dpsetconstrEL1) =>
% 130.11/17.12 (((dpsetconstrEL2) =>
% 130.11/17.12 (((dpsetconstrER) =>
% 130.11/17.12 (((funcImageSingleton) =>
% 130.11/17.12 (((apProp) =>
% 130.11/17.12 (((app) =>
% 130.11/17.12 (((infuncsetfunc) =>
% 130.11/17.12 (((ap2p) =>
% 130.11/17.12 (((funcinfuncset) =>
% 130.11/17.12 (((lamProp) =>
% 130.11/17.12 (((lamp) =>
% 130.11/17.12 (((lam2p) =>
% 130.11/17.12 (((brelnall1) =>
% 130.11/17.12 (((brelnall2) =>
% 130.11/17.12 (((ex1E2) =>
% 130.11/17.12 (((funcGraphProp1) =>
% 130.11/17.12 (((funcGraphProp3) =>
% 130.11/17.12 (((funcGraphProp2) =>
% 130.11/17.12 (((funcextLem) =>
% 130.11/17.12 (((funcGraphProp4) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq1) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq2) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (lam2lamEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifSingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifp) =>
% 130.11/17.12 ((
% 130.11/17.12 (theeq) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrue) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueorfalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setminusT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setextT) =>
% 130.11/17.12 ((
% 130.11/17.12 (subsetTI) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTELcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTERcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT1) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT2) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT3) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub2) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTnotintersectT) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementImpComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementSubsetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementInPowersetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (contraSubsetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTcontraSubset) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTILcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTIRcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion2) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (intersectInPowersetIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpNotIn1) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpInComplement1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTE) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTEcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementUnionInPowersetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule0) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_5) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all2) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1SetBreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (choice2fnsingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (setOfPairsIsBReln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all1) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compEex) =>
% 130.11/17.12 ((
% 130.11/17.12 (!!) @ (
% 130.11/17.12 (('#B') @ (
% 130.11/17.12 !!) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 !!))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#C') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1796])).
% 130.11/17.12 thf(zip_derived_cl1816, plain,
% 130.11/17.12 (~ (((cartprodpairmemER) =>
% 130.11/17.12 (((cartprodmempaircEq) =>
% 130.11/17.12 (((cartprodfstpairEq) =>
% 130.11/17.12 (((cartprodsndpairEq) =>
% 130.11/17.12 (((cartprodpairsurjEq) =>
% 130.11/17.12 (((dpsetconstrI) =>
% 130.11/17.12 (((dpsetconstrSub) =>
% 130.11/17.12 (((setOfPairsIsBReln) =>
% 130.11/17.12 (((dpsetconstrERa) =>
% 130.11/17.12 (((dpsetconstrEL1) =>
% 130.11/17.12 (((dpsetconstrEL2) =>
% 130.11/17.12 (((dpsetconstrER) =>
% 130.11/17.12 (((funcImageSingleton) =>
% 130.11/17.12 (((apProp) =>
% 130.11/17.12 (((app) =>
% 130.11/17.12 (((infuncsetfunc) =>
% 130.11/17.12 (((ap2p) =>
% 130.11/17.12 (((funcinfuncset) =>
% 130.11/17.12 (((lamProp) =>
% 130.11/17.12 (((lamp) =>
% 130.11/17.12 (((lam2p) =>
% 130.11/17.12 (((brelnall1) =>
% 130.11/17.12 (((brelnall2) =>
% 130.11/17.12 (((ex1E2) =>
% 130.11/17.12 (((funcGraphProp1) =>
% 130.11/17.12 (((funcGraphProp3) =>
% 130.11/17.12 (((funcGraphProp2) =>
% 130.11/17.12 (((funcextLem) =>
% 130.11/17.12 (((funcGraphProp4) =>
% 130.11/17.12 (((subbreln) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq1) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq2) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (lam2lamEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifSingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifp) =>
% 130.11/17.12 ((
% 130.11/17.12 (theeq) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrue) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueorfalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setminusT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setextT) =>
% 130.11/17.12 ((
% 130.11/17.12 (subsetTI) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTELcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTERcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT1) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT2) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT3) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub2) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTnotintersectT) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementImpComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementSubsetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementInPowersetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (contraSubsetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTcontraSubset) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTILcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTIRcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion2) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (intersectInPowersetIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpNotIn1) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpInComplement1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTE) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTEcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementUnionInPowersetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule0) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_5) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all2) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1SetBreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (choice2fnsingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (setOfPairsIsBReln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all1) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compEex) =>
% 130.11/17.12 ((
% 130.11/17.12 (!!) @ (
% 130.11/17.12 (('#B') @ (
% 130.11/17.12 !!) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 !!))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#C') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1807])).
% 130.11/17.12 thf(zip_derived_cl1825, plain,
% 130.11/17.12 (~ (((cartprodmempaircEq) =>
% 130.11/17.12 (((cartprodfstpairEq) =>
% 130.11/17.12 (((cartprodsndpairEq) =>
% 130.11/17.12 (((cartprodpairsurjEq) =>
% 130.11/17.12 (((dpsetconstrI) =>
% 130.11/17.12 (((dpsetconstrSub) =>
% 130.11/17.12 (((setOfPairsIsBReln) =>
% 130.11/17.12 (((dpsetconstrERa) =>
% 130.11/17.12 (((dpsetconstrEL1) =>
% 130.11/17.12 (((dpsetconstrEL2) =>
% 130.11/17.12 (((dpsetconstrER) =>
% 130.11/17.12 (((funcImageSingleton) =>
% 130.11/17.12 (((apProp) =>
% 130.11/17.12 (((app) =>
% 130.11/17.12 (((infuncsetfunc) =>
% 130.11/17.12 (((ap2p) =>
% 130.11/17.12 (((funcinfuncset) =>
% 130.11/17.12 (((lamProp) =>
% 130.11/17.12 (((lamp) =>
% 130.11/17.12 (((lam2p) =>
% 130.11/17.12 (((brelnall1) =>
% 130.11/17.12 (((brelnall2) =>
% 130.11/17.12 (((ex1E2) =>
% 130.11/17.12 (((funcGraphProp1) =>
% 130.11/17.12 (((funcGraphProp3) =>
% 130.11/17.12 (((funcGraphProp2) =>
% 130.11/17.12 (((funcextLem) =>
% 130.11/17.12 (((funcGraphProp4) =>
% 130.11/17.12 (((subbreln) =>
% 130.11/17.12 (((eqbreln) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq1) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq2) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (lam2lamEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifSingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifp) =>
% 130.11/17.12 ((
% 130.11/17.12 (theeq) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrue) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueorfalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setminusT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setextT) =>
% 130.11/17.12 ((
% 130.11/17.12 (subsetTI) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTELcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTERcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT1) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT2) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT3) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub2) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTnotintersectT) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementImpComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementSubsetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementInPowersetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (contraSubsetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTcontraSubset) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTILcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTIRcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion2) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (intersectInPowersetIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpNotIn1) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpInComplement1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTE) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTEcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementUnionInPowersetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule0) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_5) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all2) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1SetBreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (choice2fnsingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (setOfPairsIsBReln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all1) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compEex) =>
% 130.11/17.12 ((
% 130.11/17.12 (!!) @ (
% 130.11/17.12 (('#B') @ (
% 130.11/17.12 !!) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 !!))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#C') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1816])).
% 130.11/17.12 thf(zip_derived_cl1833, plain,
% 130.11/17.12 (~ (((cartprodfstpairEq) =>
% 130.11/17.12 (((cartprodsndpairEq) =>
% 130.11/17.12 (((cartprodpairsurjEq) =>
% 130.11/17.12 (((dpsetconstrI) =>
% 130.11/17.12 (((dpsetconstrSub) =>
% 130.11/17.12 (((setOfPairsIsBReln) =>
% 130.11/17.12 (((dpsetconstrERa) =>
% 130.11/17.12 (((dpsetconstrEL1) =>
% 130.11/17.12 (((dpsetconstrEL2) =>
% 130.11/17.12 (((dpsetconstrER) =>
% 130.11/17.12 (((funcImageSingleton) =>
% 130.11/17.12 (((apProp) =>
% 130.11/17.12 (((app) =>
% 130.11/17.12 (((infuncsetfunc) =>
% 130.11/17.12 (((ap2p) =>
% 130.11/17.12 (((funcinfuncset) =>
% 130.11/17.12 (((lamProp) =>
% 130.11/17.12 (((lamp) =>
% 130.11/17.12 (((lam2p) =>
% 130.11/17.12 (((brelnall1) =>
% 130.11/17.12 (((brelnall2) =>
% 130.11/17.12 (((ex1E2) =>
% 130.11/17.12 (((funcGraphProp1) =>
% 130.11/17.12 (((funcGraphProp3) =>
% 130.11/17.12 (((funcGraphProp2) =>
% 130.11/17.12 (((funcextLem) =>
% 130.11/17.12 (((funcGraphProp4) =>
% 130.11/17.12 (((subbreln) =>
% 130.11/17.12 (((eqbreln) =>
% 130.11/17.12 (((funcext) =>
% 130.11/17.12 ((
% 130.11/17.12 (funcext2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq1) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq2) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (lam2lamEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifSingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifp) =>
% 130.11/17.12 ((
% 130.11/17.12 (theeq) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrue) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueorfalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setminusT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setextT) =>
% 130.11/17.12 ((
% 130.11/17.12 (subsetTI) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTELcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTERcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT1) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT2) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT3) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub2) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTnotintersectT) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementImpComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementSubsetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementInPowersetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (contraSubsetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTcontraSubset) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTILcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTIRcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion2) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (intersectInPowersetIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpNotIn1) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpInComplement1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTE) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTEcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementUnionInPowersetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule0) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_5) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all2) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1SetBreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (choice2fnsingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (setOfPairsIsBReln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all1) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compEex) =>
% 130.11/17.12 ((
% 130.11/17.12 (!!) @ (
% 130.11/17.12 (('#B') @ (
% 130.11/17.12 !!) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 !!))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#C') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1825])).
% 130.11/17.12 thf(zip_derived_cl1840, plain,
% 130.11/17.12 (~ (((cartprodsndpairEq) =>
% 130.11/17.12 (((cartprodpairsurjEq) =>
% 130.11/17.12 (((dpsetconstrI) =>
% 130.11/17.12 (((dpsetconstrSub) =>
% 130.11/17.12 (((setOfPairsIsBReln) =>
% 130.11/17.12 (((dpsetconstrERa) =>
% 130.11/17.12 (((dpsetconstrEL1) =>
% 130.11/17.12 (((dpsetconstrEL2) =>
% 130.11/17.12 (((dpsetconstrER) =>
% 130.11/17.12 (((funcImageSingleton) =>
% 130.11/17.12 (((apProp) =>
% 130.11/17.12 (((app) =>
% 130.11/17.12 (((infuncsetfunc) =>
% 130.11/17.12 (((ap2p) =>
% 130.11/17.12 (((funcinfuncset) =>
% 130.11/17.12 (((lamProp) =>
% 130.11/17.12 (((lamp) =>
% 130.11/17.12 (((lam2p) =>
% 130.11/17.12 (((brelnall1) =>
% 130.11/17.12 (((brelnall2) =>
% 130.11/17.12 (((ex1E2) =>
% 130.11/17.12 (((funcGraphProp1) =>
% 130.11/17.12 (((funcGraphProp3) =>
% 130.11/17.12 (((funcGraphProp2) =>
% 130.11/17.12 (((funcextLem) =>
% 130.11/17.12 (((funcGraphProp4) =>
% 130.11/17.12 (((subbreln) =>
% 130.11/17.12 (((eqbreln) =>
% 130.11/17.12 (((funcext) =>
% 130.11/17.12 (((funcext2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq1) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq2) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (lam2lamEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifSingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifp) =>
% 130.11/17.12 ((
% 130.11/17.12 (theeq) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrue) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueorfalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setminusT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setextT) =>
% 130.11/17.12 ((
% 130.11/17.12 (subsetTI) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTELcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTERcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT1) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT2) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT3) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub2) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTnotintersectT) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementImpComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementSubsetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementInPowersetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (contraSubsetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTcontraSubset) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTILcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTIRcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion2) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (intersectInPowersetIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpNotIn1) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpInComplement1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTE) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTEcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementUnionInPowersetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule0) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_5) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all2) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1SetBreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (choice2fnsingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (setOfPairsIsBReln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all1) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compEex) =>
% 130.11/17.12 ((
% 130.11/17.12 (!!) @ (
% 130.11/17.12 (('#B') @ (
% 130.11/17.12 !!) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 !!))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#C') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1833])).
% 130.11/17.12 thf(zip_derived_cl1848, plain,
% 130.11/17.12 (~ (((cartprodpairsurjEq) =>
% 130.11/17.12 (((dpsetconstrI) =>
% 130.11/17.12 (((dpsetconstrSub) =>
% 130.11/17.12 (((setOfPairsIsBReln) =>
% 130.11/17.12 (((dpsetconstrERa) =>
% 130.11/17.12 (((dpsetconstrEL1) =>
% 130.11/17.12 (((dpsetconstrEL2) =>
% 130.11/17.12 (((dpsetconstrER) =>
% 130.11/17.12 (((funcImageSingleton) =>
% 130.11/17.12 (((apProp) =>
% 130.11/17.12 (((app) =>
% 130.11/17.12 (((infuncsetfunc) =>
% 130.11/17.12 (((ap2p) =>
% 130.11/17.12 (((funcinfuncset) =>
% 130.11/17.12 (((lamProp) =>
% 130.11/17.12 (((lamp) =>
% 130.11/17.12 (((lam2p) =>
% 130.11/17.12 (((brelnall1) =>
% 130.11/17.12 (((brelnall2) =>
% 130.11/17.12 (((ex1E2) =>
% 130.11/17.12 (((funcGraphProp1) =>
% 130.11/17.12 (((funcGraphProp3) =>
% 130.11/17.12 (((funcGraphProp2) =>
% 130.11/17.12 (((funcextLem) =>
% 130.11/17.12 (((funcGraphProp4) =>
% 130.11/17.12 (((subbreln) =>
% 130.11/17.12 (((eqbreln) =>
% 130.11/17.12 (((funcext) =>
% 130.11/17.12 (((funcext2) =>
% 130.11/17.12 (((ap2apEq1) =>
% 130.11/17.12 ((
% 130.11/17.12 (ap2apEq2) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (lam2lamEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifSingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifp) =>
% 130.11/17.12 ((
% 130.11/17.12 (theeq) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrue) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueorfalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setminusT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setextT) =>
% 130.11/17.12 ((
% 130.11/17.12 (subsetTI) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTELcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTERcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT1) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT2) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT3) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub2) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTnotintersectT) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementImpComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementSubsetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementInPowersetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (contraSubsetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTcontraSubset) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTILcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTIRcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion2) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (intersectInPowersetIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpNotIn1) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpInComplement1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTE) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTEcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementUnionInPowersetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule0) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_5) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all2) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1SetBreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (choice2fnsingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (setOfPairsIsBReln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all1) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compEex) =>
% 130.11/17.12 ((
% 130.11/17.12 (!!) @ (
% 130.11/17.12 (('#B') @ (
% 130.11/17.12 !!) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 !!))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#C') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1840])).
% 130.11/17.12 thf(zip_derived_cl1856, plain,
% 130.11/17.12 (~ (((dpsetconstrI) =>
% 130.11/17.12 (((dpsetconstrSub) =>
% 130.11/17.12 (((setOfPairsIsBReln) =>
% 130.11/17.12 (((dpsetconstrERa) =>
% 130.11/17.12 (((dpsetconstrEL1) =>
% 130.11/17.12 (((dpsetconstrEL2) =>
% 130.11/17.12 (((dpsetconstrER) =>
% 130.11/17.12 (((funcImageSingleton) =>
% 130.11/17.12 (((apProp) =>
% 130.11/17.12 (((app) =>
% 130.11/17.12 (((infuncsetfunc) =>
% 130.11/17.12 (((ap2p) =>
% 130.11/17.12 (((funcinfuncset) =>
% 130.11/17.12 (((lamProp) =>
% 130.11/17.12 (((lamp) =>
% 130.11/17.12 (((lam2p) =>
% 130.11/17.12 (((brelnall1) =>
% 130.11/17.12 (((brelnall2) =>
% 130.11/17.12 (((ex1E2) =>
% 130.11/17.12 (((funcGraphProp1) =>
% 130.11/17.12 (((funcGraphProp3) =>
% 130.11/17.12 (((funcGraphProp2) =>
% 130.11/17.12 (((funcextLem) =>
% 130.11/17.12 (((funcGraphProp4) =>
% 130.11/17.12 (((subbreln) =>
% 130.11/17.12 (((eqbreln) =>
% 130.11/17.12 (((funcext) =>
% 130.11/17.12 (((funcext2) =>
% 130.11/17.12 (((ap2apEq1) =>
% 130.11/17.12 (((ap2apEq2) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta1) =>
% 130.11/17.12 ((
% 130.11/17.12 (lam2lamEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (beta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (eta2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalseProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp1) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueProp2) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifSingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (ifp) =>
% 130.11/17.12 ((
% 130.11/17.12 (theeq) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrue) =>
% 130.11/17.12 ((
% 130.11/17.12 (iffalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (iftrueorfalse) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setminusT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementT_lem) =>
% 130.11/17.12 ((
% 130.11/17.12 (setextT) =>
% 130.11/17.12 ((
% 130.11/17.12 (subsetTI) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (powersetTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTELcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binintersectTERcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT1) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT2) =>
% 130.11/17.12 ((
% 130.11/17.12 (contrasubsetT3) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementI1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementE1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub1) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementSub2) =>
% 130.11/17.12 ((
% 130.11/17.12 (doubleComplementEq) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTnotintersectT) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementImpComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementSubsetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementInPowersetComplementIntersect) =>
% 130.11/17.12 ((
% 130.11/17.12 (contraSubsetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementTcontraSubset) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTILcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTIRcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInUnion2) =>
% 130.11/17.12 ((
% 130.11/17.12 (inIntersectImpInIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (intersectInPowersetIntersectUnions) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpNotIn1) =>
% 130.11/17.12 ((
% 130.11/17.12 (inComplementUnionImpInComplement1) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTE) =>
% 130.11/17.12 ((
% 130.11/17.12 (binunionTEcontra) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a1) =>
% 130.11/17.12 ((
% 130.11/17.12 (complementUnionInPowersetComplement) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan1) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2a) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b2) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2b) =>
% 130.11/17.12 ((
% 130.11/17.12 (demorgan2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule0) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz13rule4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_1) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_2) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_3) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_4) =>
% 130.11/17.12 ((
% 130.11/17.12 (woz1_5) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all2) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1SetBreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (choice2fnsingleton) =>
% 130.11/17.12 ((
% 130.11/17.12 (setOfPairsIsBReln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1all1) =>
% 130.11/17.12 ((
% 130.11/17.12 (subbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (eqbreln1) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1invE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compprop) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compI) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compE) =>
% 130.11/17.12 ((
% 130.11/17.12 (breln1compEex) =>
% 130.11/17.12 ((
% 130.11/17.12 (!!) @ (
% 130.11/17.12 (('#B') @ (
% 130.11/17.12 !!) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 !!))) @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#S') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#B') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 '#S') @
% 130.11/17.12 (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 (
% 130.11/17.12 ('#B') @ (
% 130.11/17.12 =>))) @
% 130.11/17.12 breln1)))))) @
% 130.11/17.12 (
% 130.11/17.13 (
% 130.11/17.13 ('#C') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1848])).
% 130.11/17.13 thf(zip_derived_cl1865, plain,
% 130.11/17.13 (~ (((dpsetconstrSub) =>
% 130.11/17.13 (((setOfPairsIsBReln) =>
% 130.11/17.13 (((dpsetconstrERa) =>
% 130.11/17.13 (((dpsetconstrEL1) =>
% 130.11/17.13 (((dpsetconstrEL2) =>
% 130.11/17.13 (((dpsetconstrER) =>
% 130.11/17.13 (((funcImageSingleton) =>
% 130.11/17.13 (((apProp) =>
% 130.11/17.13 (((app) =>
% 130.11/17.13 (((infuncsetfunc) =>
% 130.11/17.13 (((ap2p) =>
% 130.11/17.13 (((funcinfuncset) =>
% 130.11/17.13 (((lamProp) =>
% 130.11/17.13 (((lamp) =>
% 130.11/17.13 (((lam2p) =>
% 130.11/17.13 (((brelnall1) =>
% 130.11/17.13 (((brelnall2) =>
% 130.11/17.13 (((ex1E2) =>
% 130.11/17.13 (((funcGraphProp1) =>
% 130.11/17.13 (((funcGraphProp3) =>
% 130.11/17.13 (((funcGraphProp2) =>
% 130.11/17.13 (((funcextLem) =>
% 130.11/17.13 (((funcGraphProp4) =>
% 130.11/17.13 (((subbreln) =>
% 130.11/17.13 (((eqbreln) =>
% 130.11/17.13 (((funcext) =>
% 130.11/17.13 (((funcext2) =>
% 130.11/17.13 (((ap2apEq1) =>
% 130.11/17.13 (((ap2apEq2) =>
% 130.11/17.13 (((beta1) =>
% 130.11/17.13 ((
% 130.11/17.13 (eta1) =>
% 130.11/17.13 ((
% 130.11/17.13 (lam2lamEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (beta2) =>
% 130.11/17.13 ((
% 130.11/17.13 (eta2) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalseProp1) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalseProp2) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueProp1) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueProp2) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifSingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifp) =>
% 130.11/17.13 ((
% 130.11/17.13 (theeq) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrue) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueorfalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setminusT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setextT) =>
% 130.11/17.13 ((
% 130.11/17.13 (subsetTI) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTELcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTERcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT1) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT2) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT3) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub2) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTnotintersectT) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementImpComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementSubsetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementInPowersetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (contraSubsetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTcontraSubset) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTILcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTIRcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion2) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (intersectInPowersetIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpNotIn1) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpInComplement1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTE) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTEcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementUnionInPowersetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule0) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_5) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all2) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1SetBreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (choice2fnsingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (setOfPairsIsBReln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all1) =>
% 130.11/17.13 ((
% 130.11/17.13 (subbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (eqbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compEex) =>
% 130.11/17.13 ((
% 130.11/17.13 (!!) @ (
% 130.11/17.13 (('#B') @ (
% 130.11/17.13 !!) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 !!))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#C') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1856])).
% 130.11/17.13 thf(zip_derived_cl1874, plain,
% 130.11/17.13 (~ (((setOfPairsIsBReln) =>
% 130.11/17.13 (((dpsetconstrERa) =>
% 130.11/17.13 (((dpsetconstrEL1) =>
% 130.11/17.13 (((dpsetconstrEL2) =>
% 130.11/17.13 (((dpsetconstrER) =>
% 130.11/17.13 (((funcImageSingleton) =>
% 130.11/17.13 (((apProp) =>
% 130.11/17.13 (((app) =>
% 130.11/17.13 (((infuncsetfunc) =>
% 130.11/17.13 (((ap2p) =>
% 130.11/17.13 (((funcinfuncset) =>
% 130.11/17.13 (((lamProp) =>
% 130.11/17.13 (((lamp) =>
% 130.11/17.13 (((lam2p) =>
% 130.11/17.13 (((brelnall1) =>
% 130.11/17.13 (((brelnall2) =>
% 130.11/17.13 (((ex1E2) =>
% 130.11/17.13 (((funcGraphProp1) =>
% 130.11/17.13 (((funcGraphProp3) =>
% 130.11/17.13 (((funcGraphProp2) =>
% 130.11/17.13 (((funcextLem) =>
% 130.11/17.13 (((funcGraphProp4) =>
% 130.11/17.13 (((subbreln) =>
% 130.11/17.13 (((eqbreln) =>
% 130.11/17.13 (((funcext) =>
% 130.11/17.13 (((funcext2) =>
% 130.11/17.13 (((ap2apEq1) =>
% 130.11/17.13 (((ap2apEq2) =>
% 130.11/17.13 (((beta1) =>
% 130.11/17.13 (((eta1) =>
% 130.11/17.13 ((
% 130.11/17.13 (lam2lamEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (beta2) =>
% 130.11/17.13 ((
% 130.11/17.13 (eta2) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalseProp1) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalseProp2) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueProp1) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueProp2) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifSingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifp) =>
% 130.11/17.13 ((
% 130.11/17.13 (theeq) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrue) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueorfalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setminusT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setextT) =>
% 130.11/17.13 ((
% 130.11/17.13 (subsetTI) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTELcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTERcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT1) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT2) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT3) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub2) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTnotintersectT) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementImpComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementSubsetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementInPowersetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (contraSubsetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTcontraSubset) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTILcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTIRcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion2) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (intersectInPowersetIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpNotIn1) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpInComplement1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTE) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTEcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementUnionInPowersetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule0) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_5) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all2) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1SetBreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (choice2fnsingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (setOfPairsIsBReln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all1) =>
% 130.11/17.13 ((
% 130.11/17.13 (subbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (eqbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compEex) =>
% 130.11/17.13 ((
% 130.11/17.13 (!!) @ (
% 130.11/17.13 (('#B') @ (
% 130.11/17.13 !!) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 !!))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#C') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1865])).
% 130.11/17.13 thf(zip_derived_cl1883, plain,
% 130.11/17.13 (~ (((dpsetconstrERa) =>
% 130.11/17.13 (((dpsetconstrEL1) =>
% 130.11/17.13 (((dpsetconstrEL2) =>
% 130.11/17.13 (((dpsetconstrER) =>
% 130.11/17.13 (((funcImageSingleton) =>
% 130.11/17.13 (((apProp) =>
% 130.11/17.13 (((app) =>
% 130.11/17.13 (((infuncsetfunc) =>
% 130.11/17.13 (((ap2p) =>
% 130.11/17.13 (((funcinfuncset) =>
% 130.11/17.13 (((lamProp) =>
% 130.11/17.13 (((lamp) =>
% 130.11/17.13 (((lam2p) =>
% 130.11/17.13 (((brelnall1) =>
% 130.11/17.13 (((brelnall2) =>
% 130.11/17.13 (((ex1E2) =>
% 130.11/17.13 (((funcGraphProp1) =>
% 130.11/17.13 (((funcGraphProp3) =>
% 130.11/17.13 (((funcGraphProp2) =>
% 130.11/17.13 (((funcextLem) =>
% 130.11/17.13 (((funcGraphProp4) =>
% 130.11/17.13 (((subbreln) =>
% 130.11/17.13 (((eqbreln) =>
% 130.11/17.13 (((funcext) =>
% 130.11/17.13 (((funcext2) =>
% 130.11/17.13 (((ap2apEq1) =>
% 130.11/17.13 (((ap2apEq2) =>
% 130.11/17.13 (((beta1) =>
% 130.11/17.13 (((eta1) =>
% 130.11/17.13 (((lam2lamEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (beta2) =>
% 130.11/17.13 ((
% 130.11/17.13 (eta2) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalseProp1) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalseProp2) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueProp1) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueProp2) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifSingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifp) =>
% 130.11/17.13 ((
% 130.11/17.13 (theeq) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrue) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueorfalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setminusT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setextT) =>
% 130.11/17.13 ((
% 130.11/17.13 (subsetTI) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTELcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTERcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT1) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT2) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT3) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub2) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTnotintersectT) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementImpComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementSubsetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementInPowersetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (contraSubsetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTcontraSubset) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTILcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTIRcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion2) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (intersectInPowersetIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpNotIn1) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpInComplement1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTE) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTEcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementUnionInPowersetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule0) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_5) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all2) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1SetBreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (choice2fnsingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (setOfPairsIsBReln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all1) =>
% 130.11/17.13 ((
% 130.11/17.13 (subbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (eqbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compEex) =>
% 130.11/17.13 ((
% 130.11/17.13 (!!) @ (
% 130.11/17.13 (('#B') @ (
% 130.11/17.13 !!) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 !!))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#C') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1874])).
% 130.11/17.13 thf(zip_derived_cl1893, plain,
% 130.11/17.13 (~ (((dpsetconstrEL1) =>
% 130.11/17.13 (((dpsetconstrEL2) =>
% 130.11/17.13 (((dpsetconstrER) =>
% 130.11/17.13 (((funcImageSingleton) =>
% 130.11/17.13 (((apProp) =>
% 130.11/17.13 (((app) =>
% 130.11/17.13 (((infuncsetfunc) =>
% 130.11/17.13 (((ap2p) =>
% 130.11/17.13 (((funcinfuncset) =>
% 130.11/17.13 (((lamProp) =>
% 130.11/17.13 (((lamp) =>
% 130.11/17.13 (((lam2p) =>
% 130.11/17.13 (((brelnall1) =>
% 130.11/17.13 (((brelnall2) =>
% 130.11/17.13 (((ex1E2) =>
% 130.11/17.13 (((funcGraphProp1) =>
% 130.11/17.13 (((funcGraphProp3) =>
% 130.11/17.13 (((funcGraphProp2) =>
% 130.11/17.13 (((funcextLem) =>
% 130.11/17.13 (((funcGraphProp4) =>
% 130.11/17.13 (((subbreln) =>
% 130.11/17.13 (((eqbreln) =>
% 130.11/17.13 (((funcext) =>
% 130.11/17.13 (((funcext2) =>
% 130.11/17.13 (((ap2apEq1) =>
% 130.11/17.13 (((ap2apEq2) =>
% 130.11/17.13 (((beta1) =>
% 130.11/17.13 (((eta1) =>
% 130.11/17.13 (((lam2lamEq) =>
% 130.11/17.13 (((beta2) =>
% 130.11/17.13 ((
% 130.11/17.13 (eta2) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalseProp1) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalseProp2) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueProp1) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueProp2) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifSingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifp) =>
% 130.11/17.13 ((
% 130.11/17.13 (theeq) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrue) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueorfalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setminusT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setextT) =>
% 130.11/17.13 ((
% 130.11/17.13 (subsetTI) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTELcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTERcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT1) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT2) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT3) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub2) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTnotintersectT) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementImpComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementSubsetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementInPowersetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (contraSubsetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTcontraSubset) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTILcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTIRcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion2) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (intersectInPowersetIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpNotIn1) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpInComplement1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTE) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTEcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementUnionInPowersetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule0) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_5) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all2) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1SetBreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (choice2fnsingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (setOfPairsIsBReln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all1) =>
% 130.11/17.13 ((
% 130.11/17.13 (subbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (eqbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compEex) =>
% 130.11/17.13 ((
% 130.11/17.13 (!!) @ (
% 130.11/17.13 (('#B') @ (
% 130.11/17.13 !!) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 !!))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#C') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1883])).
% 130.11/17.13 thf(zip_derived_cl1903, plain,
% 130.11/17.13 (~ (((dpsetconstrEL2) =>
% 130.11/17.13 (((dpsetconstrER) =>
% 130.11/17.13 (((funcImageSingleton) =>
% 130.11/17.13 (((apProp) =>
% 130.11/17.13 (((app) =>
% 130.11/17.13 (((infuncsetfunc) =>
% 130.11/17.13 (((ap2p) =>
% 130.11/17.13 (((funcinfuncset) =>
% 130.11/17.13 (((lamProp) =>
% 130.11/17.13 (((lamp) =>
% 130.11/17.13 (((lam2p) =>
% 130.11/17.13 (((brelnall1) =>
% 130.11/17.13 (((brelnall2) =>
% 130.11/17.13 (((ex1E2) =>
% 130.11/17.13 (((funcGraphProp1) =>
% 130.11/17.13 (((funcGraphProp3) =>
% 130.11/17.13 (((funcGraphProp2) =>
% 130.11/17.13 (((funcextLem) =>
% 130.11/17.13 (((funcGraphProp4) =>
% 130.11/17.13 (((subbreln) =>
% 130.11/17.13 (((eqbreln) =>
% 130.11/17.13 (((funcext) =>
% 130.11/17.13 (((funcext2) =>
% 130.11/17.13 (((ap2apEq1) =>
% 130.11/17.13 (((ap2apEq2) =>
% 130.11/17.13 (((beta1) =>
% 130.11/17.13 (((eta1) =>
% 130.11/17.13 (((lam2lamEq) =>
% 130.11/17.13 (((beta2) =>
% 130.11/17.13 (((eta2) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalseProp1) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalseProp2) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueProp1) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueProp2) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifSingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifp) =>
% 130.11/17.13 ((
% 130.11/17.13 (theeq) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrue) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueorfalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setminusT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setextT) =>
% 130.11/17.13 ((
% 130.11/17.13 (subsetTI) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTELcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTERcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT1) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT2) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT3) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub2) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTnotintersectT) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementImpComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementSubsetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementInPowersetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (contraSubsetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTcontraSubset) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTILcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTIRcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion2) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (intersectInPowersetIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpNotIn1) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpInComplement1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTE) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTEcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementUnionInPowersetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule0) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_5) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all2) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1SetBreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (choice2fnsingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (setOfPairsIsBReln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all1) =>
% 130.11/17.13 ((
% 130.11/17.13 (subbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (eqbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compEex) =>
% 130.11/17.13 ((
% 130.11/17.13 (!!) @ (
% 130.11/17.13 (('#B') @ (
% 130.11/17.13 !!) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 !!))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#C') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1893])).
% 130.11/17.13 thf(zip_derived_cl1914, plain,
% 130.11/17.13 (~ (((dpsetconstrER) =>
% 130.11/17.13 (((funcImageSingleton) =>
% 130.11/17.13 (((apProp) =>
% 130.11/17.13 (((app) =>
% 130.11/17.13 (((infuncsetfunc) =>
% 130.11/17.13 (((ap2p) =>
% 130.11/17.13 (((funcinfuncset) =>
% 130.11/17.13 (((lamProp) =>
% 130.11/17.13 (((lamp) =>
% 130.11/17.13 (((lam2p) =>
% 130.11/17.13 (((brelnall1) =>
% 130.11/17.13 (((brelnall2) =>
% 130.11/17.13 (((ex1E2) =>
% 130.11/17.13 (((funcGraphProp1) =>
% 130.11/17.13 (((funcGraphProp3) =>
% 130.11/17.13 (((funcGraphProp2) =>
% 130.11/17.13 (((funcextLem) =>
% 130.11/17.13 (((funcGraphProp4) =>
% 130.11/17.13 (((subbreln) =>
% 130.11/17.13 (((eqbreln) =>
% 130.11/17.13 (((funcext) =>
% 130.11/17.13 (((funcext2) =>
% 130.11/17.13 (((ap2apEq1) =>
% 130.11/17.13 (((ap2apEq2) =>
% 130.11/17.13 (((beta1) =>
% 130.11/17.13 (((eta1) =>
% 130.11/17.13 (((lam2lamEq) =>
% 130.11/17.13 (((beta2) =>
% 130.11/17.13 (((eta2) =>
% 130.11/17.13 (((iffalseProp1) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalseProp2) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueProp1) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueProp2) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifSingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifp) =>
% 130.11/17.13 ((
% 130.11/17.13 (theeq) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrue) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueorfalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setminusT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setextT) =>
% 130.11/17.13 ((
% 130.11/17.13 (subsetTI) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTELcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTERcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT1) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT2) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT3) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub2) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTnotintersectT) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementImpComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementSubsetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementInPowersetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (contraSubsetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTcontraSubset) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTILcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTIRcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion2) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (intersectInPowersetIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpNotIn1) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpInComplement1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTE) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTEcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementUnionInPowersetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule0) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_5) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all2) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1SetBreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (choice2fnsingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (setOfPairsIsBReln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all1) =>
% 130.11/17.13 ((
% 130.11/17.13 (subbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (eqbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compEex) =>
% 130.11/17.13 ((
% 130.11/17.13 (!!) @ (
% 130.11/17.13 (('#B') @ (
% 130.11/17.13 !!) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 !!))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#C') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1903])).
% 130.11/17.13 thf(zip_derived_cl1923, plain,
% 130.11/17.13 (~ (((funcImageSingleton) =>
% 130.11/17.13 (((apProp) =>
% 130.11/17.13 (((app) =>
% 130.11/17.13 (((infuncsetfunc) =>
% 130.11/17.13 (((ap2p) =>
% 130.11/17.13 (((funcinfuncset) =>
% 130.11/17.13 (((lamProp) =>
% 130.11/17.13 (((lamp) =>
% 130.11/17.13 (((lam2p) =>
% 130.11/17.13 (((brelnall1) =>
% 130.11/17.13 (((brelnall2) =>
% 130.11/17.13 (((ex1E2) =>
% 130.11/17.13 (((funcGraphProp1) =>
% 130.11/17.13 (((funcGraphProp3) =>
% 130.11/17.13 (((funcGraphProp2) =>
% 130.11/17.13 (((funcextLem) =>
% 130.11/17.13 (((funcGraphProp4) =>
% 130.11/17.13 (((subbreln) =>
% 130.11/17.13 (((eqbreln) =>
% 130.11/17.13 (((funcext) =>
% 130.11/17.13 (((funcext2) =>
% 130.11/17.13 (((ap2apEq1) =>
% 130.11/17.13 (((ap2apEq2) =>
% 130.11/17.13 (((beta1) =>
% 130.11/17.13 (((eta1) =>
% 130.11/17.13 (((lam2lamEq) =>
% 130.11/17.13 (((beta2) =>
% 130.11/17.13 (((eta2) =>
% 130.11/17.13 (((iffalseProp1) =>
% 130.11/17.13 (((iffalseProp2) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueProp1) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueProp2) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifSingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifp) =>
% 130.11/17.13 ((
% 130.11/17.13 (theeq) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrue) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueorfalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setminusT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setextT) =>
% 130.11/17.13 ((
% 130.11/17.13 (subsetTI) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTELcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTERcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT1) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT2) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT3) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub2) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTnotintersectT) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementImpComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementSubsetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementInPowersetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (contraSubsetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTcontraSubset) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTILcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTIRcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion2) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (intersectInPowersetIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpNotIn1) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpInComplement1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTE) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTEcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementUnionInPowersetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule0) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_5) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all2) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1SetBreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (choice2fnsingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (setOfPairsIsBReln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all1) =>
% 130.11/17.13 ((
% 130.11/17.13 (subbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (eqbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compEex) =>
% 130.11/17.13 ((
% 130.11/17.13 (!!) @ (
% 130.11/17.13 (('#B') @ (
% 130.11/17.13 !!) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 !!))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#C') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1914])).
% 130.11/17.13 thf(zip_derived_cl1932, plain,
% 130.11/17.13 (~ (((apProp) =>
% 130.11/17.13 (((app) =>
% 130.11/17.13 (((infuncsetfunc) =>
% 130.11/17.13 (((ap2p) =>
% 130.11/17.13 (((funcinfuncset) =>
% 130.11/17.13 (((lamProp) =>
% 130.11/17.13 (((lamp) =>
% 130.11/17.13 (((lam2p) =>
% 130.11/17.13 (((brelnall1) =>
% 130.11/17.13 (((brelnall2) =>
% 130.11/17.13 (((ex1E2) =>
% 130.11/17.13 (((funcGraphProp1) =>
% 130.11/17.13 (((funcGraphProp3) =>
% 130.11/17.13 (((funcGraphProp2) =>
% 130.11/17.13 (((funcextLem) =>
% 130.11/17.13 (((funcGraphProp4) =>
% 130.11/17.13 (((subbreln) =>
% 130.11/17.13 (((eqbreln) =>
% 130.11/17.13 (((funcext) =>
% 130.11/17.13 (((funcext2) =>
% 130.11/17.13 (((ap2apEq1) =>
% 130.11/17.13 (((ap2apEq2) =>
% 130.11/17.13 (((beta1) =>
% 130.11/17.13 (((eta1) =>
% 130.11/17.13 (((lam2lamEq) =>
% 130.11/17.13 (((beta2) =>
% 130.11/17.13 (((eta2) =>
% 130.11/17.13 (((iffalseProp1) =>
% 130.11/17.13 (((iffalseProp2) =>
% 130.11/17.13 (((iftrueProp1) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueProp2) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifSingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifp) =>
% 130.11/17.13 ((
% 130.11/17.13 (theeq) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrue) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueorfalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setminusT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setextT) =>
% 130.11/17.13 ((
% 130.11/17.13 (subsetTI) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTELcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTERcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT1) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT2) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT3) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub2) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTnotintersectT) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementImpComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementSubsetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementInPowersetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (contraSubsetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTcontraSubset) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTILcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTIRcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion2) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (intersectInPowersetIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpNotIn1) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpInComplement1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTE) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTEcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementUnionInPowersetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule0) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_5) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all2) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1SetBreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (choice2fnsingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (setOfPairsIsBReln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all1) =>
% 130.11/17.13 ((
% 130.11/17.13 (subbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (eqbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compEex) =>
% 130.11/17.13 ((
% 130.11/17.13 (!!) @ (
% 130.11/17.13 (('#B') @ (
% 130.11/17.13 !!) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 !!))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#C') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1923])).
% 130.11/17.13 thf(zip_derived_cl1941, plain,
% 130.11/17.13 (~ (((app) =>
% 130.11/17.13 (((infuncsetfunc) =>
% 130.11/17.13 (((ap2p) =>
% 130.11/17.13 (((funcinfuncset) =>
% 130.11/17.13 (((lamProp) =>
% 130.11/17.13 (((lamp) =>
% 130.11/17.13 (((lam2p) =>
% 130.11/17.13 (((brelnall1) =>
% 130.11/17.13 (((brelnall2) =>
% 130.11/17.13 (((ex1E2) =>
% 130.11/17.13 (((funcGraphProp1) =>
% 130.11/17.13 (((funcGraphProp3) =>
% 130.11/17.13 (((funcGraphProp2) =>
% 130.11/17.13 (((funcextLem) =>
% 130.11/17.13 (((funcGraphProp4) =>
% 130.11/17.13 (((subbreln) =>
% 130.11/17.13 (((eqbreln) =>
% 130.11/17.13 (((funcext) =>
% 130.11/17.13 (((funcext2) =>
% 130.11/17.13 (((ap2apEq1) =>
% 130.11/17.13 (((ap2apEq2) =>
% 130.11/17.13 (((beta1) =>
% 130.11/17.13 (((eta1) =>
% 130.11/17.13 (((lam2lamEq) =>
% 130.11/17.13 (((beta2) =>
% 130.11/17.13 (((eta2) =>
% 130.11/17.13 (((iffalseProp1) =>
% 130.11/17.13 (((iffalseProp2) =>
% 130.11/17.13 (((iftrueProp1) =>
% 130.11/17.13 (((iftrueProp2) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifSingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifp) =>
% 130.11/17.13 ((
% 130.11/17.13 (theeq) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrue) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueorfalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setminusT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setextT) =>
% 130.11/17.13 ((
% 130.11/17.13 (subsetTI) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTELcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTERcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT1) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT2) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT3) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub2) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTnotintersectT) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementImpComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementSubsetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementInPowersetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (contraSubsetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTcontraSubset) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTILcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTIRcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion2) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (intersectInPowersetIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpNotIn1) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpInComplement1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTE) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTEcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementUnionInPowersetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule0) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_5) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all2) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1SetBreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (choice2fnsingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (setOfPairsIsBReln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all1) =>
% 130.11/17.13 ((
% 130.11/17.13 (subbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (eqbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compEex) =>
% 130.11/17.13 ((
% 130.11/17.13 (!!) @ (
% 130.11/17.13 (('#B') @ (
% 130.11/17.13 !!) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 !!))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#C') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1932])).
% 130.11/17.13 thf(zip_derived_cl1951, plain,
% 130.11/17.13 (~ (((infuncsetfunc) =>
% 130.11/17.13 (((ap2p) =>
% 130.11/17.13 (((funcinfuncset) =>
% 130.11/17.13 (((lamProp) =>
% 130.11/17.13 (((lamp) =>
% 130.11/17.13 (((lam2p) =>
% 130.11/17.13 (((brelnall1) =>
% 130.11/17.13 (((brelnall2) =>
% 130.11/17.13 (((ex1E2) =>
% 130.11/17.13 (((funcGraphProp1) =>
% 130.11/17.13 (((funcGraphProp3) =>
% 130.11/17.13 (((funcGraphProp2) =>
% 130.11/17.13 (((funcextLem) =>
% 130.11/17.13 (((funcGraphProp4) =>
% 130.11/17.13 (((subbreln) =>
% 130.11/17.13 (((eqbreln) =>
% 130.11/17.13 (((funcext) =>
% 130.11/17.13 (((funcext2) =>
% 130.11/17.13 (((ap2apEq1) =>
% 130.11/17.13 (((ap2apEq2) =>
% 130.11/17.13 (((beta1) =>
% 130.11/17.13 (((eta1) =>
% 130.11/17.13 (((lam2lamEq) =>
% 130.11/17.13 (((beta2) =>
% 130.11/17.13 (((eta2) =>
% 130.11/17.13 (((iffalseProp1) =>
% 130.11/17.13 (((iffalseProp2) =>
% 130.11/17.13 (((iftrueProp1) =>
% 130.11/17.13 (((iftrueProp2) =>
% 130.11/17.13 (((ifSingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (ifp) =>
% 130.11/17.13 ((
% 130.11/17.13 (theeq) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrue) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueorfalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setminusT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setextT) =>
% 130.11/17.13 ((
% 130.11/17.13 (subsetTI) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTELcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTERcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT1) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT2) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT3) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub2) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTnotintersectT) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementImpComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementSubsetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementInPowersetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (contraSubsetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTcontraSubset) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTILcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTIRcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion2) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (intersectInPowersetIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpNotIn1) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpInComplement1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTE) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTEcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementUnionInPowersetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule0) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_5) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all2) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1SetBreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (choice2fnsingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (setOfPairsIsBReln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all1) =>
% 130.11/17.13 ((
% 130.11/17.13 (subbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (eqbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compEex) =>
% 130.11/17.13 ((
% 130.11/17.13 (!!) @ (
% 130.11/17.13 (('#B') @ (
% 130.11/17.13 !!) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 !!))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#C') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1941])).
% 130.11/17.13 thf(zip_derived_cl1961, plain,
% 130.11/17.13 (~ (((ap2p) =>
% 130.11/17.13 (((funcinfuncset) =>
% 130.11/17.13 (((lamProp) =>
% 130.11/17.13 (((lamp) =>
% 130.11/17.13 (((lam2p) =>
% 130.11/17.13 (((brelnall1) =>
% 130.11/17.13 (((brelnall2) =>
% 130.11/17.13 (((ex1E2) =>
% 130.11/17.13 (((funcGraphProp1) =>
% 130.11/17.13 (((funcGraphProp3) =>
% 130.11/17.13 (((funcGraphProp2) =>
% 130.11/17.13 (((funcextLem) =>
% 130.11/17.13 (((funcGraphProp4) =>
% 130.11/17.13 (((subbreln) =>
% 130.11/17.13 (((eqbreln) =>
% 130.11/17.13 (((funcext) =>
% 130.11/17.13 (((funcext2) =>
% 130.11/17.13 (((ap2apEq1) =>
% 130.11/17.13 (((ap2apEq2) =>
% 130.11/17.13 (((beta1) =>
% 130.11/17.13 (((eta1) =>
% 130.11/17.13 (((lam2lamEq) =>
% 130.11/17.13 (((beta2) =>
% 130.11/17.13 (((eta2) =>
% 130.11/17.13 (((iffalseProp1) =>
% 130.11/17.13 (((iffalseProp2) =>
% 130.11/17.13 (((iftrueProp1) =>
% 130.11/17.13 (((iftrueProp2) =>
% 130.11/17.13 (((ifSingleton) =>
% 130.11/17.13 (((ifp) =>
% 130.11/17.13 ((
% 130.11/17.13 (theeq) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrue) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueorfalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setminusT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setextT) =>
% 130.11/17.13 ((
% 130.11/17.13 (subsetTI) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTELcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTERcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT1) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT2) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT3) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub2) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTnotintersectT) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementImpComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementSubsetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementInPowersetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (contraSubsetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTcontraSubset) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTILcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTIRcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion2) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (intersectInPowersetIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpNotIn1) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpInComplement1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTE) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTEcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementUnionInPowersetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule0) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_5) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all2) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1SetBreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (choice2fnsingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (setOfPairsIsBReln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all1) =>
% 130.11/17.13 ((
% 130.11/17.13 (subbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (eqbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compEex) =>
% 130.11/17.13 ((
% 130.11/17.13 (!!) @ (
% 130.11/17.13 (('#B') @ (
% 130.11/17.13 !!) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 !!))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#C') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1951])).
% 130.11/17.13 thf(zip_derived_cl1972, plain,
% 130.11/17.13 (~ (((funcinfuncset) =>
% 130.11/17.13 (((lamProp) =>
% 130.11/17.13 (((lamp) =>
% 130.11/17.13 (((lam2p) =>
% 130.11/17.13 (((brelnall1) =>
% 130.11/17.13 (((brelnall2) =>
% 130.11/17.13 (((ex1E2) =>
% 130.11/17.13 (((funcGraphProp1) =>
% 130.11/17.13 (((funcGraphProp3) =>
% 130.11/17.13 (((funcGraphProp2) =>
% 130.11/17.13 (((funcextLem) =>
% 130.11/17.13 (((funcGraphProp4) =>
% 130.11/17.13 (((subbreln) =>
% 130.11/17.13 (((eqbreln) =>
% 130.11/17.13 (((funcext) =>
% 130.11/17.13 (((funcext2) =>
% 130.11/17.13 (((ap2apEq1) =>
% 130.11/17.13 (((ap2apEq2) =>
% 130.11/17.13 (((beta1) =>
% 130.11/17.13 (((eta1) =>
% 130.11/17.13 (((lam2lamEq) =>
% 130.11/17.13 (((beta2) =>
% 130.11/17.13 (((eta2) =>
% 130.11/17.13 (((iffalseProp1) =>
% 130.11/17.13 (((iffalseProp2) =>
% 130.11/17.13 (((iftrueProp1) =>
% 130.11/17.13 (((iftrueProp2) =>
% 130.11/17.13 (((ifSingleton) =>
% 130.11/17.13 (((ifp) =>
% 130.11/17.13 (((theeq) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrue) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueorfalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setminusT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setextT) =>
% 130.11/17.13 ((
% 130.11/17.13 (subsetTI) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTELcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTERcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT1) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT2) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT3) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub2) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTnotintersectT) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementImpComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementSubsetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementInPowersetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (contraSubsetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTcontraSubset) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTILcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTIRcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion2) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (intersectInPowersetIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpNotIn1) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpInComplement1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTE) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTEcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementUnionInPowersetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule0) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_5) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all2) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1SetBreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (choice2fnsingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (setOfPairsIsBReln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all1) =>
% 130.11/17.13 ((
% 130.11/17.13 (subbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (eqbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compEex) =>
% 130.11/17.13 ((
% 130.11/17.13 (!!) @ (
% 130.11/17.13 (('#B') @ (
% 130.11/17.13 !!) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 !!))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#C') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1961])).
% 130.11/17.13 thf(zip_derived_cl1983, plain,
% 130.11/17.13 (~ (((lamProp) =>
% 130.11/17.13 (((lamp) =>
% 130.11/17.13 (((lam2p) =>
% 130.11/17.13 (((brelnall1) =>
% 130.11/17.13 (((brelnall2) =>
% 130.11/17.13 (((ex1E2) =>
% 130.11/17.13 (((funcGraphProp1) =>
% 130.11/17.13 (((funcGraphProp3) =>
% 130.11/17.13 (((funcGraphProp2) =>
% 130.11/17.13 (((funcextLem) =>
% 130.11/17.13 (((funcGraphProp4) =>
% 130.11/17.13 (((subbreln) =>
% 130.11/17.13 (((eqbreln) =>
% 130.11/17.13 (((funcext) =>
% 130.11/17.13 (((funcext2) =>
% 130.11/17.13 (((ap2apEq1) =>
% 130.11/17.13 (((ap2apEq2) =>
% 130.11/17.13 (((beta1) =>
% 130.11/17.13 (((eta1) =>
% 130.11/17.13 (((lam2lamEq) =>
% 130.11/17.13 (((beta2) =>
% 130.11/17.13 (((eta2) =>
% 130.11/17.13 (((iffalseProp1) =>
% 130.11/17.13 (((iffalseProp2) =>
% 130.11/17.13 (((iftrueProp1) =>
% 130.11/17.13 (((iftrueProp2) =>
% 130.11/17.13 (((ifSingleton) =>
% 130.11/17.13 (((ifp) =>
% 130.11/17.13 (((theeq) =>
% 130.11/17.13 (((iftrue) =>
% 130.11/17.13 ((
% 130.11/17.13 (iffalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueorfalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setminusT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setextT) =>
% 130.11/17.13 ((
% 130.11/17.13 (subsetTI) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTELcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTERcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT1) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT2) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT3) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub2) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTnotintersectT) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementImpComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementSubsetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementInPowersetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (contraSubsetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTcontraSubset) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTILcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTIRcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion2) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (intersectInPowersetIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpNotIn1) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpInComplement1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTE) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTEcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementUnionInPowersetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule0) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_5) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all2) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1SetBreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (choice2fnsingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (setOfPairsIsBReln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all1) =>
% 130.11/17.13 ((
% 130.11/17.13 (subbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (eqbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compEex) =>
% 130.11/17.13 ((
% 130.11/17.13 (!!) @ (
% 130.11/17.13 (('#B') @ (
% 130.11/17.13 !!) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 !!))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#C') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1972])).
% 130.11/17.13 thf(zip_derived_cl1993, plain,
% 130.11/17.13 (~ (((lamp) =>
% 130.11/17.13 (((lam2p) =>
% 130.11/17.13 (((brelnall1) =>
% 130.11/17.13 (((brelnall2) =>
% 130.11/17.13 (((ex1E2) =>
% 130.11/17.13 (((funcGraphProp1) =>
% 130.11/17.13 (((funcGraphProp3) =>
% 130.11/17.13 (((funcGraphProp2) =>
% 130.11/17.13 (((funcextLem) =>
% 130.11/17.13 (((funcGraphProp4) =>
% 130.11/17.13 (((subbreln) =>
% 130.11/17.13 (((eqbreln) =>
% 130.11/17.13 (((funcext) =>
% 130.11/17.13 (((funcext2) =>
% 130.11/17.13 (((ap2apEq1) =>
% 130.11/17.13 (((ap2apEq2) =>
% 130.11/17.13 (((beta1) =>
% 130.11/17.13 (((eta1) =>
% 130.11/17.13 (((lam2lamEq) =>
% 130.11/17.13 (((beta2) =>
% 130.11/17.13 (((eta2) =>
% 130.11/17.13 (((iffalseProp1) =>
% 130.11/17.13 (((iffalseProp2) =>
% 130.11/17.13 (((iftrueProp1) =>
% 130.11/17.13 (((iftrueProp2) =>
% 130.11/17.13 (((ifSingleton) =>
% 130.11/17.13 (((ifp) =>
% 130.11/17.13 (((theeq) =>
% 130.11/17.13 (((iftrue) =>
% 130.11/17.13 (((iffalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (iftrueorfalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setminusT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setextT) =>
% 130.11/17.13 ((
% 130.11/17.13 (subsetTI) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTELcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTERcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT1) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT2) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT3) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub2) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTnotintersectT) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementImpComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementSubsetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementInPowersetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (contraSubsetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTcontraSubset) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTILcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTIRcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion2) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (intersectInPowersetIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpNotIn1) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpInComplement1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTE) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTEcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementUnionInPowersetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule0) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_5) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all2) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1SetBreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (choice2fnsingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (setOfPairsIsBReln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all1) =>
% 130.11/17.13 ((
% 130.11/17.13 (subbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (eqbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compEex) =>
% 130.11/17.13 ((
% 130.11/17.13 (!!) @ (
% 130.11/17.13 (('#B') @ (
% 130.11/17.13 !!) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 !!))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#S') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#S') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 =>))) @
% 130.11/17.13 breln1)))))) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#C') @ (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.13 ('#B') @ (
% 130.11/17.13 '#B') @
% 130.11/17.13 breln1)))) @
% 130.11/17.13 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1983])).
% 130.11/17.13 thf(zip_derived_cl2003, plain,
% 130.11/17.13 (~ (((lam2p) =>
% 130.11/17.13 (((brelnall1) =>
% 130.11/17.13 (((brelnall2) =>
% 130.11/17.13 (((ex1E2) =>
% 130.11/17.13 (((funcGraphProp1) =>
% 130.11/17.13 (((funcGraphProp3) =>
% 130.11/17.13 (((funcGraphProp2) =>
% 130.11/17.13 (((funcextLem) =>
% 130.11/17.13 (((funcGraphProp4) =>
% 130.11/17.13 (((subbreln) =>
% 130.11/17.13 (((eqbreln) =>
% 130.11/17.13 (((funcext) =>
% 130.11/17.13 (((funcext2) =>
% 130.11/17.13 (((ap2apEq1) =>
% 130.11/17.13 (((ap2apEq2) =>
% 130.11/17.13 (((beta1) =>
% 130.11/17.13 (((eta1) =>
% 130.11/17.13 (((lam2lamEq) =>
% 130.11/17.13 (((beta2) =>
% 130.11/17.13 (((eta2) =>
% 130.11/17.13 (((iffalseProp1) =>
% 130.11/17.13 (((iffalseProp2) =>
% 130.11/17.13 (((iftrueProp1) =>
% 130.11/17.13 (((iftrueProp2) =>
% 130.11/17.13 (((ifSingleton) =>
% 130.11/17.13 (((ifp) =>
% 130.11/17.13 (((theeq) =>
% 130.11/17.13 (((iftrue) =>
% 130.11/17.13 (((iffalse) =>
% 130.11/17.13 (((iftrueorfalse) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setminusT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementT_lem) =>
% 130.11/17.13 ((
% 130.11/17.13 (setextT) =>
% 130.11/17.13 ((
% 130.11/17.13 (subsetTI) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (powersetTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTELcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binintersectTERcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT1) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT2) =>
% 130.11/17.13 ((
% 130.11/17.13 (contrasubsetT3) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementI1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementE1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub1) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementSub2) =>
% 130.11/17.13 ((
% 130.11/17.13 (doubleComplementEq) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTnotintersectT) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementImpComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementSubsetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementInPowersetComplementIntersect) =>
% 130.11/17.13 ((
% 130.11/17.13 (contraSubsetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementTcontraSubset) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTILcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTIRcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInUnion2) =>
% 130.11/17.13 ((
% 130.11/17.13 (inIntersectImpInIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (intersectInPowersetIntersectUnions) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpNotIn1) =>
% 130.11/17.13 ((
% 130.11/17.13 (inComplementUnionImpInComplement1) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTE) =>
% 130.11/17.13 ((
% 130.11/17.13 (binunionTEcontra) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a1) =>
% 130.11/17.13 ((
% 130.11/17.13 (complementUnionInPowersetComplement) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan1) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2a) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b2) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2b) =>
% 130.11/17.13 ((
% 130.11/17.13 (demorgan2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule0) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz13rule4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_1) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_2) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_3) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_4) =>
% 130.11/17.13 ((
% 130.11/17.13 (woz1_5) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all2) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1SetBreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (choice2fnsingleton) =>
% 130.11/17.13 ((
% 130.11/17.13 (setOfPairsIsBReln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1all1) =>
% 130.11/17.13 ((
% 130.11/17.13 (subbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (eqbreln1) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1invE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compprop) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compI) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compE) =>
% 130.11/17.13 ((
% 130.11/17.13 (breln1compEex) =>
% 130.11/17.13 ((
% 130.11/17.13 (!!) @ (
% 130.11/17.13 (('#B') @ (
% 130.11/17.13 !!) @
% 130.11/17.13 (
% 130.11/17.13 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 !!))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#C') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1993])).
% 130.11/17.14 thf(zip_derived_cl2013, plain,
% 130.11/17.14 (~ (((brelnall1) =>
% 130.11/17.14 (((brelnall2) =>
% 130.11/17.14 (((ex1E2) =>
% 130.11/17.14 (((funcGraphProp1) =>
% 130.11/17.14 (((funcGraphProp3) =>
% 130.11/17.14 (((funcGraphProp2) =>
% 130.11/17.14 (((funcextLem) =>
% 130.11/17.14 (((funcGraphProp4) =>
% 130.11/17.14 (((subbreln) =>
% 130.11/17.14 (((eqbreln) =>
% 130.11/17.14 (((funcext) =>
% 130.11/17.14 (((funcext2) =>
% 130.11/17.14 (((ap2apEq1) =>
% 130.11/17.14 (((ap2apEq2) =>
% 130.11/17.14 (((beta1) =>
% 130.11/17.14 (((eta1) =>
% 130.11/17.14 (((lam2lamEq) =>
% 130.11/17.14 (((beta2) =>
% 130.11/17.14 (((eta2) =>
% 130.11/17.14 (((iffalseProp1) =>
% 130.11/17.14 (((iffalseProp2) =>
% 130.11/17.14 (((iftrueProp1) =>
% 130.11/17.14 (((iftrueProp2) =>
% 130.11/17.14 (((ifSingleton) =>
% 130.11/17.14 (((ifp) =>
% 130.11/17.14 (((theeq) =>
% 130.11/17.14 (((iftrue) =>
% 130.11/17.14 (((iffalse) =>
% 130.11/17.14 (((iftrueorfalse) =>
% 130.11/17.14 (((binintersectT_lem) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionT_lem) =>
% 130.11/17.14 ((
% 130.11/17.14 (powersetT_lem) =>
% 130.11/17.14 ((
% 130.11/17.14 (setminusT_lem) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementT_lem) =>
% 130.11/17.14 ((
% 130.11/17.14 (setextT) =>
% 130.11/17.14 ((
% 130.11/17.14 (subsetTI) =>
% 130.11/17.14 ((
% 130.11/17.14 (powersetTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (powersetTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTELcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTERcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT1) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT2) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT3) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub2) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementEq) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTnotintersectT) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementImpComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementSubsetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementInPowersetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (contraSubsetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTcontraSubset) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTILcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTIRcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion2) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (intersectInPowersetIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpNotIn1) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpInComplement1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTE) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTEcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementUnionInPowersetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule0) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_5) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all2) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1SetBreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (choice2fnsingleton) =>
% 130.11/17.14 ((
% 130.11/17.14 (setOfPairsIsBReln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all1) =>
% 130.11/17.14 ((
% 130.11/17.14 (subbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (eqbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compEex) =>
% 130.11/17.14 ((
% 130.11/17.14 (!!) @ (
% 130.11/17.14 (('#B') @ (
% 130.11/17.14 !!) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 !!))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#C') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2003])).
% 130.11/17.14 thf(zip_derived_cl2022, plain,
% 130.11/17.14 (~ (((brelnall2) =>
% 130.11/17.14 (((ex1E2) =>
% 130.11/17.14 (((funcGraphProp1) =>
% 130.11/17.14 (((funcGraphProp3) =>
% 130.11/17.14 (((funcGraphProp2) =>
% 130.11/17.14 (((funcextLem) =>
% 130.11/17.14 (((funcGraphProp4) =>
% 130.11/17.14 (((subbreln) =>
% 130.11/17.14 (((eqbreln) =>
% 130.11/17.14 (((funcext) =>
% 130.11/17.14 (((funcext2) =>
% 130.11/17.14 (((ap2apEq1) =>
% 130.11/17.14 (((ap2apEq2) =>
% 130.11/17.14 (((beta1) =>
% 130.11/17.14 (((eta1) =>
% 130.11/17.14 (((lam2lamEq) =>
% 130.11/17.14 (((beta2) =>
% 130.11/17.14 (((eta2) =>
% 130.11/17.14 (((iffalseProp1) =>
% 130.11/17.14 (((iffalseProp2) =>
% 130.11/17.14 (((iftrueProp1) =>
% 130.11/17.14 (((iftrueProp2) =>
% 130.11/17.14 (((ifSingleton) =>
% 130.11/17.14 (((ifp) =>
% 130.11/17.14 (((theeq) =>
% 130.11/17.14 (((iftrue) =>
% 130.11/17.14 (((iffalse) =>
% 130.11/17.14 (((iftrueorfalse) =>
% 130.11/17.14 (((binintersectT_lem) =>
% 130.11/17.14 (((binunionT_lem) =>
% 130.11/17.14 ((
% 130.11/17.14 (powersetT_lem) =>
% 130.11/17.14 ((
% 130.11/17.14 (setminusT_lem) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementT_lem) =>
% 130.11/17.14 ((
% 130.11/17.14 (setextT) =>
% 130.11/17.14 ((
% 130.11/17.14 (subsetTI) =>
% 130.11/17.14 ((
% 130.11/17.14 (powersetTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (powersetTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTELcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTERcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT1) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT2) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT3) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub2) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementEq) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTnotintersectT) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementImpComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementSubsetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementInPowersetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (contraSubsetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTcontraSubset) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTILcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTIRcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion2) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (intersectInPowersetIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpNotIn1) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpInComplement1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTE) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTEcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementUnionInPowersetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule0) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_5) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all2) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1SetBreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (choice2fnsingleton) =>
% 130.11/17.14 ((
% 130.11/17.14 (setOfPairsIsBReln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all1) =>
% 130.11/17.14 ((
% 130.11/17.14 (subbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (eqbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compEex) =>
% 130.11/17.14 ((
% 130.11/17.14 (!!) @ (
% 130.11/17.14 (('#B') @ (
% 130.11/17.14 !!) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 !!))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#C') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2013])).
% 130.11/17.14 thf(zip_derived_cl2031, plain,
% 130.11/17.14 (~ (((ex1E2) =>
% 130.11/17.14 (((funcGraphProp1) =>
% 130.11/17.14 (((funcGraphProp3) =>
% 130.11/17.14 (((funcGraphProp2) =>
% 130.11/17.14 (((funcextLem) =>
% 130.11/17.14 (((funcGraphProp4) =>
% 130.11/17.14 (((subbreln) =>
% 130.11/17.14 (((eqbreln) =>
% 130.11/17.14 (((funcext) =>
% 130.11/17.14 (((funcext2) =>
% 130.11/17.14 (((ap2apEq1) =>
% 130.11/17.14 (((ap2apEq2) =>
% 130.11/17.14 (((beta1) =>
% 130.11/17.14 (((eta1) =>
% 130.11/17.14 (((lam2lamEq) =>
% 130.11/17.14 (((beta2) =>
% 130.11/17.14 (((eta2) =>
% 130.11/17.14 (((iffalseProp1) =>
% 130.11/17.14 (((iffalseProp2) =>
% 130.11/17.14 (((iftrueProp1) =>
% 130.11/17.14 (((iftrueProp2) =>
% 130.11/17.14 (((ifSingleton) =>
% 130.11/17.14 (((ifp) =>
% 130.11/17.14 (((theeq) =>
% 130.11/17.14 (((iftrue) =>
% 130.11/17.14 (((iffalse) =>
% 130.11/17.14 (((iftrueorfalse) =>
% 130.11/17.14 (((binintersectT_lem) =>
% 130.11/17.14 (((binunionT_lem) =>
% 130.11/17.14 (((powersetT_lem) =>
% 130.11/17.14 ((
% 130.11/17.14 (setminusT_lem) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementT_lem) =>
% 130.11/17.14 ((
% 130.11/17.14 (setextT) =>
% 130.11/17.14 ((
% 130.11/17.14 (subsetTI) =>
% 130.11/17.14 ((
% 130.11/17.14 (powersetTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (powersetTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTELcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTERcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT1) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT2) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT3) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub2) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementEq) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTnotintersectT) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementImpComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementSubsetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementInPowersetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (contraSubsetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTcontraSubset) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTILcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTIRcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion2) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (intersectInPowersetIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpNotIn1) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpInComplement1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTE) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTEcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementUnionInPowersetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule0) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_5) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all2) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1SetBreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (choice2fnsingleton) =>
% 130.11/17.14 ((
% 130.11/17.14 (setOfPairsIsBReln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all1) =>
% 130.11/17.14 ((
% 130.11/17.14 (subbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (eqbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compEex) =>
% 130.11/17.14 ((
% 130.11/17.14 (!!) @ (
% 130.11/17.14 (('#B') @ (
% 130.11/17.14 !!) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 !!))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#C') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2022])).
% 130.11/17.14 thf(zip_derived_cl2040, plain,
% 130.11/17.14 (~ (((funcGraphProp1) =>
% 130.11/17.14 (((funcGraphProp3) =>
% 130.11/17.14 (((funcGraphProp2) =>
% 130.11/17.14 (((funcextLem) =>
% 130.11/17.14 (((funcGraphProp4) =>
% 130.11/17.14 (((subbreln) =>
% 130.11/17.14 (((eqbreln) =>
% 130.11/17.14 (((funcext) =>
% 130.11/17.14 (((funcext2) =>
% 130.11/17.14 (((ap2apEq1) =>
% 130.11/17.14 (((ap2apEq2) =>
% 130.11/17.14 (((beta1) =>
% 130.11/17.14 (((eta1) =>
% 130.11/17.14 (((lam2lamEq) =>
% 130.11/17.14 (((beta2) =>
% 130.11/17.14 (((eta2) =>
% 130.11/17.14 (((iffalseProp1) =>
% 130.11/17.14 (((iffalseProp2) =>
% 130.11/17.14 (((iftrueProp1) =>
% 130.11/17.14 (((iftrueProp2) =>
% 130.11/17.14 (((ifSingleton) =>
% 130.11/17.14 (((ifp) =>
% 130.11/17.14 (((theeq) =>
% 130.11/17.14 (((iftrue) =>
% 130.11/17.14 (((iffalse) =>
% 130.11/17.14 (((iftrueorfalse) =>
% 130.11/17.14 (((binintersectT_lem) =>
% 130.11/17.14 (((binunionT_lem) =>
% 130.11/17.14 (((powersetT_lem) =>
% 130.11/17.14 (((setminusT_lem) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementT_lem) =>
% 130.11/17.14 ((
% 130.11/17.14 (setextT) =>
% 130.11/17.14 ((
% 130.11/17.14 (subsetTI) =>
% 130.11/17.14 ((
% 130.11/17.14 (powersetTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (powersetTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTELcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTERcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT1) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT2) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT3) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub2) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementEq) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTnotintersectT) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementImpComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementSubsetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementInPowersetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (contraSubsetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTcontraSubset) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTILcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTIRcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion2) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (intersectInPowersetIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpNotIn1) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpInComplement1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTE) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTEcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementUnionInPowersetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule0) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_5) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all2) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1SetBreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (choice2fnsingleton) =>
% 130.11/17.14 ((
% 130.11/17.14 (setOfPairsIsBReln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all1) =>
% 130.11/17.14 ((
% 130.11/17.14 (subbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (eqbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compEex) =>
% 130.11/17.14 ((
% 130.11/17.14 (!!) @ (
% 130.11/17.14 (('#B') @ (
% 130.11/17.14 !!) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 !!))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#C') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2031])).
% 130.11/17.14 thf(zip_derived_cl2049, plain,
% 130.11/17.14 (~ (((funcGraphProp3) =>
% 130.11/17.14 (((funcGraphProp2) =>
% 130.11/17.14 (((funcextLem) =>
% 130.11/17.14 (((funcGraphProp4) =>
% 130.11/17.14 (((subbreln) =>
% 130.11/17.14 (((eqbreln) =>
% 130.11/17.14 (((funcext) =>
% 130.11/17.14 (((funcext2) =>
% 130.11/17.14 (((ap2apEq1) =>
% 130.11/17.14 (((ap2apEq2) =>
% 130.11/17.14 (((beta1) =>
% 130.11/17.14 (((eta1) =>
% 130.11/17.14 (((lam2lamEq) =>
% 130.11/17.14 (((beta2) =>
% 130.11/17.14 (((eta2) =>
% 130.11/17.14 (((iffalseProp1) =>
% 130.11/17.14 (((iffalseProp2) =>
% 130.11/17.14 (((iftrueProp1) =>
% 130.11/17.14 (((iftrueProp2) =>
% 130.11/17.14 (((ifSingleton) =>
% 130.11/17.14 (((ifp) =>
% 130.11/17.14 (((theeq) =>
% 130.11/17.14 (((iftrue) =>
% 130.11/17.14 (((iffalse) =>
% 130.11/17.14 (((iftrueorfalse) =>
% 130.11/17.14 (((binintersectT_lem) =>
% 130.11/17.14 (((binunionT_lem) =>
% 130.11/17.14 (((powersetT_lem) =>
% 130.11/17.14 (((setminusT_lem) =>
% 130.11/17.14 (((complementT_lem) =>
% 130.11/17.14 ((
% 130.11/17.14 (setextT) =>
% 130.11/17.14 ((
% 130.11/17.14 (subsetTI) =>
% 130.11/17.14 ((
% 130.11/17.14 (powersetTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (powersetTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTELcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTERcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT1) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT2) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT3) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub2) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementEq) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTnotintersectT) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementImpComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementSubsetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementInPowersetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (contraSubsetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTcontraSubset) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTILcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTIRcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion2) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (intersectInPowersetIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpNotIn1) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpInComplement1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTE) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTEcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementUnionInPowersetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule0) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_5) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all2) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1SetBreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (choice2fnsingleton) =>
% 130.11/17.14 ((
% 130.11/17.14 (setOfPairsIsBReln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all1) =>
% 130.11/17.14 ((
% 130.11/17.14 (subbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (eqbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compEex) =>
% 130.11/17.14 ((
% 130.11/17.14 (!!) @ (
% 130.11/17.14 (('#B') @ (
% 130.11/17.14 !!) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 !!))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#C') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2040])).
% 130.11/17.14 thf(zip_derived_cl2060, plain,
% 130.11/17.14 (~ (((funcGraphProp2) =>
% 130.11/17.14 (((funcextLem) =>
% 130.11/17.14 (((funcGraphProp4) =>
% 130.11/17.14 (((subbreln) =>
% 130.11/17.14 (((eqbreln) =>
% 130.11/17.14 (((funcext) =>
% 130.11/17.14 (((funcext2) =>
% 130.11/17.14 (((ap2apEq1) =>
% 130.11/17.14 (((ap2apEq2) =>
% 130.11/17.14 (((beta1) =>
% 130.11/17.14 (((eta1) =>
% 130.11/17.14 (((lam2lamEq) =>
% 130.11/17.14 (((beta2) =>
% 130.11/17.14 (((eta2) =>
% 130.11/17.14 (((iffalseProp1) =>
% 130.11/17.14 (((iffalseProp2) =>
% 130.11/17.14 (((iftrueProp1) =>
% 130.11/17.14 (((iftrueProp2) =>
% 130.11/17.14 (((ifSingleton) =>
% 130.11/17.14 (((ifp) =>
% 130.11/17.14 (((theeq) =>
% 130.11/17.14 (((iftrue) =>
% 130.11/17.14 (((iffalse) =>
% 130.11/17.14 (((iftrueorfalse) =>
% 130.11/17.14 (((binintersectT_lem) =>
% 130.11/17.14 (((binunionT_lem) =>
% 130.11/17.14 (((powersetT_lem) =>
% 130.11/17.14 (((setminusT_lem) =>
% 130.11/17.14 (((complementT_lem) =>
% 130.11/17.14 (((setextT) =>
% 130.11/17.14 ((
% 130.11/17.14 (subsetTI) =>
% 130.11/17.14 ((
% 130.11/17.14 (powersetTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (powersetTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTELcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTERcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT1) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT2) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT3) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub2) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementEq) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTnotintersectT) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementImpComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementSubsetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementInPowersetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (contraSubsetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTcontraSubset) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTILcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTIRcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion2) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (intersectInPowersetIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpNotIn1) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpInComplement1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTE) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTEcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementUnionInPowersetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule0) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_5) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all2) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1SetBreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (choice2fnsingleton) =>
% 130.11/17.14 ((
% 130.11/17.14 (setOfPairsIsBReln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all1) =>
% 130.11/17.14 ((
% 130.11/17.14 (subbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (eqbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compEex) =>
% 130.11/17.14 ((
% 130.11/17.14 (!!) @ (
% 130.11/17.14 (('#B') @ (
% 130.11/17.14 !!) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 !!))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#C') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2049])).
% 130.11/17.14 thf(zip_derived_cl2072, plain,
% 130.11/17.14 (~ (((funcextLem) =>
% 130.11/17.14 (((funcGraphProp4) =>
% 130.11/17.14 (((subbreln) =>
% 130.11/17.14 (((eqbreln) =>
% 130.11/17.14 (((funcext) =>
% 130.11/17.14 (((funcext2) =>
% 130.11/17.14 (((ap2apEq1) =>
% 130.11/17.14 (((ap2apEq2) =>
% 130.11/17.14 (((beta1) =>
% 130.11/17.14 (((eta1) =>
% 130.11/17.14 (((lam2lamEq) =>
% 130.11/17.14 (((beta2) =>
% 130.11/17.14 (((eta2) =>
% 130.11/17.14 (((iffalseProp1) =>
% 130.11/17.14 (((iffalseProp2) =>
% 130.11/17.14 (((iftrueProp1) =>
% 130.11/17.14 (((iftrueProp2) =>
% 130.11/17.14 (((ifSingleton) =>
% 130.11/17.14 (((ifp) =>
% 130.11/17.14 (((theeq) =>
% 130.11/17.14 (((iftrue) =>
% 130.11/17.14 (((iffalse) =>
% 130.11/17.14 (((iftrueorfalse) =>
% 130.11/17.14 (((binintersectT_lem) =>
% 130.11/17.14 (((binunionT_lem) =>
% 130.11/17.14 (((powersetT_lem) =>
% 130.11/17.14 (((setminusT_lem) =>
% 130.11/17.14 (((complementT_lem) =>
% 130.11/17.14 (((setextT) =>
% 130.11/17.14 (((subsetTI) =>
% 130.11/17.14 ((
% 130.11/17.14 (powersetTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (powersetTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTELcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTERcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT1) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT2) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT3) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub2) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementEq) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTnotintersectT) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementImpComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementSubsetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementInPowersetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (contraSubsetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTcontraSubset) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTILcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTIRcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion2) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (intersectInPowersetIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpNotIn1) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpInComplement1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTE) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTEcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementUnionInPowersetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule0) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_5) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all2) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1SetBreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (choice2fnsingleton) =>
% 130.11/17.14 ((
% 130.11/17.14 (setOfPairsIsBReln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all1) =>
% 130.11/17.14 ((
% 130.11/17.14 (subbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (eqbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compEex) =>
% 130.11/17.14 ((
% 130.11/17.14 (!!) @ (
% 130.11/17.14 (('#B') @ (
% 130.11/17.14 !!) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 !!))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#C') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2060])).
% 130.11/17.14 thf(zip_derived_cl2084, plain,
% 130.11/17.14 (~ (((funcGraphProp4) =>
% 130.11/17.14 (((subbreln) =>
% 130.11/17.14 (((eqbreln) =>
% 130.11/17.14 (((funcext) =>
% 130.11/17.14 (((funcext2) =>
% 130.11/17.14 (((ap2apEq1) =>
% 130.11/17.14 (((ap2apEq2) =>
% 130.11/17.14 (((beta1) =>
% 130.11/17.14 (((eta1) =>
% 130.11/17.14 (((lam2lamEq) =>
% 130.11/17.14 (((beta2) =>
% 130.11/17.14 (((eta2) =>
% 130.11/17.14 (((iffalseProp1) =>
% 130.11/17.14 (((iffalseProp2) =>
% 130.11/17.14 (((iftrueProp1) =>
% 130.11/17.14 (((iftrueProp2) =>
% 130.11/17.14 (((ifSingleton) =>
% 130.11/17.14 (((ifp) =>
% 130.11/17.14 (((theeq) =>
% 130.11/17.14 (((iftrue) =>
% 130.11/17.14 (((iffalse) =>
% 130.11/17.14 (((iftrueorfalse) =>
% 130.11/17.14 (((binintersectT_lem) =>
% 130.11/17.14 (((binunionT_lem) =>
% 130.11/17.14 (((powersetT_lem) =>
% 130.11/17.14 (((setminusT_lem) =>
% 130.11/17.14 (((complementT_lem) =>
% 130.11/17.14 (((setextT) =>
% 130.11/17.14 (((subsetTI) =>
% 130.11/17.14 (((powersetTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (powersetTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTELcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTERcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT1) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT2) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT3) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub2) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementEq) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTnotintersectT) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementImpComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementSubsetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementInPowersetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (contraSubsetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTcontraSubset) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTILcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTIRcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion2) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (intersectInPowersetIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpNotIn1) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpInComplement1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTE) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTEcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementUnionInPowersetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule0) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_5) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all2) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1SetBreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (choice2fnsingleton) =>
% 130.11/17.14 ((
% 130.11/17.14 (setOfPairsIsBReln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all1) =>
% 130.11/17.14 ((
% 130.11/17.14 (subbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (eqbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compEex) =>
% 130.11/17.14 ((
% 130.11/17.14 (!!) @ (
% 130.11/17.14 (('#B') @ (
% 130.11/17.14 !!) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 !!))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#C') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2072])).
% 130.11/17.14 thf(zip_derived_cl2094, plain,
% 130.11/17.14 (~ (((subbreln) =>
% 130.11/17.14 (((eqbreln) =>
% 130.11/17.14 (((funcext) =>
% 130.11/17.14 (((funcext2) =>
% 130.11/17.14 (((ap2apEq1) =>
% 130.11/17.14 (((ap2apEq2) =>
% 130.11/17.14 (((beta1) =>
% 130.11/17.14 (((eta1) =>
% 130.11/17.14 (((lam2lamEq) =>
% 130.11/17.14 (((beta2) =>
% 130.11/17.14 (((eta2) =>
% 130.11/17.14 (((iffalseProp1) =>
% 130.11/17.14 (((iffalseProp2) =>
% 130.11/17.14 (((iftrueProp1) =>
% 130.11/17.14 (((iftrueProp2) =>
% 130.11/17.14 (((ifSingleton) =>
% 130.11/17.14 (((ifp) =>
% 130.11/17.14 (((theeq) =>
% 130.11/17.14 (((iftrue) =>
% 130.11/17.14 (((iffalse) =>
% 130.11/17.14 (((iftrueorfalse) =>
% 130.11/17.14 (((binintersectT_lem) =>
% 130.11/17.14 (((binunionT_lem) =>
% 130.11/17.14 (((powersetT_lem) =>
% 130.11/17.14 (((setminusT_lem) =>
% 130.11/17.14 (((complementT_lem) =>
% 130.11/17.14 (((setextT) =>
% 130.11/17.14 (((subsetTI) =>
% 130.11/17.14 (((powersetTI1) =>
% 130.11/17.14 (((powersetTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTELcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTERcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT1) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT2) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT3) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub2) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementEq) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTnotintersectT) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementImpComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementSubsetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementInPowersetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (contraSubsetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTcontraSubset) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTILcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTIRcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion2) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (intersectInPowersetIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpNotIn1) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpInComplement1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTE) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTEcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementUnionInPowersetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule0) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_5) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all2) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1SetBreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (choice2fnsingleton) =>
% 130.11/17.14 ((
% 130.11/17.14 (setOfPairsIsBReln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all1) =>
% 130.11/17.14 ((
% 130.11/17.14 (subbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (eqbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compEex) =>
% 130.11/17.14 ((
% 130.11/17.14 (!!) @ (
% 130.11/17.14 (('#B') @ (
% 130.11/17.14 !!) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 !!))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#C') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2084])).
% 130.11/17.14 thf(zip_derived_cl2105, plain,
% 130.11/17.14 (~ (((eqbreln) =>
% 130.11/17.14 (((funcext) =>
% 130.11/17.14 (((funcext2) =>
% 130.11/17.14 (((ap2apEq1) =>
% 130.11/17.14 (((ap2apEq2) =>
% 130.11/17.14 (((beta1) =>
% 130.11/17.14 (((eta1) =>
% 130.11/17.14 (((lam2lamEq) =>
% 130.11/17.14 (((beta2) =>
% 130.11/17.14 (((eta2) =>
% 130.11/17.14 (((iffalseProp1) =>
% 130.11/17.14 (((iffalseProp2) =>
% 130.11/17.14 (((iftrueProp1) =>
% 130.11/17.14 (((iftrueProp2) =>
% 130.11/17.14 (((ifSingleton) =>
% 130.11/17.14 (((ifp) =>
% 130.11/17.14 (((theeq) =>
% 130.11/17.14 (((iftrue) =>
% 130.11/17.14 (((iffalse) =>
% 130.11/17.14 (((iftrueorfalse) =>
% 130.11/17.14 (((binintersectT_lem) =>
% 130.11/17.14 (((binunionT_lem) =>
% 130.11/17.14 (((powersetT_lem) =>
% 130.11/17.14 (((setminusT_lem) =>
% 130.11/17.14 (((complementT_lem) =>
% 130.11/17.14 (((setextT) =>
% 130.11/17.14 (((subsetTI) =>
% 130.11/17.14 (((powersetTI1) =>
% 130.11/17.14 (((powersetTE1) =>
% 130.11/17.14 (((complementTI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTELcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTERcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT1) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT2) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT3) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub2) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementEq) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTnotintersectT) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementImpComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementSubsetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementInPowersetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (contraSubsetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTcontraSubset) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTILcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTIRcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion2) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (intersectInPowersetIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpNotIn1) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpInComplement1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTE) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTEcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementUnionInPowersetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule0) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_5) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all2) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1SetBreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (choice2fnsingleton) =>
% 130.11/17.14 ((
% 130.11/17.14 (setOfPairsIsBReln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all1) =>
% 130.11/17.14 ((
% 130.11/17.14 (subbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (eqbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compEex) =>
% 130.11/17.14 ((
% 130.11/17.14 (!!) @ (
% 130.11/17.14 (('#B') @ (
% 130.11/17.14 !!) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 !!))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#C') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2094])).
% 130.11/17.14 thf(zip_derived_cl2118, plain,
% 130.11/17.14 (~ (((funcext) =>
% 130.11/17.14 (((funcext2) =>
% 130.11/17.14 (((ap2apEq1) =>
% 130.11/17.14 (((ap2apEq2) =>
% 130.11/17.14 (((beta1) =>
% 130.11/17.14 (((eta1) =>
% 130.11/17.14 (((lam2lamEq) =>
% 130.11/17.14 (((beta2) =>
% 130.11/17.14 (((eta2) =>
% 130.11/17.14 (((iffalseProp1) =>
% 130.11/17.14 (((iffalseProp2) =>
% 130.11/17.14 (((iftrueProp1) =>
% 130.11/17.14 (((iftrueProp2) =>
% 130.11/17.14 (((ifSingleton) =>
% 130.11/17.14 (((ifp) =>
% 130.11/17.14 (((theeq) =>
% 130.11/17.14 (((iftrue) =>
% 130.11/17.14 (((iffalse) =>
% 130.11/17.14 (((iftrueorfalse) =>
% 130.11/17.14 (((binintersectT_lem) =>
% 130.11/17.14 (((binunionT_lem) =>
% 130.11/17.14 (((powersetT_lem) =>
% 130.11/17.14 (((setminusT_lem) =>
% 130.11/17.14 (((complementT_lem) =>
% 130.11/17.14 (((setextT) =>
% 130.11/17.14 (((subsetTI) =>
% 130.11/17.14 (((powersetTI1) =>
% 130.11/17.14 (((powersetTE1) =>
% 130.11/17.14 (((complementTI1) =>
% 130.11/17.14 (((complementTE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTELcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTERcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT1) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT2) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT3) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub2) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementEq) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTnotintersectT) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementImpComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementSubsetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementInPowersetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (contraSubsetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTcontraSubset) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTILcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTIRcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion2) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (intersectInPowersetIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpNotIn1) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpInComplement1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTE) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTEcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementUnionInPowersetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule0) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_5) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all2) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1SetBreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (choice2fnsingleton) =>
% 130.11/17.14 ((
% 130.11/17.14 (setOfPairsIsBReln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all1) =>
% 130.11/17.14 ((
% 130.11/17.14 (subbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (eqbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compEex) =>
% 130.11/17.14 ((
% 130.11/17.14 (!!) @ (
% 130.11/17.14 (('#B') @ (
% 130.11/17.14 !!) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 !!))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#C') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2105])).
% 130.11/17.14 thf(zip_derived_cl2133, plain,
% 130.11/17.14 (~ (((funcext2) =>
% 130.11/17.14 (((ap2apEq1) =>
% 130.11/17.14 (((ap2apEq2) =>
% 130.11/17.14 (((beta1) =>
% 130.11/17.14 (((eta1) =>
% 130.11/17.14 (((lam2lamEq) =>
% 130.11/17.14 (((beta2) =>
% 130.11/17.14 (((eta2) =>
% 130.11/17.14 (((iffalseProp1) =>
% 130.11/17.14 (((iffalseProp2) =>
% 130.11/17.14 (((iftrueProp1) =>
% 130.11/17.14 (((iftrueProp2) =>
% 130.11/17.14 (((ifSingleton) =>
% 130.11/17.14 (((ifp) =>
% 130.11/17.14 (((theeq) =>
% 130.11/17.14 (((iftrue) =>
% 130.11/17.14 (((iffalse) =>
% 130.11/17.14 (((iftrueorfalse) =>
% 130.11/17.14 (((binintersectT_lem) =>
% 130.11/17.14 (((binunionT_lem) =>
% 130.11/17.14 (((powersetT_lem) =>
% 130.11/17.14 (((setminusT_lem) =>
% 130.11/17.14 (((complementT_lem) =>
% 130.11/17.14 (((setextT) =>
% 130.11/17.14 (((subsetTI) =>
% 130.11/17.14 (((powersetTI1) =>
% 130.11/17.14 (((powersetTE1) =>
% 130.11/17.14 (((complementTI1) =>
% 130.11/17.14 (((complementTE1) =>
% 130.11/17.14 (((binintersectTELcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binintersectTERcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT1) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT2) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT3) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub2) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementEq) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTnotintersectT) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementImpComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementSubsetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementInPowersetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (contraSubsetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTcontraSubset) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTILcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTIRcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion2) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (intersectInPowersetIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpNotIn1) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpInComplement1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTE) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTEcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementUnionInPowersetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule0) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_5) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all2) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1SetBreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (choice2fnsingleton) =>
% 130.11/17.14 ((
% 130.11/17.14 (setOfPairsIsBReln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all1) =>
% 130.11/17.14 ((
% 130.11/17.14 (subbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (eqbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compEex) =>
% 130.11/17.14 ((
% 130.11/17.14 (!!) @ (
% 130.11/17.14 (('#B') @ (
% 130.11/17.14 !!) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 !!))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#C') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2118])).
% 130.11/17.14 thf(zip_derived_cl2149, plain,
% 130.11/17.14 (~ (((ap2apEq1) =>
% 130.11/17.14 (((ap2apEq2) =>
% 130.11/17.14 (((beta1) =>
% 130.11/17.14 (((eta1) =>
% 130.11/17.14 (((lam2lamEq) =>
% 130.11/17.14 (((beta2) =>
% 130.11/17.14 (((eta2) =>
% 130.11/17.14 (((iffalseProp1) =>
% 130.11/17.14 (((iffalseProp2) =>
% 130.11/17.14 (((iftrueProp1) =>
% 130.11/17.14 (((iftrueProp2) =>
% 130.11/17.14 (((ifSingleton) =>
% 130.11/17.14 (((ifp) =>
% 130.11/17.14 (((theeq) =>
% 130.11/17.14 (((iftrue) =>
% 130.11/17.14 (((iffalse) =>
% 130.11/17.14 (((iftrueorfalse) =>
% 130.11/17.14 (((binintersectT_lem) =>
% 130.11/17.14 (((binunionT_lem) =>
% 130.11/17.14 (((powersetT_lem) =>
% 130.11/17.14 (((setminusT_lem) =>
% 130.11/17.14 (((complementT_lem) =>
% 130.11/17.14 (((setextT) =>
% 130.11/17.14 (((subsetTI) =>
% 130.11/17.14 (((powersetTI1) =>
% 130.11/17.14 (((powersetTE1) =>
% 130.11/17.14 (((complementTI1) =>
% 130.11/17.14 (((complementTE1) =>
% 130.11/17.14 (((binintersectTELcontra) =>
% 130.11/17.14 (((binintersectTERcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT1) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT2) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT3) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub2) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementEq) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTnotintersectT) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementImpComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementSubsetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementInPowersetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (contraSubsetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTcontraSubset) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTILcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTIRcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion2) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (intersectInPowersetIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpNotIn1) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpInComplement1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTE) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTEcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementUnionInPowersetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule0) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_5) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all2) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1SetBreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (choice2fnsingleton) =>
% 130.11/17.14 ((
% 130.11/17.14 (setOfPairsIsBReln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all1) =>
% 130.11/17.14 ((
% 130.11/17.14 (subbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (eqbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compEex) =>
% 130.11/17.14 ((
% 130.11/17.14 (!!) @ (
% 130.11/17.14 (('#B') @ (
% 130.11/17.14 !!) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 !!))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#C') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2133])).
% 130.11/17.14 thf(zip_derived_cl2166, plain,
% 130.11/17.14 (~ (((ap2apEq2) =>
% 130.11/17.14 (((beta1) =>
% 130.11/17.14 (((eta1) =>
% 130.11/17.14 (((lam2lamEq) =>
% 130.11/17.14 (((beta2) =>
% 130.11/17.14 (((eta2) =>
% 130.11/17.14 (((iffalseProp1) =>
% 130.11/17.14 (((iffalseProp2) =>
% 130.11/17.14 (((iftrueProp1) =>
% 130.11/17.14 (((iftrueProp2) =>
% 130.11/17.14 (((ifSingleton) =>
% 130.11/17.14 (((ifp) =>
% 130.11/17.14 (((theeq) =>
% 130.11/17.14 (((iftrue) =>
% 130.11/17.14 (((iffalse) =>
% 130.11/17.14 (((iftrueorfalse) =>
% 130.11/17.14 (((binintersectT_lem) =>
% 130.11/17.14 (((binunionT_lem) =>
% 130.11/17.14 (((powersetT_lem) =>
% 130.11/17.14 (((setminusT_lem) =>
% 130.11/17.14 (((complementT_lem) =>
% 130.11/17.14 (((setextT) =>
% 130.11/17.14 (((subsetTI) =>
% 130.11/17.14 (((powersetTI1) =>
% 130.11/17.14 (((powersetTE1) =>
% 130.11/17.14 (((complementTI1) =>
% 130.11/17.14 (((complementTE1) =>
% 130.11/17.14 (((binintersectTELcontra) =>
% 130.11/17.14 (((binintersectTERcontra) =>
% 130.11/17.14 (((contrasubsetT) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT1) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT2) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT3) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub2) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementEq) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTnotintersectT) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementImpComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementSubsetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementInPowersetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (contraSubsetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTcontraSubset) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTILcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTIRcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion2) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (intersectInPowersetIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpNotIn1) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpInComplement1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTE) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTEcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementUnionInPowersetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule0) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_5) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all2) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1SetBreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (choice2fnsingleton) =>
% 130.11/17.14 ((
% 130.11/17.14 (setOfPairsIsBReln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all1) =>
% 130.11/17.14 ((
% 130.11/17.14 (subbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (eqbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compEex) =>
% 130.11/17.14 ((
% 130.11/17.14 (!!) @ (
% 130.11/17.14 (('#B') @ (
% 130.11/17.14 !!) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 !!))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#C') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2149])).
% 130.11/17.14 thf(zip_derived_cl2185, plain,
% 130.11/17.14 (~ (((beta1) =>
% 130.11/17.14 (((eta1) =>
% 130.11/17.14 (((lam2lamEq) =>
% 130.11/17.14 (((beta2) =>
% 130.11/17.14 (((eta2) =>
% 130.11/17.14 (((iffalseProp1) =>
% 130.11/17.14 (((iffalseProp2) =>
% 130.11/17.14 (((iftrueProp1) =>
% 130.11/17.14 (((iftrueProp2) =>
% 130.11/17.14 (((ifSingleton) =>
% 130.11/17.14 (((ifp) =>
% 130.11/17.14 (((theeq) =>
% 130.11/17.14 (((iftrue) =>
% 130.11/17.14 (((iffalse) =>
% 130.11/17.14 (((iftrueorfalse) =>
% 130.11/17.14 (((binintersectT_lem) =>
% 130.11/17.14 (((binunionT_lem) =>
% 130.11/17.14 (((powersetT_lem) =>
% 130.11/17.14 (((setminusT_lem) =>
% 130.11/17.14 (((complementT_lem) =>
% 130.11/17.14 (((setextT) =>
% 130.11/17.14 (((subsetTI) =>
% 130.11/17.14 (((powersetTI1) =>
% 130.11/17.14 (((powersetTE1) =>
% 130.11/17.14 (((complementTI1) =>
% 130.11/17.14 (((complementTE1) =>
% 130.11/17.14 (((binintersectTELcontra) =>
% 130.11/17.14 (((binintersectTERcontra) =>
% 130.11/17.14 (((contrasubsetT) =>
% 130.11/17.14 (((contrasubsetT1) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT2) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT3) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub2) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementEq) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTnotintersectT) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementImpComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementSubsetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementInPowersetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (contraSubsetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTcontraSubset) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTILcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTIRcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion2) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (intersectInPowersetIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpNotIn1) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpInComplement1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTE) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTEcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementUnionInPowersetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule0) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_5) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all2) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1SetBreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (choice2fnsingleton) =>
% 130.11/17.14 ((
% 130.11/17.14 (setOfPairsIsBReln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all1) =>
% 130.11/17.14 ((
% 130.11/17.14 (subbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (eqbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compEex) =>
% 130.11/17.14 ((
% 130.11/17.14 (!!) @ (
% 130.11/17.14 (('#B') @ (
% 130.11/17.14 !!) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 !!))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#C') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2166])).
% 130.11/17.14 thf(zip_derived_cl2203, plain,
% 130.11/17.14 (~ (((eta1) =>
% 130.11/17.14 (((lam2lamEq) =>
% 130.11/17.14 (((beta2) =>
% 130.11/17.14 (((eta2) =>
% 130.11/17.14 (((iffalseProp1) =>
% 130.11/17.14 (((iffalseProp2) =>
% 130.11/17.14 (((iftrueProp1) =>
% 130.11/17.14 (((iftrueProp2) =>
% 130.11/17.14 (((ifSingleton) =>
% 130.11/17.14 (((ifp) =>
% 130.11/17.14 (((theeq) =>
% 130.11/17.14 (((iftrue) =>
% 130.11/17.14 (((iffalse) =>
% 130.11/17.14 (((iftrueorfalse) =>
% 130.11/17.14 (((binintersectT_lem) =>
% 130.11/17.14 (((binunionT_lem) =>
% 130.11/17.14 (((powersetT_lem) =>
% 130.11/17.14 (((setminusT_lem) =>
% 130.11/17.14 (((complementT_lem) =>
% 130.11/17.14 (((setextT) =>
% 130.11/17.14 (((subsetTI) =>
% 130.11/17.14 (((powersetTI1) =>
% 130.11/17.14 (((powersetTE1) =>
% 130.11/17.14 (((complementTI1) =>
% 130.11/17.14 (((complementTE1) =>
% 130.11/17.14 (((binintersectTELcontra) =>
% 130.11/17.14 (((binintersectTERcontra) =>
% 130.11/17.14 (((contrasubsetT) =>
% 130.11/17.14 (((contrasubsetT1) =>
% 130.11/17.14 (((contrasubsetT2) =>
% 130.11/17.14 ((
% 130.11/17.14 (contrasubsetT3) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub2) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementEq) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTnotintersectT) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementImpComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementSubsetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementInPowersetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (contraSubsetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTcontraSubset) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTILcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTIRcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion2) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (intersectInPowersetIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpNotIn1) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpInComplement1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTE) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTEcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementUnionInPowersetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule0) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_5) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all2) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1SetBreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (choice2fnsingleton) =>
% 130.11/17.14 ((
% 130.11/17.14 (setOfPairsIsBReln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all1) =>
% 130.11/17.14 ((
% 130.11/17.14 (subbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (eqbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compprop) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compI) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compE) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1compEex) =>
% 130.11/17.14 ((
% 130.11/17.14 (!!) @ (
% 130.11/17.14 (('#B') @ (
% 130.11/17.14 !!) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 !!))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#S') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#S') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 =>))) @
% 130.11/17.14 breln1)))))) @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#C') @ (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 (
% 130.11/17.14 (
% 130.11/17.14 ('#B') @ (
% 130.11/17.14 '#B') @
% 130.11/17.14 breln1)))) @
% 130.11/17.14 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2185])).
% 130.11/17.14 thf(zip_derived_cl2219, plain,
% 130.11/17.14 (~ (((lam2lamEq) =>
% 130.11/17.14 (((beta2) =>
% 130.11/17.14 (((eta2) =>
% 130.11/17.14 (((iffalseProp1) =>
% 130.11/17.14 (((iffalseProp2) =>
% 130.11/17.14 (((iftrueProp1) =>
% 130.11/17.14 (((iftrueProp2) =>
% 130.11/17.14 (((ifSingleton) =>
% 130.11/17.14 (((ifp) =>
% 130.11/17.14 (((theeq) =>
% 130.11/17.14 (((iftrue) =>
% 130.11/17.14 (((iffalse) =>
% 130.11/17.14 (((iftrueorfalse) =>
% 130.11/17.14 (((binintersectT_lem) =>
% 130.11/17.14 (((binunionT_lem) =>
% 130.11/17.14 (((powersetT_lem) =>
% 130.11/17.14 (((setminusT_lem) =>
% 130.11/17.14 (((complementT_lem) =>
% 130.11/17.14 (((setextT) =>
% 130.11/17.14 (((subsetTI) =>
% 130.11/17.14 (((powersetTI1) =>
% 130.11/17.14 (((powersetTE1) =>
% 130.11/17.14 (((complementTI1) =>
% 130.11/17.14 (((complementTE1) =>
% 130.11/17.14 (((binintersectTELcontra) =>
% 130.11/17.14 (((binintersectTERcontra) =>
% 130.11/17.14 (((contrasubsetT) =>
% 130.11/17.14 (((contrasubsetT1) =>
% 130.11/17.14 (((contrasubsetT2) =>
% 130.11/17.14 (((contrasubsetT3) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementI1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementE1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub1) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementSub2) =>
% 130.11/17.14 ((
% 130.11/17.14 (doubleComplementEq) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTnotintersectT) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementImpComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementSubsetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementInPowersetComplementIntersect) =>
% 130.11/17.14 ((
% 130.11/17.14 (contraSubsetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementTcontraSubset) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTILcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTIRcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInUnion2) =>
% 130.11/17.14 ((
% 130.11/17.14 (inIntersectImpInIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (intersectInPowersetIntersectUnions) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpNotIn1) =>
% 130.11/17.14 ((
% 130.11/17.14 (inComplementUnionImpInComplement1) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTE) =>
% 130.11/17.14 ((
% 130.11/17.14 (binunionTEcontra) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a1) =>
% 130.11/17.14 ((
% 130.11/17.14 (complementUnionInPowersetComplement) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan1) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2a) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b2) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2b) =>
% 130.11/17.14 ((
% 130.11/17.14 (demorgan2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule0) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz13rule4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_1) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_2) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_3) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_4) =>
% 130.11/17.14 ((
% 130.11/17.14 (woz1_5) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all2) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1SetBreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (choice2fnsingleton) =>
% 130.11/17.14 ((
% 130.11/17.14 (setOfPairsIsBReln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1all1) =>
% 130.11/17.14 ((
% 130.11/17.14 (subbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (eqbreln1) =>
% 130.11/17.14 ((
% 130.11/17.14 (breln1invprop) =>
% 130.11/17.14 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2203])).
% 130.11/17.15 thf(zip_derived_cl2235, plain,
% 130.11/17.15 (~ (((beta2) =>
% 130.11/17.15 (((eta2) =>
% 130.11/17.15 (((iffalseProp1) =>
% 130.11/17.15 (((iffalseProp2) =>
% 130.11/17.15 (((iftrueProp1) =>
% 130.11/17.15 (((iftrueProp2) =>
% 130.11/17.15 (((ifSingleton) =>
% 130.11/17.15 (((ifp) =>
% 130.11/17.15 (((theeq) =>
% 130.11/17.15 (((iftrue) =>
% 130.11/17.15 (((iffalse) =>
% 130.11/17.15 (((iftrueorfalse) =>
% 130.11/17.15 (((binintersectT_lem) =>
% 130.11/17.15 (((binunionT_lem) =>
% 130.11/17.15 (((powersetT_lem) =>
% 130.11/17.15 (((setminusT_lem) =>
% 130.11/17.15 (((complementT_lem) =>
% 130.11/17.15 (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 ((
% 130.11/17.15 (doubleComplementE1) =>
% 130.11/17.15 ((
% 130.11/17.15 (doubleComplementSub1) =>
% 130.11/17.15 ((
% 130.11/17.15 (doubleComplementSub2) =>
% 130.11/17.15 ((
% 130.11/17.15 (doubleComplementEq) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementTnotintersectT) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementImpComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementSubsetComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementInPowersetComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (contraSubsetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementTcontraSubset) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTILcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTIRcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion2) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (intersectInPowersetIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2219])).
% 130.11/17.15 thf(zip_derived_cl2251, plain,
% 130.11/17.15 (~ (((eta2) =>
% 130.11/17.15 (((iffalseProp1) =>
% 130.11/17.15 (((iffalseProp2) =>
% 130.11/17.15 (((iftrueProp1) =>
% 130.11/17.15 (((iftrueProp2) =>
% 130.11/17.15 (((ifSingleton) =>
% 130.11/17.15 (((ifp) =>
% 130.11/17.15 (((theeq) =>
% 130.11/17.15 (((iftrue) =>
% 130.11/17.15 (((iffalse) =>
% 130.11/17.15 (((iftrueorfalse) =>
% 130.11/17.15 (((binintersectT_lem) =>
% 130.11/17.15 (((binunionT_lem) =>
% 130.11/17.15 (((powersetT_lem) =>
% 130.11/17.15 (((setminusT_lem) =>
% 130.11/17.15 (((complementT_lem) =>
% 130.11/17.15 (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 ((
% 130.11/17.15 (doubleComplementSub1) =>
% 130.11/17.15 ((
% 130.11/17.15 (doubleComplementSub2) =>
% 130.11/17.15 ((
% 130.11/17.15 (doubleComplementEq) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementTnotintersectT) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementImpComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementSubsetComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementInPowersetComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (contraSubsetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementTcontraSubset) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTILcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTIRcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion2) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (intersectInPowersetIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2235])).
% 130.11/17.15 thf(zip_derived_cl2268, plain,
% 130.11/17.15 (~ (((iffalseProp1) =>
% 130.11/17.15 (((iffalseProp2) =>
% 130.11/17.15 (((iftrueProp1) =>
% 130.11/17.15 (((iftrueProp2) =>
% 130.11/17.15 (((ifSingleton) =>
% 130.11/17.15 (((ifp) =>
% 130.11/17.15 (((theeq) =>
% 130.11/17.15 (((iftrue) =>
% 130.11/17.15 (((iffalse) =>
% 130.11/17.15 (((iftrueorfalse) =>
% 130.11/17.15 (((binintersectT_lem) =>
% 130.11/17.15 (((binunionT_lem) =>
% 130.11/17.15 (((powersetT_lem) =>
% 130.11/17.15 (((setminusT_lem) =>
% 130.11/17.15 (((complementT_lem) =>
% 130.11/17.15 (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 ((
% 130.11/17.15 (doubleComplementSub2) =>
% 130.11/17.15 ((
% 130.11/17.15 (doubleComplementEq) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementTnotintersectT) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementImpComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementSubsetComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementInPowersetComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (contraSubsetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementTcontraSubset) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTILcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTIRcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion2) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (intersectInPowersetIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2251])).
% 130.11/17.15 thf(zip_derived_cl2286, plain,
% 130.11/17.15 (~ (((iffalseProp2) =>
% 130.11/17.15 (((iftrueProp1) =>
% 130.11/17.15 (((iftrueProp2) =>
% 130.11/17.15 (((ifSingleton) =>
% 130.11/17.15 (((ifp) =>
% 130.11/17.15 (((theeq) =>
% 130.11/17.15 (((iftrue) =>
% 130.11/17.15 (((iffalse) =>
% 130.11/17.15 (((iftrueorfalse) =>
% 130.11/17.15 (((binintersectT_lem) =>
% 130.11/17.15 (((binunionT_lem) =>
% 130.11/17.15 (((powersetT_lem) =>
% 130.11/17.15 (((setminusT_lem) =>
% 130.11/17.15 (((complementT_lem) =>
% 130.11/17.15 (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 ((
% 130.11/17.15 (doubleComplementEq) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementTnotintersectT) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementImpComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementSubsetComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementInPowersetComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (contraSubsetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementTcontraSubset) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTILcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTIRcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion2) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (intersectInPowersetIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2268])).
% 130.11/17.15 thf(zip_derived_cl2306, plain,
% 130.11/17.15 (~ (((iftrueProp1) =>
% 130.11/17.15 (((iftrueProp2) =>
% 130.11/17.15 (((ifSingleton) =>
% 130.11/17.15 (((ifp) =>
% 130.11/17.15 (((theeq) =>
% 130.11/17.15 (((iftrue) =>
% 130.11/17.15 (((iffalse) =>
% 130.11/17.15 (((iftrueorfalse) =>
% 130.11/17.15 (((binintersectT_lem) =>
% 130.11/17.15 (((binunionT_lem) =>
% 130.11/17.15 (((powersetT_lem) =>
% 130.11/17.15 (((setminusT_lem) =>
% 130.11/17.15 (((complementT_lem) =>
% 130.11/17.15 (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 (((doubleComplementEq) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementTnotintersectT) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementImpComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementSubsetComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementInPowersetComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (contraSubsetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementTcontraSubset) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTILcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTIRcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion2) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (intersectInPowersetIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2286])).
% 130.11/17.15 thf(zip_derived_cl2328, plain,
% 130.11/17.15 (~ (((iftrueProp2) =>
% 130.11/17.15 (((ifSingleton) =>
% 130.11/17.15 (((ifp) =>
% 130.11/17.15 (((theeq) =>
% 130.11/17.15 (((iftrue) =>
% 130.11/17.15 (((iffalse) =>
% 130.11/17.15 (((iftrueorfalse) =>
% 130.11/17.15 (((binintersectT_lem) =>
% 130.11/17.15 (((binunionT_lem) =>
% 130.11/17.15 (((powersetT_lem) =>
% 130.11/17.15 (((setminusT_lem) =>
% 130.11/17.15 (((complementT_lem) =>
% 130.11/17.15 (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 (((doubleComplementEq) =>
% 130.11/17.15 (((complementTnotintersectT) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementImpComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementSubsetComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementInPowersetComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (contraSubsetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementTcontraSubset) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTILcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTIRcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion2) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (intersectInPowersetIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2306])).
% 130.11/17.15 thf(zip_derived_cl2344, plain,
% 130.11/17.15 (~ (((ifSingleton) =>
% 130.11/17.15 (((ifp) =>
% 130.11/17.15 (((theeq) =>
% 130.11/17.15 (((iftrue) =>
% 130.11/17.15 (((iffalse) =>
% 130.11/17.15 (((iftrueorfalse) =>
% 130.11/17.15 (((binintersectT_lem) =>
% 130.11/17.15 (((binunionT_lem) =>
% 130.11/17.15 (((powersetT_lem) =>
% 130.11/17.15 (((setminusT_lem) =>
% 130.11/17.15 (((complementT_lem) =>
% 130.11/17.15 (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 (((doubleComplementEq) =>
% 130.11/17.15 (((complementTnotintersectT) =>
% 130.11/17.15 (((complementImpComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementSubsetComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementInPowersetComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (contraSubsetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementTcontraSubset) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTILcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTIRcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion2) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (intersectInPowersetIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2328])).
% 130.11/17.15 thf(zip_derived_cl2360, plain,
% 130.11/17.15 (~ (((ifp) =>
% 130.11/17.15 (((theeq) =>
% 130.11/17.15 (((iftrue) =>
% 130.11/17.15 (((iffalse) =>
% 130.11/17.15 (((iftrueorfalse) =>
% 130.11/17.15 (((binintersectT_lem) =>
% 130.11/17.15 (((binunionT_lem) =>
% 130.11/17.15 (((powersetT_lem) =>
% 130.11/17.15 (((setminusT_lem) =>
% 130.11/17.15 (((complementT_lem) =>
% 130.11/17.15 (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 (((doubleComplementEq) =>
% 130.11/17.15 (((complementTnotintersectT) =>
% 130.11/17.15 (((complementImpComplementIntersect) =>
% 130.11/17.15 (((complementSubsetComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementInPowersetComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (contraSubsetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementTcontraSubset) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTILcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTIRcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion2) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (intersectInPowersetIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2344])).
% 130.11/17.15 thf(zip_derived_cl2381, plain,
% 130.11/17.15 (~ (((theeq) =>
% 130.11/17.15 (((iftrue) =>
% 130.11/17.15 (((iffalse) =>
% 130.11/17.15 (((iftrueorfalse) =>
% 130.11/17.15 (((binintersectT_lem) =>
% 130.11/17.15 (((binunionT_lem) =>
% 130.11/17.15 (((powersetT_lem) =>
% 130.11/17.15 (((setminusT_lem) =>
% 130.11/17.15 (((complementT_lem) =>
% 130.11/17.15 (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 (((doubleComplementEq) =>
% 130.11/17.15 (((complementTnotintersectT) =>
% 130.11/17.15 (((complementImpComplementIntersect) =>
% 130.11/17.15 (((complementSubsetComplementIntersect) =>
% 130.11/17.15 (((complementInPowersetComplementIntersect) =>
% 130.11/17.15 ((
% 130.11/17.15 (contraSubsetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementTcontraSubset) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTILcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTIRcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion2) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (intersectInPowersetIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2360])).
% 130.11/17.15 thf(zip_derived_cl2399, plain,
% 130.11/17.15 (~ (((iftrue) =>
% 130.11/17.15 (((iffalse) =>
% 130.11/17.15 (((iftrueorfalse) =>
% 130.11/17.15 (((binintersectT_lem) =>
% 130.11/17.15 (((binunionT_lem) =>
% 130.11/17.15 (((powersetT_lem) =>
% 130.11/17.15 (((setminusT_lem) =>
% 130.11/17.15 (((complementT_lem) =>
% 130.11/17.15 (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 (((doubleComplementEq) =>
% 130.11/17.15 (((complementTnotintersectT) =>
% 130.11/17.15 (((complementImpComplementIntersect) =>
% 130.11/17.15 (((complementSubsetComplementIntersect) =>
% 130.11/17.15 (((complementInPowersetComplementIntersect) =>
% 130.11/17.15 (((contraSubsetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementTcontraSubset) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTILcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTIRcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion2) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (intersectInPowersetIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2381])).
% 130.11/17.15 thf(zip_derived_cl2415, plain,
% 130.11/17.15 (~ (((iffalse) =>
% 130.11/17.15 (((iftrueorfalse) =>
% 130.11/17.15 (((binintersectT_lem) =>
% 130.11/17.15 (((binunionT_lem) =>
% 130.11/17.15 (((powersetT_lem) =>
% 130.11/17.15 (((setminusT_lem) =>
% 130.11/17.15 (((complementT_lem) =>
% 130.11/17.15 (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 (((doubleComplementEq) =>
% 130.11/17.15 (((complementTnotintersectT) =>
% 130.11/17.15 (((complementImpComplementIntersect) =>
% 130.11/17.15 (((complementSubsetComplementIntersect) =>
% 130.11/17.15 (((complementInPowersetComplementIntersect) =>
% 130.11/17.15 (((contraSubsetComplement) =>
% 130.11/17.15 (((complementTcontraSubset) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTILcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTIRcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion2) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (intersectInPowersetIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2399])).
% 130.11/17.15 thf(zip_derived_cl2434, plain,
% 130.11/17.15 (~ (((iftrueorfalse) =>
% 130.11/17.15 (((binintersectT_lem) =>
% 130.11/17.15 (((binunionT_lem) =>
% 130.11/17.15 (((powersetT_lem) =>
% 130.11/17.15 (((setminusT_lem) =>
% 130.11/17.15 (((complementT_lem) =>
% 130.11/17.15 (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 (((doubleComplementEq) =>
% 130.11/17.15 (((complementTnotintersectT) =>
% 130.11/17.15 (((complementImpComplementIntersect) =>
% 130.11/17.15 (((complementSubsetComplementIntersect) =>
% 130.11/17.15 (((complementInPowersetComplementIntersect) =>
% 130.11/17.15 (((contraSubsetComplement) =>
% 130.11/17.15 (((complementTcontraSubset) =>
% 130.11/17.15 (((binunionTILcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTIRcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion2) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (intersectInPowersetIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2415])).
% 130.11/17.15 thf(zip_derived_cl2449, plain,
% 130.11/17.15 (~ (((binintersectT_lem) =>
% 130.11/17.15 (((binunionT_lem) =>
% 130.11/17.15 (((powersetT_lem) =>
% 130.11/17.15 (((setminusT_lem) =>
% 130.11/17.15 (((complementT_lem) =>
% 130.11/17.15 (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 (((doubleComplementEq) =>
% 130.11/17.15 (((complementTnotintersectT) =>
% 130.11/17.15 (((complementImpComplementIntersect) =>
% 130.11/17.15 (((complementSubsetComplementIntersect) =>
% 130.11/17.15 (((complementInPowersetComplementIntersect) =>
% 130.11/17.15 (((contraSubsetComplement) =>
% 130.11/17.15 (((complementTcontraSubset) =>
% 130.11/17.15 (((binunionTILcontra) =>
% 130.11/17.15 (((binunionTIRcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion2) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (intersectInPowersetIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2434])).
% 130.11/17.15 thf(zip_derived_cl2461, plain,
% 130.11/17.15 (~ (((binunionT_lem) =>
% 130.11/17.15 (((powersetT_lem) =>
% 130.11/17.15 (((setminusT_lem) =>
% 130.11/17.15 (((complementT_lem) =>
% 130.11/17.15 (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 (((doubleComplementEq) =>
% 130.11/17.15 (((complementTnotintersectT) =>
% 130.11/17.15 (((complementImpComplementIntersect) =>
% 130.11/17.15 (((complementSubsetComplementIntersect) =>
% 130.11/17.15 (((complementInPowersetComplementIntersect) =>
% 130.11/17.15 (((contraSubsetComplement) =>
% 130.11/17.15 (((complementTcontraSubset) =>
% 130.11/17.15 (((binunionTILcontra) =>
% 130.11/17.15 (((binunionTIRcontra) =>
% 130.11/17.15 (((inIntersectImpInUnion) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInUnion2) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (intersectInPowersetIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2449])).
% 130.11/17.15 thf(zip_derived_cl2472, plain,
% 130.11/17.15 (~ (((powersetT_lem) =>
% 130.11/17.15 (((setminusT_lem) =>
% 130.11/17.15 (((complementT_lem) =>
% 130.11/17.15 (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 (((doubleComplementEq) =>
% 130.11/17.15 (((complementTnotintersectT) =>
% 130.11/17.15 (((complementImpComplementIntersect) =>
% 130.11/17.15 (((complementSubsetComplementIntersect) =>
% 130.11/17.15 (((complementInPowersetComplementIntersect) =>
% 130.11/17.15 (((contraSubsetComplement) =>
% 130.11/17.15 (((complementTcontraSubset) =>
% 130.11/17.15 (((binunionTILcontra) =>
% 130.11/17.15 (((binunionTIRcontra) =>
% 130.11/17.15 (((inIntersectImpInUnion) =>
% 130.11/17.15 (((inIntersectImpInUnion2) =>
% 130.11/17.15 ((
% 130.11/17.15 (inIntersectImpInIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (intersectInPowersetIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2461])).
% 130.11/17.15 thf(zip_derived_cl2483, plain,
% 130.11/17.15 (~ (((setminusT_lem) =>
% 130.11/17.15 (((complementT_lem) =>
% 130.11/17.15 (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 (((doubleComplementEq) =>
% 130.11/17.15 (((complementTnotintersectT) =>
% 130.11/17.15 (((complementImpComplementIntersect) =>
% 130.11/17.15 (((complementSubsetComplementIntersect) =>
% 130.11/17.15 (((complementInPowersetComplementIntersect) =>
% 130.11/17.15 (((contraSubsetComplement) =>
% 130.11/17.15 (((complementTcontraSubset) =>
% 130.11/17.15 (((binunionTILcontra) =>
% 130.11/17.15 (((binunionTIRcontra) =>
% 130.11/17.15 (((inIntersectImpInUnion) =>
% 130.11/17.15 (((inIntersectImpInUnion2) =>
% 130.11/17.15 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (intersectInPowersetIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2472])).
% 130.11/17.15 thf(zip_derived_cl2492, plain,
% 130.11/17.15 (~ (((complementT_lem) =>
% 130.11/17.15 (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 (((doubleComplementEq) =>
% 130.11/17.15 (((complementTnotintersectT) =>
% 130.11/17.15 (((complementImpComplementIntersect) =>
% 130.11/17.15 (((complementSubsetComplementIntersect) =>
% 130.11/17.15 (((complementInPowersetComplementIntersect) =>
% 130.11/17.15 (((contraSubsetComplement) =>
% 130.11/17.15 (((complementTcontraSubset) =>
% 130.11/17.15 (((binunionTILcontra) =>
% 130.11/17.15 (((binunionTIRcontra) =>
% 130.11/17.15 (((inIntersectImpInUnion) =>
% 130.11/17.15 (((inIntersectImpInUnion2) =>
% 130.11/17.15 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.15 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2483])).
% 130.11/17.15 thf(zip_derived_cl2502, plain,
% 130.11/17.15 (~ (((setextT) =>
% 130.11/17.15 (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 (((doubleComplementEq) =>
% 130.11/17.15 (((complementTnotintersectT) =>
% 130.11/17.15 (((complementImpComplementIntersect) =>
% 130.11/17.15 (((complementSubsetComplementIntersect) =>
% 130.11/17.15 (((complementInPowersetComplementIntersect) =>
% 130.11/17.15 (((contraSubsetComplement) =>
% 130.11/17.15 (((complementTcontraSubset) =>
% 130.11/17.15 (((binunionTILcontra) =>
% 130.11/17.15 (((binunionTIRcontra) =>
% 130.11/17.15 (((inIntersectImpInUnion) =>
% 130.11/17.15 (((inIntersectImpInUnion2) =>
% 130.11/17.15 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.15 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.15 (((inComplementUnionImpNotIn1) =>
% 130.11/17.15 ((
% 130.11/17.15 (inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2492])).
% 130.11/17.15 thf(zip_derived_cl2513, plain,
% 130.11/17.15 (~ (((subsetTI) =>
% 130.11/17.15 (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 (((doubleComplementEq) =>
% 130.11/17.15 (((complementTnotintersectT) =>
% 130.11/17.15 (((complementImpComplementIntersect) =>
% 130.11/17.15 (((complementSubsetComplementIntersect) =>
% 130.11/17.15 (((complementInPowersetComplementIntersect) =>
% 130.11/17.15 (((contraSubsetComplement) =>
% 130.11/17.15 (((complementTcontraSubset) =>
% 130.11/17.15 (((binunionTILcontra) =>
% 130.11/17.15 (((binunionTIRcontra) =>
% 130.11/17.15 (((inIntersectImpInUnion) =>
% 130.11/17.15 (((inIntersectImpInUnion2) =>
% 130.11/17.15 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.15 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.15 (((inComplementUnionImpNotIn1) =>
% 130.11/17.15 (((inComplementUnionImpInComplement1) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2502])).
% 130.11/17.15 thf(zip_derived_cl2525, plain,
% 130.11/17.15 (~ (((powersetTI1) =>
% 130.11/17.15 (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 (((doubleComplementEq) =>
% 130.11/17.15 (((complementTnotintersectT) =>
% 130.11/17.15 (((complementImpComplementIntersect) =>
% 130.11/17.15 (((complementSubsetComplementIntersect) =>
% 130.11/17.15 (((complementInPowersetComplementIntersect) =>
% 130.11/17.15 (((contraSubsetComplement) =>
% 130.11/17.15 (((complementTcontraSubset) =>
% 130.11/17.15 (((binunionTILcontra) =>
% 130.11/17.15 (((binunionTIRcontra) =>
% 130.11/17.15 (((inIntersectImpInUnion) =>
% 130.11/17.15 (((inIntersectImpInUnion2) =>
% 130.11/17.15 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.15 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.15 (((inComplementUnionImpNotIn1) =>
% 130.11/17.15 (((inComplementUnionImpInComplement1) =>
% 130.11/17.15 (((binunionTE) =>
% 130.11/17.15 ((
% 130.11/17.15 (binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compprop) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compI) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compE) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1compEex) =>
% 130.11/17.15 ((
% 130.11/17.15 (!!) @ (
% 130.11/17.15 (('#B') @ (
% 130.11/17.15 !!) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 !!))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#S') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#S') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 =>))) @
% 130.11/17.15 breln1)))))) @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#C') @ (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 (
% 130.11/17.15 (
% 130.11/17.15 ('#B') @ (
% 130.11/17.15 '#B') @
% 130.11/17.15 breln1)))) @
% 130.11/17.15 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2513])).
% 130.11/17.15 thf(zip_derived_cl2534, plain,
% 130.11/17.15 (~ (((powersetTE1) =>
% 130.11/17.15 (((complementTI1) =>
% 130.11/17.15 (((complementTE1) =>
% 130.11/17.15 (((binintersectTELcontra) =>
% 130.11/17.15 (((binintersectTERcontra) =>
% 130.11/17.15 (((contrasubsetT) =>
% 130.11/17.15 (((contrasubsetT1) =>
% 130.11/17.15 (((contrasubsetT2) =>
% 130.11/17.15 (((contrasubsetT3) =>
% 130.11/17.15 (((doubleComplementI1) =>
% 130.11/17.15 (((doubleComplementE1) =>
% 130.11/17.15 (((doubleComplementSub1) =>
% 130.11/17.15 (((doubleComplementSub2) =>
% 130.11/17.15 (((doubleComplementEq) =>
% 130.11/17.15 (((complementTnotintersectT) =>
% 130.11/17.15 (((complementImpComplementIntersect) =>
% 130.11/17.15 (((complementSubsetComplementIntersect) =>
% 130.11/17.15 (((complementInPowersetComplementIntersect) =>
% 130.11/17.15 (((contraSubsetComplement) =>
% 130.11/17.15 (((complementTcontraSubset) =>
% 130.11/17.15 (((binunionTILcontra) =>
% 130.11/17.15 (((binunionTIRcontra) =>
% 130.11/17.15 (((inIntersectImpInUnion) =>
% 130.11/17.15 (((inIntersectImpInUnion2) =>
% 130.11/17.15 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.15 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.15 (((inComplementUnionImpNotIn1) =>
% 130.11/17.15 (((inComplementUnionImpInComplement1) =>
% 130.11/17.15 (((binunionTE) =>
% 130.11/17.15 (((binunionTEcontra) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a1) =>
% 130.11/17.15 ((
% 130.11/17.15 (complementUnionInPowersetComplement) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan1) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2a) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b2) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2b) =>
% 130.11/17.15 ((
% 130.11/17.15 (demorgan2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule0) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz13rule4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_1) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_2) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_3) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_4) =>
% 130.11/17.15 ((
% 130.11/17.15 (woz1_5) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all2) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1SetBreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (choice2fnsingleton) =>
% 130.11/17.15 ((
% 130.11/17.15 (setOfPairsIsBReln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1all1) =>
% 130.11/17.15 ((
% 130.11/17.15 (subbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (eqbreln1) =>
% 130.11/17.15 ((
% 130.11/17.15 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2525])).
% 130.11/17.16 thf(zip_derived_cl2542, plain,
% 130.11/17.16 (~ (((complementTI1) =>
% 130.11/17.16 (((complementTE1) =>
% 130.11/17.16 (((binintersectTELcontra) =>
% 130.11/17.16 (((binintersectTERcontra) =>
% 130.11/17.16 (((contrasubsetT) =>
% 130.11/17.16 (((contrasubsetT1) =>
% 130.11/17.16 (((contrasubsetT2) =>
% 130.11/17.16 (((contrasubsetT3) =>
% 130.11/17.16 (((doubleComplementI1) =>
% 130.11/17.16 (((doubleComplementE1) =>
% 130.11/17.16 (((doubleComplementSub1) =>
% 130.11/17.16 (((doubleComplementSub2) =>
% 130.11/17.16 (((doubleComplementEq) =>
% 130.11/17.16 (((complementTnotintersectT) =>
% 130.11/17.16 (((complementImpComplementIntersect) =>
% 130.11/17.16 (((complementSubsetComplementIntersect) =>
% 130.11/17.16 (((complementInPowersetComplementIntersect) =>
% 130.11/17.16 (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 ((
% 130.11/17.16 (complementUnionInPowersetComplement) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2a2) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan1a) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan1b) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan1) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2a) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2b2) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2b) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule0) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2534])).
% 130.11/17.16 thf(zip_derived_cl2550, plain,
% 130.11/17.16 (~ (((complementTE1) =>
% 130.11/17.16 (((binintersectTELcontra) =>
% 130.11/17.16 (((binintersectTERcontra) =>
% 130.11/17.16 (((contrasubsetT) =>
% 130.11/17.16 (((contrasubsetT1) =>
% 130.11/17.16 (((contrasubsetT2) =>
% 130.11/17.16 (((contrasubsetT3) =>
% 130.11/17.16 (((doubleComplementI1) =>
% 130.11/17.16 (((doubleComplementE1) =>
% 130.11/17.16 (((doubleComplementSub1) =>
% 130.11/17.16 (((doubleComplementSub2) =>
% 130.11/17.16 (((doubleComplementEq) =>
% 130.11/17.16 (((complementTnotintersectT) =>
% 130.11/17.16 (((complementImpComplementIntersect) =>
% 130.11/17.16 (((complementSubsetComplementIntersect) =>
% 130.11/17.16 (((complementInPowersetComplementIntersect) =>
% 130.11/17.16 (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2a2) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan1a) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan1b) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan1) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2a) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2b2) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2b) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule0) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2542])).
% 130.11/17.16 thf(zip_derived_cl2558, plain,
% 130.11/17.16 (~ (((binintersectTELcontra) =>
% 130.11/17.16 (((binintersectTERcontra) =>
% 130.11/17.16 (((contrasubsetT) =>
% 130.11/17.16 (((contrasubsetT1) =>
% 130.11/17.16 (((contrasubsetT2) =>
% 130.11/17.16 (((contrasubsetT3) =>
% 130.11/17.16 (((doubleComplementI1) =>
% 130.11/17.16 (((doubleComplementE1) =>
% 130.11/17.16 (((doubleComplementSub1) =>
% 130.11/17.16 (((doubleComplementSub2) =>
% 130.11/17.16 (((doubleComplementEq) =>
% 130.11/17.16 (((complementTnotintersectT) =>
% 130.11/17.16 (((complementImpComplementIntersect) =>
% 130.11/17.16 (((complementSubsetComplementIntersect) =>
% 130.11/17.16 (((complementInPowersetComplementIntersect) =>
% 130.11/17.16 (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan1a) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan1b) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan1) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2a) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2b2) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2b) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule0) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2550])).
% 130.11/17.16 thf(zip_derived_cl2567, plain,
% 130.11/17.16 (~ (((binintersectTERcontra) =>
% 130.11/17.16 (((contrasubsetT) =>
% 130.11/17.16 (((contrasubsetT1) =>
% 130.11/17.16 (((contrasubsetT2) =>
% 130.11/17.16 (((contrasubsetT3) =>
% 130.11/17.16 (((doubleComplementI1) =>
% 130.11/17.16 (((doubleComplementE1) =>
% 130.11/17.16 (((doubleComplementSub1) =>
% 130.11/17.16 (((doubleComplementSub2) =>
% 130.11/17.16 (((doubleComplementEq) =>
% 130.11/17.16 (((complementTnotintersectT) =>
% 130.11/17.16 (((complementImpComplementIntersect) =>
% 130.11/17.16 (((complementSubsetComplementIntersect) =>
% 130.11/17.16 (((complementInPowersetComplementIntersect) =>
% 130.11/17.16 (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan1b) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan1) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2a) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2b2) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2b) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule0) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2558])).
% 130.11/17.16 thf(zip_derived_cl2577, plain,
% 130.11/17.16 (~ (((contrasubsetT) =>
% 130.11/17.16 (((contrasubsetT1) =>
% 130.11/17.16 (((contrasubsetT2) =>
% 130.11/17.16 (((contrasubsetT3) =>
% 130.11/17.16 (((doubleComplementI1) =>
% 130.11/17.16 (((doubleComplementE1) =>
% 130.11/17.16 (((doubleComplementSub1) =>
% 130.11/17.16 (((doubleComplementSub2) =>
% 130.11/17.16 (((doubleComplementEq) =>
% 130.11/17.16 (((complementTnotintersectT) =>
% 130.11/17.16 (((complementImpComplementIntersect) =>
% 130.11/17.16 (((complementSubsetComplementIntersect) =>
% 130.11/17.16 (((complementInPowersetComplementIntersect) =>
% 130.11/17.16 (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan1) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2a) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2b2) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2b) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule0) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2567])).
% 130.11/17.16 thf(zip_derived_cl2588, plain,
% 130.11/17.16 (~ (((contrasubsetT1) =>
% 130.11/17.16 (((contrasubsetT2) =>
% 130.11/17.16 (((contrasubsetT3) =>
% 130.11/17.16 (((doubleComplementI1) =>
% 130.11/17.16 (((doubleComplementE1) =>
% 130.11/17.16 (((doubleComplementSub1) =>
% 130.11/17.16 (((doubleComplementSub2) =>
% 130.11/17.16 (((doubleComplementEq) =>
% 130.11/17.16 (((complementTnotintersectT) =>
% 130.11/17.16 (((complementImpComplementIntersect) =>
% 130.11/17.16 (((complementSubsetComplementIntersect) =>
% 130.11/17.16 (((complementInPowersetComplementIntersect) =>
% 130.11/17.16 (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2a) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2b2) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2b) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule0) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2577])).
% 130.11/17.16 thf(zip_derived_cl2601, plain,
% 130.11/17.16 (~ (((contrasubsetT2) =>
% 130.11/17.16 (((contrasubsetT3) =>
% 130.11/17.16 (((doubleComplementI1) =>
% 130.11/17.16 (((doubleComplementE1) =>
% 130.11/17.16 (((doubleComplementSub1) =>
% 130.11/17.16 (((doubleComplementSub2) =>
% 130.11/17.16 (((doubleComplementEq) =>
% 130.11/17.16 (((complementTnotintersectT) =>
% 130.11/17.16 (((complementImpComplementIntersect) =>
% 130.11/17.16 (((complementSubsetComplementIntersect) =>
% 130.11/17.16 (((complementInPowersetComplementIntersect) =>
% 130.11/17.16 (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2b2) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2b) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule0) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2588])).
% 130.11/17.16 thf(zip_derived_cl2617, plain,
% 130.11/17.16 (~ (((contrasubsetT3) =>
% 130.11/17.16 (((doubleComplementI1) =>
% 130.11/17.16 (((doubleComplementE1) =>
% 130.11/17.16 (((doubleComplementSub1) =>
% 130.11/17.16 (((doubleComplementSub2) =>
% 130.11/17.16 (((doubleComplementEq) =>
% 130.11/17.16 (((complementTnotintersectT) =>
% 130.11/17.16 (((complementImpComplementIntersect) =>
% 130.11/17.16 (((complementSubsetComplementIntersect) =>
% 130.11/17.16 (((complementInPowersetComplementIntersect) =>
% 130.11/17.16 (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2b) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule0) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2601])).
% 130.11/17.16 thf(zip_derived_cl2636, plain,
% 130.11/17.16 (~ (((doubleComplementI1) =>
% 130.11/17.16 (((doubleComplementE1) =>
% 130.11/17.16 (((doubleComplementSub1) =>
% 130.11/17.16 (((doubleComplementSub2) =>
% 130.11/17.16 (((doubleComplementEq) =>
% 130.11/17.16 (((complementTnotintersectT) =>
% 130.11/17.16 (((complementImpComplementIntersect) =>
% 130.11/17.16 (((complementSubsetComplementIntersect) =>
% 130.11/17.16 (((complementInPowersetComplementIntersect) =>
% 130.11/17.16 (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 ((
% 130.11/17.16 (demorgan2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule0) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2617])).
% 130.11/17.16 thf(zip_derived_cl2655, plain,
% 130.11/17.16 (~ (((doubleComplementE1) =>
% 130.11/17.16 (((doubleComplementSub1) =>
% 130.11/17.16 (((doubleComplementSub2) =>
% 130.11/17.16 (((doubleComplementEq) =>
% 130.11/17.16 (((complementTnotintersectT) =>
% 130.11/17.16 (((complementImpComplementIntersect) =>
% 130.11/17.16 (((complementSubsetComplementIntersect) =>
% 130.11/17.16 (((complementInPowersetComplementIntersect) =>
% 130.11/17.16 (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule0) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2636])).
% 130.11/17.16 thf(zip_derived_cl2672, plain,
% 130.11/17.16 (~ (((doubleComplementSub1) =>
% 130.11/17.16 (((doubleComplementSub2) =>
% 130.11/17.16 (((doubleComplementEq) =>
% 130.11/17.16 (((complementTnotintersectT) =>
% 130.11/17.16 (((complementImpComplementIntersect) =>
% 130.11/17.16 (((complementSubsetComplementIntersect) =>
% 130.11/17.16 (((complementInPowersetComplementIntersect) =>
% 130.11/17.16 (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2655])).
% 130.11/17.16 thf(zip_derived_cl2687, plain,
% 130.11/17.16 (~ (((doubleComplementSub2) =>
% 130.11/17.16 (((doubleComplementEq) =>
% 130.11/17.16 (((complementTnotintersectT) =>
% 130.11/17.16 (((complementImpComplementIntersect) =>
% 130.11/17.16 (((complementSubsetComplementIntersect) =>
% 130.11/17.16 (((complementInPowersetComplementIntersect) =>
% 130.11/17.16 (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2672])).
% 130.11/17.16 thf(zip_derived_cl2699, plain,
% 130.11/17.16 (~ (((doubleComplementEq) =>
% 130.11/17.16 (((complementTnotintersectT) =>
% 130.11/17.16 (((complementImpComplementIntersect) =>
% 130.11/17.16 (((complementSubsetComplementIntersect) =>
% 130.11/17.16 (((complementInPowersetComplementIntersect) =>
% 130.11/17.16 (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 (((woz13rule2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2687])).
% 130.11/17.16 thf(zip_derived_cl2711, plain,
% 130.11/17.16 (~ (((complementTnotintersectT) =>
% 130.11/17.16 (((complementImpComplementIntersect) =>
% 130.11/17.16 (((complementSubsetComplementIntersect) =>
% 130.11/17.16 (((complementInPowersetComplementIntersect) =>
% 130.11/17.16 (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 (((woz13rule2) =>
% 130.11/17.16 (((woz13rule3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz13rule4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2699])).
% 130.11/17.16 thf(zip_derived_cl2723, plain,
% 130.11/17.16 (~ (((complementImpComplementIntersect) =>
% 130.11/17.16 (((complementSubsetComplementIntersect) =>
% 130.11/17.16 (((complementInPowersetComplementIntersect) =>
% 130.11/17.16 (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 (((woz13rule2) =>
% 130.11/17.16 (((woz13rule3) =>
% 130.11/17.16 (((woz13rule4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2711])).
% 130.11/17.16 thf(zip_derived_cl2735, plain,
% 130.11/17.16 (~ (((complementSubsetComplementIntersect) =>
% 130.11/17.16 (((complementInPowersetComplementIntersect) =>
% 130.11/17.16 (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 (((woz13rule2) =>
% 130.11/17.16 (((woz13rule3) =>
% 130.11/17.16 (((woz13rule4) =>
% 130.11/17.16 (((woz1_1) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2723])).
% 130.11/17.16 thf(zip_derived_cl2745, plain,
% 130.11/17.16 (~ (((complementInPowersetComplementIntersect) =>
% 130.11/17.16 (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 (((woz13rule2) =>
% 130.11/17.16 (((woz13rule3) =>
% 130.11/17.16 (((woz13rule4) =>
% 130.11/17.16 (((woz1_1) =>
% 130.11/17.16 (((woz1_2) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2735])).
% 130.11/17.16 thf(zip_derived_cl2753, plain,
% 130.11/17.16 (~ (((contraSubsetComplement) =>
% 130.11/17.16 (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 (((woz13rule2) =>
% 130.11/17.16 (((woz13rule3) =>
% 130.11/17.16 (((woz13rule4) =>
% 130.11/17.16 (((woz1_1) =>
% 130.11/17.16 (((woz1_2) =>
% 130.11/17.16 (((woz1_3) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2745])).
% 130.11/17.16 thf(zip_derived_cl2761, plain,
% 130.11/17.16 (~ (((complementTcontraSubset) =>
% 130.11/17.16 (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 (((woz13rule2) =>
% 130.11/17.16 (((woz13rule3) =>
% 130.11/17.16 (((woz13rule4) =>
% 130.11/17.16 (((woz1_1) =>
% 130.11/17.16 (((woz1_2) =>
% 130.11/17.16 (((woz1_3) =>
% 130.11/17.16 (((woz1_4) =>
% 130.11/17.16 ((
% 130.11/17.16 (woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2753])).
% 130.11/17.16 thf(zip_derived_cl2769, plain,
% 130.11/17.16 (~ (((binunionTILcontra) =>
% 130.11/17.16 (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 (((woz13rule2) =>
% 130.11/17.16 (((woz13rule3) =>
% 130.11/17.16 (((woz13rule4) =>
% 130.11/17.16 (((woz1_1) =>
% 130.11/17.16 (((woz1_2) =>
% 130.11/17.16 (((woz1_3) =>
% 130.11/17.16 (((woz1_4) =>
% 130.11/17.16 (((woz1_5) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2761])).
% 130.11/17.16 thf(zip_derived_cl2778, plain,
% 130.11/17.16 (~ (((binunionTIRcontra) =>
% 130.11/17.16 (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 (((woz13rule2) =>
% 130.11/17.16 (((woz13rule3) =>
% 130.11/17.16 (((woz13rule4) =>
% 130.11/17.16 (((woz1_1) =>
% 130.11/17.16 (((woz1_2) =>
% 130.11/17.16 (((woz1_3) =>
% 130.11/17.16 (((woz1_4) =>
% 130.11/17.16 (((woz1_5) =>
% 130.11/17.16 (((breln1all2) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2769])).
% 130.11/17.16 thf(zip_derived_cl2788, plain,
% 130.11/17.16 (~ (((inIntersectImpInUnion) =>
% 130.11/17.16 (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 (((woz13rule2) =>
% 130.11/17.16 (((woz13rule3) =>
% 130.11/17.16 (((woz13rule4) =>
% 130.11/17.16 (((woz1_1) =>
% 130.11/17.16 (((woz1_2) =>
% 130.11/17.16 (((woz1_3) =>
% 130.11/17.16 (((woz1_4) =>
% 130.11/17.16 (((woz1_5) =>
% 130.11/17.16 (((breln1all2) =>
% 130.11/17.16 (((breln1SetBreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2778])).
% 130.11/17.16 thf(zip_derived_cl2799, plain,
% 130.11/17.16 (~ (((inIntersectImpInUnion2) =>
% 130.11/17.16 (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 (((woz13rule2) =>
% 130.11/17.16 (((woz13rule3) =>
% 130.11/17.16 (((woz13rule4) =>
% 130.11/17.16 (((woz1_1) =>
% 130.11/17.16 (((woz1_2) =>
% 130.11/17.16 (((woz1_3) =>
% 130.11/17.16 (((woz1_4) =>
% 130.11/17.16 (((woz1_5) =>
% 130.11/17.16 (((breln1all2) =>
% 130.11/17.16 (((breln1SetBreln1) =>
% 130.11/17.16 (((choice2fnsingleton) =>
% 130.11/17.16 ((
% 130.11/17.16 (setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2788])).
% 130.11/17.16 thf(zip_derived_cl2810, plain,
% 130.11/17.16 (~ (((inIntersectImpInIntersectUnions) =>
% 130.11/17.16 (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 (((woz13rule2) =>
% 130.11/17.16 (((woz13rule3) =>
% 130.11/17.16 (((woz13rule4) =>
% 130.11/17.16 (((woz1_1) =>
% 130.11/17.16 (((woz1_2) =>
% 130.11/17.16 (((woz1_3) =>
% 130.11/17.16 (((woz1_4) =>
% 130.11/17.16 (((woz1_5) =>
% 130.11/17.16 (((breln1all2) =>
% 130.11/17.16 (((breln1SetBreln1) =>
% 130.11/17.16 (((choice2fnsingleton) =>
% 130.11/17.16 (((setOfPairsIsBReln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2799])).
% 130.11/17.16 thf(zip_derived_cl2820, plain,
% 130.11/17.16 (~ (((intersectInPowersetIntersectUnions) =>
% 130.11/17.16 (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 (((woz13rule2) =>
% 130.11/17.16 (((woz13rule3) =>
% 130.11/17.16 (((woz13rule4) =>
% 130.11/17.16 (((woz1_1) =>
% 130.11/17.16 (((woz1_2) =>
% 130.11/17.16 (((woz1_3) =>
% 130.11/17.16 (((woz1_4) =>
% 130.11/17.16 (((woz1_5) =>
% 130.11/17.16 (((breln1all2) =>
% 130.11/17.16 (((breln1SetBreln1) =>
% 130.11/17.16 (((choice2fnsingleton) =>
% 130.11/17.16 (((setOfPairsIsBReln1) =>
% 130.11/17.16 (((breln1all1) =>
% 130.11/17.16 ((
% 130.11/17.16 (subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2810])).
% 130.11/17.16 thf(zip_derived_cl2830, plain,
% 130.11/17.16 (~ (((inComplementUnionImpNotIn1) =>
% 130.11/17.16 (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 (((woz13rule2) =>
% 130.11/17.16 (((woz13rule3) =>
% 130.11/17.16 (((woz13rule4) =>
% 130.11/17.16 (((woz1_1) =>
% 130.11/17.16 (((woz1_2) =>
% 130.11/17.16 (((woz1_3) =>
% 130.11/17.16 (((woz1_4) =>
% 130.11/17.16 (((woz1_5) =>
% 130.11/17.16 (((breln1all2) =>
% 130.11/17.16 (((breln1SetBreln1) =>
% 130.11/17.16 (((choice2fnsingleton) =>
% 130.11/17.16 (((setOfPairsIsBReln1) =>
% 130.11/17.16 (((breln1all1) =>
% 130.11/17.16 (((subbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2820])).
% 130.11/17.16 thf(zip_derived_cl2841, plain,
% 130.11/17.16 (~ (((inComplementUnionImpInComplement1) =>
% 130.11/17.16 (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 (((woz13rule2) =>
% 130.11/17.16 (((woz13rule3) =>
% 130.11/17.16 (((woz13rule4) =>
% 130.11/17.16 (((woz1_1) =>
% 130.11/17.16 (((woz1_2) =>
% 130.11/17.16 (((woz1_3) =>
% 130.11/17.16 (((woz1_4) =>
% 130.11/17.16 (((woz1_5) =>
% 130.11/17.16 (((breln1all2) =>
% 130.11/17.16 (((breln1SetBreln1) =>
% 130.11/17.16 (((choice2fnsingleton) =>
% 130.11/17.16 (((setOfPairsIsBReln1) =>
% 130.11/17.16 (((breln1all1) =>
% 130.11/17.16 (((subbreln1) =>
% 130.11/17.16 (((eqbreln1) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2830])).
% 130.11/17.16 thf(zip_derived_cl2852, plain,
% 130.11/17.16 (~ (((binunionTE) =>
% 130.11/17.16 (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 (((woz13rule2) =>
% 130.11/17.16 (((woz13rule3) =>
% 130.11/17.16 (((woz13rule4) =>
% 130.11/17.16 (((woz1_1) =>
% 130.11/17.16 (((woz1_2) =>
% 130.11/17.16 (((woz1_3) =>
% 130.11/17.16 (((woz1_4) =>
% 130.11/17.16 (((woz1_5) =>
% 130.11/17.16 (((breln1all2) =>
% 130.11/17.16 (((breln1SetBreln1) =>
% 130.11/17.16 (((choice2fnsingleton) =>
% 130.11/17.16 (((setOfPairsIsBReln1) =>
% 130.11/17.16 (((breln1all1) =>
% 130.11/17.16 (((subbreln1) =>
% 130.11/17.16 (((eqbreln1) =>
% 130.11/17.16 (((breln1invprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#C') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2841])).
% 130.11/17.16 thf(zip_derived_cl2864, plain,
% 130.11/17.16 (~ (((binunionTEcontra) =>
% 130.11/17.16 (((demorgan2a1) =>
% 130.11/17.16 (((complementUnionInPowersetComplement) =>
% 130.11/17.16 (((demorgan2a2) =>
% 130.11/17.16 (((demorgan1a) =>
% 130.11/17.16 (((demorgan1b) =>
% 130.11/17.16 (((demorgan1) =>
% 130.11/17.16 (((demorgan2a) =>
% 130.11/17.16 (((demorgan2b2) =>
% 130.11/17.16 (((demorgan2b) =>
% 130.11/17.16 (((demorgan2) =>
% 130.11/17.16 (((woz13rule0) =>
% 130.11/17.16 (((woz13rule1) =>
% 130.11/17.16 (((woz13rule2) =>
% 130.11/17.16 (((woz13rule3) =>
% 130.11/17.16 (((woz13rule4) =>
% 130.11/17.16 (((woz1_1) =>
% 130.11/17.16 (((woz1_2) =>
% 130.11/17.16 (((woz1_3) =>
% 130.11/17.16 (((woz1_4) =>
% 130.11/17.16 (((woz1_5) =>
% 130.11/17.16 (((breln1all2) =>
% 130.11/17.16 (((breln1SetBreln1) =>
% 130.11/17.16 (((choice2fnsingleton) =>
% 130.11/17.16 (((setOfPairsIsBReln1) =>
% 130.11/17.16 (((breln1all1) =>
% 130.11/17.16 (((subbreln1) =>
% 130.11/17.16 (((eqbreln1) =>
% 130.11/17.16 (((breln1invprop) =>
% 130.11/17.16 (((breln1invI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1invE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compprop) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compI) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compE) =>
% 130.11/17.16 ((
% 130.11/17.16 (breln1compEex) =>
% 130.11/17.16 ((
% 130.11/17.16 (!!) @ (
% 130.11/17.16 (('#B') @ (
% 130.11/17.16 !!) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#S') @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 =>))) @
% 130.11/17.16 breln1)))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 !!))) @
% 130.11/17.16 (
% 130.11/17.16 (
% 130.11/17.16 ('#S') @ (
% 130.11/17.16 (
% 130.11/17.16 ('#B') @ (
% 130.11/17.16 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#C') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2852])).
% 130.11/17.17 thf(zip_derived_cl2876, plain,
% 130.11/17.17 (~ (((demorgan2a1) =>
% 130.11/17.17 (((complementUnionInPowersetComplement) =>
% 130.11/17.17 (((demorgan2a2) =>
% 130.11/17.17 (((demorgan1a) =>
% 130.11/17.17 (((demorgan1b) =>
% 130.11/17.17 (((demorgan1) =>
% 130.11/17.17 (((demorgan2a) =>
% 130.11/17.17 (((demorgan2b2) =>
% 130.11/17.17 (((demorgan2b) =>
% 130.11/17.17 (((demorgan2) =>
% 130.11/17.17 (((woz13rule0) =>
% 130.11/17.17 (((woz13rule1) =>
% 130.11/17.17 (((woz13rule2) =>
% 130.11/17.17 (((woz13rule3) =>
% 130.11/17.17 (((woz13rule4) =>
% 130.11/17.17 (((woz1_1) =>
% 130.11/17.17 (((woz1_2) =>
% 130.11/17.17 (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 ((
% 130.11/17.17 (breln1compprop) =>
% 130.11/17.17 ((
% 130.11/17.17 (breln1compI) =>
% 130.11/17.17 ((
% 130.11/17.17 (breln1compE) =>
% 130.11/17.17 ((
% 130.11/17.17 (breln1compEex) =>
% 130.11/17.17 ((
% 130.11/17.17 (!!) @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 !!) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 !!))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#C') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2864])).
% 130.11/17.17 thf(zip_derived_cl2888, plain,
% 130.11/17.17 (~ (((complementUnionInPowersetComplement) =>
% 130.11/17.17 (((demorgan2a2) =>
% 130.11/17.17 (((demorgan1a) =>
% 130.11/17.17 (((demorgan1b) =>
% 130.11/17.17 (((demorgan1) =>
% 130.11/17.17 (((demorgan2a) =>
% 130.11/17.17 (((demorgan2b2) =>
% 130.11/17.17 (((demorgan2b) =>
% 130.11/17.17 (((demorgan2) =>
% 130.11/17.17 (((woz13rule0) =>
% 130.11/17.17 (((woz13rule1) =>
% 130.11/17.17 (((woz13rule2) =>
% 130.11/17.17 (((woz13rule3) =>
% 130.11/17.17 (((woz13rule4) =>
% 130.11/17.17 (((woz1_1) =>
% 130.11/17.17 (((woz1_2) =>
% 130.11/17.17 (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 ((
% 130.11/17.17 (breln1compI) =>
% 130.11/17.17 ((
% 130.11/17.17 (breln1compE) =>
% 130.11/17.17 ((
% 130.11/17.17 (breln1compEex) =>
% 130.11/17.17 ((
% 130.11/17.17 (!!) @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 !!) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 !!))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#C') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2876])).
% 130.11/17.17 thf(zip_derived_cl2900, plain,
% 130.11/17.17 (~ (((demorgan2a2) =>
% 130.11/17.17 (((demorgan1a) =>
% 130.11/17.17 (((demorgan1b) =>
% 130.11/17.17 (((demorgan1) =>
% 130.11/17.17 (((demorgan2a) =>
% 130.11/17.17 (((demorgan2b2) =>
% 130.11/17.17 (((demorgan2b) =>
% 130.11/17.17 (((demorgan2) =>
% 130.11/17.17 (((woz13rule0) =>
% 130.11/17.17 (((woz13rule1) =>
% 130.11/17.17 (((woz13rule2) =>
% 130.11/17.17 (((woz13rule3) =>
% 130.11/17.17 (((woz13rule4) =>
% 130.11/17.17 (((woz1_1) =>
% 130.11/17.17 (((woz1_2) =>
% 130.11/17.17 (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 ((
% 130.11/17.17 (breln1compE) =>
% 130.11/17.17 ((
% 130.11/17.17 (breln1compEex) =>
% 130.11/17.17 ((
% 130.11/17.17 (!!) @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 !!) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 !!))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#C') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2888])).
% 130.11/17.17 thf(zip_derived_cl2913, plain,
% 130.11/17.17 (~ (((demorgan1a) =>
% 130.11/17.17 (((demorgan1b) =>
% 130.11/17.17 (((demorgan1) =>
% 130.11/17.17 (((demorgan2a) =>
% 130.11/17.17 (((demorgan2b2) =>
% 130.11/17.17 (((demorgan2b) =>
% 130.11/17.17 (((demorgan2) =>
% 130.11/17.17 (((woz13rule0) =>
% 130.11/17.17 (((woz13rule1) =>
% 130.11/17.17 (((woz13rule2) =>
% 130.11/17.17 (((woz13rule3) =>
% 130.11/17.17 (((woz13rule4) =>
% 130.11/17.17 (((woz1_1) =>
% 130.11/17.17 (((woz1_2) =>
% 130.11/17.17 (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 ((
% 130.11/17.17 (breln1compEex) =>
% 130.11/17.17 ((
% 130.11/17.17 (!!) @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 !!) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 !!))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#C') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2900])).
% 130.11/17.17 thf(zip_derived_cl2927, plain,
% 130.11/17.17 (~ (((demorgan1b) =>
% 130.11/17.17 (((demorgan1) =>
% 130.11/17.17 (((demorgan2a) =>
% 130.11/17.17 (((demorgan2b2) =>
% 130.11/17.17 (((demorgan2b) =>
% 130.11/17.17 (((demorgan2) =>
% 130.11/17.17 (((woz13rule0) =>
% 130.11/17.17 (((woz13rule1) =>
% 130.11/17.17 (((woz13rule2) =>
% 130.11/17.17 (((woz13rule3) =>
% 130.11/17.17 (((woz13rule4) =>
% 130.11/17.17 (((woz1_1) =>
% 130.11/17.17 (((woz1_2) =>
% 130.11/17.17 (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 ((
% 130.11/17.17 (!!) @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 !!) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 !!))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#C') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2913])).
% 130.11/17.17 thf(zip_derived_cl2940, plain,
% 130.11/17.17 (~ (((demorgan1) =>
% 130.11/17.17 (((demorgan2a) =>
% 130.11/17.17 (((demorgan2b2) =>
% 130.11/17.17 (((demorgan2b) =>
% 130.11/17.17 (((demorgan2) =>
% 130.11/17.17 (((woz13rule0) =>
% 130.11/17.17 (((woz13rule1) =>
% 130.11/17.17 (((woz13rule2) =>
% 130.11/17.17 (((woz13rule3) =>
% 130.11/17.17 (((woz13rule4) =>
% 130.11/17.17 (((woz1_1) =>
% 130.11/17.17 (((woz1_2) =>
% 130.11/17.17 (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 !!) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 !!))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#C') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2927])).
% 130.11/17.17 thf(zip_derived_cl2953, plain,
% 130.11/17.17 (~ (((demorgan2a) =>
% 130.11/17.17 (((demorgan2b2) =>
% 130.11/17.17 (((demorgan2b) =>
% 130.11/17.17 (((demorgan2) =>
% 130.11/17.17 (((woz13rule0) =>
% 130.11/17.17 (((woz13rule1) =>
% 130.11/17.17 (((woz13rule2) =>
% 130.11/17.17 (((woz13rule3) =>
% 130.11/17.17 (((woz13rule4) =>
% 130.11/17.17 (((woz1_1) =>
% 130.11/17.17 (((woz1_2) =>
% 130.11/17.17 (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 !!) @
% 130.11/17.17 ((('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 !!))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#C') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2940])).
% 130.11/17.17 thf(zip_derived_cl2965, plain,
% 130.11/17.17 (~ (((demorgan2b2) =>
% 130.11/17.17 (((demorgan2b) =>
% 130.11/17.17 (((demorgan2) =>
% 130.11/17.17 (((woz13rule0) =>
% 130.11/17.17 (((woz13rule1) =>
% 130.11/17.17 (((woz13rule2) =>
% 130.11/17.17 (((woz13rule3) =>
% 130.11/17.17 (((woz13rule4) =>
% 130.11/17.17 (((woz1_1) =>
% 130.11/17.17 (((woz1_2) =>
% 130.11/17.17 (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 !!) @
% 130.11/17.17 ((('#S') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 !!))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#C') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2953])).
% 130.11/17.17 thf(zip_derived_cl2977, plain,
% 130.11/17.17 (~ (((demorgan2b) =>
% 130.11/17.17 (((demorgan2) =>
% 130.11/17.17 (((woz13rule0) =>
% 130.11/17.17 (((woz13rule1) =>
% 130.11/17.17 (((woz13rule2) =>
% 130.11/17.17 (((woz13rule3) =>
% 130.11/17.17 (((woz13rule4) =>
% 130.11/17.17 (((woz1_1) =>
% 130.11/17.17 (((woz1_2) =>
% 130.11/17.17 (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 !!) @
% 130.11/17.17 ((('#S') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 !!))) @
% 130.11/17.17 ((('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#C') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2965])).
% 130.11/17.17 thf(zip_derived_cl2989, plain,
% 130.11/17.17 (~ (((demorgan2) =>
% 130.11/17.17 (((woz13rule0) =>
% 130.11/17.17 (((woz13rule1) =>
% 130.11/17.17 (((woz13rule2) =>
% 130.11/17.17 (((woz13rule3) =>
% 130.11/17.17 (((woz13rule4) =>
% 130.11/17.17 (((woz1_1) =>
% 130.11/17.17 (((woz1_2) =>
% 130.11/17.17 (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (
% 130.11/17.17 !!) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 !!))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#C') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2977])).
% 130.11/17.17 thf(zip_derived_cl3002, plain,
% 130.11/17.17 (~ (((woz13rule0) =>
% 130.11/17.17 (((woz13rule1) =>
% 130.11/17.17 (((woz13rule2) =>
% 130.11/17.17 (((woz13rule3) =>
% 130.11/17.17 (((woz13rule4) =>
% 130.11/17.17 (((woz1_1) =>
% 130.11/17.17 (((woz1_2) =>
% 130.11/17.17 (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (
% 130.11/17.17 !!) @
% 130.11/17.17 ((('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 !!))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#C') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2989])).
% 130.11/17.17 thf(zip_derived_cl3015, plain,
% 130.11/17.17 (~ (((woz13rule1) =>
% 130.11/17.17 (((woz13rule2) =>
% 130.11/17.17 (((woz13rule3) =>
% 130.11/17.17 (((woz13rule4) =>
% 130.11/17.17 (((woz1_1) =>
% 130.11/17.17 (((woz1_2) =>
% 130.11/17.17 (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (
% 130.11/17.17 !!) @
% 130.11/17.17 ((('#S') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 !!))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#C') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3002])).
% 130.11/17.17 thf(zip_derived_cl3029, plain,
% 130.11/17.17 (~ (((woz13rule2) =>
% 130.11/17.17 (((woz13rule3) =>
% 130.11/17.17 (((woz13rule4) =>
% 130.11/17.17 (((woz1_1) =>
% 130.11/17.17 (((woz1_2) =>
% 130.11/17.17 (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (
% 130.11/17.17 !!) @
% 130.11/17.17 ((('#S') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 !!))) @
% 130.11/17.17 ((('#S') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#C') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3015])).
% 130.11/17.17 thf(zip_derived_cl3045, plain,
% 130.11/17.17 (~ (((woz13rule3) =>
% 130.11/17.17 (((woz13rule4) =>
% 130.11/17.17 (((woz1_1) =>
% 130.11/17.17 (((woz1_2) =>
% 130.11/17.17 (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (
% 130.11/17.17 !!) @
% 130.11/17.17 ((('#S') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 !!))) @
% 130.11/17.17 ((('#S') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3029])).
% 130.11/17.17 thf(zip_derived_cl3058, plain,
% 130.11/17.17 (~ (((woz13rule4) =>
% 130.11/17.17 (((woz1_1) =>
% 130.11/17.17 (((woz1_2) =>
% 130.11/17.17 (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (=>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3045])).
% 130.11/17.17 thf(zip_derived_cl3069, plain,
% 130.11/17.17 (~ (((woz1_1) =>
% 130.11/17.17 (((woz1_2) =>
% 130.11/17.17 (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3058])).
% 130.11/17.17 thf(zip_derived_cl3081, plain,
% 130.11/17.17 (~ (((woz1_2) =>
% 130.11/17.17 (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ ((
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 !!))) @
% 130.11/17.17 ((('#S') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3069])).
% 130.11/17.17 thf(zip_derived_cl3093, plain,
% 130.11/17.17 (~ (((woz1_3) =>
% 130.11/17.17 (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (
% 130.11/17.17 !!))) @
% 130.11/17.17 ((('#S') @ ((
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 '#B') @ breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3081])).
% 130.11/17.17 thf(zip_derived_cl3105, plain,
% 130.11/17.17 (~ (((woz1_4) =>
% 130.11/17.17 (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (
% 130.11/17.17 !!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ ((
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3093])).
% 130.11/17.17 thf(zip_derived_cl3116, plain,
% 130.11/17.17 (~ (((woz1_5) =>
% 130.11/17.17 (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (=>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 (
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((
% 130.11/17.17 ('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3105])).
% 130.11/17.17 thf(zip_derived_cl3127, plain,
% 130.11/17.17 (~ (((breln1all2) =>
% 130.11/17.17 (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (=>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3116])).
% 130.11/17.17 thf(zip_derived_cl3139, plain,
% 130.11/17.17 (~ (((breln1SetBreln1) =>
% 130.11/17.17 (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (=>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3127])).
% 130.11/17.17 thf(zip_derived_cl3151, plain,
% 130.11/17.17 (~ (((choice2fnsingleton) =>
% 130.11/17.17 (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (=>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 '#B') @ breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3139])).
% 130.11/17.17 thf(zip_derived_cl3162, plain,
% 130.11/17.17 (~ (((setOfPairsIsBReln1) =>
% 130.11/17.17 (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 '#S') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (=>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ (
% 130.11/17.17 '#B') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 '#B') @ breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3151])).
% 130.11/17.17 thf(zip_derived_cl3174, plain,
% 130.11/17.17 (~ (((breln1all1) =>
% 130.11/17.17 (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 (('#B') @ (=>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ (
% 130.11/17.17 '#B') @ breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3162])).
% 130.11/17.17 thf(zip_derived_cl3187, plain,
% 130.11/17.17 (~ (((subbreln1) =>
% 130.11/17.17 (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3174])).
% 130.11/17.17 thf(zip_derived_cl3201, plain,
% 130.11/17.17 (~ (((eqbreln1) =>
% 130.11/17.17 (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (
% 130.11/17.17 =>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#B') @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3187])).
% 130.11/17.17 thf(zip_derived_cl3211, plain,
% 130.11/17.17 (~ (((breln1invprop) =>
% 130.11/17.17 (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#B') @ breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3201])).
% 130.11/17.17 thf(zip_derived_cl3221, plain,
% 130.11/17.17 (~ (((breln1invI) =>
% 130.11/17.17 (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#B') @ breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3211])).
% 130.11/17.17 thf(zip_derived_cl3232, plain,
% 130.11/17.17 (~ (((breln1invE) =>
% 130.11/17.17 (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @
% 130.11/17.17 breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#B') @ breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3221])).
% 130.11/17.17 thf(zip_derived_cl3245, plain,
% 130.11/17.17 (~ (((breln1compprop) =>
% 130.11/17.17 (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @ breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#B') @ breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3232])).
% 130.11/17.17 thf(zip_derived_cl3260, plain,
% 130.11/17.17 (~ (((breln1compI) =>
% 130.11/17.17 (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @ breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#B') @ breln1)))) @
% 130.11/17.17 binunion))))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3245])).
% 130.11/17.17 thf(zip_derived_cl3277, plain,
% 130.11/17.17 (~ (((breln1compE) =>
% 130.11/17.17 (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @ breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @
% 130.11/17.17 breln1)))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#B') @ breln1)))) @
% 130.11/17.17 binunion))))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3260])).
% 130.11/17.17 thf(zip_derived_cl3295, plain,
% 130.11/17.17 (~ (((breln1compEex) =>
% 130.11/17.17 (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @ breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @ breln1)))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#B') @ breln1)))) @
% 130.11/17.17 binunion))))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3277])).
% 130.11/17.17 thf(zip_derived_cl3312, plain,
% 130.11/17.17 (~ (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @ breln1)))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @ breln1)))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#B') @ breln1)))) @
% 130.11/17.17 binunion))))))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3295])).
% 130.11/17.17 thf(zip_derived_cl3329, plain,
% 130.11/17.17 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (breln1 @ '#sk43'))) @
% 130.11/17.17 ((('#B') @ (!!) @
% 130.11/17.17 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 130.11/17.17 (breln1 @ '#sk43'))))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (breln1 @ '#sk43'))) @ binunion))))))))))),
% 130.11/17.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3312])).
% 130.11/17.17 thf(zip_derived_cl3345, plain,
% 130.11/17.17 (~ (((breln1 @ '#sk43' @ '#sk44') =>
% 130.11/17.17 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (breln1 @ '#sk43'))) @
% 130.11/17.17 ((('#B') @ (breln1 @ '#sk43') @ (binunion @ '#sk44')))))))))),
% 130.11/17.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3329])).
% 130.11/17.17 thf(breln, axiom,(( breln @ (X1)@ (X2)@ (X0)) =
% 130.11/17.17 ((subset @ X0 @ (cartprod @ X1 @ X2))))).
% 130.11/17.17 thf('4', plain,
% 130.11/17.17 (![X2:$i,X1:$i,X0:$i]:
% 130.11/17.17 ( ( breln @ X1 @ X2 @ X0 ) = ( subset @ X0 @ ( cartprod @ X1 @ X2 ) ) )),
% 130.11/17.17 define([status(thm)])).
% 130.11/17.17 thf(breln1, axiom,(( breln1 @ (X0)@ (X1)) = ((breln @ X0 @ X0 @ X1)))).
% 130.11/17.17 thf('5', plain,
% 130.11/17.17 (![X1:$i,X0:$i]: ( ( breln1 @ X0 @ X1 ) = ( breln @ X0 @ X0 @ X1 ) )),
% 130.11/17.17 define([status(thm)])).
% 130.11/17.17 thf(zip_derived_cl3362, plain,
% 130.11/17.17 (~ (((subset @ '#sk44' @ (cartprod @ '#sk43' @ '#sk43')) =>
% 130.11/17.17 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (breln1 @ '#sk43'))) @
% 130.11/17.17 ((('#B') @ (breln1 @ '#sk43') @ (binunion @ '#sk44')))))))))),
% 130.11/17.17 inference('rw', [status(thm)], [zip_derived_cl3345, '4', '5'])).
% 130.11/17.17 thf(zip_derived_cl3364, plain,
% 130.11/17.17 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (breln1 @ '#sk43'))) @
% 130.11/17.17 ((('#B') @ (breln1 @ '#sk43') @ (binunion @ '#sk44')))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3362])).
% 130.11/17.17 thf(zip_derived_cl3380, plain,
% 130.11/17.17 (~ (((breln1 @ '#sk43' @ '#sk45') => (breln1 @ '#sk43' @
% 130.11/17.17 (binunion @ '#sk44' @ '#sk45'))))),
% 130.11/17.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3364])).
% 130.11/17.17 thf(zip_derived_cl3391, plain,
% 130.11/17.17 (~ (((subset @ '#sk45' @ (cartprod @ '#sk43' @ '#sk43')) => (subset @
% 130.11/17.17 (binunion @ '#sk44' @ '#sk45') @ (cartprod @ '#sk43' @ '#sk43'))))),
% 130.11/17.17 inference('rw', [status(thm)], [zip_derived_cl3380, '4', '4', '5', '5'])).
% 130.11/17.17 thf(zip_derived_cl3392, plain,
% 130.11/17.17 ( (subset @ '#sk45' @ (cartprod @ '#sk43' @ '#sk43'))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3391])).
% 130.11/17.17 thf(zip_derived_cl3363, plain,
% 130.11/17.17 ( (subset @ '#sk44' @ (cartprod @ '#sk43' @ '#sk43'))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3362])).
% 130.11/17.17 thf(zip_derived_cl2471, plain, ( (binunionT_lem)),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2461])).
% 130.11/17.17 thf(binunionT_lem, axiom, (binunionT_lem) =>
% 130.11/17.17 ((((!!) @ (^[Y0 : $i]:
% 130.11/17.17 (((!!) @ (^[Y1 : $i]:
% 130.11/17.17 (((in @ Y1 @ (powerset @ Y0)) =>
% 130.11/17.17 (((!!) @ (^[Y2 : $i]:
% 130.11/17.17 (((in @ Y2 @ (powerset @ Y0)) =>
% 130.11/17.17 (in @ (binunion @ Y1 @ Y2) @
% 130.11/17.17 (powerset @ Y0)))))))))))))))
% 130.11/17.17 = ($true))).
% 130.11/17.17 thf('6', plain,
% 130.11/17.17 (( binunionT_lem ) <=>
% 130.11/17.17 ( ![X5:$i,X7:$i]:
% 130.11/17.17 ( ( in @ X7 @ ( powerset @ X5 ) ) =>
% 130.11/17.17 ( ![X9:$i]:
% 130.11/17.17 ( ( in @ X9 @ ( powerset @ X5 ) ) =>
% 130.11/17.17 ( in @ ( binunion @ X7 @ X9 ) @ ( powerset @ X5 ) ) ) ) ) )),
% 130.11/17.17 inference('rw.lit', [status(esa)], [binunionT_lem])).
% 130.11/17.17 thf(zip_derived_cl2481, plain,
% 130.11/17.17 ( (((!!) @ (^[Y0 : $i]:
% 130.11/17.17 (((!!) @ (^[Y1 : $i]:
% 130.11/17.17 (((in @ Y1 @ (powerset @ Y0)) =>
% 130.11/17.17 (((!!) @ (^[Y2 : $i]:
% 130.11/17.17 (((in @ Y2 @ (powerset @ Y0)) =>
% 130.11/17.17 (in @ (binunion @ Y1 @ Y2) @
% 130.11/17.17 (powerset @ Y0)))))))))))))))),
% 130.11/17.17 inference('rw_clause', [status(thm)], [zip_derived_cl2471, '6'])).
% 130.11/17.17 thf(zip_derived_cl2488, plain,
% 130.11/17.17 ( (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @
% 130.11/17.17 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @
% 130.11/17.17 ((('#B') @ ((('#B') @ (!!))) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#B') @
% 130.11/17.17 ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @
% 130.11/17.17 ((('#B') @ ((('#C') @ in)) @ powerset)))))))) @
% 130.11/17.17 ((('#B') @ ((('#C') @ ((('#B') @ ('#C') @
% 130.11/17.17 ((('#B') @ ((('#B') @ in)) @
% 130.11/17.17 binunion)))))) @
% 130.11/17.17 powerset))))))))))))),
% 130.11/17.17 inference('comb-normalize', [status(thm)], [zip_derived_cl2481])).
% 130.11/17.17 thf(zip_derived_cl2489, plain,
% 130.11/17.17 (![X2 : $i]:
% 130.11/17.17 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 130.11/17.17 ((('#C') @ in @ (powerset @ X2))))) @
% 130.11/17.17 ((('#B') @ (!!) @
% 130.11/17.17 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 130.11/17.17 ((('#C') @ in @ (powerset @ X2))))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ ('#C') @
% 130.11/17.17 ((('#B') @ ((('#B') @ in)) @ binunion)))) @
% 130.11/17.17 (powerset @ X2)))))))))))),
% 130.11/17.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2488])).
% 130.11/17.17 thf(zip_derived_cl2497, plain,
% 130.11/17.17 (![X2 : $i, X4 : $i]:
% 130.11/17.17 (((in @ X4 @ (powerset @ X2)) =>
% 130.11/17.17 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 130.11/17.17 ((('#C') @ in @ (powerset @ X2))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ in @ (binunion @ X4))) @
% 130.11/17.17 (powerset @ X2)))))))))),
% 130.11/17.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2489])).
% 130.11/17.17 thf(zip_derived_cl2507, plain,
% 130.11/17.17 (![X2 : $i, X4 : $i]:
% 130.11/17.17 (~ (in @ X4 @ (powerset @ X2))
% 130.11/17.17 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 130.11/17.17 ((('#C') @ in @ (powerset @ X2))))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ in @ (binunion @ X4))) @
% 130.11/17.17 (powerset @ X2))))))))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2497])).
% 130.11/17.17 thf(zip_derived_cl2518, plain,
% 130.11/17.17 (![X2 : $i, X4 : $i, X6 : $i]:
% 130.11/17.17 ( (((in @ X6 @ (powerset @ X2)) => (in @ (binunion @ X4 @ X6) @
% 130.11/17.17 (powerset @ X2))))
% 130.11/17.17 | ~ (in @ X4 @ (powerset @ X2)))),
% 130.11/17.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2507])).
% 130.11/17.17 thf(zip_derived_cl2527, plain,
% 130.11/17.17 (![X2 : $i, X4 : $i, X6 : $i]:
% 130.11/17.17 (~ (in @ X6 @ (powerset @ X2))
% 130.11/17.17 | (in @ (binunion @ X4 @ X6) @ (powerset @ X2))
% 130.11/17.17 | ~ (in @ X4 @ (powerset @ X2)))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2518])).
% 130.11/17.17 thf(zip_derived_cl3393, plain,
% 130.11/17.17 (~ (subset @ (binunion @ '#sk44' @ '#sk45') @
% 130.11/17.17 (cartprod @ '#sk43' @ '#sk43'))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3391])).
% 130.11/17.17 thf(zip_derived_cl1014, plain, ( (subset2powerset)),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1000])).
% 130.11/17.17 thf(subset2powerset, axiom, (subset2powerset) =>
% 130.11/17.17 ((((!!) @ (^[Y0 : $i]:
% 130.11/17.17 (((!!) @ (^[Y1 : $i]:
% 130.11/17.17 (((subset @ Y0 @ Y1) => (in @ Y0 @
% 130.11/17.17 (powerset @ Y1))))))))))
% 130.11/17.17 = ($true))).
% 130.11/17.17 thf('7', plain,
% 130.11/17.17 (( subset2powerset ) <=>
% 130.11/17.17 ( ![X5:$i,X7:$i]:
% 130.11/17.17 ( ( subset @ X5 @ X7 ) => ( in @ X5 @ ( powerset @ X7 ) ) ) )),
% 130.11/17.17 inference('rw.lit', [status(esa)], [subset2powerset])).
% 130.11/17.17 thf(zip_derived_cl1025, plain,
% 130.11/17.17 ( (((!!) @ (^[Y0 : $i]:
% 130.11/17.17 (((!!) @ (^[Y1 : $i]:
% 130.11/17.17 (((subset @ Y0 @ Y1) => (in @ Y0 @
% 130.11/17.17 (powerset @ Y1))))))))))),
% 130.11/17.17 inference('rw_clause', [status(thm)], [zip_derived_cl1014, '7'])).
% 130.11/17.17 thf(zip_derived_cl1035, plain,
% 130.11/17.17 ( (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @ subset)))) @
% 130.11/17.17 ((('#C') @ ((('#B') @ ('#B') @ in)) @ powerset))))))))),
% 130.11/17.17 inference('comb-normalize', [status(thm)], [zip_derived_cl1025])).
% 130.11/17.17 thf(zip_derived_cl1036, plain,
% 130.11/17.17 (![X2 : $i]:
% 130.11/17.17 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (subset @ X2))) @
% 130.11/17.17 ((('#B') @ (in @ X2) @ powerset))))))),
% 130.11/17.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1035])).
% 130.11/17.17 thf(zip_derived_cl1050, plain,
% 130.11/17.17 (![X2 : $i, X4 : $i]:
% 130.11/17.17 (((subset @ X2 @ X4) => (in @ X2 @ (powerset @ X4))))),
% 130.11/17.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1036])).
% 130.11/17.17 thf(zip_derived_cl1061, plain,
% 130.11/17.17 (![X2 : $i, X4 : $i]:
% 130.11/17.17 (~ (subset @ X2 @ X4) | (in @ X2 @ (powerset @ X4)))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1050])).
% 130.11/17.17 thf(zip_derived_cl1066, plain, ( (powersetE1)),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1055])).
% 130.11/17.17 thf(powersetE1, axiom, (powersetE1) =>
% 130.11/17.17 ((((!!) @ (^[Y0 : $i]:
% 130.11/17.17 (((!!) @ (^[Y1 : $i]:
% 130.11/17.17 (((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @
% 130.11/17.17 Y0)))))))))
% 130.11/17.17 = ($true))).
% 130.11/17.17 thf('8', plain,
% 130.11/17.17 (( powersetE1 ) <=>
% 130.11/17.17 ( ![X5:$i,X7:$i]:
% 130.11/17.17 ( ( in @ X7 @ ( powerset @ X5 ) ) => ( subset @ X7 @ X5 ) ) )),
% 130.11/17.17 inference('rw.lit', [status(esa)], [powersetE1])).
% 130.11/17.17 thf(zip_derived_cl1072, plain,
% 130.11/17.17 ( (((!!) @ (^[Y0 : $i]:
% 130.11/17.17 (((!!) @ (^[Y1 : $i]:
% 130.11/17.17 (((in @ Y1 @ (powerset @ Y0)) => (subset @
% 130.11/17.17 Y1 @ Y0)))))))))),
% 130.11/17.17 inference('rw_clause', [status(thm)], [zip_derived_cl1066, '8'])).
% 130.11/17.17 thf(zip_derived_cl1078, plain,
% 130.11/17.17 ( (((!!) @ ((('#B') @ (!!) @
% 130.11/17.17 ((('#S') @ ((('#B') @ ('#S') @
% 130.11/17.17 ((('#B') @ ((('#B') @ (=>))) @
% 130.11/17.17 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @
% 130.11/17.17 ((('#C') @ subset))))))))),
% 130.11/17.17 inference('comb-normalize', [status(thm)], [zip_derived_cl1072])).
% 130.11/17.17 thf(zip_derived_cl1079, plain,
% 130.11/17.17 (![X2 : $i]:
% 130.11/17.17 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 130.11/17.17 ((('#C') @ in @ (powerset @ X2))))) @
% 130.11/17.17 ((('#C') @ subset @ X2))))))),
% 130.11/17.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1078])).
% 130.11/17.17 thf(zip_derived_cl1085, plain,
% 130.11/17.17 (![X2 : $i, X4 : $i]:
% 130.11/17.17 (((in @ X4 @ (powerset @ X2)) => (subset @ X4 @ X2)))),
% 130.11/17.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1079])).
% 130.11/17.17 thf(zip_derived_cl1091, plain,
% 130.11/17.17 (![X2 : $i, X4 : $i]:
% 130.11/17.17 (~ (in @ X4 @ (powerset @ X2)) | (subset @ X4 @ X2))),
% 130.11/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1085])).
% 130.11/17.17 thf(zip_derived_cl3528, plain, ($false),
% 130.11/17.17 inference('eprover', [status(thm)],
% 130.11/17.17 [zip_derived_cl3392, zip_derived_cl3363, zip_derived_cl2527,
% 130.11/17.17 zip_derived_cl3393, zip_derived_cl1061, zip_derived_cl1091])).
% 130.11/17.17
% 130.11/17.17 % SZS output end Refutation
% 130.11/17.17
% 130.11/17.17
% 130.11/17.17 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 130.11/17.17 % Terminating...
% 131.19/17.36 % Runner terminated.
% 131.19/17.37 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------