%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU782^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.WWLFBmX51z true
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 19:17:34 EDT 2023
% Result : Theorem 98.85s 13.41s
% Output : Refutation 100.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU782^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.WWLFBmX51z true
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 14:49:16 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % Running portfolio for 300 s
% 0.12/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.34 % Running in HO mode
% 0.19/0.64 % Total configuration time : 828
% 0.19/0.64 % Estimated wc time : 1656
% 0.19/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.19/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.19/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.19/0.73 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.19/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.19/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.19/0.74 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.19/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.19/0.74 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 98.85/13.41 % Solved by lams/40_b.comb.sh.
% 98.85/13.41 % done 333 iterations in 12.257s
% 98.85/13.41 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 98.85/13.41 % SZS output start Refutation
% 98.85/13.41 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 98.85/13.41 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 98.85/13.41 thf(notdexE_type, type, notdexE: $o).
% 98.85/13.41 thf(setunionAx_type, type, setunionAx: $o).
% 98.85/13.41 thf(setminusELneg_type, type, setminusELneg: $o).
% 98.85/13.41 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 98.85/13.41 thf(beta1_type, type, beta1: $o).
% 98.85/13.41 thf(powersetE_type, type, powersetE: $o).
% 98.85/13.41 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 98.85/13.41 thf(omegaSAx_type, type, omegaSAx: $o).
% 98.85/13.41 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 98.85/13.41 thf(exuI1_type, type, exuI1: $o).
% 98.85/13.41 thf(binunionTEcontra_type, type, binunionTEcontra: $o).
% 98.85/13.41 thf(exuI2_type, type, exuI2: $o).
% 98.85/13.41 thf(notequalI2_type, type, notequalI2: $o).
% 98.85/13.41 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 98.85/13.41 thf(demorgan1b_type, type, demorgan1b: $o).
% 98.85/13.41 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 98.85/13.41 thf(demorgan2a_type, type, demorgan2a: $o).
% 98.85/13.41 thf(subsetTI_type, type, subsetTI: $o).
% 98.85/13.41 thf(upairsubunion_type, type, upairsubunion: $o).
% 98.85/13.41 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 98.85/13.41 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 98.85/13.41 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 98.85/13.41 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 98.85/13.41 $o).
% 98.85/13.41 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 98.85/13.41 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 98.85/13.41 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 98.85/13.41 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 98.85/13.41 thf(setminusILneg_type, type, setminusILneg: $o).
% 98.85/13.41 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 98.85/13.41 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 98.85/13.41 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 98.85/13.41 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 98.85/13.41 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 98.85/13.41 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 98.85/13.41 thf(brelnall1_type, type, brelnall1: $o).
% 98.85/13.41 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 98.85/13.41 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 98.85/13.41 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 98.85/13.41 thf('#sk44_type', type, '#sk44': $i).
% 98.85/13.41 thf(complementT_lem_type, type, complementT_lem: $o).
% 98.85/13.41 thf(funcextLem_type, type, funcextLem: $o).
% 98.85/13.41 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 98.85/13.41 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 98.85/13.41 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 98.85/13.41 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 98.85/13.41 thf(demorgan2b2_type, type, demorgan2b2: $o).
% 98.85/13.41 thf(breln1compE_type, type, breln1compE: $o).
% 98.85/13.41 thf(demorgan2b_type, type, demorgan2b: $o).
% 98.85/13.41 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 98.85/13.41 thf(ex1E1_type, type, ex1E1: $o).
% 98.85/13.41 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 98.85/13.41 thf(setukpairIR_type, type, setukpairIR: $o).
% 98.85/13.41 thf(breln1invprop_type, type, breln1invprop: $o).
% 98.85/13.41 thf(binunionE_type, type, binunionE: $o).
% 98.85/13.41 thf(setext_type, type, setext: $o).
% 98.85/13.41 thf(lam2p_type, type, lam2p: $o).
% 98.85/13.41 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 98.85/13.41 thf(breln1_type, type, breln1: $i > $i > $o).
% 98.85/13.41 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 98.85/13.41 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 98.85/13.41 thf(theeq_type, type, theeq: $o).
% 98.85/13.41 thf(descr__Cong_type, type, descr__Cong: $o).
% 98.85/13.41 thf(theprop_type, type, theprop: $o).
% 98.85/13.41 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 98.85/13.41 $o).
% 98.85/13.41 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 98.85/13.41 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 98.85/13.41 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 98.85/13.41 thf(in_type, type, in: $i > $i > $o).
% 98.85/13.41 thf(lamProp_type, type, lamProp: $o).
% 98.85/13.41 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 98.85/13.41 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 98.85/13.41 thf(setextT_type, type, setextT: $o).
% 98.85/13.41 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 98.85/13.41 thf(binunion_type, type, binunion: $i > $i > $i).
% 98.85/13.41 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 98.85/13.41 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 98.85/13.41 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 98.85/13.41 thf(ap2p_type, type, ap2p: $o).
% 98.85/13.41 thf(eqbreln_type, type, eqbreln: $o).
% 98.85/13.41 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 98.85/13.41 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 98.85/13.41 thf(ex1I2_type, type, ex1I2: $o).
% 98.85/13.41 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 98.85/13.41 thf(woz1_1_type, type, woz1_1: $o).
% 98.85/13.41 thf(demorgan1_type, type, demorgan1: $o).
% 98.85/13.41 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 98.85/13.41 thf(symdiffI2_type, type, symdiffI2: $o).
% 98.85/13.41 thf(upairset2IR_type, type, upairset2IR: $o).
% 98.85/13.41 thf('#sk43_type', type, '#sk43': $i).
% 98.85/13.41 thf(breln1compI_type, type, breln1compI: $o).
% 98.85/13.41 thf(subsetE_type, type, subsetE: $o).
% 98.85/13.41 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 98.85/13.41 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 98.85/13.41 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 98.85/13.41 thf(setbeta_type, type, setbeta: $o).
% 98.85/13.41 thf(binunionTE_type, type, binunionTE: $o).
% 98.85/13.41 thf(eqinunit_type, type, eqinunit: $o).
% 98.85/13.41 thf(upairsetIL_type, type, upairsetIL: $o).
% 98.85/13.41 thf(powersetI1_type, type, powersetI1: $o).
% 98.85/13.41 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 98.85/13.41 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 98.85/13.41 thf(powersetTE1_type, type, powersetTE1: $o).
% 98.85/13.41 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 98.85/13.41 thf(app_type, type, app: $o).
% 98.85/13.41 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 98.85/13.41 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 98.85/13.41 thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1:
% 98.85/13.41 $o).
% 98.85/13.41 thf(powersetAx_type, type, powersetAx: $o).
% 98.85/13.41 thf(lamp_type, type, lamp: $o).
% 98.85/13.41 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 98.85/13.41 thf(ifSingleton_type, type, ifSingleton: $o).
% 98.85/13.41 thf(iffalse_type, type, iffalse: $o).
% 98.85/13.41 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 98.85/13.41 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 98.85/13.41 thf(powersetI_type, type, powersetI: $o).
% 98.85/13.41 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 98.85/13.41 thf(upairsetIR_type, type, upairsetIR: $o).
% 98.85/13.41 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 98.85/13.41 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 98.85/13.41 thf(funcext2_type, type, funcext2: $o).
% 98.85/13.41 thf(inCongP_type, type, inCongP: $o).
% 98.85/13.41 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 98.85/13.41 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 98.85/13.41 thf(exuE3e_type, type, exuE3e: $o).
% 98.85/13.41 thf(emptysetE_type, type, emptysetE: $o).
% 98.85/13.41 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 98.85/13.41 thf(setunionI_type, type, setunionI: $o).
% 98.85/13.41 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 98.85/13.41 thf(prop2setI_type, type, prop2setI: $o).
% 98.85/13.41 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 98.85/13.41 thf(setminusER_type, type, setminusER: $o).
% 98.85/13.41 thf(exuE2_type, type, exuE2: $o).
% 98.85/13.41 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 98.85/13.41 thf(emptyset_type, type, emptyset: $i).
% 98.85/13.41 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 98.85/13.41 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 98.85/13.41 thf(complementTI1_type, type, complementTI1: $o).
% 98.85/13.41 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o).
% 98.85/13.41 thf(breln_type, type, breln: $i > $i > $i > $o).
% 98.85/13.41 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 98.85/13.41 thf(subbreln1_type, type, subbreln1: $o).
% 98.85/13.41 thf(powersetsubset_type, type, powersetsubset: $o).
% 98.85/13.41 thf(upairequniteq_type, type, upairequniteq: $o).
% 98.85/13.41 thf(woz1_4_type, type, woz1_4: $o).
% 98.85/13.41 thf(subPowSU_type, type, subPowSU: $o).
% 98.85/13.41 thf(notequalI1_type, type, notequalI1: $o).
% 98.85/13.41 thf(notinemptyset_type, type, notinemptyset: $o).
% 98.85/13.41 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 98.85/13.41 thf(subsetTrans_type, type, subsetTrans: $o).
% 98.85/13.41 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 98.85/13.41 thf(kpairp_type, type, kpairp: $o).
% 98.85/13.41 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 98.85/13.41 thf(setminusI_type, type, setminusI: $o).
% 98.85/13.41 thf(eta1_type, type, eta1: $o).
% 98.85/13.41 thf(binunionIL_type, type, binunionIL: $o).
% 98.85/13.41 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 98.85/13.41 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 98.85/13.41 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 98.85/13.41 thf(subsetE2_type, type, subsetE2: $o).
% 98.85/13.41 thf('#sk45_type', type, '#sk45': $i).
% 98.85/13.41 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 98.85/13.41 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 98.85/13.41 thf(eta2_type, type, eta2: $o).
% 98.85/13.41 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 98.85/13.41 thf(setextsub_type, type, setextsub: $o).
% 98.85/13.41 thf(binunionLsub_type, type, binunionLsub: $o).
% 98.85/13.41 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 98.85/13.41 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 98.85/13.41 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 98.85/13.41 thf(setunionE_type, type, setunionE: $o).
% 98.85/13.41 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 98.85/13.41 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 98.85/13.41 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 98.85/13.41 thf(binunionIR_type, type, binunionIR: $o).
% 98.85/13.41 thf(iftrue_type, type, iftrue: $o).
% 98.85/13.41 thf(setadjoinE_type, type, setadjoinE: $o).
% 98.85/13.41 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 98.85/13.41 thf(woz1_5_type, type, woz1_5: $o).
% 98.85/13.41 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 98.85/13.41 thf(beta2_type, type, beta2: $o).
% 98.85/13.41 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 98.85/13.41 $o).
% 98.85/13.41 thf(brelnall2_type, type, brelnall2: $o).
% 98.85/13.41 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 98.85/13.41 thf(exuE1_type, type, exuE1: $o).
% 98.85/13.41 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 98.85/13.41 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 98.85/13.41 thf(ifp_type, type, ifp: $o).
% 98.85/13.41 thf(setminusLsub_type, type, setminusLsub: $o).
% 98.85/13.41 thf(woz1_3_type, type, woz1_3: $o).
% 98.85/13.41 thf(notinsingleton_type, type, notinsingleton: $o).
% 98.85/13.41 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 98.85/13.41 thf(exuEu_type, type, exuEu: $o).
% 98.85/13.41 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 98.85/13.41 thf(upairsetE_type, type, upairsetE: $o).
% 98.85/13.41 thf(omega0Ax_type, type, omega0Ax: $o).
% 98.85/13.41 thf(breln1invI_type, type, breln1invI: $o).
% 98.85/13.41 thf(complementTE1_type, type, complementTE1: $o).
% 98.85/13.41 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 98.85/13.41 thf(notsubsetI_type, type, notsubsetI: $o).
% 98.85/13.41 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions:
% 98.85/13.41 $o).
% 98.85/13.41 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 98.85/13.41 thf(setextAx_type, type, setextAx: $o).
% 98.85/13.41 thf(setOfPairsIsBReln1_type, type, setOfPairsIsBReln1: $o).
% 98.85/13.41 thf(breln1SetBreln1_type, type, breln1SetBreln1: $o).
% 98.85/13.41 thf(powersetE1_type, type, powersetE1: $o).
% 98.85/13.41 thf(bs114d_type, type, bs114d: $o).
% 98.85/13.41 thf(breln1all2_type, type, breln1all2: $o).
% 98.85/13.41 thf(woz13rule0_type, type, woz13rule0: $o).
% 98.85/13.41 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 98.85/13.41 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 98.85/13.41 thf(woz1_2_type, type, woz1_2: $o).
% 98.85/13.41 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 98.85/13.41 thf(subsetI1_type, type, subsetI1: $o).
% 98.85/13.41 thf(symdiffE_type, type, symdiffE: $o).
% 98.85/13.41 thf(descrp_type, type, descrp: $o).
% 98.85/13.41 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 98.85/13.41 thf(foundationAx_type, type, foundationAx: $o).
% 98.85/13.41 thf(emptysetAx_type, type, emptysetAx: $o).
% 98.85/13.41 thf(emptyI_type, type, emptyI: $o).
% 98.85/13.41 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 98.85/13.41 thf(binintersectEL_type, type, binintersectEL: $o).
% 98.85/13.41 thf(emptyE1_type, type, emptyE1: $o).
% 98.85/13.41 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 98.85/13.41 thf(demorgan2_type, type, demorgan2: $o).
% 98.85/13.41 thf(vacuousDall_type, type, vacuousDall: $o).
% 98.85/13.41 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 98.85/13.41 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 98.85/13.41 thf(ex1E2_type, type, ex1E2: $o).
% 98.85/13.41 thf(binintersectI_type, type, binintersectI: $o).
% 98.85/13.41 thf(woz13rule3_type, type, woz13rule3: $o).
% 98.85/13.41 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 98.85/13.41 thf(woz13rule2_type, type, woz13rule2: $o).
% 98.85/13.41 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 98.85/13.41 thf(breln1invE_type, type, breln1invE: $o).
% 98.85/13.41 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 98.85/13.41 thf(choice2fnsingleton_type, type, choice2fnsingleton: $o).
% 98.85/13.41 thf(apProp_type, type, apProp: $o).
% 98.85/13.41 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 98.85/13.41 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 98.85/13.41 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 98.85/13.41 thf(demorgan2a2_type, type, demorgan2a2: $o).
% 98.85/13.41 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 98.85/13.41 thf(symdiffI1_type, type, symdiffI1: $o).
% 98.85/13.41 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 98.85/13.41 thf(subsetI2_type, type, subsetI2: $o).
% 98.85/13.41 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 98.85/13.41 thf(setminusERneg_type, type, setminusERneg: $o).
% 98.85/13.41 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 98.85/13.41 thf(omega__Cong_type, type, omega__Cong: $o).
% 98.85/13.41 thf(subsetRefl_type, type, subsetRefl: $o).
% 98.85/13.41 thf(uniqinunit_type, type, uniqinunit: $o).
% 98.85/13.41 thf(breln1compprop_type, type, breln1compprop: $o).
% 98.85/13.41 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 98.85/13.41 thf(prop2setE_type, type, prop2setE: $o).
% 98.85/13.41 thf(binunionEcases_type, type, binunionEcases: $o).
% 98.85/13.41 thf(omega_type, type, omega: $i).
% 98.85/13.41 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions:
% 98.85/13.41 $o).
% 98.85/13.41 thf(nonemptyI_type, type, nonemptyI: $o).
% 98.85/13.41 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 98.85/13.41 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 98.85/13.41 thf(exuE3u_type, type, exuE3u: $o).
% 98.85/13.41 thf(setminusEL_type, type, setminusEL: $o).
% 98.85/13.41 thf(woz13rule4_type, type, woz13rule4: $o).
% 98.85/13.41 thf(breln1all1_type, type, breln1all1: $o).
% 98.85/13.41 thf(breln1compEex_type, type, breln1compEex: $o).
% 98.85/13.41 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 98.85/13.41 thf(sepSubset_type, type, sepSubset: $o).
% 98.85/13.41 thf(upairset2E_type, type, upairset2E: $o).
% 98.85/13.41 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 98.85/13.41 thf(eqbreln1_type, type, eqbreln1: $o).
% 98.85/13.41 thf(woz13rule1_type, type, woz13rule1: $o).
% 98.85/13.41 thf(exuI3_type, type, exuI3: $o).
% 98.85/13.41 thf(notdallE_type, type, notdallE: $o).
% 98.85/13.41 thf(demorgan1a_type, type, demorgan1a: $o).
% 98.85/13.41 thf(binintersectER_type, type, binintersectER: $o).
% 98.85/13.41 thf(powerset_type, type, powerset: $i > $i).
% 98.85/13.41 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 98.85/13.41 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 98.85/13.41 thf(subbreln_type, type, subbreln: $o).
% 98.85/13.41 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 98.85/13.41 thf(exu__Cong_type, type, exu__Cong: $o).
% 98.85/13.41 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 98.85/13.41 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 98.85/13.41 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 98.85/13.41 thf(powersetTI1_type, type, powersetTI1: $o).
% 98.85/13.41 thf(funcext_type, type, funcext: $o).
% 98.85/13.41 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 98.85/13.41 thf(ex1I_type, type, ex1I: $o).
% 98.85/13.41 thf(secondinupair_type, type, secondinupair: $o).
% 98.85/13.41 thf(singletonprop_type, type, singletonprop: $o).
% 98.85/13.41 thf(singletonsubset_type, type, singletonsubset: $o).
% 98.85/13.41 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 98.85/13.41 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 98.85/13.41 thf(replAx_type, type, replAx: $o).
% 98.85/13.41 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 98.85/13.41 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 98.85/13.41 thf(setukpairIL_type, type, setukpairIL: $o).
% 98.85/13.41 thf(setunionE2_type, type, setunionE2: $o).
% 98.85/13.41 thf(inPowerset_type, type, inPowerset: $o).
% 98.85/13.41 thf(demorgan2a1_type, type, demorgan2a1: $o).
% 98.85/13.41 thf(cartprod_type, type, cartprod: $i > $i > $i).
% 98.85/13.41 thf(subset_type, type, subset: $i > $i > $o).
% 98.85/13.41 thf(complementUnionInPowersetComplement_type, type, complementUnionInPowersetComplement:
% 98.85/13.41 $o).
% 98.85/13.41 thf(in__Cong_type, type, in__Cong: $o).
% 98.85/13.41 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 98.85/13.41 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 98.85/13.41 thf(binunionRsub_type, type, binunionRsub: $o).
% 98.85/13.41 thf(subset2powerset_type, type, subset2powerset: $o).
% 98.85/13.41 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 98.85/13.41 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 98.85/13.41 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 98.85/13.41 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 98.85/13.41 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 98.85/13.41 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 98.85/13.41 thf(breln1unionprop, conjecture,
% 98.85/13.41 (( setextAx ) =>
% 98.85/13.41 ( ( emptysetAx ) =>
% 98.85/13.41 ( ( setadjoinAx ) =>
% 98.85/13.41 ( ( powersetAx ) =>
% 98.85/13.41 ( ( setunionAx ) =>
% 98.85/13.41 ( ( omega0Ax ) =>
% 98.85/13.41 ( ( omegaSAx ) =>
% 98.85/13.41 ( ( omegaIndAx ) =>
% 98.85/13.41 ( ( replAx ) =>
% 98.85/13.41 ( ( foundationAx ) =>
% 98.85/13.41 ( ( wellorderingAx ) =>
% 98.85/13.41 ( ( descrp ) =>
% 98.85/13.41 ( ( dsetconstrI ) =>
% 98.85/13.41 ( ( dsetconstrEL ) =>
% 98.85/13.41 ( ( dsetconstrER ) =>
% 98.85/13.41 ( ( exuE1 ) =>
% 98.85/13.41 ( ( prop2setE ) =>
% 98.85/13.41 ( ( emptysetE ) =>
% 98.85/13.41 ( ( emptysetimpfalse ) =>
% 98.85/13.41 ( ( notinemptyset ) =>
% 98.85/13.41 ( ( exuE3e ) =>
% 98.85/13.41 ( ( setext ) =>
% 98.85/13.41 ( ( emptyI ) =>
% 98.85/13.41 ( ( noeltsimpempty ) =>
% 98.85/13.41 ( ( setbeta ) =>
% 98.85/13.41 ( ( nonemptyE1 ) =>
% 98.85/13.41 ( ( nonemptyI ) =>
% 98.85/13.41 ( ( nonemptyI1 ) =>
% 98.85/13.41 ( ( setadjoinIL ) =>
% 98.85/13.41 ( ( emptyinunitempty ) =>
% 98.85/13.41 ( ( setadjoinIR ) =>
% 98.85/13.41 ( ( setadjoinE ) =>
% 98.85/13.41 ( (
% 98.85/13.41 setadjoinOr ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setoftrueEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powersetI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 emptyinPowerset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 emptyInPowerset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powersetE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setunionI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setunionE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subPowSU ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 exuE2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 nonemptyImpWitness ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 uniqinunit ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 notinsingleton ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 eqinunit ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 singletonsswitch ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 upairsetE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 upairsetIL ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 upairsetIR ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 emptyE1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 vacuousDall ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 quantDeMorgan1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 quantDeMorgan2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 quantDeMorgan3 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 quantDeMorgan4 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 prop2setI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 prop2set2propI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 notdexE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 notdallE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 exuI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 exuI3 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 exuI2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 inCongP ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 in__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 exuE3u ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 exu__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 emptyset__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setadjoin__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powerset__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setunion__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 omega__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 exuEu ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 descr__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 dsetconstr__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subsetI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 eqimpsubset2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 eqimpsubset1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subsetI2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 emptysetsubset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subsetE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subsetE2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 notsubsetI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 notequalI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 notequalI2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subsetRefl ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subsetTrans ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setadjoinSub ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setadjoinSub2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subset2powerset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setextsub ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subsetemptysetimpeq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powersetI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powersetE1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 inPowerset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powersetsubset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 sepInPowerset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 sepSubset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionIL ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 upairset2IR ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionIR ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionEcases ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionLsub ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionRsub ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectSubset5 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectEL ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectLsub ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectSubset2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectSubset3 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectER ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 disjointsetsI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectRsub ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectSubset4 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectSubset1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 bs114d ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusEL ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusER ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusSubset2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusERneg ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusELneg ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusILneg ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusIRneg ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusLsub ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusSubset1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 symdiffE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 symdiffI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 symdiffI2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 symdiffIneg1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 symdiffIneg2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 secondinupair ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairIL ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairIR ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 kpairiskpair ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 kpairp ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 singletonsubset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 singletoninpowerset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 singletoninpowunion ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 upairset2E ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 upairsubunion ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 upairinpowunion ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ubforcartprodlem1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ubforcartprodlem2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ubforcartprodlem3 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodpairin ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodmempair1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodmempair ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setunionE2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setunionsingleton1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setunionsingleton2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setunionsingleton ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 singletonprop ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ex1E1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ex1I ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ex1I2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 singletonsuniq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairinjL1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 kfstsingleton ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 theprop ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 kfstpairEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodfstin ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairinjL2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairinjL ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairinjR11 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairinjR12 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairinjR1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 upairequniteq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairinjR2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairinjR ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ksndsingleton ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ksndpairEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 kpairsurjEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodsndin ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodpairmemEL ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodpairmemER ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodmempaircEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodfstpairEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodsndpairEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodpairsurjEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 dpsetconstrI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 dpsetconstrSub ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setOfPairsIsBReln ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 dpsetconstrERa ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 dpsetconstrEL1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 dpsetconstrEL2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 dpsetconstrER ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcImageSingleton ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 apProp ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 app ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 infuncsetfunc ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ap2p ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcinfuncset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 lamProp ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 lamp ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 lam2p ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 brelnall1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 brelnall2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ex1E2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcGraphProp1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcGraphProp3 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcGraphProp2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcextLem ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcGraphProp4 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subbreln ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 eqbreln ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcext ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcext2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ap2apEq1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ap2apEq2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 beta1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 eta1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 lam2lamEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 beta2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 eta2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 iffalseProp1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 iffalseProp2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 iftrueProp1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 iftrueProp2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ifSingleton ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ifp ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 theeq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 iftrue ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 iffalse ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 iftrueorfalse ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectT_lem ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionT_lem ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powersetT_lem ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusT_lem ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementT_lem ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setextT ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subsetTI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powersetTI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powersetTE1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementTI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementTE1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectTELcontra ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectTERcontra ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 contrasubsetT ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 contrasubsetT1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 contrasubsetT2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 contrasubsetT3 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 doubleComplementI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 doubleComplementE1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 doubleComplementSub1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 doubleComplementSub2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 doubleComplementEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementTnotintersectT ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementImpComplementIntersect ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementSubsetComplementIntersect ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementInPowersetComplementIntersect ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 contraSubsetComplement ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementTcontraSubset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionTILcontra ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionTIRcontra ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 inIntersectImpInUnion ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 inIntersectImpInUnion2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 inIntersectImpInIntersectUnions ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 intersectInPowersetIntersectUnions ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 inComplementUnionImpNotIn1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 inComplementUnionImpInComplement1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionTE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionTEcontra ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan2a1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementUnionInPowersetComplement ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan2a2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan1a ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan1b ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan2a ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan2b2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan2b ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz13rule0 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz13rule1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz13rule2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz13rule3 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz13rule4 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz1_1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz1_2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz1_3 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz1_4 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz1_5 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1all2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1SetBreln1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 choice2fnsingleton ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setOfPairsIsBReln1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1all1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subbreln1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 eqbreln1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1invprop ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1invI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1invE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1compprop ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1compI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1compE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1compEex ) =>
% 98.85/13.41 (
% 98.85/13.41 ![
% 98.85/13.41 A:$i,R:$i]:
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1 @
% 98.85/13.41 A @ R ) =>
% 98.85/13.41 (
% 98.85/13.41 ![
% 98.85/13.41 S:$i]:
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1 @
% 98.85/13.41 A @ S ) =>
% 98.85/13.41 (
% 98.85/13.41 breln1 @
% 98.85/13.41 A @
% 98.85/13.41 (
% 98.85/13.41 binunion @
% 98.85/13.41 R @ S ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 98.85/13.41 thf(zf_stmt_0, negated_conjecture,
% 98.85/13.41 (~( ( setextAx ) =>
% 98.85/13.41 ( ( emptysetAx ) =>
% 98.85/13.41 ( ( setadjoinAx ) =>
% 98.85/13.41 ( ( powersetAx ) =>
% 98.85/13.41 ( ( setunionAx ) =>
% 98.85/13.41 ( ( omega0Ax ) =>
% 98.85/13.41 ( ( omegaSAx ) =>
% 98.85/13.41 ( ( omegaIndAx ) =>
% 98.85/13.41 ( ( replAx ) =>
% 98.85/13.41 ( ( foundationAx ) =>
% 98.85/13.41 ( ( wellorderingAx ) =>
% 98.85/13.41 ( ( descrp ) =>
% 98.85/13.41 ( ( dsetconstrI ) =>
% 98.85/13.41 ( ( dsetconstrEL ) =>
% 98.85/13.41 ( ( dsetconstrER ) =>
% 98.85/13.41 ( ( exuE1 ) =>
% 98.85/13.41 ( ( prop2setE ) =>
% 98.85/13.41 ( ( emptysetE ) =>
% 98.85/13.41 ( ( emptysetimpfalse ) =>
% 98.85/13.41 ( ( notinemptyset ) =>
% 98.85/13.41 ( ( exuE3e ) =>
% 98.85/13.41 ( ( setext ) =>
% 98.85/13.41 ( ( emptyI ) =>
% 98.85/13.41 ( ( noeltsimpempty ) =>
% 98.85/13.41 ( ( setbeta ) =>
% 98.85/13.41 ( ( nonemptyE1 ) =>
% 98.85/13.41 ( ( nonemptyI ) =>
% 98.85/13.41 ( ( nonemptyI1 ) =>
% 98.85/13.41 ( ( setadjoinIL ) =>
% 98.85/13.41 ( ( emptyinunitempty ) =>
% 98.85/13.41 ( ( setadjoinIR ) =>
% 98.85/13.41 ( (
% 98.85/13.41 setadjoinE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setadjoinOr ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setoftrueEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powersetI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 emptyinPowerset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 emptyInPowerset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powersetE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setunionI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setunionE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subPowSU ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 exuE2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 nonemptyImpWitness ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 uniqinunit ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 notinsingleton ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 eqinunit ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 singletonsswitch ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 upairsetE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 upairsetIL ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 upairsetIR ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 emptyE1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 vacuousDall ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 quantDeMorgan1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 quantDeMorgan2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 quantDeMorgan3 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 quantDeMorgan4 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 prop2setI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 prop2set2propI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 notdexE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 notdallE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 exuI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 exuI3 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 exuI2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 inCongP ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 in__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 exuE3u ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 exu__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 emptyset__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setadjoin__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powerset__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setunion__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 omega__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 exuEu ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 descr__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 dsetconstr__Cong ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subsetI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 eqimpsubset2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 eqimpsubset1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subsetI2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 emptysetsubset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subsetE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subsetE2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 notsubsetI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 notequalI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 notequalI2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subsetRefl ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subsetTrans ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setadjoinSub ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setadjoinSub2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subset2powerset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setextsub ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subsetemptysetimpeq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powersetI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powersetE1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 inPowerset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powersetsubset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 sepInPowerset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 sepSubset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionIL ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 upairset2IR ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionIR ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionEcases ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionLsub ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionRsub ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectSubset5 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectEL ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectLsub ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectSubset2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectSubset3 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectER ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 disjointsetsI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectRsub ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectSubset4 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectSubset1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 bs114d ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusEL ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusER ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusSubset2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusERneg ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusELneg ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusILneg ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusIRneg ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusLsub ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusSubset1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 symdiffE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 symdiffI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 symdiffI2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 symdiffIneg1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 symdiffIneg2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 secondinupair ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairIL ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairIR ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 kpairiskpair ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 kpairp ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 singletonsubset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 singletoninpowerset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 singletoninpowunion ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 upairset2E ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 upairsubunion ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 upairinpowunion ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ubforcartprodlem1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ubforcartprodlem2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ubforcartprodlem3 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodpairin ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodmempair1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodmempair ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setunionE2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setunionsingleton1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setunionsingleton2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setunionsingleton ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 singletonprop ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ex1E1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ex1I ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ex1I2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 singletonsuniq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairinjL1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 kfstsingleton ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 theprop ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 kfstpairEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodfstin ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairinjL2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairinjL ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairinjR11 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairinjR12 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairinjR1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 upairequniteq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairinjR2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setukpairinjR ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ksndsingleton ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ksndpairEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 kpairsurjEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodsndin ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodpairmemEL ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodpairmemER ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodmempaircEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodfstpairEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodsndpairEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 cartprodpairsurjEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 dpsetconstrI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 dpsetconstrSub ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setOfPairsIsBReln ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 dpsetconstrERa ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 dpsetconstrEL1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 dpsetconstrEL2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 dpsetconstrER ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcImageSingleton ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 apProp ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 app ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 infuncsetfunc ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ap2p ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcinfuncset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 lamProp ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 lamp ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 lam2p ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 brelnall1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 brelnall2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ex1E2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcGraphProp1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcGraphProp3 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcGraphProp2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcextLem ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcGraphProp4 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subbreln ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 eqbreln ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcext ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 funcext2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ap2apEq1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ap2apEq2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 beta1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 eta1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 lam2lamEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 beta2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 eta2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 iffalseProp1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 iffalseProp2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 iftrueProp1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 iftrueProp2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ifSingleton ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 ifp ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 theeq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 iftrue ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 iffalse ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 iftrueorfalse ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectT_lem ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionT_lem ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powersetT_lem ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setminusT_lem ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementT_lem ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setextT ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subsetTI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powersetTI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 powersetTE1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementTI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementTE1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectTELcontra ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binintersectTERcontra ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 contrasubsetT ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 contrasubsetT1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 contrasubsetT2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 contrasubsetT3 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 doubleComplementI1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 doubleComplementE1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 doubleComplementSub1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 doubleComplementSub2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 doubleComplementEq ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementTnotintersectT ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementImpComplementIntersect ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementSubsetComplementIntersect ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementInPowersetComplementIntersect ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 contraSubsetComplement ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementTcontraSubset ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionTILcontra ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionTIRcontra ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 inIntersectImpInUnion ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 inIntersectImpInUnion2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 inIntersectImpInIntersectUnions ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 intersectInPowersetIntersectUnions ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 inComplementUnionImpNotIn1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 inComplementUnionImpInComplement1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionTE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 binunionTEcontra ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan2a1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 complementUnionInPowersetComplement ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan2a2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan1a ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan1b ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan2a ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan2b2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan2b ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 demorgan2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz13rule0 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz13rule1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz13rule2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz13rule3 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz13rule4 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz1_1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz1_2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz1_3 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz1_4 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 woz1_5 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1all2 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1SetBreln1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 choice2fnsingleton ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 setOfPairsIsBReln1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1all1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 subbreln1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 eqbreln1 ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1invprop ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1invI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1invE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1compprop ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1compI ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1compE ) =>
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1compEex ) =>
% 98.85/13.41 (
% 98.85/13.41 ![
% 98.85/13.41 A:$i,R:$i]:
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1 @
% 98.85/13.41 A @ R ) =>
% 98.85/13.41 (
% 98.85/13.41 ![
% 98.85/13.41 S:$i]:
% 98.85/13.41 (
% 98.85/13.41 (
% 98.85/13.41 breln1 @
% 98.85/13.41 A @ S ) =>
% 98.85/13.41 (
% 98.85/13.41 breln1 @
% 98.85/13.41 A @
% 98.85/13.41 (
% 98.85/13.41 binunion
% 98.85/13.41 @
% 98.85/13.41 R @ S ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 98.85/13.41 inference('cnf.neg', [status(esa)], [breln1unionprop])).
% 98.85/13.41 thf(zip_derived_cl0, plain,
% 98.85/13.41 (~ (((setextAx) =>
% 98.85/13.41 (((emptysetAx) =>
% 98.85/13.41 (((setadjoinAx) =>
% 98.85/13.41 (((powersetAx) =>
% 98.85/13.41 (((setunionAx) =>
% 98.85/13.41 (((omega0Ax) =>
% 98.85/13.41 (((omegaSAx) =>
% 98.85/13.41 (((omegaIndAx) =>
% 98.85/13.41 (((replAx) =>
% 98.85/13.41 (((foundationAx) =>
% 98.85/13.41 (((wellorderingAx) =>
% 98.85/13.41 (((descrp) =>
% 98.85/13.41 (((dsetconstrI) =>
% 98.85/13.41 (((dsetconstrEL) =>
% 98.85/13.41 (((dsetconstrER) =>
% 98.85/13.41 (((exuE1) =>
% 98.85/13.41 (((prop2setE) =>
% 98.85/13.41 (((emptysetE) =>
% 98.85/13.41 (((emptysetimpfalse) =>
% 98.85/13.41 (((notinemptyset) =>
% 98.85/13.41 (((exuE3e) =>
% 98.85/13.41 (((setext) =>
% 98.85/13.41 (((emptyI) =>
% 98.85/13.41 (((noeltsimpempty) =>
% 98.85/13.41 (((setbeta) =>
% 98.85/13.41 (((nonemptyE1) =>
% 98.85/13.41 (((nonemptyI) =>
% 98.85/13.41 (((nonemptyI1) =>
% 98.85/13.41 (((setadjoinIL) =>
% 98.85/13.41 (((emptyinunitempty) =>
% 98.85/13.41 ((
% 98.85/13.41 (setadjoinIR) =>
% 98.85/13.41 ((
% 98.85/13.41 (setadjoinE) =>
% 98.85/13.41 ((
% 98.85/13.41 (setadjoinOr) =>
% 98.85/13.41 ((
% 98.85/13.41 (setoftrueEq) =>
% 98.85/13.41 ((
% 98.85/13.41 (powersetI) =>
% 98.85/13.41 ((
% 98.85/13.41 (emptyinPowerset) =>
% 98.85/13.41 ((
% 98.85/13.41 (emptyInPowerset) =>
% 98.85/13.41 ((
% 98.85/13.41 (powersetE) =>
% 98.85/13.41 ((
% 98.85/13.41 (setunionI) =>
% 98.85/13.41 ((
% 98.85/13.41 (setunionE) =>
% 98.85/13.41 ((
% 98.85/13.41 (subPowSU) =>
% 98.85/13.41 ((
% 98.85/13.41 (exuE2) =>
% 98.85/13.41 ((
% 98.85/13.41 (nonemptyImpWitness) =>
% 98.85/13.41 ((
% 98.85/13.41 (uniqinunit) =>
% 98.85/13.41 ((
% 98.85/13.41 (notinsingleton) =>
% 98.85/13.41 ((
% 98.85/13.41 (eqinunit) =>
% 98.85/13.41 ((
% 98.85/13.41 (singletonsswitch) =>
% 98.85/13.41 ((
% 98.85/13.41 (upairsetE) =>
% 98.85/13.41 ((
% 98.85/13.41 (upairsetIL) =>
% 98.85/13.41 ((
% 98.85/13.41 (upairsetIR) =>
% 98.85/13.41 ((
% 98.85/13.41 (emptyE1) =>
% 98.85/13.41 ((
% 98.85/13.41 (vacuousDall) =>
% 98.85/13.41 ((
% 98.85/13.41 (quantDeMorgan1) =>
% 98.85/13.41 ((
% 98.85/13.41 (quantDeMorgan2) =>
% 98.85/13.41 ((
% 98.85/13.41 (quantDeMorgan3) =>
% 98.85/13.41 ((
% 98.85/13.41 (quantDeMorgan4) =>
% 98.85/13.41 ((
% 98.85/13.41 (prop2setI) =>
% 98.85/13.41 ((
% 98.85/13.41 (prop2set2propI) =>
% 98.85/13.41 ((
% 98.85/13.41 (notdexE) =>
% 98.85/13.41 ((
% 98.85/13.41 (notdallE) =>
% 98.85/13.41 ((
% 98.85/13.41 (exuI1) =>
% 98.85/13.41 ((
% 98.85/13.41 (exuI3) =>
% 98.85/13.41 ((
% 98.85/13.41 (exuI2) =>
% 98.85/13.41 ((
% 98.85/13.41 (inCongP) =>
% 98.85/13.41 ((
% 98.85/13.41 (in__Cong) =>
% 98.85/13.41 ((
% 98.85/13.41 (exuE3u) =>
% 98.85/13.41 ((
% 98.85/13.41 (exu__Cong) =>
% 98.85/13.41 ((
% 98.85/13.41 (emptyset__Cong) =>
% 98.85/13.41 ((
% 98.85/13.41 (setadjoin__Cong) =>
% 98.85/13.41 ((
% 98.85/13.41 (powerset__Cong) =>
% 98.85/13.41 ((
% 98.85/13.41 (setunion__Cong) =>
% 98.85/13.41 ((
% 98.85/13.41 (omega__Cong) =>
% 98.85/13.41 ((
% 98.85/13.41 (exuEu) =>
% 98.85/13.41 ((
% 98.85/13.41 (descr__Cong) =>
% 98.85/13.41 ((
% 98.85/13.41 (dsetconstr__Cong) =>
% 98.85/13.41 ((
% 98.85/13.41 (subsetI1) =>
% 98.85/13.41 ((
% 98.85/13.41 (eqimpsubset2) =>
% 98.85/13.41 ((
% 98.85/13.41 (eqimpsubset1) =>
% 98.85/13.41 ((
% 98.85/13.41 (subsetI2) =>
% 98.85/13.41 ((
% 98.85/13.41 (emptysetsubset) =>
% 98.85/13.41 ((
% 98.85/13.41 (subsetE) =>
% 98.85/13.41 ((
% 98.85/13.41 (subsetE2) =>
% 98.85/13.41 ((
% 98.85/13.41 (notsubsetI) =>
% 98.85/13.41 ((
% 98.85/13.41 (notequalI1) =>
% 98.85/13.41 ((
% 98.85/13.41 (notequalI2) =>
% 98.85/13.41 ((
% 98.85/13.41 (subsetRefl) =>
% 98.85/13.41 ((
% 98.85/13.41 (subsetTrans) =>
% 98.85/13.41 ((
% 98.85/13.41 (setadjoinSub) =>
% 98.85/13.41 ((
% 98.85/13.41 (setadjoinSub2) =>
% 98.85/13.41 ((
% 98.85/13.41 (subset2powerset) =>
% 98.85/13.41 ((
% 98.85/13.41 (setextsub) =>
% 98.85/13.41 ((
% 98.85/13.41 (subsetemptysetimpeq) =>
% 98.85/13.41 ((
% 98.85/13.41 (powersetI1) =>
% 98.85/13.41 ((
% 98.85/13.41 (powersetE1) =>
% 98.85/13.41 ((
% 98.85/13.41 (inPowerset) =>
% 98.85/13.41 ((
% 98.85/13.41 (powersetsubset) =>
% 98.85/13.41 ((
% 98.85/13.41 (sepInPowerset) =>
% 98.85/13.41 ((
% 98.85/13.41 (sepSubset) =>
% 98.85/13.41 ((
% 98.85/13.41 (binunionIL) =>
% 98.85/13.41 ((
% 98.85/13.41 (upairset2IR) =>
% 98.85/13.41 ((
% 98.85/13.41 (binunionIR) =>
% 98.85/13.41 ((
% 98.85/13.41 (binunionEcases) =>
% 98.85/13.41 ((
% 98.85/13.41 (binunionE) =>
% 98.85/13.41 ((
% 98.85/13.41 (binunionLsub) =>
% 98.85/13.41 ((
% 98.85/13.41 (binunionRsub) =>
% 98.85/13.41 ((
% 98.85/13.41 (binintersectI) =>
% 98.85/13.41 ((
% 98.85/13.41 (binintersectSubset5) =>
% 98.85/13.41 ((
% 98.85/13.41 (binintersectEL) =>
% 98.85/13.41 ((
% 98.85/13.41 (binintersectLsub) =>
% 98.85/13.41 ((
% 98.85/13.41 (binintersectSubset2) =>
% 98.85/13.41 ((
% 98.85/13.41 (binintersectSubset3) =>
% 98.85/13.41 ((
% 98.85/13.41 (binintersectER) =>
% 98.85/13.41 ((
% 98.85/13.41 (disjointsetsI1) =>
% 98.85/13.41 ((
% 98.85/13.41 (binintersectRsub) =>
% 98.85/13.41 ((
% 98.85/13.41 (binintersectSubset4) =>
% 98.85/13.41 ((
% 98.85/13.41 (binintersectSubset1) =>
% 98.85/13.41 ((
% 98.85/13.41 (bs114d) =>
% 98.85/13.41 ((
% 98.85/13.41 (setminusI) =>
% 98.85/13.41 ((
% 98.85/13.41 (setminusEL) =>
% 98.85/13.41 ((
% 98.85/13.41 (setminusER) =>
% 98.85/13.41 ((
% 98.85/13.41 (setminusSubset2) =>
% 98.85/13.41 ((
% 98.85/13.41 (setminusERneg) =>
% 98.85/13.41 ((
% 98.85/13.41 (setminusELneg) =>
% 98.85/13.41 ((
% 98.85/13.41 (setminusILneg) =>
% 98.85/13.41 ((
% 98.85/13.41 (setminusIRneg) =>
% 98.85/13.41 ((
% 98.85/13.41 (setminusLsub) =>
% 98.85/13.41 ((
% 98.85/13.41 (setminusSubset1) =>
% 98.85/13.41 ((
% 98.85/13.41 (symdiffE) =>
% 98.85/13.41 ((
% 98.85/13.41 (symdiffI1) =>
% 98.85/13.41 ((
% 98.85/13.41 (symdiffI2) =>
% 98.85/13.41 ((
% 98.85/13.41 (symdiffIneg1) =>
% 98.85/13.41 ((
% 98.85/13.41 (symdiffIneg2) =>
% 98.85/13.41 ((
% 98.85/13.41 (secondinupair) =>
% 98.85/13.41 ((
% 98.85/13.41 (setukpairIL) =>
% 98.85/13.41 ((
% 98.85/13.41 (setukpairIR) =>
% 98.85/13.41 ((
% 98.85/13.41 (kpairiskpair) =>
% 98.85/13.41 ((
% 98.85/13.41 (kpairp) =>
% 98.85/13.41 ((
% 98.85/13.41 (singletonsubset) =>
% 98.85/13.41 ((
% 98.85/13.41 (singletoninpowerset) =>
% 98.85/13.41 ((
% 98.85/13.41 (singletoninpowunion) =>
% 98.85/13.41 ((
% 98.85/13.41 (upairset2E) =>
% 98.85/13.41 ((
% 98.85/13.41 (upairsubunion) =>
% 98.85/13.41 ((
% 98.85/13.41 (upairinpowunion) =>
% 98.85/13.41 ((
% 98.85/13.41 (ubforcartprodlem1) =>
% 98.85/13.41 ((
% 98.85/13.41 (ubforcartprodlem2) =>
% 98.85/13.41 ((
% 98.85/13.41 (ubforcartprodlem3) =>
% 98.85/13.41 ((
% 98.85/13.41 (cartprodpairin) =>
% 98.85/13.41 ((
% 98.85/13.41 (cartprodmempair1) =>
% 98.85/13.41 ((
% 98.85/13.41 (cartprodmempair) =>
% 98.85/13.41 ((
% 98.85/13.41 (setunionE2) =>
% 98.85/13.41 ((
% 98.85/13.41 (setunionsingleton1) =>
% 98.85/13.41 ((
% 98.85/13.41 (setunionsingleton2) =>
% 98.85/13.41 ((
% 98.85/13.41 (setunionsingleton) =>
% 98.85/13.41 ((
% 98.85/13.41 (singletonprop) =>
% 98.85/13.41 ((
% 98.85/13.41 (ex1E1) =>
% 98.85/13.41 ((
% 98.85/13.41 (ex1I) =>
% 98.85/13.41 ((
% 98.85/13.41 (ex1I2) =>
% 98.85/13.41 ((
% 98.85/13.41 (singletonsuniq) =>
% 98.85/13.41 ((
% 98.85/13.41 (setukpairinjL1) =>
% 98.85/13.41 ((
% 98.85/13.41 (kfstsingleton) =>
% 98.85/13.41 ((
% 98.85/13.41 (theprop) =>
% 98.85/13.41 ((
% 98.85/13.41 (kfstpairEq) =>
% 98.85/13.41 ((
% 98.85/13.41 (cartprodfstin) =>
% 98.85/13.41 ((
% 98.85/13.41 (setukpairinjL2) =>
% 98.85/13.41 ((
% 98.85/13.41 (setukpairinjL) =>
% 98.85/13.41 ((
% 98.85/13.41 (setukpairinjR11) =>
% 98.85/13.41 ((
% 98.85/13.41 (setukpairinjR12) =>
% 98.85/13.41 ((
% 98.85/13.41 (setukpairinjR1) =>
% 98.85/13.41 ((
% 98.85/13.41 (upairequniteq) =>
% 98.85/13.41 ((
% 98.85/13.41 (setukpairinjR2) =>
% 98.85/13.41 ((
% 98.85/13.41 (setukpairinjR) =>
% 98.85/13.41 ((
% 98.85/13.41 (ksndsingleton) =>
% 98.85/13.41 ((
% 98.85/13.41 (ksndpairEq) =>
% 98.85/13.41 ((
% 98.85/13.41 (kpairsurjEq) =>
% 98.85/13.41 ((
% 98.85/13.41 (cartprodsndin) =>
% 98.85/13.41 ((
% 98.85/13.41 (cartprodpairmemEL) =>
% 98.85/13.41 ((
% 98.85/13.41 (cartprodpairmemER) =>
% 98.85/13.41 ((
% 98.85/13.41 (cartprodmempaircEq) =>
% 98.85/13.41 ((
% 98.85/13.41 (cartprodfstpairEq) =>
% 98.85/13.41 ((
% 98.85/13.41 (cartprodsndpairEq) =>
% 98.85/13.41 ((
% 98.85/13.41 (cartprodpairsurjEq) =>
% 98.85/13.41 ((
% 98.85/13.41 (dpsetconstrI) =>
% 98.85/13.41 ((
% 98.85/13.41 (dpsetconstrSub) =>
% 98.85/13.41 ((
% 98.85/13.41 (setOfPairsIsBReln) =>
% 98.85/13.41 ((
% 98.85/13.41 (dpsetconstrERa) =>
% 98.85/13.41 ((
% 98.85/13.41 (dpsetconstrEL1) =>
% 98.85/13.41 ((
% 98.85/13.41 (dpsetconstrEL2) =>
% 98.85/13.41 ((
% 98.85/13.41 (dpsetconstrER) =>
% 98.85/13.41 ((
% 98.85/13.41 (funcImageSingleton) =>
% 98.85/13.41 ((
% 98.85/13.41 (apProp) =>
% 98.85/13.41 ((
% 98.85/13.41 (app) =>
% 98.85/13.41 ((
% 98.85/13.41 (infuncsetfunc) =>
% 98.85/13.41 ((
% 98.85/13.41 (ap2p) =>
% 98.85/13.41 ((
% 98.85/13.41 (funcinfuncset) =>
% 98.85/13.41 ((
% 98.85/13.41 (lamProp) =>
% 98.85/13.41 ((
% 98.85/13.41 (lamp) =>
% 98.85/13.41 ((
% 98.85/13.41 (lam2p) =>
% 98.85/13.41 ((
% 98.85/13.41 (brelnall1) =>
% 98.85/13.41 ((
% 98.85/13.41 (brelnall2) =>
% 98.85/13.41 ((
% 98.85/13.41 (ex1E2) =>
% 98.85/13.41 ((
% 98.85/13.41 (funcGraphProp1) =>
% 98.85/13.41 ((
% 98.85/13.41 (funcGraphProp3) =>
% 98.85/13.41 ((
% 98.85/13.41 (funcGraphProp2) =>
% 98.85/13.41 ((
% 98.85/13.41 (funcextLem) =>
% 98.85/13.41 ((
% 98.85/13.41 (funcGraphProp4) =>
% 98.85/13.41 ((
% 98.85/13.41 (subbreln) =>
% 98.85/13.41 ((
% 98.85/13.41 (eqbreln) =>
% 98.85/13.41 ((
% 98.85/13.41 (funcext) =>
% 98.85/13.41 ((
% 98.85/13.41 (funcext2) =>
% 98.85/13.41 ((
% 98.85/13.41 (ap2apEq1) =>
% 98.85/13.41 ((
% 98.85/13.41 (ap2apEq2) =>
% 98.85/13.41 ((
% 98.85/13.41 (beta1) =>
% 98.85/13.41 ((
% 98.85/13.41 (eta1) =>
% 98.85/13.41 ((
% 98.85/13.41 (lam2lamEq) =>
% 98.85/13.41 ((
% 98.85/13.41 (beta2) =>
% 98.85/13.41 ((
% 98.85/13.41 (eta2) =>
% 98.85/13.41 ((
% 98.85/13.41 (iffalseProp1) =>
% 98.85/13.41 ((
% 98.85/13.41 (iffalseProp2) =>
% 98.85/13.41 ((
% 98.85/13.41 (iftrueProp1) =>
% 98.85/13.41 ((
% 98.85/13.41 (iftrueProp2) =>
% 98.85/13.41 ((
% 98.85/13.41 (ifSingleton) =>
% 98.85/13.41 ((
% 98.85/13.41 (ifp) =>
% 98.85/13.41 ((
% 98.85/13.41 (theeq) =>
% 98.85/13.41 ((
% 98.85/13.41 (iftrue) =>
% 98.85/13.41 ((
% 98.85/13.41 (iffalse) =>
% 98.85/13.41 ((
% 98.85/13.41 (iftrueorfalse) =>
% 98.85/13.41 ((
% 98.85/13.41 (binintersectT_lem) =>
% 98.85/13.41 ((
% 98.85/13.41 (binunionT_lem) =>
% 98.85/13.41 ((
% 98.85/13.41 (powersetT_lem) =>
% 98.85/13.41 ((
% 98.85/13.41 (setminusT_lem) =>
% 98.85/13.41 ((
% 98.85/13.41 (complementT_lem) =>
% 98.85/13.41 ((
% 98.85/13.41 (setextT) =>
% 98.85/13.41 ((
% 98.85/13.41 (subsetTI) =>
% 98.85/13.41 ((
% 98.85/13.41 (powersetTI1) =>
% 98.85/13.41 ((
% 98.85/13.41 (powersetTE1) =>
% 98.85/13.41 ((
% 98.85/13.41 (complementTI1) =>
% 98.85/13.41 ((
% 98.85/13.41 (complementTE1) =>
% 98.85/13.41 ((
% 98.85/13.41 (binintersectTELcontra) =>
% 98.85/13.41 ((
% 98.85/13.41 (binintersectTERcontra) =>
% 98.85/13.41 ((
% 98.85/13.41 (contrasubsetT) =>
% 98.85/13.41 ((
% 98.85/13.41 (contrasubsetT1) =>
% 98.85/13.41 ((
% 98.85/13.41 (contrasubsetT2) =>
% 98.85/13.41 ((
% 98.85/13.41 (contrasubsetT3) =>
% 98.85/13.41 ((
% 98.85/13.41 (doubleComplementI1) =>
% 98.85/13.41 ((
% 98.85/13.41 (doubleComplementE1) =>
% 98.85/13.41 ((
% 98.85/13.41 (doubleComplementSub1) =>
% 98.85/13.41 ((
% 98.85/13.41 (doubleComplementSub2) =>
% 98.85/13.41 ((
% 98.85/13.41 (doubleComplementEq) =>
% 98.85/13.41 ((
% 98.85/13.41 (complementTnotintersectT) =>
% 98.85/13.41 ((
% 98.85/13.41 (complementImpComplementIntersect) =>
% 98.85/13.41 ((
% 98.85/13.41 (complementSubsetComplementIntersect) =>
% 98.85/13.41 ((
% 98.85/13.41 (complementInPowersetComplementIntersect) =>
% 98.85/13.41 ((
% 98.85/13.41 (contraSubsetComplement) =>
% 98.85/13.41 ((
% 98.85/13.41 (complementTcontraSubset) =>
% 98.85/13.41 ((
% 98.85/13.41 (binunionTILcontra) =>
% 98.85/13.41 ((
% 98.85/13.41 (binunionTIRcontra) =>
% 98.85/13.41 ((
% 98.85/13.41 (inIntersectImpInUnion) =>
% 98.85/13.41 ((
% 98.85/13.41 (inIntersectImpInUnion2) =>
% 98.85/13.41 ((
% 98.85/13.41 (inIntersectImpInIntersectUnions) =>
% 98.85/13.41 ((
% 98.85/13.41 (intersectInPowersetIntersectUnions) =>
% 98.85/13.41 ((
% 98.85/13.41 (inComplementUnionImpNotIn1) =>
% 98.85/13.41 ((
% 98.85/13.41 (inComplementUnionImpInComplement1) =>
% 98.85/13.41 ((
% 98.85/13.41 (binunionTE) =>
% 98.85/13.41 ((
% 98.85/13.41 (binunionTEcontra) =>
% 98.85/13.41 ((
% 98.85/13.41 (demorgan2a1) =>
% 98.85/13.41 ((
% 98.85/13.41 (complementUnionInPowersetComplement) =>
% 98.85/13.41 ((
% 98.85/13.41 (demorgan2a2) =>
% 98.85/13.41 ((
% 98.85/13.41 (demorgan1a) =>
% 98.85/13.41 ((
% 98.85/13.41 (demorgan1b) =>
% 98.85/13.41 ((
% 98.85/13.41 (demorgan1) =>
% 98.85/13.41 ((
% 98.85/13.41 (demorgan2a) =>
% 98.85/13.41 ((
% 98.85/13.41 (demorgan2b2) =>
% 98.85/13.41 ((
% 98.85/13.41 (demorgan2b) =>
% 98.85/13.41 ((
% 98.85/13.41 (demorgan2) =>
% 98.85/13.41 ((
% 98.85/13.41 (woz13rule0) =>
% 98.85/13.41 ((
% 98.85/13.41 (woz13rule1) =>
% 98.85/13.41 ((
% 98.85/13.41 (woz13rule2) =>
% 98.85/13.41 ((
% 98.85/13.41 (woz13rule3) =>
% 98.85/13.41 ((
% 98.85/13.41 (woz13rule4) =>
% 98.85/13.41 ((
% 98.85/13.41 (woz1_1) =>
% 98.85/13.41 ((
% 98.85/13.41 (woz1_2) =>
% 98.85/13.41 ((
% 98.85/13.41 (woz1_3) =>
% 98.85/13.41 ((
% 98.85/13.41 (woz1_4) =>
% 98.85/13.41 ((
% 98.85/13.41 (woz1_5) =>
% 98.85/13.41 ((
% 98.85/13.41 (breln1all2) =>
% 98.85/13.41 ((
% 98.85/13.41 (breln1SetBreln1) =>
% 98.85/13.41 ((
% 98.85/13.41 (choice2fnsingleton) =>
% 98.85/13.41 ((
% 98.85/13.41 (setOfPairsIsBReln1) =>
% 98.85/13.41 ((
% 98.85/13.41 (breln1all1) =>
% 98.85/13.41 ((
% 98.85/13.41 (subbreln1) =>
% 98.85/13.41 ((
% 98.85/13.41 (eqbreln1) =>
% 98.85/13.41 ((
% 98.85/13.41 (breln1invprop) =>
% 98.85/13.41 ((
% 98.85/13.41 (breln1invI) =>
% 98.85/13.41 ((
% 98.85/13.41 (breln1invE) =>
% 98.85/13.41 ((
% 98.85/13.41 (breln1compprop) =>
% 98.85/13.41 ((
% 98.85/13.41 (breln1compI) =>
% 98.85/13.41 ((
% 98.85/13.41 (breln1compE) =>
% 98.85/13.41 ((
% 98.85/13.41 (breln1compEex) =>
% 98.85/13.41 ((
% 98.85/13.41 (!!) @ (
% 98.85/13.41 ^[Y0 : $i]:
% 98.85/13.41 ((
% 98.85/13.41 (!!) @ (
% 98.85/13.41 ^[Y1 : $i]:
% 98.85/13.41 ((
% 98.85/13.41 (breln1 @
% 98.85/13.41 Y0 @
% 98.85/13.41 Y1) =>
% 98.85/13.41 ((
% 98.85/13.41 (!!) @ (
% 98.85/13.41 ^[Y2 : $i]:
% 98.85/13.41 ((
% 98.85/13.41 (breln1 @
% 98.85/13.41 Y0 @
% 98.85/13.41 Y2) =>
% 98.85/13.41 (breln1 @
% 98.85/13.41 Y0 @
% 98.85/13.41 (
% 98.85/13.41 binunion @
% 98.85/13.41 Y1 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.85/13.42 inference('cnf', [status(esa)], [zf_stmt_0])).
% 98.85/13.42 thf(zip_derived_cl1, plain,
% 98.85/13.42 (~ (((setextAx) =>
% 98.85/13.42 (((emptysetAx) =>
% 98.85/13.42 (((setadjoinAx) =>
% 98.85/13.42 (((powersetAx) =>
% 98.85/13.42 (((setunionAx) =>
% 98.85/13.42 (((omega0Ax) =>
% 98.85/13.42 (((omegaSAx) =>
% 98.85/13.42 (((omegaIndAx) =>
% 98.85/13.42 (((replAx) =>
% 98.85/13.42 (((foundationAx) =>
% 98.85/13.42 (((wellorderingAx) =>
% 98.85/13.42 (((descrp) =>
% 98.85/13.42 (((dsetconstrI) =>
% 98.85/13.42 (((dsetconstrEL) =>
% 98.85/13.42 (((dsetconstrER) =>
% 98.85/13.42 (((exuE1) =>
% 98.85/13.42 (((prop2setE) =>
% 98.85/13.42 (((emptysetE) =>
% 98.85/13.42 (((emptysetimpfalse) =>
% 98.85/13.42 (((notinemptyset) =>
% 98.85/13.42 (((exuE3e) =>
% 98.85/13.42 (((setext) =>
% 98.85/13.42 (((emptyI) =>
% 98.85/13.42 (((noeltsimpempty) =>
% 98.85/13.42 (((setbeta) =>
% 98.85/13.42 (((nonemptyE1) =>
% 98.85/13.42 (((nonemptyI) =>
% 98.85/13.42 (((nonemptyI1) =>
% 98.85/13.42 (((setadjoinIL) =>
% 98.85/13.42 (((emptyinunitempty) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinE) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinOr) =>
% 98.85/13.42 ((
% 98.85/13.42 (setoftrueEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetI) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyinPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyInPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionI) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionE) =>
% 98.85/13.42 ((
% 98.85/13.42 (subPowSU) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (nonemptyImpWitness) =>
% 98.85/13.42 ((
% 98.85/13.42 (uniqinunit) =>
% 98.85/13.42 ((
% 98.85/13.42 (notinsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqinunit) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsswitch) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (vacuousDall) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan1) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan2) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan3) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan4) =>
% 98.85/13.42 ((
% 98.85/13.42 (prop2setI) =>
% 98.85/13.42 ((
% 98.85/13.42 (prop2set2propI) =>
% 98.85/13.42 ((
% 98.85/13.42 (notdexE) =>
% 98.85/13.42 ((
% 98.85/13.42 (notdallE) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI3) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (inCongP) =>
% 98.85/13.42 ((
% 98.85/13.42 (in__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuE3u) =>
% 98.85/13.42 ((
% 98.85/13.42 (exu__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyset__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoin__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (powerset__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunion__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (omega__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuEu) =>
% 98.85/13.42 ((
% 98.85/13.42 (descr__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (dsetconstr__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqimpsubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqimpsubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptysetsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (notsubsetI) =>
% 98.85/13.42 ((
% 98.85/13.42 (notequalI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (notequalI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetRefl) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetTrans) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinSub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinSub2) =>
% 98.85/13.42 ((
% 98.85/13.42 (subset2powerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (setextsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetemptysetimpeq) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (inPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (sepInPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (sepSubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairset2IR) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionEcases) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionE) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionRsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectI) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset5) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset3) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectER) =>
% 98.85/13.42 ((
% 98.85/13.42 (disjointsetsI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectRsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset4) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (bs114d) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusI) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusER) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusSubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusERneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusELneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusILneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusIRneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusSubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffE) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffIneg1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffIneg2) =>
% 98.85/13.42 ((
% 98.85/13.42 (secondinupair) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairiskpair) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairp) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletoninpowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletoninpowunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairset2E) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsubunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairinpowunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem3) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairin) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempair1) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempair) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton1) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1E1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1I) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1I2) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsuniq) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL1) =>
% 98.85/13.42 ((
% 98.85/13.42 (kfstsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (theprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (kfstpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodfstin) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR11) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR12) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR1) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairequniteq) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR) =>
% 98.85/13.42 ((
% 98.85/13.42 (ksndsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (ksndpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairsurjEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodsndin) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairmemEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairmemER) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempaircEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodfstpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodsndpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairsurjEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrI) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrSub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setOfPairsIsBReln) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrERa) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrEL1) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrEL2) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrER) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcImageSingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (apProp) =>
% 98.85/13.42 ((
% 98.85/13.42 (app) =>
% 98.85/13.42 ((
% 98.85/13.42 (infuncsetfunc) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2p) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcinfuncset) =>
% 98.85/13.42 ((
% 98.85/13.42 (lamProp) =>
% 98.85/13.42 ((
% 98.85/13.42 (lamp) =>
% 98.85/13.42 ((
% 98.85/13.42 (lam2p) =>
% 98.85/13.42 ((
% 98.85/13.42 (brelnall1) =>
% 98.85/13.42 ((
% 98.85/13.42 (brelnall2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1E2) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp3) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcextLem) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp4) =>
% 98.85/13.42 ((
% 98.85/13.42 (subbreln) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqbreln) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcext) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcext2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2apEq1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2apEq2) =>
% 98.85/13.42 ((
% 98.85/13.42 (beta1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eta1) =>
% 98.85/13.42 ((
% 98.85/13.42 (lam2lamEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (beta2) =>
% 98.85/13.42 ((
% 98.85/13.42 (eta2) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalseProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalseProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ifSingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (ifp) =>
% 98.85/13.42 ((
% 98.85/13.42 (theeq) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrue) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalse) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueorfalse) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (setextT) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetTI) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetTI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetTE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectTELcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectTERcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT1) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT2) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT3) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementSub1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementSub2) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTnotintersectT) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementImpComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementSubsetComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementInPowersetComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (contraSubsetComplement) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTcontraSubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTILcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTIRcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInUnion) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInUnion2) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInIntersectUnions) =>
% 98.85/13.42 ((
% 98.85/13.42 (intersectInPowersetIntersectUnions) =>
% 98.85/13.42 ((
% 98.85/13.42 (inComplementUnionImpNotIn1) =>
% 98.85/13.42 ((
% 98.85/13.42 (inComplementUnionImpInComplement1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTE) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTEcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementUnionInPowersetComplement) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a2) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1a) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1b) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2b2) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2b) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule0) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule1) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule3) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule4) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_1) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_3) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_4) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_5) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1all2) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1SetBreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (choice2fnsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (setOfPairsIsBReln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1all1) =>
% 98.85/13.42 ((
% 98.85/13.42 (subbreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqbreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invI) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invE) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compI) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compE) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compEex) =>
% 98.85/13.42 ((
% 98.85/13.42 (!!) @ (
% 98.85/13.42 (('#B') @ (
% 98.85/13.42 !!) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#S') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#S') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 =>))) @
% 98.85/13.42 breln1)))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 !!))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#S') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#S') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 =>))) @
% 98.85/13.42 breln1)))))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#C') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 breln1)))) @
% 98.85/13.42 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.85/13.42 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 98.85/13.42 thf(omega0Ax, axiom,(( omega0Ax ) = ((in @ emptyset @ omega)))).
% 98.85/13.42 thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 98.85/13.42 define([status(thm)])).
% 98.85/13.42 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 98.85/13.42 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))).
% 98.85/13.42 thf('1', plain,
% 98.85/13.42 (( emptyinunitempty ) =
% 98.85/13.42 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 98.85/13.42 define([status(thm)])).
% 98.85/13.42 thf(emptyset__Cong, axiom,(( emptyset__Cong ) =
% 98.85/13.42 ((((emptyset) = (emptyset)))))).
% 98.85/13.42 thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 98.85/13.42 define([status(thm)])).
% 98.85/13.42 thf(omega__Cong, axiom,(( omega__Cong ) = ((((omega) = (omega)))))).
% 98.85/13.42 thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 98.85/13.42 define([status(thm)])).
% 98.85/13.42 thf(zip_derived_cl2, plain,
% 98.85/13.42 (~ (((setextAx) =>
% 98.85/13.42 (((emptysetAx) =>
% 98.85/13.42 (((setadjoinAx) =>
% 98.85/13.42 (((powersetAx) =>
% 98.85/13.42 (((setunionAx) =>
% 98.85/13.42 (((in @ emptyset @ omega) =>
% 98.85/13.42 (((omegaSAx) =>
% 98.85/13.42 (((omegaIndAx) =>
% 98.85/13.42 (((replAx) =>
% 98.85/13.42 (((foundationAx) =>
% 98.85/13.42 (((wellorderingAx) =>
% 98.85/13.42 (((descrp) =>
% 98.85/13.42 (((dsetconstrI) =>
% 98.85/13.42 (((dsetconstrEL) =>
% 98.85/13.42 (((dsetconstrER) =>
% 98.85/13.42 (((exuE1) =>
% 98.85/13.42 (((prop2setE) =>
% 98.85/13.42 (((emptysetE) =>
% 98.85/13.42 (((emptysetimpfalse) =>
% 98.85/13.42 (((notinemptyset) =>
% 98.85/13.42 (((exuE3e) =>
% 98.85/13.42 (((setext) =>
% 98.85/13.42 (((emptyI) =>
% 98.85/13.42 (((noeltsimpempty) =>
% 98.85/13.42 (((setbeta) =>
% 98.85/13.42 (((nonemptyE1) =>
% 98.85/13.42 (((nonemptyI) =>
% 98.85/13.42 (((nonemptyI1) =>
% 98.85/13.42 (((setadjoinIL) =>
% 98.85/13.42 (((in @
% 98.85/13.42 emptyset @
% 98.85/13.42 (setadjoin @
% 98.85/13.42 emptyset @
% 98.85/13.42 emptyset)) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinE) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinOr) =>
% 98.85/13.42 ((
% 98.85/13.42 (setoftrueEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetI) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyinPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyInPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionI) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionE) =>
% 98.85/13.42 ((
% 98.85/13.42 (subPowSU) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (nonemptyImpWitness) =>
% 98.85/13.42 ((
% 98.85/13.42 (uniqinunit) =>
% 98.85/13.42 ((
% 98.85/13.42 (notinsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqinunit) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsswitch) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (vacuousDall) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan1) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan2) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan3) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan4) =>
% 98.85/13.42 ((
% 98.85/13.42 (prop2setI) =>
% 98.85/13.42 ((
% 98.85/13.42 (prop2set2propI) =>
% 98.85/13.42 ((
% 98.85/13.42 (notdexE) =>
% 98.85/13.42 ((
% 98.85/13.42 (notdallE) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI3) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (inCongP) =>
% 98.85/13.42 ((
% 98.85/13.42 (in__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuE3u) =>
% 98.85/13.42 ((
% 98.85/13.42 (exu__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 ((
% 98.85/13.42 (emptyset) =
% 98.85/13.42 (emptyset))) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoin__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (powerset__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunion__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 ((
% 98.85/13.42 (omega) =
% 98.85/13.42 (omega))) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuEu) =>
% 98.85/13.42 ((
% 98.85/13.42 (descr__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (dsetconstr__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqimpsubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqimpsubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptysetsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (notsubsetI) =>
% 98.85/13.42 ((
% 98.85/13.42 (notequalI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (notequalI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetRefl) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetTrans) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinSub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinSub2) =>
% 98.85/13.42 ((
% 98.85/13.42 (subset2powerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (setextsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetemptysetimpeq) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (inPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (sepInPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (sepSubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairset2IR) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionEcases) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionE) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionRsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectI) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset5) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset3) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectER) =>
% 98.85/13.42 ((
% 98.85/13.42 (disjointsetsI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectRsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset4) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (bs114d) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusI) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusER) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusSubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusERneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusELneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusILneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusIRneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusSubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffE) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffIneg1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffIneg2) =>
% 98.85/13.42 ((
% 98.85/13.42 (secondinupair) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairiskpair) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairp) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletoninpowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletoninpowunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairset2E) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsubunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairinpowunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem3) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairin) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempair1) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempair) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton1) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1E1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1I) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1I2) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsuniq) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL1) =>
% 98.85/13.42 ((
% 98.85/13.42 (kfstsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (theprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (kfstpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodfstin) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR11) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR12) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR1) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairequniteq) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR) =>
% 98.85/13.42 ((
% 98.85/13.42 (ksndsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (ksndpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairsurjEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodsndin) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairmemEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairmemER) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempaircEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodfstpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodsndpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairsurjEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrI) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrSub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setOfPairsIsBReln) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrERa) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrEL1) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrEL2) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrER) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcImageSingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (apProp) =>
% 98.85/13.42 ((
% 98.85/13.42 (app) =>
% 98.85/13.42 ((
% 98.85/13.42 (infuncsetfunc) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2p) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcinfuncset) =>
% 98.85/13.42 ((
% 98.85/13.42 (lamProp) =>
% 98.85/13.42 ((
% 98.85/13.42 (lamp) =>
% 98.85/13.42 ((
% 98.85/13.42 (lam2p) =>
% 98.85/13.42 ((
% 98.85/13.42 (brelnall1) =>
% 98.85/13.42 ((
% 98.85/13.42 (brelnall2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1E2) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp3) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcextLem) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp4) =>
% 98.85/13.42 ((
% 98.85/13.42 (subbreln) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqbreln) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcext) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcext2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2apEq1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2apEq2) =>
% 98.85/13.42 ((
% 98.85/13.42 (beta1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eta1) =>
% 98.85/13.42 ((
% 98.85/13.42 (lam2lamEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (beta2) =>
% 98.85/13.42 ((
% 98.85/13.42 (eta2) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalseProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalseProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ifSingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (ifp) =>
% 98.85/13.42 ((
% 98.85/13.42 (theeq) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrue) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalse) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueorfalse) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (setextT) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetTI) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetTI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetTE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectTELcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectTERcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT1) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT2) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT3) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementSub1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementSub2) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTnotintersectT) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementImpComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementSubsetComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementInPowersetComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (contraSubsetComplement) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTcontraSubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTILcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTIRcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInUnion) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInUnion2) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInIntersectUnions) =>
% 98.85/13.42 ((
% 98.85/13.42 (intersectInPowersetIntersectUnions) =>
% 98.85/13.42 ((
% 98.85/13.42 (inComplementUnionImpNotIn1) =>
% 98.85/13.42 ((
% 98.85/13.42 (inComplementUnionImpInComplement1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTE) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTEcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementUnionInPowersetComplement) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a2) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1a) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1b) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2b2) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2b) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule0) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule1) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule3) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule4) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_1) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_3) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_4) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_5) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1all2) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1SetBreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (choice2fnsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (setOfPairsIsBReln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1all1) =>
% 98.85/13.42 ((
% 98.85/13.42 (subbreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqbreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invI) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invE) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compI) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compE) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compEex) =>
% 98.85/13.42 ((
% 98.85/13.42 (!!) @ (
% 98.85/13.42 (('#B') @ (
% 98.85/13.42 !!) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#S') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#S') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 =>))) @
% 98.85/13.42 breln1)))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 !!))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#S') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#S') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 =>))) @
% 98.85/13.42 breln1)))))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#C') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 breln1)))) @
% 98.85/13.42 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.85/13.42 inference('rw', [status(thm)], [zip_derived_cl1, '0', '1', '2', '3'])).
% 98.85/13.42 thf(zip_derived_cl3, plain,
% 98.85/13.42 (~ (((setextAx) =>
% 98.85/13.42 (((emptysetAx) =>
% 98.85/13.42 (((setadjoinAx) =>
% 98.85/13.42 (((powersetAx) =>
% 98.85/13.42 (((setunionAx) =>
% 98.85/13.42 (((in @ emptyset @ omega) =>
% 98.85/13.42 (((omegaSAx) =>
% 98.85/13.42 (((omegaIndAx) =>
% 98.85/13.42 (((replAx) =>
% 98.85/13.42 (((foundationAx) =>
% 98.85/13.42 (((wellorderingAx) =>
% 98.85/13.42 (((descrp) =>
% 98.85/13.42 (((dsetconstrI) =>
% 98.85/13.42 (((dsetconstrEL) =>
% 98.85/13.42 (((dsetconstrER) =>
% 98.85/13.42 (((exuE1) =>
% 98.85/13.42 (((prop2setE) =>
% 98.85/13.42 (((emptysetE) =>
% 98.85/13.42 (((emptysetimpfalse) =>
% 98.85/13.42 (((notinemptyset) =>
% 98.85/13.42 (((exuE3e) =>
% 98.85/13.42 (((setext) =>
% 98.85/13.42 (((emptyI) =>
% 98.85/13.42 (((noeltsimpempty) =>
% 98.85/13.42 (((setbeta) =>
% 98.85/13.42 (((nonemptyE1) =>
% 98.85/13.42 (((nonemptyI) =>
% 98.85/13.42 (((nonemptyI1) =>
% 98.85/13.42 (((setadjoinIL) =>
% 98.85/13.42 (((in @
% 98.85/13.42 emptyset @
% 98.85/13.42 (setadjoin @
% 98.85/13.42 emptyset @
% 98.85/13.42 emptyset)) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinE) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinOr) =>
% 98.85/13.42 ((
% 98.85/13.42 (setoftrueEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetI) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyinPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyInPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionI) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionE) =>
% 98.85/13.42 ((
% 98.85/13.42 (subPowSU) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (nonemptyImpWitness) =>
% 98.85/13.42 ((
% 98.85/13.42 (uniqinunit) =>
% 98.85/13.42 ((
% 98.85/13.42 (notinsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqinunit) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsswitch) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (vacuousDall) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan1) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan2) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan3) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan4) =>
% 98.85/13.42 ((
% 98.85/13.42 (prop2setI) =>
% 98.85/13.42 ((
% 98.85/13.42 (prop2set2propI) =>
% 98.85/13.42 ((
% 98.85/13.42 (notdexE) =>
% 98.85/13.42 ((
% 98.85/13.42 (notdallE) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI3) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (inCongP) =>
% 98.85/13.42 ((
% 98.85/13.42 (in__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuE3u) =>
% 98.85/13.42 ((
% 98.85/13.42 (exu__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoin__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (powerset__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunion__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuEu) =>
% 98.85/13.42 ((
% 98.85/13.42 (descr__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (dsetconstr__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqimpsubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqimpsubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptysetsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (notsubsetI) =>
% 98.85/13.42 ((
% 98.85/13.42 (notequalI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (notequalI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetRefl) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetTrans) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinSub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinSub2) =>
% 98.85/13.42 ((
% 98.85/13.42 (subset2powerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (setextsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetemptysetimpeq) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (inPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (sepInPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (sepSubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairset2IR) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionEcases) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionE) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionRsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectI) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset5) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset3) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectER) =>
% 98.85/13.42 ((
% 98.85/13.42 (disjointsetsI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectRsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset4) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (bs114d) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusI) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusER) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusSubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusERneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusELneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusILneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusIRneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusSubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffE) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffIneg1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffIneg2) =>
% 98.85/13.42 ((
% 98.85/13.42 (secondinupair) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairiskpair) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairp) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletoninpowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletoninpowunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairset2E) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsubunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairinpowunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem3) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairin) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempair1) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempair) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton1) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1E1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1I) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1I2) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsuniq) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL1) =>
% 98.85/13.42 ((
% 98.85/13.42 (kfstsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (theprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (kfstpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodfstin) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR11) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR12) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR1) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairequniteq) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR) =>
% 98.85/13.42 ((
% 98.85/13.42 (ksndsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (ksndpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairsurjEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodsndin) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairmemEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairmemER) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempaircEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodfstpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodsndpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairsurjEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrI) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrSub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setOfPairsIsBReln) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrERa) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrEL1) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrEL2) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrER) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcImageSingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (apProp) =>
% 98.85/13.42 ((
% 98.85/13.42 (app) =>
% 98.85/13.42 ((
% 98.85/13.42 (infuncsetfunc) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2p) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcinfuncset) =>
% 98.85/13.42 ((
% 98.85/13.42 (lamProp) =>
% 98.85/13.42 ((
% 98.85/13.42 (lamp) =>
% 98.85/13.42 ((
% 98.85/13.42 (lam2p) =>
% 98.85/13.42 ((
% 98.85/13.42 (brelnall1) =>
% 98.85/13.42 ((
% 98.85/13.42 (brelnall2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1E2) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp3) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcextLem) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp4) =>
% 98.85/13.42 ((
% 98.85/13.42 (subbreln) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqbreln) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcext) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcext2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2apEq1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2apEq2) =>
% 98.85/13.42 ((
% 98.85/13.42 (beta1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eta1) =>
% 98.85/13.42 ((
% 98.85/13.42 (lam2lamEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (beta2) =>
% 98.85/13.42 ((
% 98.85/13.42 (eta2) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalseProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalseProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ifSingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (ifp) =>
% 98.85/13.42 ((
% 98.85/13.42 (theeq) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrue) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalse) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueorfalse) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (setextT) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetTI) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetTI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetTE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectTELcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectTERcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT1) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT2) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT3) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementSub1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementSub2) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTnotintersectT) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementImpComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementSubsetComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementInPowersetComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (contraSubsetComplement) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTcontraSubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTILcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTIRcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInUnion) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInUnion2) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInIntersectUnions) =>
% 98.85/13.42 ((
% 98.85/13.42 (intersectInPowersetIntersectUnions) =>
% 98.85/13.42 ((
% 98.85/13.42 (inComplementUnionImpNotIn1) =>
% 98.85/13.42 ((
% 98.85/13.42 (inComplementUnionImpInComplement1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTE) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTEcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementUnionInPowersetComplement) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a2) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1a) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1b) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2b2) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2b) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule0) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule1) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule3) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule4) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_1) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_3) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_4) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_5) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1all2) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1SetBreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (choice2fnsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (setOfPairsIsBReln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1all1) =>
% 98.85/13.42 ((
% 98.85/13.42 (subbreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqbreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invI) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invE) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compI) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compE) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compEex) =>
% 98.85/13.42 ((
% 98.85/13.42 (!!) @ (
% 98.85/13.42 (('#B') @ (
% 98.85/13.42 !!) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#S') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#S') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 =>))) @
% 98.85/13.42 breln1)))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 !!))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#S') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#S') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 =>))) @
% 98.85/13.42 breln1)))))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#C') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 breln1)))) @
% 98.85/13.42 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.85/13.42 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl2])).
% 98.85/13.42 thf(zip_derived_cl5, plain,
% 98.85/13.42 (~ (((emptysetAx) =>
% 98.85/13.42 (((setadjoinAx) =>
% 98.85/13.42 (((powersetAx) =>
% 98.85/13.42 (((setunionAx) =>
% 98.85/13.42 (((in @ emptyset @ omega) =>
% 98.85/13.42 (((omegaSAx) =>
% 98.85/13.42 (((omegaIndAx) =>
% 98.85/13.42 (((replAx) =>
% 98.85/13.42 (((foundationAx) =>
% 98.85/13.42 (((wellorderingAx) =>
% 98.85/13.42 (((descrp) =>
% 98.85/13.42 (((dsetconstrI) =>
% 98.85/13.42 (((dsetconstrEL) =>
% 98.85/13.42 (((dsetconstrER) =>
% 98.85/13.42 (((exuE1) =>
% 98.85/13.42 (((prop2setE) =>
% 98.85/13.42 (((emptysetE) =>
% 98.85/13.42 (((emptysetimpfalse) =>
% 98.85/13.42 (((notinemptyset) =>
% 98.85/13.42 (((exuE3e) =>
% 98.85/13.42 (((setext) =>
% 98.85/13.42 (((emptyI) =>
% 98.85/13.42 (((noeltsimpempty) =>
% 98.85/13.42 (((setbeta) =>
% 98.85/13.42 (((nonemptyE1) =>
% 98.85/13.42 (((nonemptyI) =>
% 98.85/13.42 (((nonemptyI1) =>
% 98.85/13.42 (((setadjoinIL) =>
% 98.85/13.42 (((in @
% 98.85/13.42 emptyset @
% 98.85/13.42 (setadjoin @
% 98.85/13.42 emptyset @
% 98.85/13.42 emptyset)) =>
% 98.85/13.42 (((setadjoinIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinE) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinOr) =>
% 98.85/13.42 ((
% 98.85/13.42 (setoftrueEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetI) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyinPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyInPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionI) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionE) =>
% 98.85/13.42 ((
% 98.85/13.42 (subPowSU) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (nonemptyImpWitness) =>
% 98.85/13.42 ((
% 98.85/13.42 (uniqinunit) =>
% 98.85/13.42 ((
% 98.85/13.42 (notinsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqinunit) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsswitch) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (vacuousDall) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan1) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan2) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan3) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan4) =>
% 98.85/13.42 ((
% 98.85/13.42 (prop2setI) =>
% 98.85/13.42 ((
% 98.85/13.42 (prop2set2propI) =>
% 98.85/13.42 ((
% 98.85/13.42 (notdexE) =>
% 98.85/13.42 ((
% 98.85/13.42 (notdallE) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI3) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (inCongP) =>
% 98.85/13.42 ((
% 98.85/13.42 (in__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuE3u) =>
% 98.85/13.42 ((
% 98.85/13.42 (exu__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoin__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (powerset__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunion__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuEu) =>
% 98.85/13.42 ((
% 98.85/13.42 (descr__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (dsetconstr__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqimpsubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqimpsubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptysetsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (notsubsetI) =>
% 98.85/13.42 ((
% 98.85/13.42 (notequalI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (notequalI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetRefl) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetTrans) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinSub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinSub2) =>
% 98.85/13.42 ((
% 98.85/13.42 (subset2powerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (setextsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetemptysetimpeq) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (inPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (sepInPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (sepSubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairset2IR) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionEcases) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionE) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionRsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectI) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset5) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset3) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectER) =>
% 98.85/13.42 ((
% 98.85/13.42 (disjointsetsI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectRsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset4) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (bs114d) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusI) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusER) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusSubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusERneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusELneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusILneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusIRneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusSubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffE) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffIneg1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffIneg2) =>
% 98.85/13.42 ((
% 98.85/13.42 (secondinupair) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairiskpair) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairp) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletoninpowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletoninpowunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairset2E) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsubunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairinpowunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem3) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairin) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempair1) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempair) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton1) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1E1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1I) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1I2) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsuniq) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL1) =>
% 98.85/13.42 ((
% 98.85/13.42 (kfstsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (theprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (kfstpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodfstin) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR11) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR12) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR1) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairequniteq) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR) =>
% 98.85/13.42 ((
% 98.85/13.42 (ksndsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (ksndpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairsurjEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodsndin) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairmemEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairmemER) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempaircEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodfstpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodsndpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairsurjEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrI) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrSub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setOfPairsIsBReln) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrERa) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrEL1) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrEL2) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrER) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcImageSingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (apProp) =>
% 98.85/13.42 ((
% 98.85/13.42 (app) =>
% 98.85/13.42 ((
% 98.85/13.42 (infuncsetfunc) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2p) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcinfuncset) =>
% 98.85/13.42 ((
% 98.85/13.42 (lamProp) =>
% 98.85/13.42 ((
% 98.85/13.42 (lamp) =>
% 98.85/13.42 ((
% 98.85/13.42 (lam2p) =>
% 98.85/13.42 ((
% 98.85/13.42 (brelnall1) =>
% 98.85/13.42 ((
% 98.85/13.42 (brelnall2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1E2) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp3) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcextLem) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp4) =>
% 98.85/13.42 ((
% 98.85/13.42 (subbreln) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqbreln) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcext) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcext2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2apEq1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2apEq2) =>
% 98.85/13.42 ((
% 98.85/13.42 (beta1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eta1) =>
% 98.85/13.42 ((
% 98.85/13.42 (lam2lamEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (beta2) =>
% 98.85/13.42 ((
% 98.85/13.42 (eta2) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalseProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalseProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ifSingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (ifp) =>
% 98.85/13.42 ((
% 98.85/13.42 (theeq) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrue) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalse) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueorfalse) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (setextT) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetTI) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetTI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetTE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectTELcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectTERcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT1) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT2) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT3) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementSub1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementSub2) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTnotintersectT) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementImpComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementSubsetComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementInPowersetComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (contraSubsetComplement) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTcontraSubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTILcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTIRcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInUnion) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInUnion2) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInIntersectUnions) =>
% 98.85/13.42 ((
% 98.85/13.42 (intersectInPowersetIntersectUnions) =>
% 98.85/13.42 ((
% 98.85/13.42 (inComplementUnionImpNotIn1) =>
% 98.85/13.42 ((
% 98.85/13.42 (inComplementUnionImpInComplement1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTE) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTEcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementUnionInPowersetComplement) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a2) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1a) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1b) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2b2) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2b) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule0) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule1) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule3) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule4) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_1) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_3) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_4) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_5) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1all2) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1SetBreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (choice2fnsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (setOfPairsIsBReln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1all1) =>
% 98.85/13.42 ((
% 98.85/13.42 (subbreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqbreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invI) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invE) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compI) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compE) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compEex) =>
% 98.85/13.42 ((
% 98.85/13.42 (!!) @ (
% 98.85/13.42 (('#B') @ (
% 98.85/13.42 !!) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#S') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#S') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 =>))) @
% 98.85/13.42 breln1)))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 !!))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#S') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#S') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 =>))) @
% 98.85/13.42 breln1)))))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#C') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 breln1)))) @
% 98.85/13.42 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.85/13.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])).
% 98.85/13.42 thf(zip_derived_cl8, plain,
% 98.85/13.42 (~ (((setadjoinAx) =>
% 98.85/13.42 (((powersetAx) =>
% 98.85/13.42 (((setunionAx) =>
% 98.85/13.42 (((in @ emptyset @ omega) =>
% 98.85/13.42 (((omegaSAx) =>
% 98.85/13.42 (((omegaIndAx) =>
% 98.85/13.42 (((replAx) =>
% 98.85/13.42 (((foundationAx) =>
% 98.85/13.42 (((wellorderingAx) =>
% 98.85/13.42 (((descrp) =>
% 98.85/13.42 (((dsetconstrI) =>
% 98.85/13.42 (((dsetconstrEL) =>
% 98.85/13.42 (((dsetconstrER) =>
% 98.85/13.42 (((exuE1) =>
% 98.85/13.42 (((prop2setE) =>
% 98.85/13.42 (((emptysetE) =>
% 98.85/13.42 (((emptysetimpfalse) =>
% 98.85/13.42 (((notinemptyset) =>
% 98.85/13.42 (((exuE3e) =>
% 98.85/13.42 (((setext) =>
% 98.85/13.42 (((emptyI) =>
% 98.85/13.42 (((noeltsimpempty) =>
% 98.85/13.42 (((setbeta) =>
% 98.85/13.42 (((nonemptyE1) =>
% 98.85/13.42 (((nonemptyI) =>
% 98.85/13.42 (((nonemptyI1) =>
% 98.85/13.42 (((setadjoinIL) =>
% 98.85/13.42 (((in @
% 98.85/13.42 emptyset @
% 98.85/13.42 (setadjoin @
% 98.85/13.42 emptyset @
% 98.85/13.42 emptyset)) =>
% 98.85/13.42 (((setadjoinIR) =>
% 98.85/13.42 (((setadjoinE) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinOr) =>
% 98.85/13.42 ((
% 98.85/13.42 (setoftrueEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetI) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyinPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyInPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionI) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionE) =>
% 98.85/13.42 ((
% 98.85/13.42 (subPowSU) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (nonemptyImpWitness) =>
% 98.85/13.42 ((
% 98.85/13.42 (uniqinunit) =>
% 98.85/13.42 ((
% 98.85/13.42 (notinsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqinunit) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsswitch) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (vacuousDall) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan1) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan2) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan3) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan4) =>
% 98.85/13.42 ((
% 98.85/13.42 (prop2setI) =>
% 98.85/13.42 ((
% 98.85/13.42 (prop2set2propI) =>
% 98.85/13.42 ((
% 98.85/13.42 (notdexE) =>
% 98.85/13.42 ((
% 98.85/13.42 (notdallE) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI3) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (inCongP) =>
% 98.85/13.42 ((
% 98.85/13.42 (in__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuE3u) =>
% 98.85/13.42 ((
% 98.85/13.42 (exu__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoin__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (powerset__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunion__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuEu) =>
% 98.85/13.42 ((
% 98.85/13.42 (descr__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (dsetconstr__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqimpsubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqimpsubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptysetsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (notsubsetI) =>
% 98.85/13.42 ((
% 98.85/13.42 (notequalI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (notequalI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetRefl) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetTrans) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinSub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinSub2) =>
% 98.85/13.42 ((
% 98.85/13.42 (subset2powerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (setextsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetemptysetimpeq) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (inPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (sepInPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (sepSubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairset2IR) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionEcases) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionE) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionRsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectI) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset5) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset3) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectER) =>
% 98.85/13.42 ((
% 98.85/13.42 (disjointsetsI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectRsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset4) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (bs114d) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusI) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusER) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusSubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusERneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusELneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusILneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusIRneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusSubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffE) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffIneg1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffIneg2) =>
% 98.85/13.42 ((
% 98.85/13.42 (secondinupair) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairiskpair) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairp) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletoninpowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletoninpowunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairset2E) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsubunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairinpowunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem3) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairin) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempair1) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempair) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton1) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1E1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1I) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1I2) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsuniq) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL1) =>
% 98.85/13.42 ((
% 98.85/13.42 (kfstsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (theprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (kfstpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodfstin) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR11) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR12) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR1) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairequniteq) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR) =>
% 98.85/13.42 ((
% 98.85/13.42 (ksndsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (ksndpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairsurjEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodsndin) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairmemEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairmemER) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempaircEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodfstpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodsndpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairsurjEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrI) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrSub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setOfPairsIsBReln) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrERa) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrEL1) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrEL2) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrER) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcImageSingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (apProp) =>
% 98.85/13.42 ((
% 98.85/13.42 (app) =>
% 98.85/13.42 ((
% 98.85/13.42 (infuncsetfunc) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2p) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcinfuncset) =>
% 98.85/13.42 ((
% 98.85/13.42 (lamProp) =>
% 98.85/13.42 ((
% 98.85/13.42 (lamp) =>
% 98.85/13.42 ((
% 98.85/13.42 (lam2p) =>
% 98.85/13.42 ((
% 98.85/13.42 (brelnall1) =>
% 98.85/13.42 ((
% 98.85/13.42 (brelnall2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1E2) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp3) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcextLem) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp4) =>
% 98.85/13.42 ((
% 98.85/13.42 (subbreln) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqbreln) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcext) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcext2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2apEq1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2apEq2) =>
% 98.85/13.42 ((
% 98.85/13.42 (beta1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eta1) =>
% 98.85/13.42 ((
% 98.85/13.42 (lam2lamEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (beta2) =>
% 98.85/13.42 ((
% 98.85/13.42 (eta2) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalseProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalseProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ifSingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (ifp) =>
% 98.85/13.42 ((
% 98.85/13.42 (theeq) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrue) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalse) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueorfalse) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (setextT) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetTI) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetTI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetTE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectTELcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectTERcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT1) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT2) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT3) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementSub1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementSub2) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTnotintersectT) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementImpComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementSubsetComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementInPowersetComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (contraSubsetComplement) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTcontraSubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTILcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTIRcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInUnion) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInUnion2) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInIntersectUnions) =>
% 98.85/13.42 ((
% 98.85/13.42 (intersectInPowersetIntersectUnions) =>
% 98.85/13.42 ((
% 98.85/13.42 (inComplementUnionImpNotIn1) =>
% 98.85/13.42 ((
% 98.85/13.42 (inComplementUnionImpInComplement1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTE) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTEcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementUnionInPowersetComplement) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a2) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1a) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1b) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2b2) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2b) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule0) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule1) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule3) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule4) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_1) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_3) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_4) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_5) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1all2) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1SetBreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (choice2fnsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (setOfPairsIsBReln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1all1) =>
% 98.85/13.42 ((
% 98.85/13.42 (subbreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqbreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invI) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invE) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compI) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compE) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compEex) =>
% 98.85/13.42 ((
% 98.85/13.42 (!!) @ (
% 98.85/13.42 (('#B') @ (
% 98.85/13.42 !!) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#S') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#S') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 =>))) @
% 98.85/13.42 breln1)))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 !!))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#S') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#S') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 =>))) @
% 98.85/13.42 breln1)))))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#C') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 breln1)))) @
% 98.85/13.42 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.85/13.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])).
% 98.85/13.42 thf(zip_derived_cl13, plain,
% 98.85/13.42 (~ (((powersetAx) =>
% 98.85/13.42 (((setunionAx) =>
% 98.85/13.42 (((in @ emptyset @ omega) =>
% 98.85/13.42 (((omegaSAx) =>
% 98.85/13.42 (((omegaIndAx) =>
% 98.85/13.42 (((replAx) =>
% 98.85/13.42 (((foundationAx) =>
% 98.85/13.42 (((wellorderingAx) =>
% 98.85/13.42 (((descrp) =>
% 98.85/13.42 (((dsetconstrI) =>
% 98.85/13.42 (((dsetconstrEL) =>
% 98.85/13.42 (((dsetconstrER) =>
% 98.85/13.42 (((exuE1) =>
% 98.85/13.42 (((prop2setE) =>
% 98.85/13.42 (((emptysetE) =>
% 98.85/13.42 (((emptysetimpfalse) =>
% 98.85/13.42 (((notinemptyset) =>
% 98.85/13.42 (((exuE3e) =>
% 98.85/13.42 (((setext) =>
% 98.85/13.42 (((emptyI) =>
% 98.85/13.42 (((noeltsimpempty) =>
% 98.85/13.42 (((setbeta) =>
% 98.85/13.42 (((nonemptyE1) =>
% 98.85/13.42 (((nonemptyI) =>
% 98.85/13.42 (((nonemptyI1) =>
% 98.85/13.42 (((setadjoinIL) =>
% 98.85/13.42 (((in @
% 98.85/13.42 emptyset @
% 98.85/13.42 (setadjoin @
% 98.85/13.42 emptyset @
% 98.85/13.42 emptyset)) =>
% 98.85/13.42 (((setadjoinIR) =>
% 98.85/13.42 (((setadjoinE) =>
% 98.85/13.42 (((setadjoinOr) =>
% 98.85/13.42 ((
% 98.85/13.42 (setoftrueEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetI) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyinPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyInPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionI) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionE) =>
% 98.85/13.42 ((
% 98.85/13.42 (subPowSU) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (nonemptyImpWitness) =>
% 98.85/13.42 ((
% 98.85/13.42 (uniqinunit) =>
% 98.85/13.42 ((
% 98.85/13.42 (notinsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqinunit) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsswitch) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (vacuousDall) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan1) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan2) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan3) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan4) =>
% 98.85/13.42 ((
% 98.85/13.42 (prop2setI) =>
% 98.85/13.42 ((
% 98.85/13.42 (prop2set2propI) =>
% 98.85/13.42 ((
% 98.85/13.42 (notdexE) =>
% 98.85/13.42 ((
% 98.85/13.42 (notdallE) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI3) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (inCongP) =>
% 98.85/13.42 ((
% 98.85/13.42 (in__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuE3u) =>
% 98.85/13.42 ((
% 98.85/13.42 (exu__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoin__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (powerset__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunion__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuEu) =>
% 98.85/13.42 ((
% 98.85/13.42 (descr__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (dsetconstr__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqimpsubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqimpsubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptysetsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (notsubsetI) =>
% 98.85/13.42 ((
% 98.85/13.42 (notequalI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (notequalI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetRefl) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetTrans) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinSub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinSub2) =>
% 98.85/13.42 ((
% 98.85/13.42 (subset2powerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (setextsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetemptysetimpeq) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (inPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (sepInPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (sepSubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairset2IR) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionEcases) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionE) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionRsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectI) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset5) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset3) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectER) =>
% 98.85/13.42 ((
% 98.85/13.42 (disjointsetsI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectRsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset4) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (bs114d) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusI) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusER) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusSubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusERneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusELneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusILneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusIRneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusSubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffE) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffIneg1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffIneg2) =>
% 98.85/13.42 ((
% 98.85/13.42 (secondinupair) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairiskpair) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairp) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletoninpowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletoninpowunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairset2E) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsubunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairinpowunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem3) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairin) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempair1) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempair) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton1) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1E1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1I) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1I2) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsuniq) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL1) =>
% 98.85/13.42 ((
% 98.85/13.42 (kfstsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (theprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (kfstpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodfstin) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR11) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR12) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR1) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairequniteq) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR) =>
% 98.85/13.42 ((
% 98.85/13.42 (ksndsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (ksndpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairsurjEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodsndin) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairmemEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairmemER) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempaircEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodfstpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodsndpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairsurjEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrI) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrSub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setOfPairsIsBReln) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrERa) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrEL1) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrEL2) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrER) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcImageSingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (apProp) =>
% 98.85/13.42 ((
% 98.85/13.42 (app) =>
% 98.85/13.42 ((
% 98.85/13.42 (infuncsetfunc) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2p) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcinfuncset) =>
% 98.85/13.42 ((
% 98.85/13.42 (lamProp) =>
% 98.85/13.42 ((
% 98.85/13.42 (lamp) =>
% 98.85/13.42 ((
% 98.85/13.42 (lam2p) =>
% 98.85/13.42 ((
% 98.85/13.42 (brelnall1) =>
% 98.85/13.42 ((
% 98.85/13.42 (brelnall2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1E2) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp3) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcextLem) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp4) =>
% 98.85/13.42 ((
% 98.85/13.42 (subbreln) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqbreln) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcext) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcext2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2apEq1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2apEq2) =>
% 98.85/13.42 ((
% 98.85/13.42 (beta1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eta1) =>
% 98.85/13.42 ((
% 98.85/13.42 (lam2lamEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (beta2) =>
% 98.85/13.42 ((
% 98.85/13.42 (eta2) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalseProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalseProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ifSingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (ifp) =>
% 98.85/13.42 ((
% 98.85/13.42 (theeq) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrue) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalse) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueorfalse) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (setextT) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetTI) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetTI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetTE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectTELcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectTERcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT1) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT2) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT3) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementSub1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementSub2) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTnotintersectT) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementImpComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementSubsetComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementInPowersetComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (contraSubsetComplement) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTcontraSubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTILcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTIRcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInUnion) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInUnion2) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInIntersectUnions) =>
% 98.85/13.42 ((
% 98.85/13.42 (intersectInPowersetIntersectUnions) =>
% 98.85/13.42 ((
% 98.85/13.42 (inComplementUnionImpNotIn1) =>
% 98.85/13.42 ((
% 98.85/13.42 (inComplementUnionImpInComplement1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTE) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTEcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementUnionInPowersetComplement) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a2) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1a) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1b) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2b2) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2b) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule0) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule1) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule3) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule4) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_1) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_3) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_4) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_5) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1all2) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1SetBreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (choice2fnsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (setOfPairsIsBReln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1all1) =>
% 98.85/13.42 ((
% 98.85/13.42 (subbreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqbreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invI) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1invE) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compI) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compE) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1compEex) =>
% 98.85/13.42 ((
% 98.85/13.42 (!!) @ (
% 98.85/13.42 (('#B') @ (
% 98.85/13.42 !!) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#S') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#S') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 =>))) @
% 98.85/13.42 breln1)))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 !!))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#S') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#S') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 =>))) @
% 98.85/13.42 breln1)))))) @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#C') @ (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 (
% 98.85/13.42 (
% 98.85/13.42 ('#B') @ (
% 98.85/13.42 '#B') @
% 98.85/13.42 breln1)))) @
% 98.85/13.42 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.85/13.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])).
% 98.85/13.42 thf(zip_derived_cl19, plain,
% 98.85/13.42 (~ (((setunionAx) =>
% 98.85/13.42 (((in @ emptyset @ omega) =>
% 98.85/13.42 (((omegaSAx) =>
% 98.85/13.42 (((omegaIndAx) =>
% 98.85/13.42 (((replAx) =>
% 98.85/13.42 (((foundationAx) =>
% 98.85/13.42 (((wellorderingAx) =>
% 98.85/13.42 (((descrp) =>
% 98.85/13.42 (((dsetconstrI) =>
% 98.85/13.42 (((dsetconstrEL) =>
% 98.85/13.42 (((dsetconstrER) =>
% 98.85/13.42 (((exuE1) =>
% 98.85/13.42 (((prop2setE) =>
% 98.85/13.42 (((emptysetE) =>
% 98.85/13.42 (((emptysetimpfalse) =>
% 98.85/13.42 (((notinemptyset) =>
% 98.85/13.42 (((exuE3e) =>
% 98.85/13.42 (((setext) =>
% 98.85/13.42 (((emptyI) =>
% 98.85/13.42 (((noeltsimpempty) =>
% 98.85/13.42 (((setbeta) =>
% 98.85/13.42 (((nonemptyE1) =>
% 98.85/13.42 (((nonemptyI) =>
% 98.85/13.42 (((nonemptyI1) =>
% 98.85/13.42 (((setadjoinIL) =>
% 98.85/13.42 (((in @ emptyset @
% 98.85/13.42 (setadjoin @
% 98.85/13.42 emptyset @
% 98.85/13.42 emptyset)) =>
% 98.85/13.42 (((setadjoinIR) =>
% 98.85/13.42 (((setadjoinE) =>
% 98.85/13.42 (((setadjoinOr) =>
% 98.85/13.42 (((setoftrueEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetI) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyinPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyInPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionI) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionE) =>
% 98.85/13.42 ((
% 98.85/13.42 (subPowSU) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (nonemptyImpWitness) =>
% 98.85/13.42 ((
% 98.85/13.42 (uniqinunit) =>
% 98.85/13.42 ((
% 98.85/13.42 (notinsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqinunit) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsswitch) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsetIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptyE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (vacuousDall) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan1) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan2) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan3) =>
% 98.85/13.42 ((
% 98.85/13.42 (quantDeMorgan4) =>
% 98.85/13.42 ((
% 98.85/13.42 (prop2setI) =>
% 98.85/13.42 ((
% 98.85/13.42 (prop2set2propI) =>
% 98.85/13.42 ((
% 98.85/13.42 (notdexE) =>
% 98.85/13.42 ((
% 98.85/13.42 (notdallE) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI3) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (inCongP) =>
% 98.85/13.42 ((
% 98.85/13.42 (in__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuE3u) =>
% 98.85/13.42 ((
% 98.85/13.42 (exu__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoin__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (powerset__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunion__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (exuEu) =>
% 98.85/13.42 ((
% 98.85/13.42 (descr__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (dsetconstr__Cong) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqimpsubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqimpsubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (emptysetsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetE) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (notsubsetI) =>
% 98.85/13.42 ((
% 98.85/13.42 (notequalI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (notequalI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetRefl) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetTrans) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinSub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setadjoinSub2) =>
% 98.85/13.42 ((
% 98.85/13.42 (subset2powerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (setextsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetemptysetimpeq) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (inPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (sepInPowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (sepSubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairset2IR) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionEcases) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionE) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionRsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectI) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset5) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset3) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectER) =>
% 98.85/13.42 ((
% 98.85/13.42 (disjointsetsI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectRsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset4) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectSubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (bs114d) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusI) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusER) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusSubset2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusERneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusELneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusILneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusIRneg) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusLsub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusSubset1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffE) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffI2) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffIneg1) =>
% 98.85/13.42 ((
% 98.85/13.42 (symdiffIneg2) =>
% 98.85/13.42 ((
% 98.85/13.42 (secondinupair) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairIL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairIR) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairiskpair) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairp) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletoninpowerset) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletoninpowunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairset2E) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairsubunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairinpowunion) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ubforcartprodlem3) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairin) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempair1) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempair) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionE2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton1) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setunionsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1E1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1I) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1I2) =>
% 98.85/13.42 ((
% 98.85/13.42 (singletonsuniq) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL1) =>
% 98.85/13.42 ((
% 98.85/13.42 (kfstsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (theprop) =>
% 98.85/13.42 ((
% 98.85/13.42 (kfstpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodfstin) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjL) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR11) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR12) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR1) =>
% 98.85/13.42 ((
% 98.85/13.42 (upairequniteq) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR2) =>
% 98.85/13.42 ((
% 98.85/13.42 (setukpairinjR) =>
% 98.85/13.42 ((
% 98.85/13.42 (ksndsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (ksndpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (kpairsurjEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodsndin) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairmemEL) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairmemER) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodmempaircEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodfstpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodsndpairEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (cartprodpairsurjEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrI) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrSub) =>
% 98.85/13.42 ((
% 98.85/13.42 (setOfPairsIsBReln) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrERa) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrEL1) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrEL2) =>
% 98.85/13.42 ((
% 98.85/13.42 (dpsetconstrER) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcImageSingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (apProp) =>
% 98.85/13.42 ((
% 98.85/13.42 (app) =>
% 98.85/13.42 ((
% 98.85/13.42 (infuncsetfunc) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2p) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcinfuncset) =>
% 98.85/13.42 ((
% 98.85/13.42 (lamProp) =>
% 98.85/13.42 ((
% 98.85/13.42 (lamp) =>
% 98.85/13.42 ((
% 98.85/13.42 (lam2p) =>
% 98.85/13.42 ((
% 98.85/13.42 (brelnall1) =>
% 98.85/13.42 ((
% 98.85/13.42 (brelnall2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ex1E2) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp3) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcextLem) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcGraphProp4) =>
% 98.85/13.42 ((
% 98.85/13.42 (subbreln) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqbreln) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcext) =>
% 98.85/13.42 ((
% 98.85/13.42 (funcext2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2apEq1) =>
% 98.85/13.42 ((
% 98.85/13.42 (ap2apEq2) =>
% 98.85/13.42 ((
% 98.85/13.42 (beta1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eta1) =>
% 98.85/13.42 ((
% 98.85/13.42 (lam2lamEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (beta2) =>
% 98.85/13.42 ((
% 98.85/13.42 (eta2) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalseProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalseProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueProp1) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueProp2) =>
% 98.85/13.42 ((
% 98.85/13.42 (ifSingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (ifp) =>
% 98.85/13.42 ((
% 98.85/13.42 (theeq) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrue) =>
% 98.85/13.42 ((
% 98.85/13.42 (iffalse) =>
% 98.85/13.42 ((
% 98.85/13.42 (iftrueorfalse) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (setminusT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementT_lem) =>
% 98.85/13.42 ((
% 98.85/13.42 (setextT) =>
% 98.85/13.42 ((
% 98.85/13.42 (subsetTI) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetTI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (powersetTE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectTELcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (binintersectTERcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT1) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT2) =>
% 98.85/13.42 ((
% 98.85/13.42 (contrasubsetT3) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementI1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementE1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementSub1) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementSub2) =>
% 98.85/13.42 ((
% 98.85/13.42 (doubleComplementEq) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTnotintersectT) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementImpComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementSubsetComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementInPowersetComplementIntersect) =>
% 98.85/13.42 ((
% 98.85/13.42 (contraSubsetComplement) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementTcontraSubset) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTILcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTIRcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInUnion) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInUnion2) =>
% 98.85/13.42 ((
% 98.85/13.42 (inIntersectImpInIntersectUnions) =>
% 98.85/13.42 ((
% 98.85/13.42 (intersectInPowersetIntersectUnions) =>
% 98.85/13.42 ((
% 98.85/13.42 (inComplementUnionImpNotIn1) =>
% 98.85/13.42 ((
% 98.85/13.42 (inComplementUnionImpInComplement1) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTE) =>
% 98.85/13.42 ((
% 98.85/13.42 (binunionTEcontra) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a1) =>
% 98.85/13.42 ((
% 98.85/13.42 (complementUnionInPowersetComplement) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a2) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1a) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1b) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan1) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2a) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2b2) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2b) =>
% 98.85/13.42 ((
% 98.85/13.42 (demorgan2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule0) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule1) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule3) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz13rule4) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_1) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_2) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_3) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_4) =>
% 98.85/13.42 ((
% 98.85/13.42 (woz1_5) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1all2) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1SetBreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (choice2fnsingleton) =>
% 98.85/13.42 ((
% 98.85/13.42 (setOfPairsIsBReln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (breln1all1) =>
% 98.85/13.42 ((
% 98.85/13.42 (subbreln1) =>
% 98.85/13.42 ((
% 98.85/13.42 (eqbreln1) =>
% 98.85/13.42 ((
% 99.25/13.42 (breln1invprop) =>
% 99.25/13.42 ((
% 99.25/13.42 (breln1invI) =>
% 99.25/13.42 ((
% 99.25/13.42 (breln1invE) =>
% 99.25/13.42 ((
% 99.25/13.42 (breln1compprop) =>
% 99.25/13.42 ((
% 99.25/13.42 (breln1compI) =>
% 99.25/13.42 ((
% 99.25/13.42 (breln1compE) =>
% 99.25/13.42 ((
% 99.25/13.42 (breln1compEex) =>
% 99.25/13.42 ((
% 99.25/13.42 (!!) @ (
% 99.25/13.42 (('#B') @ (
% 99.25/13.42 !!) @
% 99.25/13.42 (
% 99.25/13.42 (
% 99.25/13.42 ('#S') @ (
% 99.25/13.42 (
% 99.25/13.42 ('#B') @ (
% 99.25/13.42 '#S') @
% 99.25/13.42 (
% 99.25/13.42 (
% 99.25/13.42 ('#B') @ (
% 99.25/13.42 (
% 99.25/13.42 ('#B') @ (
% 99.25/13.42 =>))) @
% 99.25/13.42 breln1)))) @
% 99.25/13.42 (
% 99.25/13.42 (
% 99.25/13.42 ('#B') @ (
% 99.25/13.42 (
% 99.25/13.42 ('#B') @ (
% 99.25/13.42 !!))) @
% 99.25/13.42 (
% 99.25/13.42 (
% 99.25/13.42 ('#S') @ (
% 99.25/13.42 (
% 99.25/13.42 ('#B') @ (
% 99.25/13.42 '#B') @
% 99.25/13.42 (
% 99.25/13.42 (
% 99.25/13.42 ('#B') @ (
% 99.25/13.42 '#S') @
% 99.25/13.42 (
% 99.25/13.42 (
% 99.25/13.42 ('#B') @ (
% 99.25/13.42 (
% 99.25/13.42 ('#B') @ (
% 99.25/13.42 =>))) @
% 99.25/13.42 breln1)))))) @
% 99.25/13.42 (
% 99.25/13.42 (
% 99.25/13.42 ('#C') @ (
% 99.25/13.42 (
% 99.25/13.42 ('#B') @ (
% 99.25/13.42 '#B') @
% 99.25/13.42 (
% 99.25/13.42 (
% 99.25/13.42 ('#B') @ (
% 99.25/13.42 '#B') @
% 99.25/13.42 breln1)))) @
% 99.25/13.42 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])).
% 99.25/13.42 thf(zip_derived_cl25, plain,
% 99.25/13.42 (~ (((in @ emptyset @ omega) =>
% 99.25/13.42 (((omegaSAx) =>
% 99.25/13.42 (((omegaIndAx) =>
% 99.25/13.42 (((replAx) =>
% 99.25/13.42 (((foundationAx) =>
% 99.25/13.42 (((wellorderingAx) =>
% 99.25/13.42 (((descrp) =>
% 99.25/13.42 (((dsetconstrI) =>
% 99.25/13.42 (((dsetconstrEL) =>
% 99.25/13.42 (((dsetconstrER) =>
% 99.25/13.42 (((exuE1) =>
% 99.25/13.42 (((prop2setE) =>
% 99.25/13.42 (((emptysetE) =>
% 99.25/13.42 (((emptysetimpfalse) =>
% 99.25/13.42 (((notinemptyset) =>
% 99.25/13.42 (((exuE3e) =>
% 99.25/13.42 (((setext) =>
% 99.25/13.42 (((emptyI) =>
% 99.25/13.42 (((noeltsimpempty) =>
% 99.25/13.42 (((setbeta) =>
% 99.25/13.42 (((nonemptyE1) =>
% 99.25/13.42 (((nonemptyI) =>
% 99.25/13.42 (((nonemptyI1) =>
% 99.25/13.42 (((setadjoinIL) =>
% 99.25/13.42 (((in @ emptyset @
% 99.25/13.42 (setadjoin @
% 99.25/13.42 emptyset @ emptyset)) =>
% 99.25/13.42 (((setadjoinIR) =>
% 99.25/13.42 (((setadjoinE) =>
% 99.25/13.42 (((setadjoinOr) =>
% 99.25/13.42 (((setoftrueEq) =>
% 99.25/13.42 (((powersetI) =>
% 99.25/13.42 ((
% 99.25/13.42 (emptyinPowerset) =>
% 99.25/13.42 ((
% 99.25/13.42 (emptyInPowerset) =>
% 99.25/13.42 ((
% 99.25/13.42 (powersetE) =>
% 99.25/13.42 ((
% 99.25/13.42 (setunionI) =>
% 99.25/13.42 ((
% 99.25/13.42 (setunionE) =>
% 99.25/13.42 ((
% 99.25/13.42 (subPowSU) =>
% 99.25/13.42 ((
% 99.25/13.42 (exuE2) =>
% 99.25/13.42 ((
% 99.25/13.42 (nonemptyImpWitness) =>
% 99.25/13.42 ((
% 99.25/13.42 (uniqinunit) =>
% 99.25/13.42 ((
% 99.25/13.42 (notinsingleton) =>
% 99.25/13.42 ((
% 99.25/13.42 (eqinunit) =>
% 99.25/13.42 ((
% 99.25/13.42 (singletonsswitch) =>
% 99.25/13.42 ((
% 99.25/13.42 (upairsetE) =>
% 99.25/13.42 ((
% 99.25/13.42 (upairsetIL) =>
% 99.25/13.42 ((
% 99.25/13.42 (upairsetIR) =>
% 99.25/13.42 ((
% 99.25/13.42 (emptyE1) =>
% 99.25/13.42 ((
% 99.25/13.42 (vacuousDall) =>
% 99.25/13.42 ((
% 99.25/13.42 (quantDeMorgan1) =>
% 99.25/13.42 ((
% 99.25/13.42 (quantDeMorgan2) =>
% 99.25/13.42 ((
% 99.25/13.42 (quantDeMorgan3) =>
% 99.25/13.42 ((
% 99.25/13.42 (quantDeMorgan4) =>
% 99.25/13.42 ((
% 99.25/13.42 (prop2setI) =>
% 99.25/13.42 ((
% 99.25/13.42 (prop2set2propI) =>
% 99.25/13.42 ((
% 99.25/13.42 (notdexE) =>
% 99.25/13.42 ((
% 99.25/13.42 (notdallE) =>
% 99.25/13.42 ((
% 99.25/13.42 (exuI1) =>
% 99.25/13.42 ((
% 99.25/13.42 (exuI3) =>
% 99.25/13.42 ((
% 99.25/13.42 (exuI2) =>
% 99.25/13.42 ((
% 99.25/13.42 (inCongP) =>
% 99.25/13.42 ((
% 99.25/13.42 (in__Cong) =>
% 99.25/13.42 ((
% 99.25/13.42 (exuE3u) =>
% 99.25/13.42 ((
% 99.25/13.42 (exu__Cong) =>
% 99.25/13.42 ((
% 99.25/13.42 (setadjoin__Cong) =>
% 99.25/13.42 ((
% 99.25/13.42 (powerset__Cong) =>
% 99.25/13.42 ((
% 99.25/13.42 (setunion__Cong) =>
% 99.25/13.42 ((
% 99.25/13.42 (exuEu) =>
% 99.25/13.42 ((
% 99.25/13.42 (descr__Cong) =>
% 99.25/13.42 ((
% 99.25/13.42 (dsetconstr__Cong) =>
% 99.25/13.42 ((
% 99.25/13.42 (subsetI1) =>
% 99.25/13.42 ((
% 99.25/13.42 (eqimpsubset2) =>
% 99.25/13.42 ((
% 99.25/13.42 (eqimpsubset1) =>
% 99.25/13.42 ((
% 99.25/13.42 (subsetI2) =>
% 99.25/13.42 ((
% 99.25/13.42 (emptysetsubset) =>
% 99.25/13.42 ((
% 99.25/13.42 (subsetE) =>
% 99.25/13.42 ((
% 99.25/13.42 (subsetE2) =>
% 99.25/13.42 ((
% 99.25/13.42 (notsubsetI) =>
% 99.25/13.42 ((
% 99.25/13.42 (notequalI1) =>
% 99.25/13.42 ((
% 99.25/13.42 (notequalI2) =>
% 99.25/13.42 ((
% 99.25/13.42 (subsetRefl) =>
% 99.25/13.42 ((
% 99.25/13.42 (subsetTrans) =>
% 99.25/13.42 ((
% 99.25/13.42 (setadjoinSub) =>
% 99.25/13.42 ((
% 99.25/13.42 (setadjoinSub2) =>
% 99.25/13.42 ((
% 99.25/13.42 (subset2powerset) =>
% 99.25/13.42 ((
% 99.25/13.42 (setextsub) =>
% 99.25/13.42 ((
% 99.25/13.42 (subsetemptysetimpeq) =>
% 99.25/13.42 ((
% 99.25/13.42 (powersetI1) =>
% 99.25/13.42 ((
% 99.25/13.42 (powersetE1) =>
% 99.25/13.42 ((
% 99.25/13.42 (inPowerset) =>
% 99.25/13.42 ((
% 99.25/13.42 (powersetsubset) =>
% 99.25/13.42 ((
% 99.25/13.42 (sepInPowerset) =>
% 99.25/13.42 ((
% 99.25/13.42 (sepSubset) =>
% 99.25/13.42 ((
% 99.25/13.42 (binunionIL) =>
% 99.25/13.42 ((
% 99.25/13.42 (upairset2IR) =>
% 99.25/13.42 ((
% 99.25/13.42 (binunionIR) =>
% 99.25/13.42 ((
% 99.25/13.42 (binunionEcases) =>
% 99.25/13.42 ((
% 99.25/13.42 (binunionE) =>
% 99.25/13.42 ((
% 99.25/13.42 (binunionLsub) =>
% 99.25/13.42 ((
% 99.25/13.42 (binunionRsub) =>
% 99.25/13.42 ((
% 99.25/13.42 (binintersectI) =>
% 99.25/13.42 ((
% 99.25/13.42 (binintersectSubset5) =>
% 99.25/13.42 ((
% 99.25/13.42 (binintersectEL) =>
% 99.25/13.42 ((
% 99.25/13.42 (binintersectLsub) =>
% 99.25/13.42 ((
% 99.25/13.42 (binintersectSubset2) =>
% 99.25/13.42 ((
% 99.25/13.42 (binintersectSubset3) =>
% 99.25/13.42 ((
% 99.25/13.42 (binintersectER) =>
% 99.25/13.42 ((
% 99.25/13.42 (disjointsetsI1) =>
% 99.25/13.42 ((
% 99.25/13.42 (binintersectRsub) =>
% 99.25/13.42 ((
% 99.25/13.42 (binintersectSubset4) =>
% 99.25/13.42 ((
% 99.25/13.42 (binintersectSubset1) =>
% 99.25/13.42 ((
% 99.25/13.42 (bs114d) =>
% 99.25/13.42 ((
% 99.25/13.42 (setminusI) =>
% 99.25/13.42 ((
% 99.25/13.42 (setminusEL) =>
% 99.25/13.42 ((
% 99.25/13.42 (setminusER) =>
% 99.25/13.42 ((
% 99.25/13.42 (setminusSubset2) =>
% 99.25/13.42 ((
% 99.25/13.42 (setminusERneg) =>
% 99.25/13.42 ((
% 99.25/13.42 (setminusELneg) =>
% 99.25/13.42 ((
% 99.25/13.42 (setminusILneg) =>
% 99.25/13.42 ((
% 99.25/13.42 (setminusIRneg) =>
% 99.25/13.42 ((
% 99.25/13.42 (setminusLsub) =>
% 99.25/13.42 ((
% 99.25/13.42 (setminusSubset1) =>
% 99.25/13.42 ((
% 99.25/13.42 (symdiffE) =>
% 99.25/13.42 ((
% 99.25/13.42 (symdiffI1) =>
% 99.25/13.42 ((
% 99.25/13.42 (symdiffI2) =>
% 99.25/13.42 ((
% 99.25/13.42 (symdiffIneg1) =>
% 99.25/13.42 ((
% 99.25/13.42 (symdiffIneg2) =>
% 99.25/13.42 ((
% 99.25/13.42 (secondinupair) =>
% 99.25/13.42 ((
% 99.25/13.42 (setukpairIL) =>
% 99.25/13.42 ((
% 99.25/13.42 (setukpairIR) =>
% 99.25/13.42 ((
% 99.25/13.42 (kpairiskpair) =>
% 99.25/13.42 ((
% 99.25/13.42 (kpairp) =>
% 99.25/13.42 ((
% 99.25/13.42 (singletonsubset) =>
% 99.25/13.42 ((
% 99.25/13.42 (singletoninpowerset) =>
% 99.25/13.42 ((
% 99.25/13.42 (singletoninpowunion) =>
% 99.25/13.42 ((
% 99.25/13.42 (upairset2E) =>
% 99.25/13.42 ((
% 99.25/13.42 (upairsubunion) =>
% 99.25/13.42 ((
% 99.25/13.42 (upairinpowunion) =>
% 99.25/13.42 ((
% 99.25/13.42 (ubforcartprodlem1) =>
% 99.25/13.42 ((
% 99.25/13.42 (ubforcartprodlem2) =>
% 99.25/13.42 ((
% 99.25/13.42 (ubforcartprodlem3) =>
% 99.25/13.42 ((
% 99.25/13.42 (cartprodpairin) =>
% 99.25/13.42 ((
% 99.25/13.42 (cartprodmempair1) =>
% 99.25/13.42 ((
% 99.25/13.42 (cartprodmempair) =>
% 99.25/13.42 ((
% 99.25/13.42 (setunionE2) =>
% 99.25/13.42 ((
% 99.25/13.42 (setunionsingleton1) =>
% 99.25/13.42 ((
% 99.25/13.42 (setunionsingleton2) =>
% 99.25/13.42 ((
% 99.25/13.42 (setunionsingleton) =>
% 99.25/13.42 ((
% 99.25/13.42 (singletonprop) =>
% 99.25/13.42 ((
% 99.25/13.42 (ex1E1) =>
% 99.25/13.42 ((
% 99.25/13.42 (ex1I) =>
% 99.25/13.42 ((
% 99.25/13.42 (ex1I2) =>
% 99.25/13.42 ((
% 99.25/13.42 (singletonsuniq) =>
% 99.25/13.42 ((
% 99.25/13.42 (setukpairinjL1) =>
% 99.25/13.42 ((
% 99.25/13.42 (kfstsingleton) =>
% 99.25/13.42 ((
% 99.25/13.42 (theprop) =>
% 99.25/13.42 ((
% 99.25/13.42 (kfstpairEq) =>
% 99.25/13.42 ((
% 99.25/13.42 (cartprodfstin) =>
% 99.25/13.42 ((
% 99.25/13.42 (setukpairinjL2) =>
% 99.25/13.42 ((
% 99.25/13.42 (setukpairinjL) =>
% 99.25/13.42 ((
% 99.25/13.42 (setukpairinjR11) =>
% 99.25/13.42 ((
% 99.25/13.42 (setukpairinjR12) =>
% 99.25/13.42 ((
% 99.25/13.42 (setukpairinjR1) =>
% 99.25/13.42 ((
% 99.25/13.42 (upairequniteq) =>
% 99.25/13.42 ((
% 99.25/13.42 (setukpairinjR2) =>
% 99.25/13.42 ((
% 99.25/13.42 (setukpairinjR) =>
% 99.25/13.42 ((
% 99.25/13.42 (ksndsingleton) =>
% 99.25/13.42 ((
% 99.25/13.42 (ksndpairEq) =>
% 99.25/13.42 ((
% 99.25/13.42 (kpairsurjEq) =>
% 99.25/13.42 ((
% 99.25/13.42 (cartprodsndin) =>
% 99.25/13.42 ((
% 99.25/13.42 (cartprodpairmemEL) =>
% 99.25/13.42 ((
% 99.25/13.42 (cartprodpairmemER) =>
% 99.25/13.42 ((
% 99.25/13.42 (cartprodmempaircEq) =>
% 99.25/13.42 ((
% 99.25/13.42 (cartprodfstpairEq) =>
% 99.25/13.42 ((
% 99.25/13.42 (cartprodsndpairEq) =>
% 99.25/13.42 ((
% 99.25/13.42 (cartprodpairsurjEq) =>
% 99.25/13.42 ((
% 99.25/13.42 (dpsetconstrI) =>
% 99.25/13.42 ((
% 99.25/13.42 (dpsetconstrSub) =>
% 99.25/13.42 ((
% 99.25/13.42 (setOfPairsIsBReln) =>
% 99.25/13.42 ((
% 99.25/13.42 (dpsetconstrERa) =>
% 99.25/13.42 ((
% 99.25/13.42 (dpsetconstrEL1) =>
% 99.25/13.42 ((
% 99.25/13.42 (dpsetconstrEL2) =>
% 99.25/13.42 ((
% 99.25/13.42 (dpsetconstrER) =>
% 99.25/13.42 ((
% 99.25/13.42 (funcImageSingleton) =>
% 99.25/13.42 ((
% 99.25/13.42 (apProp) =>
% 99.25/13.42 ((
% 99.25/13.42 (app) =>
% 99.25/13.42 ((
% 99.25/13.42 (infuncsetfunc) =>
% 99.25/13.42 ((
% 99.25/13.42 (ap2p) =>
% 99.25/13.42 ((
% 99.25/13.42 (funcinfuncset) =>
% 99.25/13.42 ((
% 99.25/13.42 (lamProp) =>
% 99.25/13.42 ((
% 99.25/13.42 (lamp) =>
% 99.25/13.42 ((
% 99.25/13.42 (lam2p) =>
% 99.25/13.42 ((
% 99.25/13.42 (brelnall1) =>
% 99.25/13.42 ((
% 99.25/13.42 (brelnall2) =>
% 99.25/13.42 ((
% 99.25/13.42 (ex1E2) =>
% 99.25/13.42 ((
% 99.25/13.42 (funcGraphProp1) =>
% 99.25/13.42 ((
% 99.25/13.42 (funcGraphProp3) =>
% 99.25/13.42 ((
% 99.25/13.42 (funcGraphProp2) =>
% 99.25/13.42 ((
% 99.25/13.42 (funcextLem) =>
% 99.25/13.42 ((
% 99.25/13.42 (funcGraphProp4) =>
% 99.25/13.42 ((
% 99.25/13.42 (subbreln) =>
% 99.25/13.42 ((
% 99.25/13.42 (eqbreln) =>
% 99.25/13.42 ((
% 99.25/13.42 (funcext) =>
% 99.25/13.42 ((
% 99.25/13.42 (funcext2) =>
% 99.25/13.42 ((
% 99.25/13.42 (ap2apEq1) =>
% 99.25/13.42 ((
% 99.25/13.42 (ap2apEq2) =>
% 99.25/13.42 ((
% 99.25/13.42 (beta1) =>
% 99.25/13.42 ((
% 99.25/13.42 (eta1) =>
% 99.25/13.42 ((
% 99.25/13.42 (lam2lamEq) =>
% 99.25/13.42 ((
% 99.25/13.42 (beta2) =>
% 99.25/13.42 ((
% 99.25/13.42 (eta2) =>
% 99.25/13.42 ((
% 99.25/13.42 (iffalseProp1) =>
% 99.25/13.42 ((
% 99.25/13.42 (iffalseProp2) =>
% 99.25/13.42 ((
% 99.25/13.42 (iftrueProp1) =>
% 99.25/13.42 ((
% 99.25/13.42 (iftrueProp2) =>
% 99.25/13.42 ((
% 99.25/13.42 (ifSingleton) =>
% 99.25/13.42 ((
% 99.25/13.42 (ifp) =>
% 99.25/13.42 ((
% 99.25/13.42 (theeq) =>
% 99.25/13.42 ((
% 99.25/13.42 (iftrue) =>
% 99.25/13.42 ((
% 99.25/13.42 (iffalse) =>
% 99.25/13.42 ((
% 99.25/13.42 (iftrueorfalse) =>
% 99.25/13.42 ((
% 99.25/13.42 (binintersectT_lem) =>
% 99.25/13.42 ((
% 99.25/13.42 (binunionT_lem) =>
% 99.25/13.42 ((
% 99.25/13.42 (powersetT_lem) =>
% 99.25/13.42 ((
% 99.25/13.42 (setminusT_lem) =>
% 99.25/13.42 ((
% 99.25/13.42 (complementT_lem) =>
% 99.25/13.42 ((
% 99.25/13.42 (setextT) =>
% 99.25/13.42 ((
% 99.25/13.42 (subsetTI) =>
% 99.25/13.42 ((
% 99.25/13.42 (powersetTI1) =>
% 99.25/13.42 ((
% 99.25/13.42 (powersetTE1) =>
% 99.25/13.42 ((
% 99.25/13.42 (complementTI1) =>
% 99.25/13.42 ((
% 99.25/13.42 (complementTE1) =>
% 99.25/13.42 ((
% 99.25/13.42 (binintersectTELcontra) =>
% 99.25/13.42 ((
% 99.25/13.42 (binintersectTERcontra) =>
% 99.25/13.42 ((
% 99.25/13.42 (contrasubsetT) =>
% 99.25/13.42 ((
% 99.25/13.42 (contrasubsetT1) =>
% 99.25/13.42 ((
% 99.25/13.42 (contrasubsetT2) =>
% 99.25/13.42 ((
% 99.25/13.42 (contrasubsetT3) =>
% 99.25/13.42 ((
% 99.25/13.42 (doubleComplementI1) =>
% 99.25/13.42 ((
% 99.25/13.42 (doubleComplementE1) =>
% 99.25/13.42 ((
% 99.25/13.42 (doubleComplementSub1) =>
% 99.25/13.42 ((
% 99.25/13.42 (doubleComplementSub2) =>
% 99.25/13.42 ((
% 99.25/13.42 (doubleComplementEq) =>
% 99.25/13.42 ((
% 99.25/13.42 (complementTnotintersectT) =>
% 99.25/13.42 ((
% 99.25/13.42 (complementImpComplementIntersect) =>
% 99.25/13.42 ((
% 99.25/13.42 (complementSubsetComplementIntersect) =>
% 99.25/13.42 ((
% 99.25/13.42 (complementInPowersetComplementIntersect) =>
% 99.25/13.42 ((
% 99.25/13.42 (contraSubsetComplement) =>
% 99.25/13.42 ((
% 99.25/13.42 (complementTcontraSubset) =>
% 99.25/13.42 ((
% 99.25/13.42 (binunionTILcontra) =>
% 99.25/13.42 ((
% 99.25/13.42 (binunionTIRcontra) =>
% 99.25/13.42 ((
% 99.25/13.42 (inIntersectImpInUnion) =>
% 99.25/13.42 ((
% 99.25/13.42 (inIntersectImpInUnion2) =>
% 99.25/13.42 ((
% 99.25/13.42 (inIntersectImpInIntersectUnions) =>
% 99.25/13.42 ((
% 99.25/13.42 (intersectInPowersetIntersectUnions) =>
% 99.25/13.42 ((
% 99.25/13.42 (inComplementUnionImpNotIn1) =>
% 99.25/13.42 ((
% 99.25/13.42 (inComplementUnionImpInComplement1) =>
% 99.25/13.42 ((
% 99.25/13.42 (binunionTE) =>
% 99.25/13.42 ((
% 99.25/13.42 (binunionTEcontra) =>
% 99.25/13.42 ((
% 99.25/13.42 (demorgan2a1) =>
% 99.25/13.42 ((
% 99.25/13.42 (complementUnionInPowersetComplement) =>
% 99.25/13.42 ((
% 99.25/13.42 (demorgan2a2) =>
% 99.25/13.42 ((
% 99.25/13.42 (demorgan1a) =>
% 99.25/13.42 ((
% 99.25/13.42 (demorgan1b) =>
% 99.25/13.42 ((
% 99.25/13.42 (demorgan1) =>
% 99.25/13.42 ((
% 99.25/13.42 (demorgan2a) =>
% 99.25/13.42 ((
% 99.25/13.42 (demorgan2b2) =>
% 99.25/13.42 ((
% 99.25/13.42 (demorgan2b) =>
% 99.25/13.42 ((
% 99.25/13.42 (demorgan2) =>
% 99.25/13.42 ((
% 99.25/13.42 (woz13rule0) =>
% 99.25/13.42 ((
% 99.25/13.42 (woz13rule1) =>
% 99.25/13.42 ((
% 99.25/13.42 (woz13rule2) =>
% 99.25/13.42 ((
% 99.25/13.42 (woz13rule3) =>
% 99.25/13.42 ((
% 99.25/13.42 (woz13rule4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_1) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_3) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_5) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all2) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1SetBreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (choice2fnsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (setOfPairsIsBReln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compEex) =>
% 99.25/13.43 ((
% 99.25/13.43 (!!) @ (
% 99.25/13.43 (('#B') @ (
% 99.25/13.43 !!) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 !!))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#C') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])).
% 99.25/13.43 thf(zip_derived_cl33, plain,
% 99.25/13.43 (~ (((omegaSAx) =>
% 99.25/13.43 (((omegaIndAx) =>
% 99.25/13.43 (((replAx) =>
% 99.25/13.43 (((foundationAx) =>
% 99.25/13.43 (((wellorderingAx) =>
% 99.25/13.43 (((descrp) =>
% 99.25/13.43 (((dsetconstrI) =>
% 99.25/13.43 (((dsetconstrEL) =>
% 99.25/13.43 (((dsetconstrER) =>
% 99.25/13.43 (((exuE1) =>
% 99.25/13.43 (((prop2setE) =>
% 99.25/13.43 (((emptysetE) =>
% 99.25/13.43 (((emptysetimpfalse) =>
% 99.25/13.43 (((notinemptyset) =>
% 99.25/13.43 (((exuE3e) =>
% 99.25/13.43 (((setext) =>
% 99.25/13.43 (((emptyI) =>
% 99.25/13.43 (((noeltsimpempty) =>
% 99.25/13.43 (((setbeta) =>
% 99.25/13.43 (((nonemptyE1) =>
% 99.25/13.43 (((nonemptyI) =>
% 99.25/13.43 (((nonemptyI1) =>
% 99.25/13.43 (((setadjoinIL) =>
% 99.25/13.43 (((in @ emptyset @
% 99.25/13.43 (setadjoin @
% 99.25/13.43 emptyset @ emptyset)) =>
% 99.25/13.43 (((setadjoinIR) =>
% 99.25/13.43 (((setadjoinE) =>
% 99.25/13.43 (((setadjoinOr) =>
% 99.25/13.43 (((setoftrueEq) =>
% 99.25/13.43 (((powersetI) =>
% 99.25/13.43 (((emptyinPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptyInPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionI) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionE) =>
% 99.25/13.43 ((
% 99.25/13.43 (subPowSU) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (nonemptyImpWitness) =>
% 99.25/13.43 ((
% 99.25/13.43 (uniqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (notinsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsswitch) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptyE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (vacuousDall) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan1) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan2) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan3) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan4) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2setI) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2set2propI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdexE) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdallE) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI3) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (inCongP) =>
% 99.25/13.43 ((
% 99.25/13.43 (in__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuE3u) =>
% 99.25/13.43 ((
% 99.25/13.43 (exu__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoin__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (powerset__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunion__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuEu) =>
% 99.25/13.43 ((
% 99.25/13.43 (descr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (dsetconstr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptysetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (notsubsetI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetRefl) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetTrans) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subset2powerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (setextsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetemptysetimpeq) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (inPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepInPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepSubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2IR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionEcases) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionE) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectI) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset5) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset3) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectER) =>
% 99.25/13.43 ((
% 99.25/13.43 (disjointsetsI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset4) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (bs114d) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusI) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusER) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusERneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusELneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusILneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusIRneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffE) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg2) =>
% 99.25/13.43 ((
% 99.25/13.43 (secondinupair) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairiskpair) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairp) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2E) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsubunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairinpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem3) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairin) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempair1) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempair) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton1) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1E1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1I) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1I2) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsuniq) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL1) =>
% 99.25/13.43 ((
% 99.25/13.43 (kfstsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (theprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (kfstpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodfstin) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR11) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR12) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR1) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairequniteq) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR) =>
% 99.25/13.43 ((
% 99.25/13.43 (ksndsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (ksndpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairsurjEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodsndin) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairmemEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairmemER) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempaircEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodfstpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodsndpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairsurjEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrI) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrSub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setOfPairsIsBReln) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrERa) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrEL1) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrEL2) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrER) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcImageSingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (apProp) =>
% 99.25/13.43 ((
% 99.25/13.43 (app) =>
% 99.25/13.43 ((
% 99.25/13.43 (infuncsetfunc) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2p) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcinfuncset) =>
% 99.25/13.43 ((
% 99.25/13.43 (lamProp) =>
% 99.25/13.43 ((
% 99.25/13.43 (lamp) =>
% 99.25/13.43 ((
% 99.25/13.43 (lam2p) =>
% 99.25/13.43 ((
% 99.25/13.43 (brelnall1) =>
% 99.25/13.43 ((
% 99.25/13.43 (brelnall2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1E2) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp3) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcextLem) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp4) =>
% 99.25/13.43 ((
% 99.25/13.43 (subbreln) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqbreln) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcext) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcext2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2apEq1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2apEq2) =>
% 99.25/13.43 ((
% 99.25/13.43 (beta1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eta1) =>
% 99.25/13.43 ((
% 99.25/13.43 (lam2lamEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (beta2) =>
% 99.25/13.43 ((
% 99.25/13.43 (eta2) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalseProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalseProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ifSingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (ifp) =>
% 99.25/13.43 ((
% 99.25/13.43 (theeq) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrue) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalse) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueorfalse) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (setextT) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetTI) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetTI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetTE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectTELcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectTERcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT1) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT2) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT3) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementSub1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementSub2) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTnotintersectT) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementImpComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementSubsetComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementInPowersetComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (contraSubsetComplement) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTcontraSubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTILcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTIRcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInUnion) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInUnion2) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInIntersectUnions) =>
% 99.25/13.43 ((
% 99.25/13.43 (intersectInPowersetIntersectUnions) =>
% 99.25/13.43 ((
% 99.25/13.43 (inComplementUnionImpNotIn1) =>
% 99.25/13.43 ((
% 99.25/13.43 (inComplementUnionImpInComplement1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTE) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTEcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementUnionInPowersetComplement) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a2) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1a) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1b) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2b2) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2b) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule0) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule1) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule3) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_1) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_3) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_5) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all2) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1SetBreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (choice2fnsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (setOfPairsIsBReln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compEex) =>
% 99.25/13.43 ((
% 99.25/13.43 (!!) @ (
% 99.25/13.43 (('#B') @ (
% 99.25/13.43 !!) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 !!))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#C') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])).
% 99.25/13.43 thf(zip_derived_cl40, plain,
% 99.25/13.43 (~ (((omegaIndAx) =>
% 99.25/13.43 (((replAx) =>
% 99.25/13.43 (((foundationAx) =>
% 99.25/13.43 (((wellorderingAx) =>
% 99.25/13.43 (((descrp) =>
% 99.25/13.43 (((dsetconstrI) =>
% 99.25/13.43 (((dsetconstrEL) =>
% 99.25/13.43 (((dsetconstrER) =>
% 99.25/13.43 (((exuE1) =>
% 99.25/13.43 (((prop2setE) =>
% 99.25/13.43 (((emptysetE) =>
% 99.25/13.43 (((emptysetimpfalse) =>
% 99.25/13.43 (((notinemptyset) =>
% 99.25/13.43 (((exuE3e) =>
% 99.25/13.43 (((setext) =>
% 99.25/13.43 (((emptyI) =>
% 99.25/13.43 (((noeltsimpempty) =>
% 99.25/13.43 (((setbeta) =>
% 99.25/13.43 (((nonemptyE1) =>
% 99.25/13.43 (((nonemptyI) =>
% 99.25/13.43 (((nonemptyI1) =>
% 99.25/13.43 (((setadjoinIL) =>
% 99.25/13.43 (((in @ emptyset @
% 99.25/13.43 (setadjoin @ emptyset @
% 99.25/13.43 emptyset)) =>
% 99.25/13.43 (((setadjoinIR) =>
% 99.25/13.43 (((setadjoinE) =>
% 99.25/13.43 (((setadjoinOr) =>
% 99.25/13.43 (((setoftrueEq) =>
% 99.25/13.43 (((powersetI) =>
% 99.25/13.43 (((emptyinPowerset) =>
% 99.25/13.43 (((emptyInPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionI) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionE) =>
% 99.25/13.43 ((
% 99.25/13.43 (subPowSU) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (nonemptyImpWitness) =>
% 99.25/13.43 ((
% 99.25/13.43 (uniqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (notinsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsswitch) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptyE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (vacuousDall) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan1) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan2) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan3) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan4) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2setI) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2set2propI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdexE) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdallE) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI3) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (inCongP) =>
% 99.25/13.43 ((
% 99.25/13.43 (in__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuE3u) =>
% 99.25/13.43 ((
% 99.25/13.43 (exu__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoin__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (powerset__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunion__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuEu) =>
% 99.25/13.43 ((
% 99.25/13.43 (descr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (dsetconstr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptysetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (notsubsetI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetRefl) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetTrans) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subset2powerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (setextsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetemptysetimpeq) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (inPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepInPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepSubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2IR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionEcases) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionE) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectI) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset5) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset3) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectER) =>
% 99.25/13.43 ((
% 99.25/13.43 (disjointsetsI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset4) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (bs114d) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusI) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusER) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusERneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusELneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusILneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusIRneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffE) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg2) =>
% 99.25/13.43 ((
% 99.25/13.43 (secondinupair) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairiskpair) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairp) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2E) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsubunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairinpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem3) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairin) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempair1) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempair) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton1) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1E1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1I) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1I2) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsuniq) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL1) =>
% 99.25/13.43 ((
% 99.25/13.43 (kfstsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (theprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (kfstpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodfstin) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR11) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR12) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR1) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairequniteq) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR) =>
% 99.25/13.43 ((
% 99.25/13.43 (ksndsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (ksndpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairsurjEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodsndin) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairmemEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairmemER) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempaircEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodfstpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodsndpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairsurjEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrI) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrSub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setOfPairsIsBReln) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrERa) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrEL1) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrEL2) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrER) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcImageSingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (apProp) =>
% 99.25/13.43 ((
% 99.25/13.43 (app) =>
% 99.25/13.43 ((
% 99.25/13.43 (infuncsetfunc) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2p) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcinfuncset) =>
% 99.25/13.43 ((
% 99.25/13.43 (lamProp) =>
% 99.25/13.43 ((
% 99.25/13.43 (lamp) =>
% 99.25/13.43 ((
% 99.25/13.43 (lam2p) =>
% 99.25/13.43 ((
% 99.25/13.43 (brelnall1) =>
% 99.25/13.43 ((
% 99.25/13.43 (brelnall2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1E2) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp3) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcextLem) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp4) =>
% 99.25/13.43 ((
% 99.25/13.43 (subbreln) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqbreln) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcext) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcext2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2apEq1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2apEq2) =>
% 99.25/13.43 ((
% 99.25/13.43 (beta1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eta1) =>
% 99.25/13.43 ((
% 99.25/13.43 (lam2lamEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (beta2) =>
% 99.25/13.43 ((
% 99.25/13.43 (eta2) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalseProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalseProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ifSingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (ifp) =>
% 99.25/13.43 ((
% 99.25/13.43 (theeq) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrue) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalse) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueorfalse) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (setextT) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetTI) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetTI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetTE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectTELcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectTERcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT1) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT2) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT3) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementSub1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementSub2) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTnotintersectT) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementImpComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementSubsetComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementInPowersetComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (contraSubsetComplement) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTcontraSubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTILcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTIRcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInUnion) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInUnion2) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInIntersectUnions) =>
% 99.25/13.43 ((
% 99.25/13.43 (intersectInPowersetIntersectUnions) =>
% 99.25/13.43 ((
% 99.25/13.43 (inComplementUnionImpNotIn1) =>
% 99.25/13.43 ((
% 99.25/13.43 (inComplementUnionImpInComplement1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTE) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTEcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementUnionInPowersetComplement) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a2) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1a) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1b) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2b2) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2b) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule0) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule1) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule3) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_1) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_3) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_5) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all2) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1SetBreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (choice2fnsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (setOfPairsIsBReln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compEex) =>
% 99.25/13.43 ((
% 99.25/13.43 (!!) @ (
% 99.25/13.43 (('#B') @ (
% 99.25/13.43 !!) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 !!))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#C') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
% 99.25/13.43 thf(zip_derived_cl46, plain,
% 99.25/13.43 (~ (((replAx) =>
% 99.25/13.43 (((foundationAx) =>
% 99.25/13.43 (((wellorderingAx) =>
% 99.25/13.43 (((descrp) =>
% 99.25/13.43 (((dsetconstrI) =>
% 99.25/13.43 (((dsetconstrEL) =>
% 99.25/13.43 (((dsetconstrER) =>
% 99.25/13.43 (((exuE1) =>
% 99.25/13.43 (((prop2setE) =>
% 99.25/13.43 (((emptysetE) =>
% 99.25/13.43 (((emptysetimpfalse) =>
% 99.25/13.43 (((notinemptyset) =>
% 99.25/13.43 (((exuE3e) =>
% 99.25/13.43 (((setext) =>
% 99.25/13.43 (((emptyI) =>
% 99.25/13.43 (((noeltsimpempty) =>
% 99.25/13.43 (((setbeta) =>
% 99.25/13.43 (((nonemptyE1) =>
% 99.25/13.43 (((nonemptyI) =>
% 99.25/13.43 (((nonemptyI1) =>
% 99.25/13.43 (((setadjoinIL) =>
% 99.25/13.43 (((in @ emptyset @
% 99.25/13.43 (setadjoin @ emptyset @
% 99.25/13.43 emptyset)) =>
% 99.25/13.43 (((setadjoinIR) =>
% 99.25/13.43 (((setadjoinE) =>
% 99.25/13.43 (((setadjoinOr) =>
% 99.25/13.43 (((setoftrueEq) =>
% 99.25/13.43 (((powersetI) =>
% 99.25/13.43 (((emptyinPowerset) =>
% 99.25/13.43 (((emptyInPowerset) =>
% 99.25/13.43 (((powersetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionI) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionE) =>
% 99.25/13.43 ((
% 99.25/13.43 (subPowSU) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (nonemptyImpWitness) =>
% 99.25/13.43 ((
% 99.25/13.43 (uniqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (notinsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsswitch) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptyE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (vacuousDall) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan1) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan2) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan3) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan4) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2setI) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2set2propI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdexE) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdallE) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI3) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (inCongP) =>
% 99.25/13.43 ((
% 99.25/13.43 (in__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuE3u) =>
% 99.25/13.43 ((
% 99.25/13.43 (exu__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoin__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (powerset__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunion__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuEu) =>
% 99.25/13.43 ((
% 99.25/13.43 (descr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (dsetconstr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptysetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (notsubsetI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetRefl) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetTrans) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subset2powerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (setextsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetemptysetimpeq) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (inPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepInPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepSubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2IR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionEcases) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionE) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectI) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset5) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset3) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectER) =>
% 99.25/13.43 ((
% 99.25/13.43 (disjointsetsI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset4) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (bs114d) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusI) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusER) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusERneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusELneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusILneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusIRneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffE) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg2) =>
% 99.25/13.43 ((
% 99.25/13.43 (secondinupair) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairiskpair) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairp) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2E) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsubunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairinpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem3) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairin) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempair1) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempair) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton1) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1E1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1I) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1I2) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsuniq) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL1) =>
% 99.25/13.43 ((
% 99.25/13.43 (kfstsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (theprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (kfstpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodfstin) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR11) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR12) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR1) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairequniteq) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR) =>
% 99.25/13.43 ((
% 99.25/13.43 (ksndsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (ksndpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairsurjEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodsndin) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairmemEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairmemER) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempaircEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodfstpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodsndpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairsurjEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrI) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrSub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setOfPairsIsBReln) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrERa) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrEL1) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrEL2) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrER) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcImageSingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (apProp) =>
% 99.25/13.43 ((
% 99.25/13.43 (app) =>
% 99.25/13.43 ((
% 99.25/13.43 (infuncsetfunc) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2p) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcinfuncset) =>
% 99.25/13.43 ((
% 99.25/13.43 (lamProp) =>
% 99.25/13.43 ((
% 99.25/13.43 (lamp) =>
% 99.25/13.43 ((
% 99.25/13.43 (lam2p) =>
% 99.25/13.43 ((
% 99.25/13.43 (brelnall1) =>
% 99.25/13.43 ((
% 99.25/13.43 (brelnall2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1E2) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp3) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcextLem) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp4) =>
% 99.25/13.43 ((
% 99.25/13.43 (subbreln) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqbreln) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcext) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcext2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2apEq1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2apEq2) =>
% 99.25/13.43 ((
% 99.25/13.43 (beta1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eta1) =>
% 99.25/13.43 ((
% 99.25/13.43 (lam2lamEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (beta2) =>
% 99.25/13.43 ((
% 99.25/13.43 (eta2) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalseProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalseProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ifSingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (ifp) =>
% 99.25/13.43 ((
% 99.25/13.43 (theeq) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrue) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalse) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueorfalse) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (setextT) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetTI) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetTI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetTE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectTELcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectTERcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT1) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT2) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT3) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementSub1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementSub2) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTnotintersectT) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementImpComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementSubsetComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementInPowersetComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (contraSubsetComplement) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTcontraSubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTILcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTIRcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInUnion) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInUnion2) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInIntersectUnions) =>
% 99.25/13.43 ((
% 99.25/13.43 (intersectInPowersetIntersectUnions) =>
% 99.25/13.43 ((
% 99.25/13.43 (inComplementUnionImpNotIn1) =>
% 99.25/13.43 ((
% 99.25/13.43 (inComplementUnionImpInComplement1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTE) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTEcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementUnionInPowersetComplement) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a2) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1a) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1b) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2b2) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2b) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule0) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule1) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule3) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_1) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_3) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_5) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all2) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1SetBreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (choice2fnsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (setOfPairsIsBReln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compEex) =>
% 99.25/13.43 ((
% 99.25/13.43 (!!) @ (
% 99.25/13.43 (('#B') @ (
% 99.25/13.43 !!) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 !!))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#C') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])).
% 99.25/13.43 thf(zip_derived_cl52, plain,
% 99.25/13.43 (~ (((foundationAx) =>
% 99.25/13.43 (((wellorderingAx) =>
% 99.25/13.43 (((descrp) =>
% 99.25/13.43 (((dsetconstrI) =>
% 99.25/13.43 (((dsetconstrEL) =>
% 99.25/13.43 (((dsetconstrER) =>
% 99.25/13.43 (((exuE1) =>
% 99.25/13.43 (((prop2setE) =>
% 99.25/13.43 (((emptysetE) =>
% 99.25/13.43 (((emptysetimpfalse) =>
% 99.25/13.43 (((notinemptyset) =>
% 99.25/13.43 (((exuE3e) =>
% 99.25/13.43 (((setext) =>
% 99.25/13.43 (((emptyI) =>
% 99.25/13.43 (((noeltsimpempty) =>
% 99.25/13.43 (((setbeta) =>
% 99.25/13.43 (((nonemptyE1) =>
% 99.25/13.43 (((nonemptyI) =>
% 99.25/13.43 (((nonemptyI1) =>
% 99.25/13.43 (((setadjoinIL) =>
% 99.25/13.43 (((in @ emptyset @
% 99.25/13.43 (setadjoin @ emptyset @
% 99.25/13.43 emptyset)) =>
% 99.25/13.43 (((setadjoinIR) =>
% 99.25/13.43 (((setadjoinE) =>
% 99.25/13.43 (((setadjoinOr) =>
% 99.25/13.43 (((setoftrueEq) =>
% 99.25/13.43 (((powersetI) =>
% 99.25/13.43 (((emptyinPowerset) =>
% 99.25/13.43 (((emptyInPowerset) =>
% 99.25/13.43 (((powersetE) =>
% 99.25/13.43 (((setunionI) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionE) =>
% 99.25/13.43 ((
% 99.25/13.43 (subPowSU) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (nonemptyImpWitness) =>
% 99.25/13.43 ((
% 99.25/13.43 (uniqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (notinsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsswitch) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptyE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (vacuousDall) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan1) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan2) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan3) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan4) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2setI) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2set2propI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdexE) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdallE) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI3) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (inCongP) =>
% 99.25/13.43 ((
% 99.25/13.43 (in__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuE3u) =>
% 99.25/13.43 ((
% 99.25/13.43 (exu__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoin__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (powerset__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunion__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuEu) =>
% 99.25/13.43 ((
% 99.25/13.43 (descr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (dsetconstr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptysetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (notsubsetI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetRefl) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetTrans) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subset2powerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (setextsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetemptysetimpeq) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (inPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepInPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepSubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2IR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionEcases) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionE) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectI) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset5) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset3) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectER) =>
% 99.25/13.43 ((
% 99.25/13.43 (disjointsetsI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset4) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (bs114d) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusI) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusER) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusERneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusELneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusILneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusIRneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffE) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg2) =>
% 99.25/13.43 ((
% 99.25/13.43 (secondinupair) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairiskpair) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairp) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2E) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsubunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairinpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem3) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairin) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempair1) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempair) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton1) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1E1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1I) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1I2) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsuniq) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL1) =>
% 99.25/13.43 ((
% 99.25/13.43 (kfstsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (theprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (kfstpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodfstin) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR11) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR12) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR1) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairequniteq) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR) =>
% 99.25/13.43 ((
% 99.25/13.43 (ksndsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (ksndpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairsurjEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodsndin) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairmemEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairmemER) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempaircEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodfstpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodsndpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairsurjEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrI) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrSub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setOfPairsIsBReln) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrERa) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrEL1) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrEL2) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrER) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcImageSingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (apProp) =>
% 99.25/13.43 ((
% 99.25/13.43 (app) =>
% 99.25/13.43 ((
% 99.25/13.43 (infuncsetfunc) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2p) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcinfuncset) =>
% 99.25/13.43 ((
% 99.25/13.43 (lamProp) =>
% 99.25/13.43 ((
% 99.25/13.43 (lamp) =>
% 99.25/13.43 ((
% 99.25/13.43 (lam2p) =>
% 99.25/13.43 ((
% 99.25/13.43 (brelnall1) =>
% 99.25/13.43 ((
% 99.25/13.43 (brelnall2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1E2) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp3) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcextLem) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp4) =>
% 99.25/13.43 ((
% 99.25/13.43 (subbreln) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqbreln) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcext) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcext2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2apEq1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2apEq2) =>
% 99.25/13.43 ((
% 99.25/13.43 (beta1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eta1) =>
% 99.25/13.43 ((
% 99.25/13.43 (lam2lamEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (beta2) =>
% 99.25/13.43 ((
% 99.25/13.43 (eta2) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalseProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalseProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ifSingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (ifp) =>
% 99.25/13.43 ((
% 99.25/13.43 (theeq) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrue) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalse) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueorfalse) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (setextT) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetTI) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetTI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetTE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectTELcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectTERcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT1) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT2) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT3) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementSub1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementSub2) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTnotintersectT) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementImpComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementSubsetComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementInPowersetComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (contraSubsetComplement) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTcontraSubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTILcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTIRcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInUnion) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInUnion2) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInIntersectUnions) =>
% 99.25/13.43 ((
% 99.25/13.43 (intersectInPowersetIntersectUnions) =>
% 99.25/13.43 ((
% 99.25/13.43 (inComplementUnionImpNotIn1) =>
% 99.25/13.43 ((
% 99.25/13.43 (inComplementUnionImpInComplement1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTE) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTEcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementUnionInPowersetComplement) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a2) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1a) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1b) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2b2) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2b) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule0) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule1) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule3) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_1) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_3) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_5) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all2) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1SetBreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (choice2fnsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (setOfPairsIsBReln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compEex) =>
% 99.25/13.43 ((
% 99.25/13.43 (!!) @ (
% 99.25/13.43 (('#B') @ (
% 99.25/13.43 !!) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 !!))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#C') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])).
% 99.25/13.43 thf(zip_derived_cl58, plain,
% 99.25/13.43 (~ (((wellorderingAx) =>
% 99.25/13.43 (((descrp) =>
% 99.25/13.43 (((dsetconstrI) =>
% 99.25/13.43 (((dsetconstrEL) =>
% 99.25/13.43 (((dsetconstrER) =>
% 99.25/13.43 (((exuE1) =>
% 99.25/13.43 (((prop2setE) =>
% 99.25/13.43 (((emptysetE) =>
% 99.25/13.43 (((emptysetimpfalse) =>
% 99.25/13.43 (((notinemptyset) =>
% 99.25/13.43 (((exuE3e) =>
% 99.25/13.43 (((setext) =>
% 99.25/13.43 (((emptyI) =>
% 99.25/13.43 (((noeltsimpempty) =>
% 99.25/13.43 (((setbeta) =>
% 99.25/13.43 (((nonemptyE1) =>
% 99.25/13.43 (((nonemptyI) =>
% 99.25/13.43 (((nonemptyI1) =>
% 99.25/13.43 (((setadjoinIL) =>
% 99.25/13.43 (((in @ emptyset @
% 99.25/13.43 (setadjoin @ emptyset @
% 99.25/13.43 emptyset)) =>
% 99.25/13.43 (((setadjoinIR) =>
% 99.25/13.43 (((setadjoinE) =>
% 99.25/13.43 (((setadjoinOr) =>
% 99.25/13.43 (((setoftrueEq) =>
% 99.25/13.43 (((powersetI) =>
% 99.25/13.43 (((emptyinPowerset) =>
% 99.25/13.43 (((emptyInPowerset) =>
% 99.25/13.43 (((powersetE) =>
% 99.25/13.43 (((setunionI) =>
% 99.25/13.43 (((setunionE) =>
% 99.25/13.43 ((
% 99.25/13.43 (subPowSU) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (nonemptyImpWitness) =>
% 99.25/13.43 ((
% 99.25/13.43 (uniqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (notinsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsswitch) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptyE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (vacuousDall) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan1) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan2) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan3) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan4) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2setI) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2set2propI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdexE) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdallE) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI3) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (inCongP) =>
% 99.25/13.43 ((
% 99.25/13.43 (in__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuE3u) =>
% 99.25/13.43 ((
% 99.25/13.43 (exu__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoin__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (powerset__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunion__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuEu) =>
% 99.25/13.43 ((
% 99.25/13.43 (descr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (dsetconstr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptysetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (notsubsetI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetRefl) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetTrans) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subset2powerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (setextsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetemptysetimpeq) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (inPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepInPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepSubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2IR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionEcases) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionE) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectI) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset5) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset3) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectER) =>
% 99.25/13.43 ((
% 99.25/13.43 (disjointsetsI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset4) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (bs114d) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusI) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusER) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusERneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusELneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusILneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusIRneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffE) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg2) =>
% 99.25/13.43 ((
% 99.25/13.43 (secondinupair) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairiskpair) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairp) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2E) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsubunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairinpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem3) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairin) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempair1) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempair) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton1) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1E1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1I) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1I2) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsuniq) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL1) =>
% 99.25/13.43 ((
% 99.25/13.43 (kfstsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (theprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (kfstpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodfstin) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR11) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR12) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR1) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairequniteq) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR) =>
% 99.25/13.43 ((
% 99.25/13.43 (ksndsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (ksndpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairsurjEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodsndin) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairmemEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairmemER) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempaircEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodfstpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodsndpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairsurjEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrI) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrSub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setOfPairsIsBReln) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrERa) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrEL1) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrEL2) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrER) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcImageSingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (apProp) =>
% 99.25/13.43 ((
% 99.25/13.43 (app) =>
% 99.25/13.43 ((
% 99.25/13.43 (infuncsetfunc) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2p) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcinfuncset) =>
% 99.25/13.43 ((
% 99.25/13.43 (lamProp) =>
% 99.25/13.43 ((
% 99.25/13.43 (lamp) =>
% 99.25/13.43 ((
% 99.25/13.43 (lam2p) =>
% 99.25/13.43 ((
% 99.25/13.43 (brelnall1) =>
% 99.25/13.43 ((
% 99.25/13.43 (brelnall2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1E2) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp3) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcextLem) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp4) =>
% 99.25/13.43 ((
% 99.25/13.43 (subbreln) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqbreln) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcext) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcext2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2apEq1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2apEq2) =>
% 99.25/13.43 ((
% 99.25/13.43 (beta1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eta1) =>
% 99.25/13.43 ((
% 99.25/13.43 (lam2lamEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (beta2) =>
% 99.25/13.43 ((
% 99.25/13.43 (eta2) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalseProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalseProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ifSingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (ifp) =>
% 99.25/13.43 ((
% 99.25/13.43 (theeq) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrue) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalse) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueorfalse) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (setextT) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetTI) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetTI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetTE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectTELcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectTERcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT1) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT2) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT3) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementSub1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementSub2) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTnotintersectT) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementImpComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementSubsetComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementInPowersetComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (contraSubsetComplement) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTcontraSubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTILcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTIRcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInUnion) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInUnion2) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInIntersectUnions) =>
% 99.25/13.43 ((
% 99.25/13.43 (intersectInPowersetIntersectUnions) =>
% 99.25/13.43 ((
% 99.25/13.43 (inComplementUnionImpNotIn1) =>
% 99.25/13.43 ((
% 99.25/13.43 (inComplementUnionImpInComplement1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTE) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTEcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementUnionInPowersetComplement) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a2) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1a) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1b) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2b2) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2b) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule0) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule1) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule3) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_1) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_3) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_5) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all2) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1SetBreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (choice2fnsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (setOfPairsIsBReln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compEex) =>
% 99.25/13.43 ((
% 99.25/13.43 (!!) @ (
% 99.25/13.43 (('#B') @ (
% 99.25/13.43 !!) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 !!))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#C') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])).
% 99.25/13.43 thf(zip_derived_cl64, plain,
% 99.25/13.43 (~ (((descrp) =>
% 99.25/13.43 (((dsetconstrI) =>
% 99.25/13.43 (((dsetconstrEL) =>
% 99.25/13.43 (((dsetconstrER) =>
% 99.25/13.43 (((exuE1) =>
% 99.25/13.43 (((prop2setE) =>
% 99.25/13.43 (((emptysetE) =>
% 99.25/13.43 (((emptysetimpfalse) =>
% 99.25/13.43 (((notinemptyset) =>
% 99.25/13.43 (((exuE3e) =>
% 99.25/13.43 (((setext) =>
% 99.25/13.43 (((emptyI) =>
% 99.25/13.43 (((noeltsimpempty) =>
% 99.25/13.43 (((setbeta) =>
% 99.25/13.43 (((nonemptyE1) =>
% 99.25/13.43 (((nonemptyI) =>
% 99.25/13.43 (((nonemptyI1) =>
% 99.25/13.43 (((setadjoinIL) =>
% 99.25/13.43 (((in @ emptyset @
% 99.25/13.43 (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.43 (((setadjoinIR) =>
% 99.25/13.43 (((setadjoinE) =>
% 99.25/13.43 (((setadjoinOr) =>
% 99.25/13.43 (((setoftrueEq) =>
% 99.25/13.43 (((powersetI) =>
% 99.25/13.43 (((emptyinPowerset) =>
% 99.25/13.43 (((emptyInPowerset) =>
% 99.25/13.43 (((powersetE) =>
% 99.25/13.43 (((setunionI) =>
% 99.25/13.43 (((setunionE) =>
% 99.25/13.43 (((subPowSU) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (nonemptyImpWitness) =>
% 99.25/13.43 ((
% 99.25/13.43 (uniqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (notinsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsswitch) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptyE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (vacuousDall) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan1) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan2) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan3) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan4) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2setI) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2set2propI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdexE) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdallE) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI3) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (inCongP) =>
% 99.25/13.43 ((
% 99.25/13.43 (in__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuE3u) =>
% 99.25/13.43 ((
% 99.25/13.43 (exu__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoin__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (powerset__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunion__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuEu) =>
% 99.25/13.43 ((
% 99.25/13.43 (descr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (dsetconstr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptysetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (notsubsetI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetRefl) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetTrans) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subset2powerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (setextsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetemptysetimpeq) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (inPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepInPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepSubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2IR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionEcases) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionE) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectI) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset5) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset3) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectER) =>
% 99.25/13.43 ((
% 99.25/13.43 (disjointsetsI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset4) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (bs114d) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusI) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusER) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusERneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusELneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusILneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusIRneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffE) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg2) =>
% 99.25/13.43 ((
% 99.25/13.43 (secondinupair) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairiskpair) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairp) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2E) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsubunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairinpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem3) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairin) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempair1) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempair) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton1) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1E1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1I) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1I2) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsuniq) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL1) =>
% 99.25/13.43 ((
% 99.25/13.43 (kfstsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (theprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (kfstpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodfstin) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR11) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR12) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR1) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairequniteq) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR) =>
% 99.25/13.43 ((
% 99.25/13.43 (ksndsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (ksndpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairsurjEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodsndin) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairmemEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairmemER) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempaircEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodfstpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodsndpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairsurjEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrI) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrSub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setOfPairsIsBReln) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrERa) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrEL1) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrEL2) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrER) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcImageSingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (apProp) =>
% 99.25/13.43 ((
% 99.25/13.43 (app) =>
% 99.25/13.43 ((
% 99.25/13.43 (infuncsetfunc) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2p) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcinfuncset) =>
% 99.25/13.43 ((
% 99.25/13.43 (lamProp) =>
% 99.25/13.43 ((
% 99.25/13.43 (lamp) =>
% 99.25/13.43 ((
% 99.25/13.43 (lam2p) =>
% 99.25/13.43 ((
% 99.25/13.43 (brelnall1) =>
% 99.25/13.43 ((
% 99.25/13.43 (brelnall2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1E2) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp3) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcextLem) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp4) =>
% 99.25/13.43 ((
% 99.25/13.43 (subbreln) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqbreln) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcext) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcext2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2apEq1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2apEq2) =>
% 99.25/13.43 ((
% 99.25/13.43 (beta1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eta1) =>
% 99.25/13.43 ((
% 99.25/13.43 (lam2lamEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (beta2) =>
% 99.25/13.43 ((
% 99.25/13.43 (eta2) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalseProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalseProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ifSingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (ifp) =>
% 99.25/13.43 ((
% 99.25/13.43 (theeq) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrue) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalse) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueorfalse) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (setextT) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetTI) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetTI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetTE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectTELcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectTERcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT1) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT2) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT3) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementSub1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementSub2) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTnotintersectT) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementImpComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementSubsetComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementInPowersetComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (contraSubsetComplement) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTcontraSubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTILcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTIRcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInUnion) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInUnion2) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInIntersectUnions) =>
% 99.25/13.43 ((
% 99.25/13.43 (intersectInPowersetIntersectUnions) =>
% 99.25/13.43 ((
% 99.25/13.43 (inComplementUnionImpNotIn1) =>
% 99.25/13.43 ((
% 99.25/13.43 (inComplementUnionImpInComplement1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTE) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTEcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementUnionInPowersetComplement) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a2) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1a) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1b) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2b2) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2b) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule0) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule1) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule3) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_1) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_3) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_5) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all2) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1SetBreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (choice2fnsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (setOfPairsIsBReln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compEex) =>
% 99.25/13.43 ((
% 99.25/13.43 (!!) @ (
% 99.25/13.43 (('#B') @ (
% 99.25/13.43 !!) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 !!))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#C') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])).
% 99.25/13.43 thf(zip_derived_cl71, plain,
% 99.25/13.43 (~ (((dsetconstrI) =>
% 99.25/13.43 (((dsetconstrEL) =>
% 99.25/13.43 (((dsetconstrER) =>
% 99.25/13.43 (((exuE1) =>
% 99.25/13.43 (((prop2setE) =>
% 99.25/13.43 (((emptysetE) =>
% 99.25/13.43 (((emptysetimpfalse) =>
% 99.25/13.43 (((notinemptyset) =>
% 99.25/13.43 (((exuE3e) =>
% 99.25/13.43 (((setext) =>
% 99.25/13.43 (((emptyI) =>
% 99.25/13.43 (((noeltsimpempty) =>
% 99.25/13.43 (((setbeta) =>
% 99.25/13.43 (((nonemptyE1) =>
% 99.25/13.43 (((nonemptyI) =>
% 99.25/13.43 (((nonemptyI1) =>
% 99.25/13.43 (((setadjoinIL) =>
% 99.25/13.43 (((in @ emptyset @
% 99.25/13.43 (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.43 (((setadjoinIR) =>
% 99.25/13.43 (((setadjoinE) =>
% 99.25/13.43 (((setadjoinOr) =>
% 99.25/13.43 (((setoftrueEq) =>
% 99.25/13.43 (((powersetI) =>
% 99.25/13.43 (((emptyinPowerset) =>
% 99.25/13.43 (((emptyInPowerset) =>
% 99.25/13.43 (((powersetE) =>
% 99.25/13.43 (((setunionI) =>
% 99.25/13.43 (((setunionE) =>
% 99.25/13.43 (((subPowSU) =>
% 99.25/13.43 (((exuE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (nonemptyImpWitness) =>
% 99.25/13.43 ((
% 99.25/13.43 (uniqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (notinsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsswitch) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptyE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (vacuousDall) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan1) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan2) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan3) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan4) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2setI) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2set2propI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdexE) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdallE) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI3) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (inCongP) =>
% 99.25/13.43 ((
% 99.25/13.43 (in__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuE3u) =>
% 99.25/13.43 ((
% 99.25/13.43 (exu__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoin__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (powerset__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunion__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuEu) =>
% 99.25/13.43 ((
% 99.25/13.43 (descr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (dsetconstr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptysetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (notsubsetI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetRefl) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetTrans) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subset2powerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (setextsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetemptysetimpeq) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (inPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepInPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepSubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2IR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionEcases) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionE) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectI) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset5) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset3) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectER) =>
% 99.25/13.43 ((
% 99.25/13.43 (disjointsetsI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset4) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (bs114d) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusI) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusER) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusERneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusELneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusILneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusIRneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffE) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg2) =>
% 99.25/13.43 ((
% 99.25/13.43 (secondinupair) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairiskpair) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairp) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2E) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsubunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairinpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem3) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairin) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempair1) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempair) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton1) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1E1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1I) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1I2) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsuniq) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL1) =>
% 99.25/13.43 ((
% 99.25/13.43 (kfstsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (theprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (kfstpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodfstin) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR11) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR12) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR1) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairequniteq) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR) =>
% 99.25/13.43 ((
% 99.25/13.43 (ksndsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (ksndpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairsurjEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodsndin) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairmemEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairmemER) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempaircEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodfstpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodsndpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairsurjEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrI) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrSub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setOfPairsIsBReln) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrERa) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrEL1) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrEL2) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrER) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcImageSingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (apProp) =>
% 99.25/13.43 ((
% 99.25/13.43 (app) =>
% 99.25/13.43 ((
% 99.25/13.43 (infuncsetfunc) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2p) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcinfuncset) =>
% 99.25/13.43 ((
% 99.25/13.43 (lamProp) =>
% 99.25/13.43 ((
% 99.25/13.43 (lamp) =>
% 99.25/13.43 ((
% 99.25/13.43 (lam2p) =>
% 99.25/13.43 ((
% 99.25/13.43 (brelnall1) =>
% 99.25/13.43 ((
% 99.25/13.43 (brelnall2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1E2) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp3) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcextLem) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp4) =>
% 99.25/13.43 ((
% 99.25/13.43 (subbreln) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqbreln) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcext) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcext2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2apEq1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2apEq2) =>
% 99.25/13.43 ((
% 99.25/13.43 (beta1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eta1) =>
% 99.25/13.43 ((
% 99.25/13.43 (lam2lamEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (beta2) =>
% 99.25/13.43 ((
% 99.25/13.43 (eta2) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalseProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalseProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ifSingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (ifp) =>
% 99.25/13.43 ((
% 99.25/13.43 (theeq) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrue) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalse) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueorfalse) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (setextT) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetTI) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetTI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetTE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectTELcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectTERcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT1) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT2) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT3) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementSub1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementSub2) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTnotintersectT) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementImpComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementSubsetComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementInPowersetComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (contraSubsetComplement) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTcontraSubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTILcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTIRcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInUnion) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInUnion2) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInIntersectUnions) =>
% 99.25/13.43 ((
% 99.25/13.43 (intersectInPowersetIntersectUnions) =>
% 99.25/13.43 ((
% 99.25/13.43 (inComplementUnionImpNotIn1) =>
% 99.25/13.43 ((
% 99.25/13.43 (inComplementUnionImpInComplement1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTE) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTEcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementUnionInPowersetComplement) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a2) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1a) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1b) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2b2) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2b) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule0) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule1) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule3) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_1) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_3) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_5) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all2) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1SetBreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (choice2fnsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (setOfPairsIsBReln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compEex) =>
% 99.25/13.43 ((
% 99.25/13.43 (!!) @ (
% 99.25/13.43 (('#B') @ (
% 99.25/13.43 !!) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 !!))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#C') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])).
% 99.25/13.43 thf(zip_derived_cl79, plain,
% 99.25/13.43 (~ (((dsetconstrEL) =>
% 99.25/13.43 (((dsetconstrER) =>
% 99.25/13.43 (((exuE1) =>
% 99.25/13.43 (((prop2setE) =>
% 99.25/13.43 (((emptysetE) =>
% 99.25/13.43 (((emptysetimpfalse) =>
% 99.25/13.43 (((notinemptyset) =>
% 99.25/13.43 (((exuE3e) =>
% 99.25/13.43 (((setext) =>
% 99.25/13.43 (((emptyI) =>
% 99.25/13.43 (((noeltsimpempty) =>
% 99.25/13.43 (((setbeta) =>
% 99.25/13.43 (((nonemptyE1) =>
% 99.25/13.43 (((nonemptyI) =>
% 99.25/13.43 (((nonemptyI1) =>
% 99.25/13.43 (((setadjoinIL) =>
% 99.25/13.43 (((in @ emptyset @
% 99.25/13.43 (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.43 (((setadjoinIR) =>
% 99.25/13.43 (((setadjoinE) =>
% 99.25/13.43 (((setadjoinOr) =>
% 99.25/13.43 (((setoftrueEq) =>
% 99.25/13.43 (((powersetI) =>
% 99.25/13.43 (((emptyinPowerset) =>
% 99.25/13.43 (((emptyInPowerset) =>
% 99.25/13.43 (((powersetE) =>
% 99.25/13.43 (((setunionI) =>
% 99.25/13.43 (((setunionE) =>
% 99.25/13.43 (((subPowSU) =>
% 99.25/13.43 (((exuE2) =>
% 99.25/13.43 (((nonemptyImpWitness) =>
% 99.25/13.43 ((
% 99.25/13.43 (uniqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (notinsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsswitch) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptyE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (vacuousDall) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan1) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan2) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan3) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan4) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2setI) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2set2propI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdexE) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdallE) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI3) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (inCongP) =>
% 99.25/13.43 ((
% 99.25/13.43 (in__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuE3u) =>
% 99.25/13.43 ((
% 99.25/13.43 (exu__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoin__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (powerset__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunion__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuEu) =>
% 99.25/13.43 ((
% 99.25/13.43 (descr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (dsetconstr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptysetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (notsubsetI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetRefl) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetTrans) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subset2powerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (setextsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetemptysetimpeq) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (inPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepInPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepSubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2IR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionEcases) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionE) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectI) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset5) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset3) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectER) =>
% 99.25/13.43 ((
% 99.25/13.43 (disjointsetsI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset4) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (bs114d) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusI) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusER) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusERneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusELneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusILneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusIRneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffE) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg2) =>
% 99.25/13.43 ((
% 99.25/13.43 (secondinupair) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairiskpair) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairp) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2E) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsubunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairinpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem3) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairin) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempair1) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempair) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton1) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunionsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1E1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1I) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1I2) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsuniq) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL1) =>
% 99.25/13.43 ((
% 99.25/13.43 (kfstsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (theprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (kfstpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodfstin) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR11) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR12) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR1) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairequniteq) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairinjR) =>
% 99.25/13.43 ((
% 99.25/13.43 (ksndsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (ksndpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairsurjEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodsndin) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairmemEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairmemER) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodmempaircEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodfstpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodsndpairEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (cartprodpairsurjEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrI) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrSub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setOfPairsIsBReln) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrERa) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrEL1) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrEL2) =>
% 99.25/13.43 ((
% 99.25/13.43 (dpsetconstrER) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcImageSingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (apProp) =>
% 99.25/13.43 ((
% 99.25/13.43 (app) =>
% 99.25/13.43 ((
% 99.25/13.43 (infuncsetfunc) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2p) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcinfuncset) =>
% 99.25/13.43 ((
% 99.25/13.43 (lamProp) =>
% 99.25/13.43 ((
% 99.25/13.43 (lamp) =>
% 99.25/13.43 ((
% 99.25/13.43 (lam2p) =>
% 99.25/13.43 ((
% 99.25/13.43 (brelnall1) =>
% 99.25/13.43 ((
% 99.25/13.43 (brelnall2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ex1E2) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp3) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcextLem) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcGraphProp4) =>
% 99.25/13.43 ((
% 99.25/13.43 (subbreln) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqbreln) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcext) =>
% 99.25/13.43 ((
% 99.25/13.43 (funcext2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2apEq1) =>
% 99.25/13.43 ((
% 99.25/13.43 (ap2apEq2) =>
% 99.25/13.43 ((
% 99.25/13.43 (beta1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eta1) =>
% 99.25/13.43 ((
% 99.25/13.43 (lam2lamEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (beta2) =>
% 99.25/13.43 ((
% 99.25/13.43 (eta2) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalseProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalseProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueProp1) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueProp2) =>
% 99.25/13.43 ((
% 99.25/13.43 (ifSingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (ifp) =>
% 99.25/13.43 ((
% 99.25/13.43 (theeq) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrue) =>
% 99.25/13.43 ((
% 99.25/13.43 (iffalse) =>
% 99.25/13.43 ((
% 99.25/13.43 (iftrueorfalse) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementT_lem) =>
% 99.25/13.43 ((
% 99.25/13.43 (setextT) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetTI) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetTI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetTE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectTELcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectTERcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT1) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT2) =>
% 99.25/13.43 ((
% 99.25/13.43 (contrasubsetT3) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementSub1) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementSub2) =>
% 99.25/13.43 ((
% 99.25/13.43 (doubleComplementEq) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTnotintersectT) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementImpComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementSubsetComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementInPowersetComplementIntersect) =>
% 99.25/13.43 ((
% 99.25/13.43 (contraSubsetComplement) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementTcontraSubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTILcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTIRcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInUnion) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInUnion2) =>
% 99.25/13.43 ((
% 99.25/13.43 (inIntersectImpInIntersectUnions) =>
% 99.25/13.43 ((
% 99.25/13.43 (intersectInPowersetIntersectUnions) =>
% 99.25/13.43 ((
% 99.25/13.43 (inComplementUnionImpNotIn1) =>
% 99.25/13.43 ((
% 99.25/13.43 (inComplementUnionImpInComplement1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTE) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionTEcontra) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a1) =>
% 99.25/13.43 ((
% 99.25/13.43 (complementUnionInPowersetComplement) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a2) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1a) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1b) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan1) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2a) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2b2) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2b) =>
% 99.25/13.43 ((
% 99.25/13.43 (demorgan2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule0) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule1) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule3) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz13rule4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_1) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_2) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_3) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_4) =>
% 99.25/13.43 ((
% 99.25/13.43 (woz1_5) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all2) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1SetBreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (choice2fnsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (setOfPairsIsBReln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1all1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqbreln1) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1invE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compprop) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compI) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compE) =>
% 99.25/13.43 ((
% 99.25/13.43 (breln1compEex) =>
% 99.25/13.43 ((
% 99.25/13.43 (!!) @ (
% 99.25/13.43 (('#B') @ (
% 99.25/13.43 !!) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 !!))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#S') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#S') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 =>))) @
% 99.25/13.43 breln1)))))) @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#C') @ (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 (
% 99.25/13.43 (
% 99.25/13.43 ('#B') @ (
% 99.25/13.43 '#B') @
% 99.25/13.43 breln1)))) @
% 99.25/13.43 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])).
% 99.25/13.43 thf(zip_derived_cl89, plain,
% 99.25/13.43 (~ (((dsetconstrER) =>
% 99.25/13.43 (((exuE1) =>
% 99.25/13.43 (((prop2setE) =>
% 99.25/13.43 (((emptysetE) =>
% 99.25/13.43 (((emptysetimpfalse) =>
% 99.25/13.43 (((notinemptyset) =>
% 99.25/13.43 (((exuE3e) =>
% 99.25/13.43 (((setext) =>
% 99.25/13.43 (((emptyI) =>
% 99.25/13.43 (((noeltsimpempty) =>
% 99.25/13.43 (((setbeta) =>
% 99.25/13.43 (((nonemptyE1) =>
% 99.25/13.43 (((nonemptyI) =>
% 99.25/13.43 (((nonemptyI1) =>
% 99.25/13.43 (((setadjoinIL) =>
% 99.25/13.43 (((in @ emptyset @
% 99.25/13.43 (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.43 (((setadjoinIR) =>
% 99.25/13.43 (((setadjoinE) =>
% 99.25/13.43 (((setadjoinOr) =>
% 99.25/13.43 (((setoftrueEq) =>
% 99.25/13.43 (((powersetI) =>
% 99.25/13.43 (((emptyinPowerset) =>
% 99.25/13.43 (((emptyInPowerset) =>
% 99.25/13.43 (((powersetE) =>
% 99.25/13.43 (((setunionI) =>
% 99.25/13.43 (((setunionE) =>
% 99.25/13.43 (((subPowSU) =>
% 99.25/13.43 (((exuE2) =>
% 99.25/13.43 (((nonemptyImpWitness) =>
% 99.25/13.43 (((uniqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (notinsingleton) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqinunit) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsswitch) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsetIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptyE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (vacuousDall) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan1) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan2) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan3) =>
% 99.25/13.43 ((
% 99.25/13.43 (quantDeMorgan4) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2setI) =>
% 99.25/13.43 ((
% 99.25/13.43 (prop2set2propI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdexE) =>
% 99.25/13.43 ((
% 99.25/13.43 (notdallE) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI3) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (inCongP) =>
% 99.25/13.43 ((
% 99.25/13.43 (in__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuE3u) =>
% 99.25/13.43 ((
% 99.25/13.43 (exu__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoin__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (powerset__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (setunion__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (exuEu) =>
% 99.25/13.43 ((
% 99.25/13.43 (descr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (dsetconstr__Cong) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (eqimpsubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (emptysetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetE2) =>
% 99.25/13.43 ((
% 99.25/13.43 (notsubsetI) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (notequalI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetRefl) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetTrans) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setadjoinSub2) =>
% 99.25/13.43 ((
% 99.25/13.43 (subset2powerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (setextsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (subsetemptysetimpeq) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetE1) =>
% 99.25/13.43 ((
% 99.25/13.43 (inPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (powersetsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepInPowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (sepSubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2IR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionEcases) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionE) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binunionRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectI) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset5) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset3) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectER) =>
% 99.25/13.43 ((
% 99.25/13.43 (disjointsetsI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectRsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset4) =>
% 99.25/13.43 ((
% 99.25/13.43 (binintersectSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (bs114d) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusI) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusEL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusER) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset2) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusERneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusELneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusILneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusIRneg) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusLsub) =>
% 99.25/13.43 ((
% 99.25/13.43 (setminusSubset1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffE) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffI2) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg1) =>
% 99.25/13.43 ((
% 99.25/13.43 (symdiffIneg2) =>
% 99.25/13.43 ((
% 99.25/13.43 (secondinupair) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIL) =>
% 99.25/13.43 ((
% 99.25/13.43 (setukpairIR) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairiskpair) =>
% 99.25/13.43 ((
% 99.25/13.43 (kpairp) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletonsubset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowerset) =>
% 99.25/13.43 ((
% 99.25/13.43 (singletoninpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairset2E) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairsubunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (upairinpowunion) =>
% 99.25/13.43 ((
% 99.25/13.43 (ubforcartprodlem1) =>
% 99.25/13.43 ((
% 99.25/13.44 (ubforcartprodlem2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem3) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair1) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton1) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I2) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsuniq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (theprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstin) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR11) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR12) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR1) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairequniteq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemER) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempaircEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrI) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrERa) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrER) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcImageSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (apProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (app) =>
% 99.25/13.44 ((
% 99.25/13.44 (infuncsetfunc) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcinfuncset) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall1) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp3) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcextLem) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp4) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq2) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2lamEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifp) =>
% 99.25/13.44 ((
% 99.25/13.44 (theeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrue) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueorfalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextT) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTI) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTELcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTERcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT1) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT2) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT3) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTnotintersectT) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementImpComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementSubsetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementInPowersetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (contraSubsetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTcontraSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTILcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTIRcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (intersectInPowersetIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpNotIn1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpInComplement1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTEcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementUnionInPowersetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule0) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_5) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all2) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1SetBreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (choice2fnsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compEex) =>
% 99.25/13.44 ((
% 99.25/13.44 (!!) @ (
% 99.25/13.44 (('#B') @ (
% 99.25/13.44 !!) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 !!))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#C') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 99.25/13.44 thf(zip_derived_cl105, plain,
% 99.25/13.44 (~ (((exuE1) =>
% 99.25/13.44 (((prop2setE) =>
% 99.25/13.44 (((emptysetE) =>
% 99.25/13.44 (((emptysetimpfalse) =>
% 99.25/13.44 (((notinemptyset) =>
% 99.25/13.44 (((exuE3e) =>
% 99.25/13.44 (((setext) =>
% 99.25/13.44 (((emptyI) =>
% 99.25/13.44 (((noeltsimpempty) =>
% 99.25/13.44 (((setbeta) =>
% 99.25/13.44 (((nonemptyE1) =>
% 99.25/13.44 (((nonemptyI) =>
% 99.25/13.44 (((nonemptyI1) =>
% 99.25/13.44 (((setadjoinIL) =>
% 99.25/13.44 (((in @ emptyset @
% 99.25/13.44 (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.44 (((setadjoinIR) =>
% 99.25/13.44 (((setadjoinE) =>
% 99.25/13.44 (((setadjoinOr) =>
% 99.25/13.44 (((setoftrueEq) =>
% 99.25/13.44 (((powersetI) =>
% 99.25/13.44 (((emptyinPowerset) =>
% 99.25/13.44 (((emptyInPowerset) =>
% 99.25/13.44 (((powersetE) =>
% 99.25/13.44 (((setunionI) =>
% 99.25/13.44 (((setunionE) =>
% 99.25/13.44 (((subPowSU) =>
% 99.25/13.44 (((exuE2) =>
% 99.25/13.44 (((nonemptyImpWitness) =>
% 99.25/13.44 (((uniqinunit) =>
% 99.25/13.44 (((notinsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqinunit) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsswitch) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsetE) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsetIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsetIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (emptyE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (vacuousDall) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan3) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan4) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2setI) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2set2propI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdexE) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdallE) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI3) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inCongP) =>
% 99.25/13.44 ((
% 99.25/13.44 (in__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuE3u) =>
% 99.25/13.44 ((
% 99.25/13.44 (exu__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoin__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (powerset__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunion__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuEu) =>
% 99.25/13.44 ((
% 99.25/13.44 (descr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (dsetconstr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (emptysetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (notsubsetI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetRefl) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTrans) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subset2powerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetemptysetimpeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepInPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2IR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionEcases) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectI) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset5) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset3) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectER) =>
% 99.25/13.44 ((
% 99.25/13.44 (disjointsetsI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset4) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (bs114d) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusI) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusER) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusERneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusELneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusILneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusIRneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffE) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg2) =>
% 99.25/13.44 ((
% 99.25/13.44 (secondinupair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairiskpair) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairp) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2E) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsubunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairinpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem3) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair1) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton1) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I2) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsuniq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (theprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstin) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR11) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR12) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR1) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairequniteq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemER) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempaircEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrI) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrERa) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrER) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcImageSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (apProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (app) =>
% 99.25/13.44 ((
% 99.25/13.44 (infuncsetfunc) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcinfuncset) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall1) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp3) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcextLem) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp4) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq2) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2lamEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifp) =>
% 99.25/13.44 ((
% 99.25/13.44 (theeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrue) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueorfalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextT) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTI) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTELcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTERcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT1) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT2) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT3) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTnotintersectT) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementImpComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementSubsetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementInPowersetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (contraSubsetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTcontraSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTILcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTIRcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (intersectInPowersetIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpNotIn1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpInComplement1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTEcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementUnionInPowersetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule0) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_5) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all2) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1SetBreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (choice2fnsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compEex) =>
% 99.25/13.44 ((
% 99.25/13.44 (!!) @ (
% 99.25/13.44 (('#B') @ (
% 99.25/13.44 !!) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 !!))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#C') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl89])).
% 99.25/13.44 thf(zip_derived_cl123, plain,
% 99.25/13.44 (~ (((prop2setE) =>
% 99.25/13.44 (((emptysetE) =>
% 99.25/13.44 (((emptysetimpfalse) =>
% 99.25/13.44 (((notinemptyset) =>
% 99.25/13.44 (((exuE3e) =>
% 99.25/13.44 (((setext) =>
% 99.25/13.44 (((emptyI) =>
% 99.25/13.44 (((noeltsimpempty) =>
% 99.25/13.44 (((setbeta) =>
% 99.25/13.44 (((nonemptyE1) =>
% 99.25/13.44 (((nonemptyI) =>
% 99.25/13.44 (((nonemptyI1) =>
% 99.25/13.44 (((setadjoinIL) =>
% 99.25/13.44 (((in @ emptyset @
% 99.25/13.44 (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.44 (((setadjoinIR) =>
% 99.25/13.44 (((setadjoinE) =>
% 99.25/13.44 (((setadjoinOr) =>
% 99.25/13.44 (((setoftrueEq) =>
% 99.25/13.44 (((powersetI) =>
% 99.25/13.44 (((emptyinPowerset) =>
% 99.25/13.44 (((emptyInPowerset) =>
% 99.25/13.44 (((powersetE) =>
% 99.25/13.44 (((setunionI) =>
% 99.25/13.44 (((setunionE) =>
% 99.25/13.44 (((subPowSU) =>
% 99.25/13.44 (((exuE2) =>
% 99.25/13.44 (((nonemptyImpWitness) =>
% 99.25/13.44 (((uniqinunit) =>
% 99.25/13.44 (((notinsingleton) =>
% 99.25/13.44 (((eqinunit) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsswitch) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsetE) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsetIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsetIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (emptyE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (vacuousDall) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan3) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan4) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2setI) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2set2propI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdexE) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdallE) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI3) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inCongP) =>
% 99.25/13.44 ((
% 99.25/13.44 (in__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuE3u) =>
% 99.25/13.44 ((
% 99.25/13.44 (exu__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoin__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (powerset__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunion__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuEu) =>
% 99.25/13.44 ((
% 99.25/13.44 (descr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (dsetconstr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (emptysetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (notsubsetI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetRefl) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTrans) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subset2powerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetemptysetimpeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepInPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2IR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionEcases) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectI) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset5) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset3) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectER) =>
% 99.25/13.44 ((
% 99.25/13.44 (disjointsetsI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset4) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (bs114d) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusI) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusER) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusERneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusELneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusILneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusIRneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffE) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg2) =>
% 99.25/13.44 ((
% 99.25/13.44 (secondinupair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairiskpair) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairp) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2E) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsubunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairinpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem3) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair1) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton1) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I2) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsuniq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (theprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstin) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR11) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR12) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR1) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairequniteq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemER) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempaircEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrI) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrERa) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrER) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcImageSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (apProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (app) =>
% 99.25/13.44 ((
% 99.25/13.44 (infuncsetfunc) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcinfuncset) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall1) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp3) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcextLem) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp4) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq2) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2lamEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifp) =>
% 99.25/13.44 ((
% 99.25/13.44 (theeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrue) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueorfalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextT) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTI) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTELcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTERcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT1) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT2) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT3) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTnotintersectT) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementImpComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementSubsetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementInPowersetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (contraSubsetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTcontraSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTILcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTIRcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (intersectInPowersetIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpNotIn1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpInComplement1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTEcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementUnionInPowersetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule0) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_5) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all2) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1SetBreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (choice2fnsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compEex) =>
% 99.25/13.44 ((
% 99.25/13.44 (!!) @ (
% 99.25/13.44 (('#B') @ (
% 99.25/13.44 !!) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 !!))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#C') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])).
% 99.25/13.44 thf(zip_derived_cl142, plain,
% 99.25/13.44 (~ (((emptysetE) =>
% 99.25/13.44 (((emptysetimpfalse) =>
% 99.25/13.44 (((notinemptyset) =>
% 99.25/13.44 (((exuE3e) =>
% 99.25/13.44 (((setext) =>
% 99.25/13.44 (((emptyI) =>
% 99.25/13.44 (((noeltsimpempty) =>
% 99.25/13.44 (((setbeta) =>
% 99.25/13.44 (((nonemptyE1) =>
% 99.25/13.44 (((nonemptyI) =>
% 99.25/13.44 (((nonemptyI1) =>
% 99.25/13.44 (((setadjoinIL) =>
% 99.25/13.44 (((in @ emptyset @
% 99.25/13.44 (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.44 (((setadjoinIR) =>
% 99.25/13.44 (((setadjoinE) =>
% 99.25/13.44 (((setadjoinOr) =>
% 99.25/13.44 (((setoftrueEq) =>
% 99.25/13.44 (((powersetI) =>
% 99.25/13.44 (((emptyinPowerset) =>
% 99.25/13.44 (((emptyInPowerset) =>
% 99.25/13.44 (((powersetE) =>
% 99.25/13.44 (((setunionI) =>
% 99.25/13.44 (((setunionE) =>
% 99.25/13.44 (((subPowSU) =>
% 99.25/13.44 (((exuE2) =>
% 99.25/13.44 (((nonemptyImpWitness) =>
% 99.25/13.44 (((uniqinunit) =>
% 99.25/13.44 (((notinsingleton) =>
% 99.25/13.44 (((eqinunit) =>
% 99.25/13.44 (((singletonsswitch) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsetE) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsetIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsetIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (emptyE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (vacuousDall) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan3) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan4) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2setI) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2set2propI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdexE) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdallE) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI3) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inCongP) =>
% 99.25/13.44 ((
% 99.25/13.44 (in__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuE3u) =>
% 99.25/13.44 ((
% 99.25/13.44 (exu__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoin__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (powerset__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunion__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuEu) =>
% 99.25/13.44 ((
% 99.25/13.44 (descr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (dsetconstr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (emptysetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (notsubsetI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetRefl) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTrans) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subset2powerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetemptysetimpeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepInPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2IR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionEcases) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectI) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset5) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset3) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectER) =>
% 99.25/13.44 ((
% 99.25/13.44 (disjointsetsI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset4) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (bs114d) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusI) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusER) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusERneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusELneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusILneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusIRneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffE) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg2) =>
% 99.25/13.44 ((
% 99.25/13.44 (secondinupair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairiskpair) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairp) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2E) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsubunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairinpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem3) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair1) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton1) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I2) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsuniq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (theprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstin) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR11) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR12) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR1) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairequniteq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemER) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempaircEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrI) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrERa) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrER) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcImageSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (apProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (app) =>
% 99.25/13.44 ((
% 99.25/13.44 (infuncsetfunc) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcinfuncset) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall1) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp3) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcextLem) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp4) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq2) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2lamEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifp) =>
% 99.25/13.44 ((
% 99.25/13.44 (theeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrue) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueorfalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextT) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTI) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTELcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTERcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT1) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT2) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT3) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTnotintersectT) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementImpComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementSubsetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementInPowersetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (contraSubsetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTcontraSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTILcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTIRcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (intersectInPowersetIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpNotIn1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpInComplement1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTEcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementUnionInPowersetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule0) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_5) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all2) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1SetBreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (choice2fnsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compEex) =>
% 99.25/13.44 ((
% 99.25/13.44 (!!) @ (
% 99.25/13.44 (('#B') @ (
% 99.25/13.44 !!) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 !!))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#C') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])).
% 99.25/13.44 thf(zip_derived_cl158, plain,
% 99.25/13.44 (~ (((emptysetimpfalse) =>
% 99.25/13.44 (((notinemptyset) =>
% 99.25/13.44 (((exuE3e) =>
% 99.25/13.44 (((setext) =>
% 99.25/13.44 (((emptyI) =>
% 99.25/13.44 (((noeltsimpempty) =>
% 99.25/13.44 (((setbeta) =>
% 99.25/13.44 (((nonemptyE1) =>
% 99.25/13.44 (((nonemptyI) =>
% 99.25/13.44 (((nonemptyI1) =>
% 99.25/13.44 (((setadjoinIL) =>
% 99.25/13.44 (((in @ emptyset @
% 99.25/13.44 (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.44 (((setadjoinIR) =>
% 99.25/13.44 (((setadjoinE) =>
% 99.25/13.44 (((setadjoinOr) =>
% 99.25/13.44 (((setoftrueEq) =>
% 99.25/13.44 (((powersetI) =>
% 99.25/13.44 (((emptyinPowerset) =>
% 99.25/13.44 (((emptyInPowerset) =>
% 99.25/13.44 (((powersetE) =>
% 99.25/13.44 (((setunionI) =>
% 99.25/13.44 (((setunionE) =>
% 99.25/13.44 (((subPowSU) =>
% 99.25/13.44 (((exuE2) =>
% 99.25/13.44 (((nonemptyImpWitness) =>
% 99.25/13.44 (((uniqinunit) =>
% 99.25/13.44 (((notinsingleton) =>
% 99.25/13.44 (((eqinunit) =>
% 99.25/13.44 (((singletonsswitch) =>
% 99.25/13.44 (((upairsetE) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsetIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsetIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (emptyE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (vacuousDall) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan3) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan4) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2setI) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2set2propI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdexE) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdallE) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI3) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inCongP) =>
% 99.25/13.44 ((
% 99.25/13.44 (in__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuE3u) =>
% 99.25/13.44 ((
% 99.25/13.44 (exu__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoin__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (powerset__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunion__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuEu) =>
% 99.25/13.44 ((
% 99.25/13.44 (descr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (dsetconstr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (emptysetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (notsubsetI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetRefl) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTrans) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subset2powerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetemptysetimpeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepInPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2IR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionEcases) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectI) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset5) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset3) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectER) =>
% 99.25/13.44 ((
% 99.25/13.44 (disjointsetsI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset4) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (bs114d) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusI) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusER) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusERneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusELneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusILneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusIRneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffE) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg2) =>
% 99.25/13.44 ((
% 99.25/13.44 (secondinupair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairiskpair) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairp) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2E) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsubunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairinpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem3) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair1) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton1) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I2) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsuniq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (theprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstin) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR11) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR12) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR1) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairequniteq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemER) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempaircEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrI) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrERa) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrER) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcImageSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (apProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (app) =>
% 99.25/13.44 ((
% 99.25/13.44 (infuncsetfunc) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcinfuncset) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall1) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp3) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcextLem) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp4) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq2) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2lamEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifp) =>
% 99.25/13.44 ((
% 99.25/13.44 (theeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrue) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueorfalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextT) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTI) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTELcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTERcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT1) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT2) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT3) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTnotintersectT) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementImpComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementSubsetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementInPowersetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (contraSubsetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTcontraSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTILcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTIRcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (intersectInPowersetIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpNotIn1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpInComplement1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTEcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementUnionInPowersetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule0) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_5) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all2) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1SetBreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (choice2fnsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compEex) =>
% 99.25/13.44 ((
% 99.25/13.44 (!!) @ (
% 99.25/13.44 (('#B') @ (
% 99.25/13.44 !!) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 !!))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#C') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])).
% 99.25/13.44 thf(zip_derived_cl174, plain,
% 99.25/13.44 (~ (((notinemptyset) =>
% 99.25/13.44 (((exuE3e) =>
% 99.25/13.44 (((setext) =>
% 99.25/13.44 (((emptyI) =>
% 99.25/13.44 (((noeltsimpempty) =>
% 99.25/13.44 (((setbeta) =>
% 99.25/13.44 (((nonemptyE1) =>
% 99.25/13.44 (((nonemptyI) =>
% 99.25/13.44 (((nonemptyI1) =>
% 99.25/13.44 (((setadjoinIL) =>
% 99.25/13.44 (((in @ emptyset @
% 99.25/13.44 (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.44 (((setadjoinIR) =>
% 99.25/13.44 (((setadjoinE) =>
% 99.25/13.44 (((setadjoinOr) =>
% 99.25/13.44 (((setoftrueEq) =>
% 99.25/13.44 (((powersetI) =>
% 99.25/13.44 (((emptyinPowerset) =>
% 99.25/13.44 (((emptyInPowerset) =>
% 99.25/13.44 (((powersetE) =>
% 99.25/13.44 (((setunionI) =>
% 99.25/13.44 (((setunionE) =>
% 99.25/13.44 (((subPowSU) =>
% 99.25/13.44 (((exuE2) =>
% 99.25/13.44 (((nonemptyImpWitness) =>
% 99.25/13.44 (((uniqinunit) =>
% 99.25/13.44 (((notinsingleton) =>
% 99.25/13.44 (((eqinunit) =>
% 99.25/13.44 (((singletonsswitch) =>
% 99.25/13.44 (((upairsetE) =>
% 99.25/13.44 (((upairsetIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsetIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (emptyE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (vacuousDall) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan3) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan4) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2setI) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2set2propI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdexE) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdallE) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI3) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inCongP) =>
% 99.25/13.44 ((
% 99.25/13.44 (in__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuE3u) =>
% 99.25/13.44 ((
% 99.25/13.44 (exu__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoin__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (powerset__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunion__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuEu) =>
% 99.25/13.44 ((
% 99.25/13.44 (descr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (dsetconstr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (emptysetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (notsubsetI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetRefl) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTrans) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subset2powerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetemptysetimpeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepInPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2IR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionEcases) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectI) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset5) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset3) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectER) =>
% 99.25/13.44 ((
% 99.25/13.44 (disjointsetsI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset4) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (bs114d) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusI) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusER) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusERneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusELneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusILneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusIRneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffE) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg2) =>
% 99.25/13.44 ((
% 99.25/13.44 (secondinupair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairiskpair) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairp) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2E) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsubunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairinpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem3) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair1) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton1) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I2) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsuniq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (theprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstin) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR11) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR12) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR1) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairequniteq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemER) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempaircEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrI) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrERa) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrER) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcImageSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (apProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (app) =>
% 99.25/13.44 ((
% 99.25/13.44 (infuncsetfunc) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcinfuncset) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall1) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp3) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcextLem) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp4) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq2) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2lamEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifp) =>
% 99.25/13.44 ((
% 99.25/13.44 (theeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrue) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueorfalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextT) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTI) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTELcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTERcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT1) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT2) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT3) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTnotintersectT) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementImpComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementSubsetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementInPowersetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (contraSubsetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTcontraSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTILcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTIRcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (intersectInPowersetIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpNotIn1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpInComplement1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTEcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementUnionInPowersetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule0) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_5) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all2) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1SetBreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (choice2fnsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compEex) =>
% 99.25/13.44 ((
% 99.25/13.44 (!!) @ (
% 99.25/13.44 (('#B') @ (
% 99.25/13.44 !!) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 !!))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#C') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])).
% 99.25/13.44 thf(zip_derived_cl189, plain,
% 99.25/13.44 (~ (((exuE3e) =>
% 99.25/13.44 (((setext) =>
% 99.25/13.44 (((emptyI) =>
% 99.25/13.44 (((noeltsimpempty) =>
% 99.25/13.44 (((setbeta) =>
% 99.25/13.44 (((nonemptyE1) =>
% 99.25/13.44 (((nonemptyI) =>
% 99.25/13.44 (((nonemptyI1) =>
% 99.25/13.44 (((setadjoinIL) =>
% 99.25/13.44 (((in @ emptyset @
% 99.25/13.44 (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.44 (((setadjoinIR) =>
% 99.25/13.44 (((setadjoinE) =>
% 99.25/13.44 (((setadjoinOr) =>
% 99.25/13.44 (((setoftrueEq) =>
% 99.25/13.44 (((powersetI) =>
% 99.25/13.44 (((emptyinPowerset) =>
% 99.25/13.44 (((emptyInPowerset) =>
% 99.25/13.44 (((powersetE) =>
% 99.25/13.44 (((setunionI) =>
% 99.25/13.44 (((setunionE) =>
% 99.25/13.44 (((subPowSU) =>
% 99.25/13.44 (((exuE2) =>
% 99.25/13.44 (((nonemptyImpWitness) =>
% 99.25/13.44 (((uniqinunit) =>
% 99.25/13.44 (((notinsingleton) =>
% 99.25/13.44 (((eqinunit) =>
% 99.25/13.44 (((singletonsswitch) =>
% 99.25/13.44 (((upairsetE) =>
% 99.25/13.44 (((upairsetIL) =>
% 99.25/13.44 (((upairsetIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (emptyE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (vacuousDall) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan3) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan4) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2setI) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2set2propI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdexE) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdallE) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI3) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inCongP) =>
% 99.25/13.44 ((
% 99.25/13.44 (in__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuE3u) =>
% 99.25/13.44 ((
% 99.25/13.44 (exu__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoin__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (powerset__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunion__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuEu) =>
% 99.25/13.44 ((
% 99.25/13.44 (descr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (dsetconstr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (emptysetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (notsubsetI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetRefl) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTrans) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subset2powerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetemptysetimpeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepInPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2IR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionEcases) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectI) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset5) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset3) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectER) =>
% 99.25/13.44 ((
% 99.25/13.44 (disjointsetsI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset4) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (bs114d) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusI) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusER) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusERneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusELneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusILneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusIRneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffE) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg2) =>
% 99.25/13.44 ((
% 99.25/13.44 (secondinupair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairiskpair) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairp) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2E) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsubunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairinpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem3) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair1) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton1) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I2) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsuniq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (theprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstin) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR11) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR12) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR1) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairequniteq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemER) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempaircEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrI) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrERa) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrER) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcImageSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (apProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (app) =>
% 99.25/13.44 ((
% 99.25/13.44 (infuncsetfunc) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcinfuncset) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall1) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp3) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcextLem) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp4) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq2) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2lamEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifp) =>
% 99.25/13.44 ((
% 99.25/13.44 (theeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrue) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueorfalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextT) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTI) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTELcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTERcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT1) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT2) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT3) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTnotintersectT) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementImpComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementSubsetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementInPowersetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (contraSubsetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTcontraSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTILcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTIRcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (intersectInPowersetIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpNotIn1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpInComplement1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTEcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementUnionInPowersetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule0) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_5) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all2) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1SetBreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (choice2fnsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compEex) =>
% 99.25/13.44 ((
% 99.25/13.44 (!!) @ (
% 99.25/13.44 (('#B') @ (
% 99.25/13.44 !!) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 !!))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#C') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl174])).
% 99.25/13.44 thf(zip_derived_cl206, plain,
% 99.25/13.44 (~ (((setext) =>
% 99.25/13.44 (((emptyI) =>
% 99.25/13.44 (((noeltsimpempty) =>
% 99.25/13.44 (((setbeta) =>
% 99.25/13.44 (((nonemptyE1) =>
% 99.25/13.44 (((nonemptyI) =>
% 99.25/13.44 (((nonemptyI1) =>
% 99.25/13.44 (((setadjoinIL) =>
% 99.25/13.44 (((in @ emptyset @
% 99.25/13.44 (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.44 (((setadjoinIR) =>
% 99.25/13.44 (((setadjoinE) =>
% 99.25/13.44 (((setadjoinOr) =>
% 99.25/13.44 (((setoftrueEq) =>
% 99.25/13.44 (((powersetI) =>
% 99.25/13.44 (((emptyinPowerset) =>
% 99.25/13.44 (((emptyInPowerset) =>
% 99.25/13.44 (((powersetE) =>
% 99.25/13.44 (((setunionI) =>
% 99.25/13.44 (((setunionE) =>
% 99.25/13.44 (((subPowSU) =>
% 99.25/13.44 (((exuE2) =>
% 99.25/13.44 (((nonemptyImpWitness) =>
% 99.25/13.44 (((uniqinunit) =>
% 99.25/13.44 (((notinsingleton) =>
% 99.25/13.44 (((eqinunit) =>
% 99.25/13.44 (((singletonsswitch) =>
% 99.25/13.44 (((upairsetE) =>
% 99.25/13.44 (((upairsetIL) =>
% 99.25/13.44 (((upairsetIR) =>
% 99.25/13.44 (((emptyE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (vacuousDall) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan3) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan4) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2setI) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2set2propI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdexE) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdallE) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI3) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inCongP) =>
% 99.25/13.44 ((
% 99.25/13.44 (in__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuE3u) =>
% 99.25/13.44 ((
% 99.25/13.44 (exu__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoin__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (powerset__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunion__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuEu) =>
% 99.25/13.44 ((
% 99.25/13.44 (descr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (dsetconstr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (emptysetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (notsubsetI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetRefl) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTrans) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subset2powerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetemptysetimpeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepInPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2IR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionEcases) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectI) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset5) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset3) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectER) =>
% 99.25/13.44 ((
% 99.25/13.44 (disjointsetsI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset4) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (bs114d) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusI) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusER) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusERneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusELneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusILneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusIRneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffE) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg2) =>
% 99.25/13.44 ((
% 99.25/13.44 (secondinupair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairiskpair) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairp) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2E) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsubunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairinpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem3) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair1) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton1) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I2) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsuniq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (theprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstin) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR11) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR12) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR1) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairequniteq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemER) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempaircEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrI) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrERa) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrER) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcImageSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (apProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (app) =>
% 99.25/13.44 ((
% 99.25/13.44 (infuncsetfunc) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcinfuncset) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall1) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp3) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcextLem) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp4) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq2) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2lamEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifp) =>
% 99.25/13.44 ((
% 99.25/13.44 (theeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrue) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueorfalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextT) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTI) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTELcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTERcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT1) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT2) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT3) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTnotintersectT) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementImpComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementSubsetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementInPowersetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (contraSubsetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTcontraSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTILcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTIRcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (intersectInPowersetIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpNotIn1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpInComplement1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTEcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementUnionInPowersetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule0) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_5) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all2) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1SetBreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (choice2fnsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compEex) =>
% 99.25/13.44 ((
% 99.25/13.44 (!!) @ (
% 99.25/13.44 (('#B') @ (
% 99.25/13.44 !!) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 !!))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#C') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl189])).
% 99.25/13.44 thf(zip_derived_cl222, plain,
% 99.25/13.44 (~ (((emptyI) =>
% 99.25/13.44 (((noeltsimpempty) =>
% 99.25/13.44 (((setbeta) =>
% 99.25/13.44 (((nonemptyE1) =>
% 99.25/13.44 (((nonemptyI) =>
% 99.25/13.44 (((nonemptyI1) =>
% 99.25/13.44 (((setadjoinIL) =>
% 99.25/13.44 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.44 (((setadjoinIR) =>
% 99.25/13.44 (((setadjoinE) =>
% 99.25/13.44 (((setadjoinOr) =>
% 99.25/13.44 (((setoftrueEq) =>
% 99.25/13.44 (((powersetI) =>
% 99.25/13.44 (((emptyinPowerset) =>
% 99.25/13.44 (((emptyInPowerset) =>
% 99.25/13.44 (((powersetE) =>
% 99.25/13.44 (((setunionI) =>
% 99.25/13.44 (((setunionE) =>
% 99.25/13.44 (((subPowSU) =>
% 99.25/13.44 (((exuE2) =>
% 99.25/13.44 (((nonemptyImpWitness) =>
% 99.25/13.44 (((uniqinunit) =>
% 99.25/13.44 (((notinsingleton) =>
% 99.25/13.44 (((eqinunit) =>
% 99.25/13.44 (((singletonsswitch) =>
% 99.25/13.44 (((upairsetE) =>
% 99.25/13.44 (((upairsetIL) =>
% 99.25/13.44 (((upairsetIR) =>
% 99.25/13.44 (((emptyE1) =>
% 99.25/13.44 (((vacuousDall) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan3) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan4) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2setI) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2set2propI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdexE) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdallE) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI3) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inCongP) =>
% 99.25/13.44 ((
% 99.25/13.44 (in__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuE3u) =>
% 99.25/13.44 ((
% 99.25/13.44 (exu__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoin__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (powerset__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunion__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuEu) =>
% 99.25/13.44 ((
% 99.25/13.44 (descr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (dsetconstr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (emptysetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (notsubsetI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetRefl) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTrans) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subset2powerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetemptysetimpeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepInPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2IR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionEcases) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectI) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset5) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset3) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectER) =>
% 99.25/13.44 ((
% 99.25/13.44 (disjointsetsI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset4) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (bs114d) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusI) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusER) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusERneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusELneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusILneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusIRneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffE) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg2) =>
% 99.25/13.44 ((
% 99.25/13.44 (secondinupair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairiskpair) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairp) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2E) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsubunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairinpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem3) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair1) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton1) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I2) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsuniq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (theprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstin) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR11) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR12) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR1) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairequniteq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemER) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempaircEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrI) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrERa) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrEL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrER) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcImageSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (apProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (app) =>
% 99.25/13.44 ((
% 99.25/13.44 (infuncsetfunc) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcinfuncset) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamProp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lamp) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2p) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall1) =>
% 99.25/13.44 ((
% 99.25/13.44 (brelnall2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp3) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcextLem) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcGraphProp4) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext) =>
% 99.25/13.44 ((
% 99.25/13.44 (funcext2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ap2apEq2) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta1) =>
% 99.25/13.44 ((
% 99.25/13.44 (lam2lamEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (beta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eta2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalseProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp1) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueProp2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifSingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ifp) =>
% 99.25/13.44 ((
% 99.25/13.44 (theeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrue) =>
% 99.25/13.44 ((
% 99.25/13.44 (iffalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (iftrueorfalse) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementT_lem) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextT) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTI) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTELcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectTERcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT1) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT2) =>
% 99.25/13.44 ((
% 99.25/13.44 (contrasubsetT3) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub1) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (doubleComplementEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTnotintersectT) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementImpComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementSubsetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementInPowersetComplementIntersect) =>
% 99.25/13.44 ((
% 99.25/13.44 (contraSubsetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementTcontraSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTILcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTIRcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInUnion2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inIntersectImpInIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (intersectInPowersetIntersectUnions) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpNotIn1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inComplementUnionImpInComplement1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionTEcontra) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a1) =>
% 99.25/13.44 ((
% 99.25/13.44 (complementUnionInPowersetComplement) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2a) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b2) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2b) =>
% 99.25/13.44 ((
% 99.25/13.44 (demorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule0) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz13rule4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_1) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_2) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_3) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_4) =>
% 99.25/13.44 ((
% 99.25/13.44 (woz1_5) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all2) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1SetBreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (choice2fnsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1all1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqbreln1) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1invE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compI) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compE) =>
% 99.25/13.44 ((
% 99.25/13.44 (breln1compEex) =>
% 99.25/13.44 ((
% 99.25/13.44 (!!) @ (
% 99.25/13.44 (('#B') @ (
% 99.25/13.44 !!) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 !!))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#S') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#S') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 =>))) @
% 99.25/13.44 breln1)))))) @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#C') @ (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 (
% 99.25/13.44 (
% 99.25/13.44 ('#B') @ (
% 99.25/13.44 '#B') @
% 99.25/13.44 breln1)))) @
% 99.25/13.44 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])).
% 99.25/13.44 thf(zip_derived_cl236, plain,
% 99.25/13.44 (~ (((noeltsimpempty) =>
% 99.25/13.44 (((setbeta) =>
% 99.25/13.44 (((nonemptyE1) =>
% 99.25/13.44 (((nonemptyI) =>
% 99.25/13.44 (((nonemptyI1) =>
% 99.25/13.44 (((setadjoinIL) =>
% 99.25/13.44 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.44 (((setadjoinIR) =>
% 99.25/13.44 (((setadjoinE) =>
% 99.25/13.44 (((setadjoinOr) =>
% 99.25/13.44 (((setoftrueEq) =>
% 99.25/13.44 (((powersetI) =>
% 99.25/13.44 (((emptyinPowerset) =>
% 99.25/13.44 (((emptyInPowerset) =>
% 99.25/13.44 (((powersetE) =>
% 99.25/13.44 (((setunionI) =>
% 99.25/13.44 (((setunionE) =>
% 99.25/13.44 (((subPowSU) =>
% 99.25/13.44 (((exuE2) =>
% 99.25/13.44 (((nonemptyImpWitness) =>
% 99.25/13.44 (((uniqinunit) =>
% 99.25/13.44 (((notinsingleton) =>
% 99.25/13.44 (((eqinunit) =>
% 99.25/13.44 (((singletonsswitch) =>
% 99.25/13.44 (((upairsetE) =>
% 99.25/13.44 (((upairsetIL) =>
% 99.25/13.44 (((upairsetIR) =>
% 99.25/13.44 (((emptyE1) =>
% 99.25/13.44 (((vacuousDall) =>
% 99.25/13.44 (((quantDeMorgan1) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan2) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan3) =>
% 99.25/13.44 ((
% 99.25/13.44 (quantDeMorgan4) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2setI) =>
% 99.25/13.44 ((
% 99.25/13.44 (prop2set2propI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdexE) =>
% 99.25/13.44 ((
% 99.25/13.44 (notdallE) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI3) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (inCongP) =>
% 99.25/13.44 ((
% 99.25/13.44 (in__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuE3u) =>
% 99.25/13.44 ((
% 99.25/13.44 (exu__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoin__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (powerset__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunion__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (exuEu) =>
% 99.25/13.44 ((
% 99.25/13.44 (descr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (dsetconstr__Cong) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (eqimpsubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (emptysetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (notsubsetI) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (notequalI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetRefl) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetTrans) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setadjoinSub2) =>
% 99.25/13.44 ((
% 99.25/13.44 (subset2powerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (setextsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (subsetemptysetimpeq) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetE1) =>
% 99.25/13.44 ((
% 99.25/13.44 (inPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (powersetsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepInPowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (sepSubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2IR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionEcases) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionE) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binunionRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectI) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset5) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset3) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectER) =>
% 99.25/13.44 ((
% 99.25/13.44 (disjointsetsI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectRsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset4) =>
% 99.25/13.44 ((
% 99.25/13.44 (binintersectSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (bs114d) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusI) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusER) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusERneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusELneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusILneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusIRneg) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusLsub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setminusSubset1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffE) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffI2) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg1) =>
% 99.25/13.44 ((
% 99.25/13.44 (symdiffIneg2) =>
% 99.25/13.44 ((
% 99.25/13.44 (secondinupair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairIR) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairiskpair) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairp) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsubset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowerset) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletoninpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairset2E) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairsubunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairinpowunion) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem2) =>
% 99.25/13.44 ((
% 99.25/13.44 (ubforcartprodlem3) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair1) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempair) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionE2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton1) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setunionsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1E1) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I) =>
% 99.25/13.44 ((
% 99.25/13.44 (ex1I2) =>
% 99.25/13.44 ((
% 99.25/13.44 (singletonsuniq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL1) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (theprop) =>
% 99.25/13.44 ((
% 99.25/13.44 (kfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstin) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjL) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR11) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR12) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR1) =>
% 99.25/13.44 ((
% 99.25/13.44 (upairequniteq) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR2) =>
% 99.25/13.44 ((
% 99.25/13.44 (setukpairinjR) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndsingleton) =>
% 99.25/13.44 ((
% 99.25/13.44 (ksndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (kpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndin) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemEL) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairmemER) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodmempaircEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodfstpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodsndpairEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (cartprodpairsurjEq) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrI) =>
% 99.25/13.44 ((
% 99.25/13.44 (dpsetconstrSub) =>
% 99.25/13.44 ((
% 99.25/13.44 (setOfPairsIsBReln) =>
% 99.25/13.44 ((
% 99.25/13.45 (dpsetconstrERa) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrER) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcImageSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (apProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (app) =>
% 99.25/13.45 ((
% 99.25/13.45 (infuncsetfunc) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcinfuncset) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall1) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp3) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcextLem) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp4) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq2) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2lamEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifp) =>
% 99.25/13.45 ((
% 99.25/13.45 (theeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrue) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueorfalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextT) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTI) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTELcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTERcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT1) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT2) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT3) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTnotintersectT) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementImpComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementSubsetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementInPowersetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (contraSubsetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTcontraSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTILcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTIRcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (intersectInPowersetIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpNotIn1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpInComplement1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTEcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementUnionInPowersetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule0) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_5) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all2) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1SetBreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (choice2fnsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compEex) =>
% 99.25/13.45 ((
% 99.25/13.45 (!!) @ (
% 99.25/13.45 (('#B') @ (
% 99.25/13.45 !!) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 !!))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#C') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl222])).
% 99.25/13.45 thf(zip_derived_cl251, plain,
% 99.25/13.45 (~ (((setbeta) =>
% 99.25/13.45 (((nonemptyE1) =>
% 99.25/13.45 (((nonemptyI) =>
% 99.25/13.45 (((nonemptyI1) =>
% 99.25/13.45 (((setadjoinIL) =>
% 99.25/13.45 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.45 (((setadjoinIR) =>
% 99.25/13.45 (((setadjoinE) =>
% 99.25/13.45 (((setadjoinOr) =>
% 99.25/13.45 (((setoftrueEq) =>
% 99.25/13.45 (((powersetI) =>
% 99.25/13.45 (((emptyinPowerset) =>
% 99.25/13.45 (((emptyInPowerset) =>
% 99.25/13.45 (((powersetE) =>
% 99.25/13.45 (((setunionI) =>
% 99.25/13.45 (((setunionE) =>
% 99.25/13.45 (((subPowSU) =>
% 99.25/13.45 (((exuE2) =>
% 99.25/13.45 (((nonemptyImpWitness) =>
% 99.25/13.45 (((uniqinunit) =>
% 99.25/13.45 (((notinsingleton) =>
% 99.25/13.45 (((eqinunit) =>
% 99.25/13.45 (((singletonsswitch) =>
% 99.25/13.45 (((upairsetE) =>
% 99.25/13.45 (((upairsetIL) =>
% 99.25/13.45 (((upairsetIR) =>
% 99.25/13.45 (((emptyE1) =>
% 99.25/13.45 (((vacuousDall) =>
% 99.25/13.45 (((quantDeMorgan1) =>
% 99.25/13.45 (((quantDeMorgan2) =>
% 99.25/13.45 ((
% 99.25/13.45 (quantDeMorgan3) =>
% 99.25/13.45 ((
% 99.25/13.45 (quantDeMorgan4) =>
% 99.25/13.45 ((
% 99.25/13.45 (prop2setI) =>
% 99.25/13.45 ((
% 99.25/13.45 (prop2set2propI) =>
% 99.25/13.45 ((
% 99.25/13.45 (notdexE) =>
% 99.25/13.45 ((
% 99.25/13.45 (notdallE) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI3) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inCongP) =>
% 99.25/13.45 ((
% 99.25/13.45 (in__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuE3u) =>
% 99.25/13.45 ((
% 99.25/13.45 (exu__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoin__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (powerset__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunion__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuEu) =>
% 99.25/13.45 ((
% 99.25/13.45 (descr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (dsetconstr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (emptysetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (notsubsetI) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetRefl) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTrans) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subset2powerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetemptysetimpeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepInPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2IR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionEcases) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectI) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset5) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset3) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectER) =>
% 99.25/13.45 ((
% 99.25/13.45 (disjointsetsI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset4) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (bs114d) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusI) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusER) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusERneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusELneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusILneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusIRneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffE) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg2) =>
% 99.25/13.45 ((
% 99.25/13.45 (secondinupair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairiskpair) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairp) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2E) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairsubunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairinpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem3) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair1) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton1) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I2) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsuniq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (theprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstin) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR11) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR12) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR1) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairequniteq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemER) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempaircEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrI) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrERa) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrER) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcImageSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (apProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (app) =>
% 99.25/13.45 ((
% 99.25/13.45 (infuncsetfunc) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcinfuncset) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall1) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp3) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcextLem) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp4) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq2) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2lamEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifp) =>
% 99.25/13.45 ((
% 99.25/13.45 (theeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrue) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueorfalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextT) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTI) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTELcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTERcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT1) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT2) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT3) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTnotintersectT) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementImpComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementSubsetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementInPowersetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (contraSubsetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTcontraSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTILcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTIRcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (intersectInPowersetIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpNotIn1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpInComplement1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTEcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementUnionInPowersetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule0) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_5) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all2) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1SetBreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (choice2fnsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compEex) =>
% 99.25/13.45 ((
% 99.25/13.45 (!!) @ (
% 99.25/13.45 (('#B') @ (
% 99.25/13.45 !!) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 !!))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#C') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl236])).
% 99.25/13.45 thf(zip_derived_cl264, plain,
% 99.25/13.45 (~ (((nonemptyE1) =>
% 99.25/13.45 (((nonemptyI) =>
% 99.25/13.45 (((nonemptyI1) =>
% 99.25/13.45 (((setadjoinIL) =>
% 99.25/13.45 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.45 (((setadjoinIR) =>
% 99.25/13.45 (((setadjoinE) =>
% 99.25/13.45 (((setadjoinOr) =>
% 99.25/13.45 (((setoftrueEq) =>
% 99.25/13.45 (((powersetI) =>
% 99.25/13.45 (((emptyinPowerset) =>
% 99.25/13.45 (((emptyInPowerset) =>
% 99.25/13.45 (((powersetE) =>
% 99.25/13.45 (((setunionI) =>
% 99.25/13.45 (((setunionE) =>
% 99.25/13.45 (((subPowSU) =>
% 99.25/13.45 (((exuE2) =>
% 99.25/13.45 (((nonemptyImpWitness) =>
% 99.25/13.45 (((uniqinunit) =>
% 99.25/13.45 (((notinsingleton) =>
% 99.25/13.45 (((eqinunit) =>
% 99.25/13.45 (((singletonsswitch) =>
% 99.25/13.45 (((upairsetE) =>
% 99.25/13.45 (((upairsetIL) =>
% 99.25/13.45 (((upairsetIR) =>
% 99.25/13.45 (((emptyE1) =>
% 99.25/13.45 (((vacuousDall) =>
% 99.25/13.45 (((quantDeMorgan1) =>
% 99.25/13.45 (((quantDeMorgan2) =>
% 99.25/13.45 (((quantDeMorgan3) =>
% 99.25/13.45 ((
% 99.25/13.45 (quantDeMorgan4) =>
% 99.25/13.45 ((
% 99.25/13.45 (prop2setI) =>
% 99.25/13.45 ((
% 99.25/13.45 (prop2set2propI) =>
% 99.25/13.45 ((
% 99.25/13.45 (notdexE) =>
% 99.25/13.45 ((
% 99.25/13.45 (notdallE) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI3) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inCongP) =>
% 99.25/13.45 ((
% 99.25/13.45 (in__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuE3u) =>
% 99.25/13.45 ((
% 99.25/13.45 (exu__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoin__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (powerset__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunion__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuEu) =>
% 99.25/13.45 ((
% 99.25/13.45 (descr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (dsetconstr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (emptysetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (notsubsetI) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetRefl) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTrans) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subset2powerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetemptysetimpeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepInPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2IR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionEcases) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectI) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset5) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset3) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectER) =>
% 99.25/13.45 ((
% 99.25/13.45 (disjointsetsI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset4) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (bs114d) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusI) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusER) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusERneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusELneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusILneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusIRneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffE) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg2) =>
% 99.25/13.45 ((
% 99.25/13.45 (secondinupair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairiskpair) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairp) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2E) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairsubunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairinpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem3) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair1) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton1) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I2) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsuniq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (theprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstin) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR11) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR12) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR1) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairequniteq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemER) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempaircEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrI) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrERa) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrER) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcImageSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (apProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (app) =>
% 99.25/13.45 ((
% 99.25/13.45 (infuncsetfunc) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcinfuncset) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall1) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp3) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcextLem) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp4) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq2) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2lamEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifp) =>
% 99.25/13.45 ((
% 99.25/13.45 (theeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrue) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueorfalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextT) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTI) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTELcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTERcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT1) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT2) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT3) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTnotintersectT) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementImpComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementSubsetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementInPowersetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (contraSubsetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTcontraSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTILcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTIRcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (intersectInPowersetIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpNotIn1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpInComplement1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTEcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementUnionInPowersetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule0) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_5) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all2) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1SetBreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (choice2fnsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compEex) =>
% 99.25/13.45 ((
% 99.25/13.45 (!!) @ (
% 99.25/13.45 (('#B') @ (
% 99.25/13.45 !!) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 !!))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#C') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl251])).
% 99.25/13.45 thf(zip_derived_cl280, plain,
% 99.25/13.45 (~ (((nonemptyI) =>
% 99.25/13.45 (((nonemptyI1) =>
% 99.25/13.45 (((setadjoinIL) =>
% 99.25/13.45 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.45 (((setadjoinIR) =>
% 99.25/13.45 (((setadjoinE) =>
% 99.25/13.45 (((setadjoinOr) =>
% 99.25/13.45 (((setoftrueEq) =>
% 99.25/13.45 (((powersetI) =>
% 99.25/13.45 (((emptyinPowerset) =>
% 99.25/13.45 (((emptyInPowerset) =>
% 99.25/13.45 (((powersetE) =>
% 99.25/13.45 (((setunionI) =>
% 99.25/13.45 (((setunionE) =>
% 99.25/13.45 (((subPowSU) =>
% 99.25/13.45 (((exuE2) =>
% 99.25/13.45 (((nonemptyImpWitness) =>
% 99.25/13.45 (((uniqinunit) =>
% 99.25/13.45 (((notinsingleton) =>
% 99.25/13.45 (((eqinunit) =>
% 99.25/13.45 (((singletonsswitch) =>
% 99.25/13.45 (((upairsetE) =>
% 99.25/13.45 (((upairsetIL) =>
% 99.25/13.45 (((upairsetIR) =>
% 99.25/13.45 (((emptyE1) =>
% 99.25/13.45 (((vacuousDall) =>
% 99.25/13.45 (((quantDeMorgan1) =>
% 99.25/13.45 (((quantDeMorgan2) =>
% 99.25/13.45 (((quantDeMorgan3) =>
% 99.25/13.45 (((quantDeMorgan4) =>
% 99.25/13.45 ((
% 99.25/13.45 (prop2setI) =>
% 99.25/13.45 ((
% 99.25/13.45 (prop2set2propI) =>
% 99.25/13.45 ((
% 99.25/13.45 (notdexE) =>
% 99.25/13.45 ((
% 99.25/13.45 (notdallE) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI3) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inCongP) =>
% 99.25/13.45 ((
% 99.25/13.45 (in__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuE3u) =>
% 99.25/13.45 ((
% 99.25/13.45 (exu__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoin__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (powerset__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunion__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuEu) =>
% 99.25/13.45 ((
% 99.25/13.45 (descr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (dsetconstr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (emptysetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (notsubsetI) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetRefl) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTrans) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subset2powerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetemptysetimpeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepInPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2IR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionEcases) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectI) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset5) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset3) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectER) =>
% 99.25/13.45 ((
% 99.25/13.45 (disjointsetsI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset4) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (bs114d) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusI) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusER) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusERneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusELneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusILneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusIRneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffE) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg2) =>
% 99.25/13.45 ((
% 99.25/13.45 (secondinupair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairiskpair) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairp) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2E) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairsubunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairinpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem3) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair1) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton1) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I2) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsuniq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (theprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstin) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR11) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR12) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR1) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairequniteq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemER) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempaircEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrI) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrERa) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrER) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcImageSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (apProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (app) =>
% 99.25/13.45 ((
% 99.25/13.45 (infuncsetfunc) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcinfuncset) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall1) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp3) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcextLem) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp4) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq2) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2lamEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifp) =>
% 99.25/13.45 ((
% 99.25/13.45 (theeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrue) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueorfalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextT) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTI) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTELcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTERcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT1) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT2) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT3) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTnotintersectT) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementImpComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementSubsetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementInPowersetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (contraSubsetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTcontraSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTILcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTIRcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (intersectInPowersetIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpNotIn1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpInComplement1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTEcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementUnionInPowersetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule0) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_5) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all2) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1SetBreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (choice2fnsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compEex) =>
% 99.25/13.45 ((
% 99.25/13.45 (!!) @ (
% 99.25/13.45 (('#B') @ (
% 99.25/13.45 !!) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 !!))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#C') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl264])).
% 99.25/13.45 thf(zip_derived_cl293, plain,
% 99.25/13.45 (~ (((nonemptyI1) =>
% 99.25/13.45 (((setadjoinIL) =>
% 99.25/13.45 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.45 (((setadjoinIR) =>
% 99.25/13.45 (((setadjoinE) =>
% 99.25/13.45 (((setadjoinOr) =>
% 99.25/13.45 (((setoftrueEq) =>
% 99.25/13.45 (((powersetI) =>
% 99.25/13.45 (((emptyinPowerset) =>
% 99.25/13.45 (((emptyInPowerset) =>
% 99.25/13.45 (((powersetE) =>
% 99.25/13.45 (((setunionI) =>
% 99.25/13.45 (((setunionE) =>
% 99.25/13.45 (((subPowSU) =>
% 99.25/13.45 (((exuE2) =>
% 99.25/13.45 (((nonemptyImpWitness) =>
% 99.25/13.45 (((uniqinunit) =>
% 99.25/13.45 (((notinsingleton) =>
% 99.25/13.45 (((eqinunit) =>
% 99.25/13.45 (((singletonsswitch) =>
% 99.25/13.45 (((upairsetE) =>
% 99.25/13.45 (((upairsetIL) =>
% 99.25/13.45 (((upairsetIR) =>
% 99.25/13.45 (((emptyE1) =>
% 99.25/13.45 (((vacuousDall) =>
% 99.25/13.45 (((quantDeMorgan1) =>
% 99.25/13.45 (((quantDeMorgan2) =>
% 99.25/13.45 (((quantDeMorgan3) =>
% 99.25/13.45 (((quantDeMorgan4) =>
% 99.25/13.45 (((prop2setI) =>
% 99.25/13.45 ((
% 99.25/13.45 (prop2set2propI) =>
% 99.25/13.45 ((
% 99.25/13.45 (notdexE) =>
% 99.25/13.45 ((
% 99.25/13.45 (notdallE) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI3) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inCongP) =>
% 99.25/13.45 ((
% 99.25/13.45 (in__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuE3u) =>
% 99.25/13.45 ((
% 99.25/13.45 (exu__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoin__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (powerset__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunion__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuEu) =>
% 99.25/13.45 ((
% 99.25/13.45 (descr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (dsetconstr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (emptysetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (notsubsetI) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetRefl) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTrans) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subset2powerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetemptysetimpeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepInPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2IR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionEcases) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectI) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset5) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset3) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectER) =>
% 99.25/13.45 ((
% 99.25/13.45 (disjointsetsI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset4) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (bs114d) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusI) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusER) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusERneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusELneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusILneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusIRneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffE) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg2) =>
% 99.25/13.45 ((
% 99.25/13.45 (secondinupair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairiskpair) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairp) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2E) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairsubunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairinpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem3) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair1) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton1) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I2) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsuniq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (theprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstin) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR11) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR12) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR1) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairequniteq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemER) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempaircEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrI) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrERa) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrER) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcImageSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (apProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (app) =>
% 99.25/13.45 ((
% 99.25/13.45 (infuncsetfunc) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcinfuncset) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall1) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp3) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcextLem) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp4) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq2) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2lamEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifp) =>
% 99.25/13.45 ((
% 99.25/13.45 (theeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrue) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueorfalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextT) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTI) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTELcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTERcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT1) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT2) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT3) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTnotintersectT) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementImpComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementSubsetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementInPowersetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (contraSubsetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTcontraSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTILcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTIRcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (intersectInPowersetIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpNotIn1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpInComplement1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTEcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementUnionInPowersetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule0) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_5) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all2) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1SetBreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (choice2fnsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compEex) =>
% 99.25/13.45 ((
% 99.25/13.45 (!!) @ (
% 99.25/13.45 (('#B') @ (
% 99.25/13.45 !!) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 !!))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#C') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl280])).
% 99.25/13.45 thf(zip_derived_cl307, plain,
% 99.25/13.45 (~ (((setadjoinIL) =>
% 99.25/13.45 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.45 (((setadjoinIR) =>
% 99.25/13.45 (((setadjoinE) =>
% 99.25/13.45 (((setadjoinOr) =>
% 99.25/13.45 (((setoftrueEq) =>
% 99.25/13.45 (((powersetI) =>
% 99.25/13.45 (((emptyinPowerset) =>
% 99.25/13.45 (((emptyInPowerset) =>
% 99.25/13.45 (((powersetE) =>
% 99.25/13.45 (((setunionI) =>
% 99.25/13.45 (((setunionE) =>
% 99.25/13.45 (((subPowSU) =>
% 99.25/13.45 (((exuE2) =>
% 99.25/13.45 (((nonemptyImpWitness) =>
% 99.25/13.45 (((uniqinunit) =>
% 99.25/13.45 (((notinsingleton) =>
% 99.25/13.45 (((eqinunit) =>
% 99.25/13.45 (((singletonsswitch) =>
% 99.25/13.45 (((upairsetE) =>
% 99.25/13.45 (((upairsetIL) =>
% 99.25/13.45 (((upairsetIR) =>
% 99.25/13.45 (((emptyE1) =>
% 99.25/13.45 (((vacuousDall) =>
% 99.25/13.45 (((quantDeMorgan1) =>
% 99.25/13.45 (((quantDeMorgan2) =>
% 99.25/13.45 (((quantDeMorgan3) =>
% 99.25/13.45 (((quantDeMorgan4) =>
% 99.25/13.45 (((prop2setI) =>
% 99.25/13.45 (((prop2set2propI) =>
% 99.25/13.45 ((
% 99.25/13.45 (notdexE) =>
% 99.25/13.45 ((
% 99.25/13.45 (notdallE) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI3) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inCongP) =>
% 99.25/13.45 ((
% 99.25/13.45 (in__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuE3u) =>
% 99.25/13.45 ((
% 99.25/13.45 (exu__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoin__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (powerset__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunion__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuEu) =>
% 99.25/13.45 ((
% 99.25/13.45 (descr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (dsetconstr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (emptysetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (notsubsetI) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetRefl) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTrans) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subset2powerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetemptysetimpeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepInPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2IR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionEcases) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectI) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset5) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset3) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectER) =>
% 99.25/13.45 ((
% 99.25/13.45 (disjointsetsI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset4) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (bs114d) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusI) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusER) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusERneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusELneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusILneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusIRneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffE) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg2) =>
% 99.25/13.45 ((
% 99.25/13.45 (secondinupair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairiskpair) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairp) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2E) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairsubunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairinpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem3) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair1) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton1) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I2) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsuniq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (theprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstin) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR11) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR12) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR1) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairequniteq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemER) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempaircEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrI) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrERa) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrER) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcImageSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (apProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (app) =>
% 99.25/13.45 ((
% 99.25/13.45 (infuncsetfunc) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcinfuncset) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall1) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp3) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcextLem) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp4) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq2) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2lamEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifp) =>
% 99.25/13.45 ((
% 99.25/13.45 (theeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrue) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueorfalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextT) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTI) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTELcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTERcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT1) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT2) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT3) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTnotintersectT) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementImpComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementSubsetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementInPowersetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (contraSubsetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTcontraSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTILcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTIRcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (intersectInPowersetIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpNotIn1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpInComplement1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTEcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementUnionInPowersetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule0) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_5) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all2) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1SetBreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (choice2fnsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compEex) =>
% 99.25/13.45 ((
% 99.25/13.45 (!!) @ (
% 99.25/13.45 (('#B') @ (
% 99.25/13.45 !!) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 !!))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#C') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl293])).
% 99.25/13.45 thf(zip_derived_cl322, plain,
% 99.25/13.45 (~ (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 99.25/13.45 (((setadjoinIR) =>
% 99.25/13.45 (((setadjoinE) =>
% 99.25/13.45 (((setadjoinOr) =>
% 99.25/13.45 (((setoftrueEq) =>
% 99.25/13.45 (((powersetI) =>
% 99.25/13.45 (((emptyinPowerset) =>
% 99.25/13.45 (((emptyInPowerset) =>
% 99.25/13.45 (((powersetE) =>
% 99.25/13.45 (((setunionI) =>
% 99.25/13.45 (((setunionE) =>
% 99.25/13.45 (((subPowSU) =>
% 99.25/13.45 (((exuE2) =>
% 99.25/13.45 (((nonemptyImpWitness) =>
% 99.25/13.45 (((uniqinunit) =>
% 99.25/13.45 (((notinsingleton) =>
% 99.25/13.45 (((eqinunit) =>
% 99.25/13.45 (((singletonsswitch) =>
% 99.25/13.45 (((upairsetE) =>
% 99.25/13.45 (((upairsetIL) =>
% 99.25/13.45 (((upairsetIR) =>
% 99.25/13.45 (((emptyE1) =>
% 99.25/13.45 (((vacuousDall) =>
% 99.25/13.45 (((quantDeMorgan1) =>
% 99.25/13.45 (((quantDeMorgan2) =>
% 99.25/13.45 (((quantDeMorgan3) =>
% 99.25/13.45 (((quantDeMorgan4) =>
% 99.25/13.45 (((prop2setI) =>
% 99.25/13.45 (((prop2set2propI) =>
% 99.25/13.45 (((notdexE) =>
% 99.25/13.45 ((
% 99.25/13.45 (notdallE) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI3) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inCongP) =>
% 99.25/13.45 ((
% 99.25/13.45 (in__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuE3u) =>
% 99.25/13.45 ((
% 99.25/13.45 (exu__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoin__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (powerset__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunion__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuEu) =>
% 99.25/13.45 ((
% 99.25/13.45 (descr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (dsetconstr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (emptysetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (notsubsetI) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetRefl) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTrans) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subset2powerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetemptysetimpeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepInPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2IR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionEcases) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectI) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset5) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset3) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectER) =>
% 99.25/13.45 ((
% 99.25/13.45 (disjointsetsI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset4) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (bs114d) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusI) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusER) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusERneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusELneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusILneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusIRneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffE) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg2) =>
% 99.25/13.45 ((
% 99.25/13.45 (secondinupair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairiskpair) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairp) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2E) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairsubunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairinpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem3) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair1) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton1) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I2) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsuniq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (theprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstin) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR11) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR12) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR1) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairequniteq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemER) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempaircEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrI) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrERa) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrER) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcImageSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (apProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (app) =>
% 99.25/13.45 ((
% 99.25/13.45 (infuncsetfunc) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcinfuncset) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall1) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp3) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcextLem) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp4) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq2) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2lamEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifp) =>
% 99.25/13.45 ((
% 99.25/13.45 (theeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrue) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueorfalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextT) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTI) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTELcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTERcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT1) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT2) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT3) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTnotintersectT) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementImpComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementSubsetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementInPowersetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (contraSubsetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTcontraSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTILcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTIRcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (intersectInPowersetIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpNotIn1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpInComplement1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTEcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementUnionInPowersetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule0) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_5) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all2) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1SetBreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (choice2fnsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compEex) =>
% 99.25/13.45 ((
% 99.25/13.45 (!!) @ (
% 99.25/13.45 (('#B') @ (
% 99.25/13.45 !!) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 !!))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#C') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl307])).
% 99.25/13.45 thf(zip_derived_cl337, plain,
% 99.25/13.45 (~ (((setadjoinIR) =>
% 99.25/13.45 (((setadjoinE) =>
% 99.25/13.45 (((setadjoinOr) =>
% 99.25/13.45 (((setoftrueEq) =>
% 99.25/13.45 (((powersetI) =>
% 99.25/13.45 (((emptyinPowerset) =>
% 99.25/13.45 (((emptyInPowerset) =>
% 99.25/13.45 (((powersetE) =>
% 99.25/13.45 (((setunionI) =>
% 99.25/13.45 (((setunionE) =>
% 99.25/13.45 (((subPowSU) =>
% 99.25/13.45 (((exuE2) =>
% 99.25/13.45 (((nonemptyImpWitness) =>
% 99.25/13.45 (((uniqinunit) =>
% 99.25/13.45 (((notinsingleton) =>
% 99.25/13.45 (((eqinunit) =>
% 99.25/13.45 (((singletonsswitch) =>
% 99.25/13.45 (((upairsetE) =>
% 99.25/13.45 (((upairsetIL) =>
% 99.25/13.45 (((upairsetIR) =>
% 99.25/13.45 (((emptyE1) =>
% 99.25/13.45 (((vacuousDall) =>
% 99.25/13.45 (((quantDeMorgan1) =>
% 99.25/13.45 (((quantDeMorgan2) =>
% 99.25/13.45 (((quantDeMorgan3) =>
% 99.25/13.45 (((quantDeMorgan4) =>
% 99.25/13.45 (((prop2setI) =>
% 99.25/13.45 (((prop2set2propI) =>
% 99.25/13.45 (((notdexE) =>
% 99.25/13.45 (((notdallE) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI3) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inCongP) =>
% 99.25/13.45 ((
% 99.25/13.45 (in__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuE3u) =>
% 99.25/13.45 ((
% 99.25/13.45 (exu__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoin__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (powerset__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunion__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuEu) =>
% 99.25/13.45 ((
% 99.25/13.45 (descr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (dsetconstr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (emptysetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (notsubsetI) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetRefl) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTrans) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subset2powerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetemptysetimpeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepInPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2IR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionEcases) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectI) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset5) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset3) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectER) =>
% 99.25/13.45 ((
% 99.25/13.45 (disjointsetsI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset4) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (bs114d) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusI) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusER) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusERneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusELneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusILneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusIRneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffE) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg2) =>
% 99.25/13.45 ((
% 99.25/13.45 (secondinupair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairiskpair) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairp) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2E) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairsubunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairinpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem3) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair1) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton1) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I2) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsuniq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (theprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstin) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR11) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR12) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR1) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairequniteq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemER) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempaircEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrI) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrERa) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrER) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcImageSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (apProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (app) =>
% 99.25/13.45 ((
% 99.25/13.45 (infuncsetfunc) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcinfuncset) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall1) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp3) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcextLem) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp4) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq2) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2lamEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifp) =>
% 99.25/13.45 ((
% 99.25/13.45 (theeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrue) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueorfalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextT) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTI) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTELcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTERcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT1) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT2) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT3) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTnotintersectT) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementImpComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementSubsetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementInPowersetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (contraSubsetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTcontraSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTILcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTIRcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (intersectInPowersetIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpNotIn1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpInComplement1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTEcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementUnionInPowersetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule0) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_5) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all2) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1SetBreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (choice2fnsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compEex) =>
% 99.25/13.45 ((
% 99.25/13.45 (!!) @ (
% 99.25/13.45 (('#B') @ (
% 99.25/13.45 !!) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 !!))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#C') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl322])).
% 99.25/13.45 thf(zip_derived_cl349, plain,
% 99.25/13.45 (~ (((setadjoinE) =>
% 99.25/13.45 (((setadjoinOr) =>
% 99.25/13.45 (((setoftrueEq) =>
% 99.25/13.45 (((powersetI) =>
% 99.25/13.45 (((emptyinPowerset) =>
% 99.25/13.45 (((emptyInPowerset) =>
% 99.25/13.45 (((powersetE) =>
% 99.25/13.45 (((setunionI) =>
% 99.25/13.45 (((setunionE) =>
% 99.25/13.45 (((subPowSU) =>
% 99.25/13.45 (((exuE2) =>
% 99.25/13.45 (((nonemptyImpWitness) =>
% 99.25/13.45 (((uniqinunit) =>
% 99.25/13.45 (((notinsingleton) =>
% 99.25/13.45 (((eqinunit) =>
% 99.25/13.45 (((singletonsswitch) =>
% 99.25/13.45 (((upairsetE) =>
% 99.25/13.45 (((upairsetIL) =>
% 99.25/13.45 (((upairsetIR) =>
% 99.25/13.45 (((emptyE1) =>
% 99.25/13.45 (((vacuousDall) =>
% 99.25/13.45 (((quantDeMorgan1) =>
% 99.25/13.45 (((quantDeMorgan2) =>
% 99.25/13.45 (((quantDeMorgan3) =>
% 99.25/13.45 (((quantDeMorgan4) =>
% 99.25/13.45 (((prop2setI) =>
% 99.25/13.45 (((prop2set2propI) =>
% 99.25/13.45 (((notdexE) =>
% 99.25/13.45 (((notdallE) =>
% 99.25/13.45 (((exuI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI3) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inCongP) =>
% 99.25/13.45 ((
% 99.25/13.45 (in__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuE3u) =>
% 99.25/13.45 ((
% 99.25/13.45 (exu__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoin__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (powerset__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunion__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuEu) =>
% 99.25/13.45 ((
% 99.25/13.45 (descr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (dsetconstr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (emptysetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (notsubsetI) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetRefl) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTrans) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subset2powerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetemptysetimpeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepInPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2IR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionEcases) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectI) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset5) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset3) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectER) =>
% 99.25/13.45 ((
% 99.25/13.45 (disjointsetsI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset4) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (bs114d) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusI) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusER) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusERneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusELneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusILneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusIRneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffE) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg2) =>
% 99.25/13.45 ((
% 99.25/13.45 (secondinupair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairiskpair) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairp) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2E) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairsubunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairinpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem3) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair1) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton1) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I2) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsuniq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (theprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstin) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR11) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR12) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR1) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairequniteq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemER) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempaircEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrI) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrERa) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrER) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcImageSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (apProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (app) =>
% 99.25/13.45 ((
% 99.25/13.45 (infuncsetfunc) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcinfuncset) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall1) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp3) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcextLem) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp4) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq2) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2lamEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifp) =>
% 99.25/13.45 ((
% 99.25/13.45 (theeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrue) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueorfalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextT) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTI) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTELcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTERcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT1) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT2) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT3) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTnotintersectT) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementImpComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementSubsetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementInPowersetComplementIntersect) =>
% 99.25/13.45 ((
% 99.25/13.45 (contraSubsetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTcontraSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTILcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTIRcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInUnion2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inIntersectImpInIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (intersectInPowersetIntersectUnions) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpNotIn1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inComplementUnionImpInComplement1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionTEcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementUnionInPowersetComplement) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan1) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2a) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b2) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2b) =>
% 99.25/13.45 ((
% 99.25/13.45 (demorgan2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule0) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz13rule4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_1) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_2) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_3) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_4) =>
% 99.25/13.45 ((
% 99.25/13.45 (woz1_5) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all2) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1SetBreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (choice2fnsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1all1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln1) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1invE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compI) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compE) =>
% 99.25/13.45 ((
% 99.25/13.45 (breln1compEex) =>
% 99.25/13.45 ((
% 99.25/13.45 (!!) @ (
% 99.25/13.45 (('#B') @ (
% 99.25/13.45 !!) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 !!))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#S') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#S') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 =>))) @
% 99.25/13.45 breln1)))))) @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#C') @ (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 (
% 99.25/13.45 (
% 99.25/13.45 ('#B') @ (
% 99.25/13.45 '#B') @
% 99.25/13.45 breln1)))) @
% 99.25/13.45 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl337])).
% 99.25/13.45 thf(zip_derived_cl355, plain,
% 99.25/13.45 (~ (((setadjoinOr) =>
% 99.25/13.45 (((setoftrueEq) =>
% 99.25/13.45 (((powersetI) =>
% 99.25/13.45 (((emptyinPowerset) =>
% 99.25/13.45 (((emptyInPowerset) =>
% 99.25/13.45 (((powersetE) =>
% 99.25/13.45 (((setunionI) =>
% 99.25/13.45 (((setunionE) =>
% 99.25/13.45 (((subPowSU) =>
% 99.25/13.45 (((exuE2) =>
% 99.25/13.45 (((nonemptyImpWitness) =>
% 99.25/13.45 (((uniqinunit) =>
% 99.25/13.45 (((notinsingleton) =>
% 99.25/13.45 (((eqinunit) =>
% 99.25/13.45 (((singletonsswitch) =>
% 99.25/13.45 (((upairsetE) =>
% 99.25/13.45 (((upairsetIL) =>
% 99.25/13.45 (((upairsetIR) =>
% 99.25/13.45 (((emptyE1) =>
% 99.25/13.45 (((vacuousDall) =>
% 99.25/13.45 (((quantDeMorgan1) =>
% 99.25/13.45 (((quantDeMorgan2) =>
% 99.25/13.45 (((quantDeMorgan3) =>
% 99.25/13.45 (((quantDeMorgan4) =>
% 99.25/13.45 (((prop2setI) =>
% 99.25/13.45 (((prop2set2propI) =>
% 99.25/13.45 (((notdexE) =>
% 99.25/13.45 (((notdallE) =>
% 99.25/13.45 (((exuI1) =>
% 99.25/13.45 (((exuI3) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (inCongP) =>
% 99.25/13.45 ((
% 99.25/13.45 (in__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuE3u) =>
% 99.25/13.45 ((
% 99.25/13.45 (exu__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoin__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (powerset__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunion__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (exuEu) =>
% 99.25/13.45 ((
% 99.25/13.45 (descr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (dsetconstr__Cong) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqimpsubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (emptysetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (notsubsetI) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (notequalI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetRefl) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTrans) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setadjoinSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (subset2powerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetemptysetimpeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (inPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepInPowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (sepSubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2IR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionEcases) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionE) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectI) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset5) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset3) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectER) =>
% 99.25/13.45 ((
% 99.25/13.45 (disjointsetsI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectRsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset4) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (bs114d) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusI) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusER) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusERneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusELneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusILneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusIRneg) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusLsub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusSubset1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffE) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffI2) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg1) =>
% 99.25/13.45 ((
% 99.25/13.45 (symdiffIneg2) =>
% 99.25/13.45 ((
% 99.25/13.45 (secondinupair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairIR) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairiskpair) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairp) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsubset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowerset) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletoninpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairset2E) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairsubunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairinpowunion) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ubforcartprodlem3) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair1) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempair) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionE2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton1) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setunionsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1I2) =>
% 99.25/13.45 ((
% 99.25/13.45 (singletonsuniq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (theprop) =>
% 99.25/13.45 ((
% 99.25/13.45 (kfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstin) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjL) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR11) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR12) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR1) =>
% 99.25/13.45 ((
% 99.25/13.45 (upairequniteq) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR2) =>
% 99.25/13.45 ((
% 99.25/13.45 (setukpairinjR) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndsingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ksndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (kpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndin) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemEL) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairmemER) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodmempaircEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodfstpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodsndpairEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (cartprodpairsurjEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrI) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrSub) =>
% 99.25/13.45 ((
% 99.25/13.45 (setOfPairsIsBReln) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrERa) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL1) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrEL2) =>
% 99.25/13.45 ((
% 99.25/13.45 (dpsetconstrER) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcImageSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (apProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (app) =>
% 99.25/13.45 ((
% 99.25/13.45 (infuncsetfunc) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcinfuncset) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamProp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lamp) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2p) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall1) =>
% 99.25/13.45 ((
% 99.25/13.45 (brelnall2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ex1E2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp3) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcextLem) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcGraphProp4) =>
% 99.25/13.45 ((
% 99.25/13.45 (subbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (eqbreln) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext) =>
% 99.25/13.45 ((
% 99.25/13.45 (funcext2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq1) =>
% 99.25/13.45 ((
% 99.25/13.45 (ap2apEq2) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta1) =>
% 99.25/13.45 ((
% 99.25/13.45 (lam2lamEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (beta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (eta2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalseProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp1) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueProp2) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifSingleton) =>
% 99.25/13.45 ((
% 99.25/13.45 (ifp) =>
% 99.25/13.45 ((
% 99.25/13.45 (theeq) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrue) =>
% 99.25/13.45 ((
% 99.25/13.45 (iffalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (iftrueorfalse) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (binunionT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setminusT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementT_lem) =>
% 99.25/13.45 ((
% 99.25/13.45 (setextT) =>
% 99.25/13.45 ((
% 99.25/13.45 (subsetTI) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (powersetTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTELcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (binintersectTERcontra) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT1) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT2) =>
% 99.25/13.45 ((
% 99.25/13.45 (contrasubsetT3) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementI1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementE1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub1) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementSub2) =>
% 99.25/13.45 ((
% 99.25/13.45 (doubleComplementEq) =>
% 99.25/13.45 ((
% 99.25/13.45 (complementTnotintersectT) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementImpComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementSubsetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementInPowersetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (contraSubsetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTcontraSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTILcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTIRcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion2) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (intersectInPowersetIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpNotIn1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpInComplement1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTEcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementUnionInPowersetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule0) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_5) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all2) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1SetBreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (choice2fnsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compEex) =>
% 99.25/13.46 ((
% 99.25/13.46 (!!) @ (
% 99.25/13.46 (('#B') @ (
% 99.25/13.46 !!) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 !!))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#C') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl349])).
% 99.25/13.46 thf(zip_derived_cl362, plain,
% 99.25/13.46 (~ (((setoftrueEq) =>
% 99.25/13.46 (((powersetI) =>
% 99.25/13.46 (((emptyinPowerset) =>
% 99.25/13.46 (((emptyInPowerset) =>
% 99.25/13.46 (((powersetE) =>
% 99.25/13.46 (((setunionI) =>
% 99.25/13.46 (((setunionE) =>
% 99.25/13.46 (((subPowSU) =>
% 99.25/13.46 (((exuE2) =>
% 99.25/13.46 (((nonemptyImpWitness) =>
% 99.25/13.46 (((uniqinunit) =>
% 99.25/13.46 (((notinsingleton) =>
% 99.25/13.46 (((eqinunit) =>
% 99.25/13.46 (((singletonsswitch) =>
% 99.25/13.46 (((upairsetE) =>
% 99.25/13.46 (((upairsetIL) =>
% 99.25/13.46 (((upairsetIR) =>
% 99.25/13.46 (((emptyE1) =>
% 99.25/13.46 (((vacuousDall) =>
% 99.25/13.46 (((quantDeMorgan1) =>
% 99.25/13.46 (((quantDeMorgan2) =>
% 99.25/13.46 (((quantDeMorgan3) =>
% 99.25/13.46 (((quantDeMorgan4) =>
% 99.25/13.46 (((prop2setI) =>
% 99.25/13.46 (((prop2set2propI) =>
% 99.25/13.46 (((notdexE) =>
% 99.25/13.46 (((notdallE) =>
% 99.25/13.46 (((exuI1) =>
% 99.25/13.46 (((exuI3) =>
% 99.25/13.46 (((exuI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (inCongP) =>
% 99.25/13.46 ((
% 99.25/13.46 (in__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (exuE3u) =>
% 99.25/13.46 ((
% 99.25/13.46 (exu__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoin__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (powerset__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunion__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (exuEu) =>
% 99.25/13.46 ((
% 99.25/13.46 (descr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (dsetconstr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (emptysetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (notsubsetI) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetRefl) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTrans) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subset2powerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetemptysetimpeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepInPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2IR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionEcases) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectI) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset5) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset3) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectER) =>
% 99.25/13.46 ((
% 99.25/13.46 (disjointsetsI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset4) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (bs114d) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusI) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusER) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusERneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusELneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusILneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusIRneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffE) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg2) =>
% 99.25/13.46 ((
% 99.25/13.46 (secondinupair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairiskpair) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairp) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2E) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairsubunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairinpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem3) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair1) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton1) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I2) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsuniq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (theprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstin) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR11) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR12) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR1) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairequniteq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemER) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempaircEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrI) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrERa) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrER) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcImageSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (apProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (app) =>
% 99.25/13.46 ((
% 99.25/13.46 (infuncsetfunc) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcinfuncset) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall1) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp3) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcextLem) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp4) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq2) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2lamEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifp) =>
% 99.25/13.46 ((
% 99.25/13.46 (theeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrue) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueorfalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextT) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTI) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTELcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTERcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT1) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT2) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT3) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTnotintersectT) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementImpComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementSubsetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementInPowersetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (contraSubsetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTcontraSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTILcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTIRcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion2) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (intersectInPowersetIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpNotIn1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpInComplement1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTEcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementUnionInPowersetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule0) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_5) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all2) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1SetBreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (choice2fnsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compEex) =>
% 99.25/13.46 ((
% 99.25/13.46 (!!) @ (
% 99.25/13.46 (('#B') @ (
% 99.25/13.46 !!) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 !!))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#C') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl355])).
% 99.25/13.46 thf(zip_derived_cl369, plain,
% 99.25/13.46 (~ (((powersetI) =>
% 99.25/13.46 (((emptyinPowerset) =>
% 99.25/13.46 (((emptyInPowerset) =>
% 99.25/13.46 (((powersetE) =>
% 99.25/13.46 (((setunionI) =>
% 99.25/13.46 (((setunionE) =>
% 99.25/13.46 (((subPowSU) =>
% 99.25/13.46 (((exuE2) =>
% 99.25/13.46 (((nonemptyImpWitness) =>
% 99.25/13.46 (((uniqinunit) =>
% 99.25/13.46 (((notinsingleton) =>
% 99.25/13.46 (((eqinunit) =>
% 99.25/13.46 (((singletonsswitch) =>
% 99.25/13.46 (((upairsetE) =>
% 99.25/13.46 (((upairsetIL) =>
% 99.25/13.46 (((upairsetIR) =>
% 99.25/13.46 (((emptyE1) =>
% 99.25/13.46 (((vacuousDall) =>
% 99.25/13.46 (((quantDeMorgan1) =>
% 99.25/13.46 (((quantDeMorgan2) =>
% 99.25/13.46 (((quantDeMorgan3) =>
% 99.25/13.46 (((quantDeMorgan4) =>
% 99.25/13.46 (((prop2setI) =>
% 99.25/13.46 (((prop2set2propI) =>
% 99.25/13.46 (((notdexE) =>
% 99.25/13.46 (((notdallE) =>
% 99.25/13.46 (((exuI1) =>
% 99.25/13.46 (((exuI3) =>
% 99.25/13.46 (((exuI2) =>
% 99.25/13.46 (((inCongP) =>
% 99.25/13.46 ((
% 99.25/13.46 (in__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (exuE3u) =>
% 99.25/13.46 ((
% 99.25/13.46 (exu__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoin__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (powerset__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunion__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (exuEu) =>
% 99.25/13.46 ((
% 99.25/13.46 (descr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (dsetconstr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (emptysetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (notsubsetI) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetRefl) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTrans) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subset2powerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetemptysetimpeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepInPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2IR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionEcases) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectI) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset5) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset3) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectER) =>
% 99.25/13.46 ((
% 99.25/13.46 (disjointsetsI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset4) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (bs114d) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusI) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusER) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusERneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusELneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusILneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusIRneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffE) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg2) =>
% 99.25/13.46 ((
% 99.25/13.46 (secondinupair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairiskpair) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairp) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2E) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairsubunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairinpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem3) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair1) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton1) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I2) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsuniq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (theprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstin) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR11) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR12) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR1) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairequniteq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemER) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempaircEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrI) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrERa) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrER) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcImageSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (apProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (app) =>
% 99.25/13.46 ((
% 99.25/13.46 (infuncsetfunc) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcinfuncset) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall1) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp3) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcextLem) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp4) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq2) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2lamEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifp) =>
% 99.25/13.46 ((
% 99.25/13.46 (theeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrue) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueorfalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextT) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTI) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTELcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTERcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT1) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT2) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT3) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTnotintersectT) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementImpComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementSubsetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementInPowersetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (contraSubsetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTcontraSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTILcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTIRcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion2) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (intersectInPowersetIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpNotIn1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpInComplement1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTEcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementUnionInPowersetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule0) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_5) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all2) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1SetBreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (choice2fnsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compEex) =>
% 99.25/13.46 ((
% 99.25/13.46 (!!) @ (
% 99.25/13.46 (('#B') @ (
% 99.25/13.46 !!) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 !!))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#C') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl362])).
% 99.25/13.46 thf(zip_derived_cl376, plain,
% 99.25/13.46 (~ (((emptyinPowerset) =>
% 99.25/13.46 (((emptyInPowerset) =>
% 99.25/13.46 (((powersetE) =>
% 99.25/13.46 (((setunionI) =>
% 99.25/13.46 (((setunionE) =>
% 99.25/13.46 (((subPowSU) =>
% 99.25/13.46 (((exuE2) =>
% 99.25/13.46 (((nonemptyImpWitness) =>
% 99.25/13.46 (((uniqinunit) =>
% 99.25/13.46 (((notinsingleton) =>
% 99.25/13.46 (((eqinunit) =>
% 99.25/13.46 (((singletonsswitch) =>
% 99.25/13.46 (((upairsetE) =>
% 99.25/13.46 (((upairsetIL) =>
% 99.25/13.46 (((upairsetIR) =>
% 99.25/13.46 (((emptyE1) =>
% 99.25/13.46 (((vacuousDall) =>
% 99.25/13.46 (((quantDeMorgan1) =>
% 99.25/13.46 (((quantDeMorgan2) =>
% 99.25/13.46 (((quantDeMorgan3) =>
% 99.25/13.46 (((quantDeMorgan4) =>
% 99.25/13.46 (((prop2setI) =>
% 99.25/13.46 (((prop2set2propI) =>
% 99.25/13.46 (((notdexE) =>
% 99.25/13.46 (((notdallE) =>
% 99.25/13.46 (((exuI1) =>
% 99.25/13.46 (((exuI3) =>
% 99.25/13.46 (((exuI2) =>
% 99.25/13.46 (((inCongP) =>
% 99.25/13.46 (((in__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (exuE3u) =>
% 99.25/13.46 ((
% 99.25/13.46 (exu__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoin__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (powerset__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunion__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (exuEu) =>
% 99.25/13.46 ((
% 99.25/13.46 (descr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (dsetconstr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (emptysetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (notsubsetI) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetRefl) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTrans) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subset2powerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetemptysetimpeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepInPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2IR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionEcases) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectI) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset5) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset3) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectER) =>
% 99.25/13.46 ((
% 99.25/13.46 (disjointsetsI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset4) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (bs114d) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusI) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusER) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusERneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusELneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusILneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusIRneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffE) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg2) =>
% 99.25/13.46 ((
% 99.25/13.46 (secondinupair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairiskpair) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairp) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2E) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairsubunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairinpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem3) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair1) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton1) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I2) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsuniq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (theprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstin) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR11) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR12) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR1) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairequniteq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemER) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempaircEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrI) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrERa) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrER) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcImageSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (apProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (app) =>
% 99.25/13.46 ((
% 99.25/13.46 (infuncsetfunc) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcinfuncset) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall1) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp3) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcextLem) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp4) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq2) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2lamEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifp) =>
% 99.25/13.46 ((
% 99.25/13.46 (theeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrue) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueorfalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextT) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTI) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTELcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTERcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT1) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT2) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT3) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTnotintersectT) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementImpComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementSubsetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementInPowersetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (contraSubsetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTcontraSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTILcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTIRcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion2) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (intersectInPowersetIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpNotIn1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpInComplement1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTEcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementUnionInPowersetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule0) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_5) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all2) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1SetBreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (choice2fnsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compEex) =>
% 99.25/13.46 ((
% 99.25/13.46 (!!) @ (
% 99.25/13.46 (('#B') @ (
% 99.25/13.46 !!) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 !!))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#C') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl369])).
% 99.25/13.46 thf(zip_derived_cl384, plain,
% 99.25/13.46 (~ (((emptyInPowerset) =>
% 99.25/13.46 (((powersetE) =>
% 99.25/13.46 (((setunionI) =>
% 99.25/13.46 (((setunionE) =>
% 99.25/13.46 (((subPowSU) =>
% 99.25/13.46 (((exuE2) =>
% 99.25/13.46 (((nonemptyImpWitness) =>
% 99.25/13.46 (((uniqinunit) =>
% 99.25/13.46 (((notinsingleton) =>
% 99.25/13.46 (((eqinunit) =>
% 99.25/13.46 (((singletonsswitch) =>
% 99.25/13.46 (((upairsetE) =>
% 99.25/13.46 (((upairsetIL) =>
% 99.25/13.46 (((upairsetIR) =>
% 99.25/13.46 (((emptyE1) =>
% 99.25/13.46 (((vacuousDall) =>
% 99.25/13.46 (((quantDeMorgan1) =>
% 99.25/13.46 (((quantDeMorgan2) =>
% 99.25/13.46 (((quantDeMorgan3) =>
% 99.25/13.46 (((quantDeMorgan4) =>
% 99.25/13.46 (((prop2setI) =>
% 99.25/13.46 (((prop2set2propI) =>
% 99.25/13.46 (((notdexE) =>
% 99.25/13.46 (((notdallE) =>
% 99.25/13.46 (((exuI1) =>
% 99.25/13.46 (((exuI3) =>
% 99.25/13.46 (((exuI2) =>
% 99.25/13.46 (((inCongP) =>
% 99.25/13.46 (((in__Cong) =>
% 99.25/13.46 (((exuE3u) =>
% 99.25/13.46 ((
% 99.25/13.46 (exu__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoin__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (powerset__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunion__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (exuEu) =>
% 99.25/13.46 ((
% 99.25/13.46 (descr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (dsetconstr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (emptysetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (notsubsetI) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetRefl) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTrans) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subset2powerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetemptysetimpeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepInPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2IR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionEcases) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectI) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset5) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset3) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectER) =>
% 99.25/13.46 ((
% 99.25/13.46 (disjointsetsI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset4) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (bs114d) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusI) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusER) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusERneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusELneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusILneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusIRneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffE) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg2) =>
% 99.25/13.46 ((
% 99.25/13.46 (secondinupair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairiskpair) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairp) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2E) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairsubunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairinpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem3) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair1) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton1) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I2) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsuniq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (theprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstin) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR11) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR12) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR1) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairequniteq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemER) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempaircEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrI) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrERa) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrER) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcImageSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (apProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (app) =>
% 99.25/13.46 ((
% 99.25/13.46 (infuncsetfunc) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcinfuncset) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall1) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp3) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcextLem) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp4) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq2) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2lamEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifp) =>
% 99.25/13.46 ((
% 99.25/13.46 (theeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrue) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueorfalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextT) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTI) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTELcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTERcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT1) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT2) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT3) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTnotintersectT) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementImpComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementSubsetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementInPowersetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (contraSubsetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTcontraSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTILcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTIRcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion2) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (intersectInPowersetIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpNotIn1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpInComplement1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTEcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementUnionInPowersetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule0) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_5) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all2) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1SetBreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (choice2fnsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compEex) =>
% 99.25/13.46 ((
% 99.25/13.46 (!!) @ (
% 99.25/13.46 (('#B') @ (
% 99.25/13.46 !!) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 !!))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#C') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl376])).
% 99.25/13.46 thf(zip_derived_cl392, plain,
% 99.25/13.46 (~ (((powersetE) =>
% 99.25/13.46 (((setunionI) =>
% 99.25/13.46 (((setunionE) =>
% 99.25/13.46 (((subPowSU) =>
% 99.25/13.46 (((exuE2) =>
% 99.25/13.46 (((nonemptyImpWitness) =>
% 99.25/13.46 (((uniqinunit) =>
% 99.25/13.46 (((notinsingleton) =>
% 99.25/13.46 (((eqinunit) =>
% 99.25/13.46 (((singletonsswitch) =>
% 99.25/13.46 (((upairsetE) =>
% 99.25/13.46 (((upairsetIL) =>
% 99.25/13.46 (((upairsetIR) =>
% 99.25/13.46 (((emptyE1) =>
% 99.25/13.46 (((vacuousDall) =>
% 99.25/13.46 (((quantDeMorgan1) =>
% 99.25/13.46 (((quantDeMorgan2) =>
% 99.25/13.46 (((quantDeMorgan3) =>
% 99.25/13.46 (((quantDeMorgan4) =>
% 99.25/13.46 (((prop2setI) =>
% 99.25/13.46 (((prop2set2propI) =>
% 99.25/13.46 (((notdexE) =>
% 99.25/13.46 (((notdallE) =>
% 99.25/13.46 (((exuI1) =>
% 99.25/13.46 (((exuI3) =>
% 99.25/13.46 (((exuI2) =>
% 99.25/13.46 (((inCongP) =>
% 99.25/13.46 (((in__Cong) =>
% 99.25/13.46 (((exuE3u) =>
% 99.25/13.46 (((exu__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoin__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (powerset__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunion__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (exuEu) =>
% 99.25/13.46 ((
% 99.25/13.46 (descr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (dsetconstr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (emptysetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (notsubsetI) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetRefl) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTrans) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subset2powerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetemptysetimpeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepInPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2IR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionEcases) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectI) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset5) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset3) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectER) =>
% 99.25/13.46 ((
% 99.25/13.46 (disjointsetsI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset4) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (bs114d) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusI) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusER) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusERneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusELneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusILneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusIRneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffE) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg2) =>
% 99.25/13.46 ((
% 99.25/13.46 (secondinupair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairiskpair) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairp) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2E) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairsubunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairinpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem3) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair1) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton1) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I2) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsuniq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (theprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstin) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR11) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR12) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR1) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairequniteq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemER) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempaircEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrI) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrERa) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrER) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcImageSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (apProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (app) =>
% 99.25/13.46 ((
% 99.25/13.46 (infuncsetfunc) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcinfuncset) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall1) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp3) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcextLem) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp4) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq2) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2lamEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifp) =>
% 99.25/13.46 ((
% 99.25/13.46 (theeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrue) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueorfalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextT) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTI) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTELcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTERcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT1) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT2) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT3) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTnotintersectT) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementImpComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementSubsetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementInPowersetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (contraSubsetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTcontraSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTILcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTIRcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion2) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (intersectInPowersetIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpNotIn1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpInComplement1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTEcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementUnionInPowersetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule0) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_5) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all2) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1SetBreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (choice2fnsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compEex) =>
% 99.25/13.46 ((
% 99.25/13.46 (!!) @ (
% 99.25/13.46 (('#B') @ (
% 99.25/13.46 !!) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 !!))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#C') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl384])).
% 99.25/13.46 thf(zip_derived_cl400, plain,
% 99.25/13.46 (~ (((setunionI) =>
% 99.25/13.46 (((setunionE) =>
% 99.25/13.46 (((subPowSU) =>
% 99.25/13.46 (((exuE2) =>
% 99.25/13.46 (((nonemptyImpWitness) =>
% 99.25/13.46 (((uniqinunit) =>
% 99.25/13.46 (((notinsingleton) =>
% 99.25/13.46 (((eqinunit) =>
% 99.25/13.46 (((singletonsswitch) =>
% 99.25/13.46 (((upairsetE) =>
% 99.25/13.46 (((upairsetIL) =>
% 99.25/13.46 (((upairsetIR) =>
% 99.25/13.46 (((emptyE1) =>
% 99.25/13.46 (((vacuousDall) =>
% 99.25/13.46 (((quantDeMorgan1) =>
% 99.25/13.46 (((quantDeMorgan2) =>
% 99.25/13.46 (((quantDeMorgan3) =>
% 99.25/13.46 (((quantDeMorgan4) =>
% 99.25/13.46 (((prop2setI) =>
% 99.25/13.46 (((prop2set2propI) =>
% 99.25/13.46 (((notdexE) =>
% 99.25/13.46 (((notdallE) =>
% 99.25/13.46 (((exuI1) =>
% 99.25/13.46 (((exuI3) =>
% 99.25/13.46 (((exuI2) =>
% 99.25/13.46 (((inCongP) =>
% 99.25/13.46 (((in__Cong) =>
% 99.25/13.46 (((exuE3u) =>
% 99.25/13.46 (((exu__Cong) =>
% 99.25/13.46 (((setadjoin__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (powerset__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunion__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (exuEu) =>
% 99.25/13.46 ((
% 99.25/13.46 (descr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (dsetconstr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (emptysetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (notsubsetI) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetRefl) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTrans) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subset2powerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetemptysetimpeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepInPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2IR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionEcases) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectI) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset5) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset3) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectER) =>
% 99.25/13.46 ((
% 99.25/13.46 (disjointsetsI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset4) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (bs114d) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusI) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusER) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusERneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusELneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusILneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusIRneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffE) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg2) =>
% 99.25/13.46 ((
% 99.25/13.46 (secondinupair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairiskpair) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairp) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2E) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairsubunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairinpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem3) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair1) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton1) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I2) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsuniq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (theprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstin) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR11) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR12) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR1) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairequniteq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemER) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempaircEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrI) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrERa) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrER) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcImageSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (apProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (app) =>
% 99.25/13.46 ((
% 99.25/13.46 (infuncsetfunc) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcinfuncset) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall1) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp3) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcextLem) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp4) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq2) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2lamEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifp) =>
% 99.25/13.46 ((
% 99.25/13.46 (theeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrue) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueorfalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextT) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTI) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTELcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTERcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT1) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT2) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT3) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTnotintersectT) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementImpComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementSubsetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementInPowersetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (contraSubsetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTcontraSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTILcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTIRcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion2) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (intersectInPowersetIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpNotIn1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpInComplement1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTEcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementUnionInPowersetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule0) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_5) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all2) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1SetBreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (choice2fnsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compEex) =>
% 99.25/13.46 ((
% 99.25/13.46 (!!) @ (
% 99.25/13.46 (('#B') @ (
% 99.25/13.46 !!) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 !!))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#C') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl392])).
% 99.25/13.46 thf(zip_derived_cl408, plain,
% 99.25/13.46 (~ (((setunionE) =>
% 99.25/13.46 (((subPowSU) =>
% 99.25/13.46 (((exuE2) =>
% 99.25/13.46 (((nonemptyImpWitness) =>
% 99.25/13.46 (((uniqinunit) =>
% 99.25/13.46 (((notinsingleton) =>
% 99.25/13.46 (((eqinunit) =>
% 99.25/13.46 (((singletonsswitch) =>
% 99.25/13.46 (((upairsetE) =>
% 99.25/13.46 (((upairsetIL) =>
% 99.25/13.46 (((upairsetIR) =>
% 99.25/13.46 (((emptyE1) =>
% 99.25/13.46 (((vacuousDall) =>
% 99.25/13.46 (((quantDeMorgan1) =>
% 99.25/13.46 (((quantDeMorgan2) =>
% 99.25/13.46 (((quantDeMorgan3) =>
% 99.25/13.46 (((quantDeMorgan4) =>
% 99.25/13.46 (((prop2setI) =>
% 99.25/13.46 (((prop2set2propI) =>
% 99.25/13.46 (((notdexE) =>
% 99.25/13.46 (((notdallE) =>
% 99.25/13.46 (((exuI1) =>
% 99.25/13.46 (((exuI3) =>
% 99.25/13.46 (((exuI2) =>
% 99.25/13.46 (((inCongP) =>
% 99.25/13.46 (((in__Cong) =>
% 99.25/13.46 (((exuE3u) =>
% 99.25/13.46 (((exu__Cong) =>
% 99.25/13.46 (((setadjoin__Cong) =>
% 99.25/13.46 (((powerset__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunion__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (exuEu) =>
% 99.25/13.46 ((
% 99.25/13.46 (descr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (dsetconstr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (emptysetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (notsubsetI) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetRefl) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTrans) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subset2powerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetemptysetimpeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepInPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2IR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionEcases) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectI) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset5) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset3) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectER) =>
% 99.25/13.46 ((
% 99.25/13.46 (disjointsetsI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset4) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (bs114d) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusI) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusER) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusERneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusELneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusILneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusIRneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffE) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg2) =>
% 99.25/13.46 ((
% 99.25/13.46 (secondinupair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairiskpair) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairp) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2E) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairsubunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairinpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem3) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair1) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton1) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I2) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsuniq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (theprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstin) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR11) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR12) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR1) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairequniteq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemER) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempaircEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrI) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrERa) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrER) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcImageSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (apProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (app) =>
% 99.25/13.46 ((
% 99.25/13.46 (infuncsetfunc) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcinfuncset) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall1) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp3) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcextLem) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp4) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq2) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2lamEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifp) =>
% 99.25/13.46 ((
% 99.25/13.46 (theeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrue) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueorfalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextT) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTI) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTELcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTERcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT1) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT2) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT3) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTnotintersectT) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementImpComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementSubsetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementInPowersetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (contraSubsetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTcontraSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTILcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTIRcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion2) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (intersectInPowersetIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpNotIn1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpInComplement1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTEcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementUnionInPowersetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule0) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_5) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all2) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1SetBreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (choice2fnsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compEex) =>
% 99.25/13.46 ((
% 99.25/13.46 (!!) @ (
% 99.25/13.46 (('#B') @ (
% 99.25/13.46 !!) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 !!))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#C') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl400])).
% 99.25/13.46 thf(zip_derived_cl417, plain,
% 99.25/13.46 (~ (((subPowSU) =>
% 99.25/13.46 (((exuE2) =>
% 99.25/13.46 (((nonemptyImpWitness) =>
% 99.25/13.46 (((uniqinunit) =>
% 99.25/13.46 (((notinsingleton) =>
% 99.25/13.46 (((eqinunit) =>
% 99.25/13.46 (((singletonsswitch) =>
% 99.25/13.46 (((upairsetE) =>
% 99.25/13.46 (((upairsetIL) =>
% 99.25/13.46 (((upairsetIR) =>
% 99.25/13.46 (((emptyE1) =>
% 99.25/13.46 (((vacuousDall) =>
% 99.25/13.46 (((quantDeMorgan1) =>
% 99.25/13.46 (((quantDeMorgan2) =>
% 99.25/13.46 (((quantDeMorgan3) =>
% 99.25/13.46 (((quantDeMorgan4) =>
% 99.25/13.46 (((prop2setI) =>
% 99.25/13.46 (((prop2set2propI) =>
% 99.25/13.46 (((notdexE) =>
% 99.25/13.46 (((notdallE) =>
% 99.25/13.46 (((exuI1) =>
% 99.25/13.46 (((exuI3) =>
% 99.25/13.46 (((exuI2) =>
% 99.25/13.46 (((inCongP) =>
% 99.25/13.46 (((in__Cong) =>
% 99.25/13.46 (((exuE3u) =>
% 99.25/13.46 (((exu__Cong) =>
% 99.25/13.46 (((setadjoin__Cong) =>
% 99.25/13.46 (((powerset__Cong) =>
% 99.25/13.46 (((setunion__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (exuEu) =>
% 99.25/13.46 ((
% 99.25/13.46 (descr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (dsetconstr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (emptysetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (notsubsetI) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetRefl) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTrans) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subset2powerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetemptysetimpeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepInPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2IR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionEcases) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectI) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset5) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset3) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectER) =>
% 99.25/13.46 ((
% 99.25/13.46 (disjointsetsI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset4) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (bs114d) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusI) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusER) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusERneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusELneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusILneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusIRneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffE) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg2) =>
% 99.25/13.46 ((
% 99.25/13.46 (secondinupair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairiskpair) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairp) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2E) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairsubunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairinpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem3) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair1) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton1) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I2) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsuniq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (theprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstin) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR11) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR12) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR1) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairequniteq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemER) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempaircEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrI) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrERa) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrER) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcImageSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (apProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (app) =>
% 99.25/13.46 ((
% 99.25/13.46 (infuncsetfunc) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcinfuncset) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall1) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp3) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcextLem) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp4) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq2) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2lamEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifp) =>
% 99.25/13.46 ((
% 99.25/13.46 (theeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrue) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueorfalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextT) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTI) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTELcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTERcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT1) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT2) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT3) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTnotintersectT) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementImpComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementSubsetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementInPowersetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (contraSubsetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTcontraSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTILcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTIRcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion2) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (intersectInPowersetIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpNotIn1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpInComplement1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTEcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementUnionInPowersetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule0) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_5) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all2) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1SetBreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (choice2fnsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compEex) =>
% 99.25/13.46 ((
% 99.25/13.46 (!!) @ (
% 99.25/13.46 (('#B') @ (
% 99.25/13.46 !!) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 !!))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#C') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl408])).
% 99.25/13.46 thf(zip_derived_cl428, plain,
% 99.25/13.46 (~ (((exuE2) =>
% 99.25/13.46 (((nonemptyImpWitness) =>
% 99.25/13.46 (((uniqinunit) =>
% 99.25/13.46 (((notinsingleton) =>
% 99.25/13.46 (((eqinunit) =>
% 99.25/13.46 (((singletonsswitch) =>
% 99.25/13.46 (((upairsetE) =>
% 99.25/13.46 (((upairsetIL) =>
% 99.25/13.46 (((upairsetIR) =>
% 99.25/13.46 (((emptyE1) =>
% 99.25/13.46 (((vacuousDall) =>
% 99.25/13.46 (((quantDeMorgan1) =>
% 99.25/13.46 (((quantDeMorgan2) =>
% 99.25/13.46 (((quantDeMorgan3) =>
% 99.25/13.46 (((quantDeMorgan4) =>
% 99.25/13.46 (((prop2setI) =>
% 99.25/13.46 (((prop2set2propI) =>
% 99.25/13.46 (((notdexE) =>
% 99.25/13.46 (((notdallE) =>
% 99.25/13.46 (((exuI1) =>
% 99.25/13.46 (((exuI3) =>
% 99.25/13.46 (((exuI2) =>
% 99.25/13.46 (((inCongP) =>
% 99.25/13.46 (((in__Cong) =>
% 99.25/13.46 (((exuE3u) =>
% 99.25/13.46 (((exu__Cong) =>
% 99.25/13.46 (((setadjoin__Cong) =>
% 99.25/13.46 (((powerset__Cong) =>
% 99.25/13.46 (((setunion__Cong) =>
% 99.25/13.46 (((exuEu) =>
% 99.25/13.46 ((
% 99.25/13.46 (descr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (dsetconstr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (emptysetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (notsubsetI) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetRefl) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTrans) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subset2powerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetemptysetimpeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepInPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2IR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionEcases) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectI) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset5) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset3) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectER) =>
% 99.25/13.46 ((
% 99.25/13.46 (disjointsetsI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset4) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (bs114d) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusI) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusER) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusERneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusELneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusILneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusIRneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffE) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg2) =>
% 99.25/13.46 ((
% 99.25/13.46 (secondinupair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairiskpair) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairp) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2E) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairsubunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairinpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem3) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair1) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton1) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I2) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsuniq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (theprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstin) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR11) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR12) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR1) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairequniteq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemER) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempaircEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrI) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrERa) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrEL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (dpsetconstrER) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcImageSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (apProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (app) =>
% 99.25/13.46 ((
% 99.25/13.46 (infuncsetfunc) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcinfuncset) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamProp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lamp) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2p) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall1) =>
% 99.25/13.46 ((
% 99.25/13.46 (brelnall2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp3) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcextLem) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcGraphProp4) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext) =>
% 99.25/13.46 ((
% 99.25/13.46 (funcext2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ap2apEq2) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta1) =>
% 99.25/13.46 ((
% 99.25/13.46 (lam2lamEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (beta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eta2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalseProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp1) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueProp2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifSingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ifp) =>
% 99.25/13.46 ((
% 99.25/13.46 (theeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrue) =>
% 99.25/13.46 ((
% 99.25/13.46 (iffalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (iftrueorfalse) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementT_lem) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextT) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTI) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTELcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectTERcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT1) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT2) =>
% 99.25/13.46 ((
% 99.25/13.46 (contrasubsetT3) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub1) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (doubleComplementEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTnotintersectT) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementImpComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementSubsetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementInPowersetComplementIntersect) =>
% 99.25/13.46 ((
% 99.25/13.46 (contraSubsetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementTcontraSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTILcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTIRcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInUnion2) =>
% 99.25/13.46 ((
% 99.25/13.46 (inIntersectImpInIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (intersectInPowersetIntersectUnions) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpNotIn1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inComplementUnionImpInComplement1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionTEcontra) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a1) =>
% 99.25/13.46 ((
% 99.25/13.46 (complementUnionInPowersetComplement) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan1) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2a) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b2) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2b) =>
% 99.25/13.46 ((
% 99.25/13.46 (demorgan2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule0) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz13rule4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_1) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_2) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_3) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_4) =>
% 99.25/13.46 ((
% 99.25/13.46 (woz1_5) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all2) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1SetBreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (choice2fnsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (setOfPairsIsBReln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1all1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqbreln1) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1invE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compI) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compE) =>
% 99.25/13.46 ((
% 99.25/13.46 (breln1compEex) =>
% 99.25/13.46 ((
% 99.25/13.46 (!!) @ (
% 99.25/13.46 (('#B') @ (
% 99.25/13.46 !!) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 !!))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#S') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#S') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 =>))) @
% 99.25/13.46 breln1)))))) @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#C') @ (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 (
% 99.25/13.46 (
% 99.25/13.46 ('#B') @ (
% 99.25/13.46 '#B') @
% 99.25/13.46 breln1)))) @
% 99.25/13.46 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl417])).
% 99.25/13.46 thf(zip_derived_cl439, plain,
% 99.25/13.46 (~ (((nonemptyImpWitness) =>
% 99.25/13.46 (((uniqinunit) =>
% 99.25/13.46 (((notinsingleton) =>
% 99.25/13.46 (((eqinunit) =>
% 99.25/13.46 (((singletonsswitch) =>
% 99.25/13.46 (((upairsetE) =>
% 99.25/13.46 (((upairsetIL) =>
% 99.25/13.46 (((upairsetIR) =>
% 99.25/13.46 (((emptyE1) =>
% 99.25/13.46 (((vacuousDall) =>
% 99.25/13.46 (((quantDeMorgan1) =>
% 99.25/13.46 (((quantDeMorgan2) =>
% 99.25/13.46 (((quantDeMorgan3) =>
% 99.25/13.46 (((quantDeMorgan4) =>
% 99.25/13.46 (((prop2setI) =>
% 99.25/13.46 (((prop2set2propI) =>
% 99.25/13.46 (((notdexE) =>
% 99.25/13.46 (((notdallE) =>
% 99.25/13.46 (((exuI1) =>
% 99.25/13.46 (((exuI3) =>
% 99.25/13.46 (((exuI2) =>
% 99.25/13.46 (((inCongP) =>
% 99.25/13.46 (((in__Cong) =>
% 99.25/13.46 (((exuE3u) =>
% 99.25/13.46 (((exu__Cong) =>
% 99.25/13.46 (((setadjoin__Cong) =>
% 99.25/13.46 (((powerset__Cong) =>
% 99.25/13.46 (((setunion__Cong) =>
% 99.25/13.46 (((exuEu) =>
% 99.25/13.46 (((descr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (dsetconstr__Cong) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (eqimpsubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (emptysetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (notsubsetI) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (notequalI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetRefl) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetTrans) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setadjoinSub2) =>
% 99.25/13.46 ((
% 99.25/13.46 (subset2powerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (setextsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (subsetemptysetimpeq) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetE1) =>
% 99.25/13.46 ((
% 99.25/13.46 (inPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (powersetsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepInPowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (sepSubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2IR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionEcases) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionE) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binunionRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectI) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset5) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset3) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectER) =>
% 99.25/13.46 ((
% 99.25/13.46 (disjointsetsI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectRsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset4) =>
% 99.25/13.46 ((
% 99.25/13.46 (binintersectSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (bs114d) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusI) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusER) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusERneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusELneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusILneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusIRneg) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusLsub) =>
% 99.25/13.46 ((
% 99.25/13.46 (setminusSubset1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffE) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffI2) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg1) =>
% 99.25/13.46 ((
% 99.25/13.46 (symdiffIneg2) =>
% 99.25/13.46 ((
% 99.25/13.46 (secondinupair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairIR) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairiskpair) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairp) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsubset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowerset) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletoninpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairset2E) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairsubunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairinpowunion) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem2) =>
% 99.25/13.46 ((
% 99.25/13.46 (ubforcartprodlem3) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair1) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodmempair) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionE2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton1) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setunionsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1E1) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I) =>
% 99.25/13.46 ((
% 99.25/13.46 (ex1I2) =>
% 99.25/13.46 ((
% 99.25/13.46 (singletonsuniq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL1) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (theprop) =>
% 99.25/13.46 ((
% 99.25/13.46 (kfstpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodfstin) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjL) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR11) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR12) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR1) =>
% 99.25/13.46 ((
% 99.25/13.46 (upairequniteq) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR2) =>
% 99.25/13.46 ((
% 99.25/13.46 (setukpairinjR) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndsingleton) =>
% 99.25/13.46 ((
% 99.25/13.46 (ksndpairEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (kpairsurjEq) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodsndin) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemEL) =>
% 99.25/13.46 ((
% 99.25/13.46 (cartprodpairmemER) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempaircEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrI) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrERa) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrER) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcImageSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (apProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (app) =>
% 99.25/13.47 ((
% 99.25/13.47 (infuncsetfunc) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcinfuncset) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall1) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp3) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcextLem) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp4) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq2) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2lamEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifp) =>
% 99.25/13.47 ((
% 99.25/13.47 (theeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrue) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueorfalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextT) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTI) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTELcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTERcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT1) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT2) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT3) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTnotintersectT) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementImpComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementSubsetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementInPowersetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (contraSubsetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTcontraSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTILcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTIRcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion2) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (intersectInPowersetIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpNotIn1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpInComplement1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTEcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementUnionInPowersetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule0) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_5) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all2) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1SetBreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (choice2fnsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all1) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compEex) =>
% 99.25/13.47 ((
% 99.25/13.47 (!!) @ (
% 99.25/13.47 (('#B') @ (
% 99.25/13.47 !!) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 !!))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#C') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])).
% 99.25/13.47 thf(zip_derived_cl449, plain,
% 99.25/13.47 (~ (((uniqinunit) =>
% 99.25/13.47 (((notinsingleton) =>
% 99.25/13.47 (((eqinunit) =>
% 99.25/13.47 (((singletonsswitch) =>
% 99.25/13.47 (((upairsetE) =>
% 99.25/13.47 (((upairsetIL) =>
% 99.25/13.47 (((upairsetIR) =>
% 99.25/13.47 (((emptyE1) =>
% 99.25/13.47 (((vacuousDall) =>
% 99.25/13.47 (((quantDeMorgan1) =>
% 99.25/13.47 (((quantDeMorgan2) =>
% 99.25/13.47 (((quantDeMorgan3) =>
% 99.25/13.47 (((quantDeMorgan4) =>
% 99.25/13.47 (((prop2setI) =>
% 99.25/13.47 (((prop2set2propI) =>
% 99.25/13.47 (((notdexE) =>
% 99.25/13.47 (((notdallE) =>
% 99.25/13.47 (((exuI1) =>
% 99.25/13.47 (((exuI3) =>
% 99.25/13.47 (((exuI2) =>
% 99.25/13.47 (((inCongP) =>
% 99.25/13.47 (((in__Cong) =>
% 99.25/13.47 (((exuE3u) =>
% 99.25/13.47 (((exu__Cong) =>
% 99.25/13.47 (((setadjoin__Cong) =>
% 99.25/13.47 (((powerset__Cong) =>
% 99.25/13.47 (((setunion__Cong) =>
% 99.25/13.47 (((exuEu) =>
% 99.25/13.47 (((descr__Cong) =>
% 99.25/13.47 (((dsetconstr__Cong) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqimpsubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqimpsubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (emptysetsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetE) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (notsubsetI) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetRefl) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTrans) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subset2powerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetemptysetimpeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepInPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2IR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionEcases) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectI) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset5) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset3) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectER) =>
% 99.25/13.47 ((
% 99.25/13.47 (disjointsetsI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset4) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (bs114d) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusI) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusER) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusERneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusELneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusILneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusIRneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffE) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg2) =>
% 99.25/13.47 ((
% 99.25/13.47 (secondinupair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairiskpair) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairp) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2E) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairsubunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairinpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem3) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair1) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton1) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I2) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsuniq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (theprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstin) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR11) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR12) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR1) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairequniteq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemER) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempaircEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrI) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrERa) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrER) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcImageSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (apProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (app) =>
% 99.25/13.47 ((
% 99.25/13.47 (infuncsetfunc) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcinfuncset) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall1) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp3) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcextLem) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp4) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq2) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2lamEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifp) =>
% 99.25/13.47 ((
% 99.25/13.47 (theeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrue) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueorfalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextT) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTI) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTELcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTERcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT1) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT2) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT3) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTnotintersectT) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementImpComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementSubsetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementInPowersetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (contraSubsetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTcontraSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTILcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTIRcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion2) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (intersectInPowersetIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpNotIn1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpInComplement1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTEcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementUnionInPowersetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule0) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_5) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all2) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1SetBreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (choice2fnsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all1) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compEex) =>
% 99.25/13.47 ((
% 99.25/13.47 (!!) @ (
% 99.25/13.47 (('#B') @ (
% 99.25/13.47 !!) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 !!))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#C') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl439])).
% 99.25/13.47 thf(zip_derived_cl458, plain,
% 99.25/13.47 (~ (((notinsingleton) =>
% 99.25/13.47 (((eqinunit) =>
% 99.25/13.47 (((singletonsswitch) =>
% 99.25/13.47 (((upairsetE) =>
% 99.25/13.47 (((upairsetIL) =>
% 99.25/13.47 (((upairsetIR) =>
% 99.25/13.47 (((emptyE1) =>
% 99.25/13.47 (((vacuousDall) =>
% 99.25/13.47 (((quantDeMorgan1) =>
% 99.25/13.47 (((quantDeMorgan2) =>
% 99.25/13.47 (((quantDeMorgan3) =>
% 99.25/13.47 (((quantDeMorgan4) =>
% 99.25/13.47 (((prop2setI) =>
% 99.25/13.47 (((prop2set2propI) =>
% 99.25/13.47 (((notdexE) =>
% 99.25/13.47 (((notdallE) =>
% 99.25/13.47 (((exuI1) =>
% 99.25/13.47 (((exuI3) =>
% 99.25/13.47 (((exuI2) =>
% 99.25/13.47 (((inCongP) =>
% 99.25/13.47 (((in__Cong) =>
% 99.25/13.47 (((exuE3u) =>
% 99.25/13.47 (((exu__Cong) =>
% 99.25/13.47 (((setadjoin__Cong) =>
% 99.25/13.47 (((powerset__Cong) =>
% 99.25/13.47 (((setunion__Cong) =>
% 99.25/13.47 (((exuEu) =>
% 99.25/13.47 (((descr__Cong) =>
% 99.25/13.47 (((dsetconstr__Cong) =>
% 99.25/13.47 (((subsetI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqimpsubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqimpsubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (emptysetsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetE) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (notsubsetI) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetRefl) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTrans) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subset2powerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetemptysetimpeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepInPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2IR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionEcases) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectI) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset5) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset3) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectER) =>
% 99.25/13.47 ((
% 99.25/13.47 (disjointsetsI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset4) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (bs114d) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusI) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusER) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusERneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusELneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusILneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusIRneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffE) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg2) =>
% 99.25/13.47 ((
% 99.25/13.47 (secondinupair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairiskpair) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairp) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2E) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairsubunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairinpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem3) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair1) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton1) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I2) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsuniq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (theprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstin) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR11) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR12) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR1) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairequniteq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemER) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempaircEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrI) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrERa) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrER) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcImageSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (apProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (app) =>
% 99.25/13.47 ((
% 99.25/13.47 (infuncsetfunc) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcinfuncset) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall1) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp3) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcextLem) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp4) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq2) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2lamEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifp) =>
% 99.25/13.47 ((
% 99.25/13.47 (theeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrue) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueorfalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextT) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTI) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTELcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTERcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT1) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT2) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT3) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTnotintersectT) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementImpComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementSubsetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementInPowersetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (contraSubsetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTcontraSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTILcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTIRcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion2) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (intersectInPowersetIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpNotIn1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpInComplement1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTEcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementUnionInPowersetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule0) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_5) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all2) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1SetBreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (choice2fnsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all1) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compEex) =>
% 99.25/13.47 ((
% 99.25/13.47 (!!) @ (
% 99.25/13.47 (('#B') @ (
% 99.25/13.47 !!) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 !!))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#C') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl449])).
% 99.25/13.47 thf(zip_derived_cl467, plain,
% 99.25/13.47 (~ (((eqinunit) =>
% 99.25/13.47 (((singletonsswitch) =>
% 99.25/13.47 (((upairsetE) =>
% 99.25/13.47 (((upairsetIL) =>
% 99.25/13.47 (((upairsetIR) =>
% 99.25/13.47 (((emptyE1) =>
% 99.25/13.47 (((vacuousDall) =>
% 99.25/13.47 (((quantDeMorgan1) =>
% 99.25/13.47 (((quantDeMorgan2) =>
% 99.25/13.47 (((quantDeMorgan3) =>
% 99.25/13.47 (((quantDeMorgan4) =>
% 99.25/13.47 (((prop2setI) =>
% 99.25/13.47 (((prop2set2propI) =>
% 99.25/13.47 (((notdexE) =>
% 99.25/13.47 (((notdallE) =>
% 99.25/13.47 (((exuI1) =>
% 99.25/13.47 (((exuI3) =>
% 99.25/13.47 (((exuI2) =>
% 99.25/13.47 (((inCongP) =>
% 99.25/13.47 (((in__Cong) =>
% 99.25/13.47 (((exuE3u) =>
% 99.25/13.47 (((exu__Cong) =>
% 99.25/13.47 (((setadjoin__Cong) =>
% 99.25/13.47 (((powerset__Cong) =>
% 99.25/13.47 (((setunion__Cong) =>
% 99.25/13.47 (((exuEu) =>
% 99.25/13.47 (((descr__Cong) =>
% 99.25/13.47 (((dsetconstr__Cong) =>
% 99.25/13.47 (((subsetI1) =>
% 99.25/13.47 (((eqimpsubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqimpsubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (emptysetsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetE) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (notsubsetI) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetRefl) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTrans) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subset2powerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetemptysetimpeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepInPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2IR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionEcases) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectI) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset5) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset3) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectER) =>
% 99.25/13.47 ((
% 99.25/13.47 (disjointsetsI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset4) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (bs114d) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusI) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusER) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusERneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusELneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusILneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusIRneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffE) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg2) =>
% 99.25/13.47 ((
% 99.25/13.47 (secondinupair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairiskpair) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairp) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2E) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairsubunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairinpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem3) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair1) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton1) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I2) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsuniq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (theprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstin) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR11) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR12) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR1) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairequniteq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemER) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempaircEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrI) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrERa) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrER) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcImageSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (apProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (app) =>
% 99.25/13.47 ((
% 99.25/13.47 (infuncsetfunc) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcinfuncset) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall1) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp3) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcextLem) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp4) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq2) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2lamEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifp) =>
% 99.25/13.47 ((
% 99.25/13.47 (theeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrue) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueorfalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextT) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTI) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTELcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTERcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT1) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT2) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT3) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTnotintersectT) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementImpComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementSubsetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementInPowersetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (contraSubsetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTcontraSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTILcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTIRcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion2) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (intersectInPowersetIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpNotIn1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpInComplement1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTEcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementUnionInPowersetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule0) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_5) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all2) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1SetBreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (choice2fnsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all1) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compEex) =>
% 99.25/13.47 ((
% 99.25/13.47 (!!) @ (
% 99.25/13.47 (('#B') @ (
% 99.25/13.47 !!) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 !!))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#C') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl458])).
% 99.25/13.47 thf(zip_derived_cl475, plain,
% 99.25/13.47 (~ (((singletonsswitch) =>
% 99.25/13.47 (((upairsetE) =>
% 99.25/13.47 (((upairsetIL) =>
% 99.25/13.47 (((upairsetIR) =>
% 99.25/13.47 (((emptyE1) =>
% 99.25/13.47 (((vacuousDall) =>
% 99.25/13.47 (((quantDeMorgan1) =>
% 99.25/13.47 (((quantDeMorgan2) =>
% 99.25/13.47 (((quantDeMorgan3) =>
% 99.25/13.47 (((quantDeMorgan4) =>
% 99.25/13.47 (((prop2setI) =>
% 99.25/13.47 (((prop2set2propI) =>
% 99.25/13.47 (((notdexE) =>
% 99.25/13.47 (((notdallE) =>
% 99.25/13.47 (((exuI1) =>
% 99.25/13.47 (((exuI3) =>
% 99.25/13.47 (((exuI2) =>
% 99.25/13.47 (((inCongP) =>
% 99.25/13.47 (((in__Cong) =>
% 99.25/13.47 (((exuE3u) =>
% 99.25/13.47 (((exu__Cong) =>
% 99.25/13.47 (((setadjoin__Cong) =>
% 99.25/13.47 (((powerset__Cong) =>
% 99.25/13.47 (((setunion__Cong) =>
% 99.25/13.47 (((exuEu) =>
% 99.25/13.47 (((descr__Cong) =>
% 99.25/13.47 (((dsetconstr__Cong) =>
% 99.25/13.47 (((subsetI1) =>
% 99.25/13.47 (((eqimpsubset2) =>
% 99.25/13.47 (((eqimpsubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (emptysetsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetE) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (notsubsetI) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetRefl) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTrans) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subset2powerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetemptysetimpeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepInPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2IR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionEcases) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectI) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset5) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset3) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectER) =>
% 99.25/13.47 ((
% 99.25/13.47 (disjointsetsI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset4) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (bs114d) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusI) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusER) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusERneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusELneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusILneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusIRneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffE) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg2) =>
% 99.25/13.47 ((
% 99.25/13.47 (secondinupair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairiskpair) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairp) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2E) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairsubunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairinpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem3) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair1) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton1) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I2) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsuniq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (theprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstin) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR11) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR12) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR1) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairequniteq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemER) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempaircEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrI) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrERa) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrER) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcImageSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (apProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (app) =>
% 99.25/13.47 ((
% 99.25/13.47 (infuncsetfunc) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcinfuncset) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall1) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp3) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcextLem) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp4) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq2) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2lamEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifp) =>
% 99.25/13.47 ((
% 99.25/13.47 (theeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrue) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueorfalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextT) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTI) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTELcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTERcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT1) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT2) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT3) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTnotintersectT) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementImpComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementSubsetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementInPowersetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (contraSubsetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTcontraSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTILcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTIRcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion2) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (intersectInPowersetIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpNotIn1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpInComplement1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTEcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementUnionInPowersetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule0) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_5) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all2) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1SetBreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (choice2fnsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all1) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compEex) =>
% 99.25/13.47 ((
% 99.25/13.47 (!!) @ (
% 99.25/13.47 (('#B') @ (
% 99.25/13.47 !!) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 !!))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#C') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl467])).
% 99.25/13.47 thf(zip_derived_cl485, plain,
% 99.25/13.47 (~ (((upairsetE) =>
% 99.25/13.47 (((upairsetIL) =>
% 99.25/13.47 (((upairsetIR) =>
% 99.25/13.47 (((emptyE1) =>
% 99.25/13.47 (((vacuousDall) =>
% 99.25/13.47 (((quantDeMorgan1) =>
% 99.25/13.47 (((quantDeMorgan2) =>
% 99.25/13.47 (((quantDeMorgan3) =>
% 99.25/13.47 (((quantDeMorgan4) =>
% 99.25/13.47 (((prop2setI) =>
% 99.25/13.47 (((prop2set2propI) =>
% 99.25/13.47 (((notdexE) =>
% 99.25/13.47 (((notdallE) =>
% 99.25/13.47 (((exuI1) =>
% 99.25/13.47 (((exuI3) =>
% 99.25/13.47 (((exuI2) =>
% 99.25/13.47 (((inCongP) =>
% 99.25/13.47 (((in__Cong) =>
% 99.25/13.47 (((exuE3u) =>
% 99.25/13.47 (((exu__Cong) =>
% 99.25/13.47 (((setadjoin__Cong) =>
% 99.25/13.47 (((powerset__Cong) =>
% 99.25/13.47 (((setunion__Cong) =>
% 99.25/13.47 (((exuEu) =>
% 99.25/13.47 (((descr__Cong) =>
% 99.25/13.47 (((dsetconstr__Cong) =>
% 99.25/13.47 (((subsetI1) =>
% 99.25/13.47 (((eqimpsubset2) =>
% 99.25/13.47 (((eqimpsubset1) =>
% 99.25/13.47 (((subsetI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (emptysetsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetE) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (notsubsetI) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetRefl) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTrans) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subset2powerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetemptysetimpeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepInPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2IR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionEcases) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectI) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset5) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset3) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectER) =>
% 99.25/13.47 ((
% 99.25/13.47 (disjointsetsI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset4) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (bs114d) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusI) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusER) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusERneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusELneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusILneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusIRneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffE) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg2) =>
% 99.25/13.47 ((
% 99.25/13.47 (secondinupair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairiskpair) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairp) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2E) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairsubunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairinpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem3) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair1) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton1) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I2) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsuniq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (theprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstin) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR11) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR12) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR1) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairequniteq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemER) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempaircEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrI) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrERa) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrER) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcImageSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (apProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (app) =>
% 99.25/13.47 ((
% 99.25/13.47 (infuncsetfunc) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcinfuncset) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall1) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp3) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcextLem) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp4) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq2) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2lamEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifp) =>
% 99.25/13.47 ((
% 99.25/13.47 (theeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrue) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueorfalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextT) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTI) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTELcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTERcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT1) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT2) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT3) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTnotintersectT) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementImpComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementSubsetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementInPowersetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (contraSubsetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTcontraSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTILcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTIRcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion2) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (intersectInPowersetIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpNotIn1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpInComplement1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTEcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementUnionInPowersetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule0) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_5) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all2) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1SetBreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (choice2fnsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all1) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compEex) =>
% 99.25/13.47 ((
% 99.25/13.47 (!!) @ (
% 99.25/13.47 (('#B') @ (
% 99.25/13.47 !!) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 !!))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#C') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl475])).
% 99.25/13.47 thf(zip_derived_cl496, plain,
% 99.25/13.47 (~ (((upairsetIL) =>
% 99.25/13.47 (((upairsetIR) =>
% 99.25/13.47 (((emptyE1) =>
% 99.25/13.47 (((vacuousDall) =>
% 99.25/13.47 (((quantDeMorgan1) =>
% 99.25/13.47 (((quantDeMorgan2) =>
% 99.25/13.47 (((quantDeMorgan3) =>
% 99.25/13.47 (((quantDeMorgan4) =>
% 99.25/13.47 (((prop2setI) =>
% 99.25/13.47 (((prop2set2propI) =>
% 99.25/13.47 (((notdexE) =>
% 99.25/13.47 (((notdallE) =>
% 99.25/13.47 (((exuI1) =>
% 99.25/13.47 (((exuI3) =>
% 99.25/13.47 (((exuI2) =>
% 99.25/13.47 (((inCongP) =>
% 99.25/13.47 (((in__Cong) =>
% 99.25/13.47 (((exuE3u) =>
% 99.25/13.47 (((exu__Cong) =>
% 99.25/13.47 (((setadjoin__Cong) =>
% 99.25/13.47 (((powerset__Cong) =>
% 99.25/13.47 (((setunion__Cong) =>
% 99.25/13.47 (((exuEu) =>
% 99.25/13.47 (((descr__Cong) =>
% 99.25/13.47 (((dsetconstr__Cong) =>
% 99.25/13.47 (((subsetI1) =>
% 99.25/13.47 (((eqimpsubset2) =>
% 99.25/13.47 (((eqimpsubset1) =>
% 99.25/13.47 (((subsetI2) =>
% 99.25/13.47 (((emptysetsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetE) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (notsubsetI) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetRefl) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTrans) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subset2powerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetemptysetimpeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepInPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2IR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionEcases) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectI) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset5) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset3) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectER) =>
% 99.25/13.47 ((
% 99.25/13.47 (disjointsetsI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset4) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (bs114d) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusI) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusER) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusERneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusELneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusILneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusIRneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffE) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg2) =>
% 99.25/13.47 ((
% 99.25/13.47 (secondinupair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairiskpair) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairp) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2E) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairsubunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairinpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem3) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair1) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton1) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I2) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsuniq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (theprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstin) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR11) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR12) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR1) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairequniteq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemER) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempaircEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrI) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrERa) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrER) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcImageSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (apProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (app) =>
% 99.25/13.47 ((
% 99.25/13.47 (infuncsetfunc) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcinfuncset) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall1) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp3) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcextLem) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp4) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq2) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2lamEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifp) =>
% 99.25/13.47 ((
% 99.25/13.47 (theeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrue) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueorfalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextT) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTI) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTELcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTERcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT1) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT2) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT3) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTnotintersectT) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementImpComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementSubsetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementInPowersetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (contraSubsetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTcontraSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTILcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTIRcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion2) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (intersectInPowersetIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpNotIn1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpInComplement1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTEcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementUnionInPowersetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule0) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_5) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all2) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1SetBreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (choice2fnsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all1) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compEex) =>
% 99.25/13.47 ((
% 99.25/13.47 (!!) @ (
% 99.25/13.47 (('#B') @ (
% 99.25/13.47 !!) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 !!))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#C') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl485])).
% 99.25/13.47 thf(zip_derived_cl507, plain,
% 99.25/13.47 (~ (((upairsetIR) =>
% 99.25/13.47 (((emptyE1) =>
% 99.25/13.47 (((vacuousDall) =>
% 99.25/13.47 (((quantDeMorgan1) =>
% 99.25/13.47 (((quantDeMorgan2) =>
% 99.25/13.47 (((quantDeMorgan3) =>
% 99.25/13.47 (((quantDeMorgan4) =>
% 99.25/13.47 (((prop2setI) =>
% 99.25/13.47 (((prop2set2propI) =>
% 99.25/13.47 (((notdexE) =>
% 99.25/13.47 (((notdallE) =>
% 99.25/13.47 (((exuI1) =>
% 99.25/13.47 (((exuI3) =>
% 99.25/13.47 (((exuI2) =>
% 99.25/13.47 (((inCongP) =>
% 99.25/13.47 (((in__Cong) =>
% 99.25/13.47 (((exuE3u) =>
% 99.25/13.47 (((exu__Cong) =>
% 99.25/13.47 (((setadjoin__Cong) =>
% 99.25/13.47 (((powerset__Cong) =>
% 99.25/13.47 (((setunion__Cong) =>
% 99.25/13.47 (((exuEu) =>
% 99.25/13.47 (((descr__Cong) =>
% 99.25/13.47 (((dsetconstr__Cong) =>
% 99.25/13.47 (((subsetI1) =>
% 99.25/13.47 (((eqimpsubset2) =>
% 99.25/13.47 (((eqimpsubset1) =>
% 99.25/13.47 (((subsetI2) =>
% 99.25/13.47 (((emptysetsubset) =>
% 99.25/13.47 (((subsetE) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (notsubsetI) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetRefl) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTrans) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subset2powerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetemptysetimpeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepInPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2IR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionEcases) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectI) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset5) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset3) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectER) =>
% 99.25/13.47 ((
% 99.25/13.47 (disjointsetsI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset4) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (bs114d) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusI) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusER) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusERneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusELneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusILneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusIRneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffE) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg2) =>
% 99.25/13.47 ((
% 99.25/13.47 (secondinupair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairiskpair) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairp) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2E) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairsubunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairinpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem3) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair1) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton1) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I2) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsuniq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (theprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstin) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR11) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR12) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR1) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairequniteq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemER) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempaircEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrI) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrERa) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrER) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcImageSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (apProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (app) =>
% 99.25/13.47 ((
% 99.25/13.47 (infuncsetfunc) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcinfuncset) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall1) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp3) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcextLem) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp4) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq2) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2lamEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifp) =>
% 99.25/13.47 ((
% 99.25/13.47 (theeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrue) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueorfalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextT) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTI) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTELcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTERcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT1) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT2) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT3) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTnotintersectT) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementImpComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementSubsetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementInPowersetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (contraSubsetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTcontraSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTILcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTIRcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion2) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (intersectInPowersetIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpNotIn1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpInComplement1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTEcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementUnionInPowersetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule0) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_5) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all2) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1SetBreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (choice2fnsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all1) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compEex) =>
% 99.25/13.47 ((
% 99.25/13.47 (!!) @ (
% 99.25/13.47 (('#B') @ (
% 99.25/13.47 !!) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 !!))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#C') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl496])).
% 99.25/13.47 thf(zip_derived_cl517, plain,
% 99.25/13.47 (~ (((emptyE1) =>
% 99.25/13.47 (((vacuousDall) =>
% 99.25/13.47 (((quantDeMorgan1) =>
% 99.25/13.47 (((quantDeMorgan2) =>
% 99.25/13.47 (((quantDeMorgan3) =>
% 99.25/13.47 (((quantDeMorgan4) =>
% 99.25/13.47 (((prop2setI) =>
% 99.25/13.47 (((prop2set2propI) =>
% 99.25/13.47 (((notdexE) =>
% 99.25/13.47 (((notdallE) =>
% 99.25/13.47 (((exuI1) =>
% 99.25/13.47 (((exuI3) =>
% 99.25/13.47 (((exuI2) =>
% 99.25/13.47 (((inCongP) =>
% 99.25/13.47 (((in__Cong) =>
% 99.25/13.47 (((exuE3u) =>
% 99.25/13.47 (((exu__Cong) =>
% 99.25/13.47 (((setadjoin__Cong) =>
% 99.25/13.47 (((powerset__Cong) =>
% 99.25/13.47 (((setunion__Cong) =>
% 99.25/13.47 (((exuEu) =>
% 99.25/13.47 (((descr__Cong) =>
% 99.25/13.47 (((dsetconstr__Cong) =>
% 99.25/13.47 (((subsetI1) =>
% 99.25/13.47 (((eqimpsubset2) =>
% 99.25/13.47 (((eqimpsubset1) =>
% 99.25/13.47 (((subsetI2) =>
% 99.25/13.47 (((emptysetsubset) =>
% 99.25/13.47 (((subsetE) =>
% 99.25/13.47 (((subsetE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (notsubsetI) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetRefl) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTrans) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subset2powerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetemptysetimpeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepInPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2IR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionEcases) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectI) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset5) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset3) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectER) =>
% 99.25/13.47 ((
% 99.25/13.47 (disjointsetsI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset4) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (bs114d) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusI) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusER) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusERneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusELneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusILneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusIRneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffE) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg2) =>
% 99.25/13.47 ((
% 99.25/13.47 (secondinupair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairiskpair) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairp) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2E) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairsubunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairinpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem3) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair1) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton1) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I2) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsuniq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (theprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstin) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR11) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR12) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR1) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairequniteq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemER) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempaircEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrI) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrERa) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrER) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcImageSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (apProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (app) =>
% 99.25/13.47 ((
% 99.25/13.47 (infuncsetfunc) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcinfuncset) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall1) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp3) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcextLem) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp4) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq2) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2lamEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifp) =>
% 99.25/13.47 ((
% 99.25/13.47 (theeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrue) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueorfalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextT) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTI) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTELcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTERcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT1) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT2) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT3) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTnotintersectT) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementImpComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementSubsetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementInPowersetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (contraSubsetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTcontraSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTILcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTIRcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion2) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (intersectInPowersetIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpNotIn1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpInComplement1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTEcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementUnionInPowersetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule0) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_5) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all2) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1SetBreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (choice2fnsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all1) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compEex) =>
% 99.25/13.47 ((
% 99.25/13.47 (!!) @ (
% 99.25/13.47 (('#B') @ (
% 99.25/13.47 !!) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 !!))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#C') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl507])).
% 99.25/13.47 thf(zip_derived_cl528, plain,
% 99.25/13.47 (~ (((vacuousDall) =>
% 99.25/13.47 (((quantDeMorgan1) =>
% 99.25/13.47 (((quantDeMorgan2) =>
% 99.25/13.47 (((quantDeMorgan3) =>
% 99.25/13.47 (((quantDeMorgan4) =>
% 99.25/13.47 (((prop2setI) =>
% 99.25/13.47 (((prop2set2propI) =>
% 99.25/13.47 (((notdexE) =>
% 99.25/13.47 (((notdallE) =>
% 99.25/13.47 (((exuI1) =>
% 99.25/13.47 (((exuI3) =>
% 99.25/13.47 (((exuI2) =>
% 99.25/13.47 (((inCongP) =>
% 99.25/13.47 (((in__Cong) =>
% 99.25/13.47 (((exuE3u) =>
% 99.25/13.47 (((exu__Cong) =>
% 99.25/13.47 (((setadjoin__Cong) =>
% 99.25/13.47 (((powerset__Cong) =>
% 99.25/13.47 (((setunion__Cong) =>
% 99.25/13.47 (((exuEu) =>
% 99.25/13.47 (((descr__Cong) =>
% 99.25/13.47 (((dsetconstr__Cong) =>
% 99.25/13.47 (((subsetI1) =>
% 99.25/13.47 (((eqimpsubset2) =>
% 99.25/13.47 (((eqimpsubset1) =>
% 99.25/13.47 (((subsetI2) =>
% 99.25/13.47 (((emptysetsubset) =>
% 99.25/13.47 (((subsetE) =>
% 99.25/13.47 (((subsetE2) =>
% 99.25/13.47 (((notsubsetI) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetRefl) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTrans) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subset2powerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetemptysetimpeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepInPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2IR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionEcases) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectI) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset5) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset3) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectER) =>
% 99.25/13.47 ((
% 99.25/13.47 (disjointsetsI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset4) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (bs114d) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusI) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusER) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusERneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusELneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusILneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusIRneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffE) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg2) =>
% 99.25/13.47 ((
% 99.25/13.47 (secondinupair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairiskpair) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairp) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2E) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairsubunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairinpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem3) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair1) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton1) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I2) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsuniq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (theprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstin) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR11) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR12) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR1) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairequniteq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemER) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempaircEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrI) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrERa) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrER) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcImageSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (apProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (app) =>
% 99.25/13.47 ((
% 99.25/13.47 (infuncsetfunc) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcinfuncset) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall1) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp3) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcextLem) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcGraphProp4) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcext2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2apEq2) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta1) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2lamEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (beta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (eta2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalseProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp1) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueProp2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ifp) =>
% 99.25/13.47 ((
% 99.25/13.47 (theeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrue) =>
% 99.25/13.47 ((
% 99.25/13.47 (iffalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (iftrueorfalse) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementT_lem) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextT) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTI) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTELcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectTERcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT1) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT2) =>
% 99.25/13.47 ((
% 99.25/13.47 (contrasubsetT3) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub1) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (doubleComplementEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTnotintersectT) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementImpComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementSubsetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementInPowersetComplementIntersect) =>
% 99.25/13.47 ((
% 99.25/13.47 (contraSubsetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementTcontraSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTILcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTIRcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInUnion2) =>
% 99.25/13.47 ((
% 99.25/13.47 (inIntersectImpInIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (intersectInPowersetIntersectUnions) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpNotIn1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inComplementUnionImpInComplement1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionTEcontra) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a1) =>
% 99.25/13.47 ((
% 99.25/13.47 (complementUnionInPowersetComplement) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan1) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2a) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b2) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2b) =>
% 99.25/13.47 ((
% 99.25/13.47 (demorgan2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule0) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz13rule4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_1) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_2) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_3) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_4) =>
% 99.25/13.47 ((
% 99.25/13.47 (woz1_5) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all2) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1SetBreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (choice2fnsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1all1) =>
% 99.25/13.47 ((
% 99.25/13.47 (subbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (eqbreln1) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1invE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compI) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compE) =>
% 99.25/13.47 ((
% 99.25/13.47 (breln1compEex) =>
% 99.25/13.47 ((
% 99.25/13.47 (!!) @ (
% 99.25/13.47 (('#B') @ (
% 99.25/13.47 !!) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 !!))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#S') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#S') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 =>))) @
% 99.25/13.47 breln1)))))) @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#C') @ (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 (
% 99.25/13.47 (
% 99.25/13.47 ('#B') @ (
% 99.25/13.47 '#B') @
% 99.25/13.47 breln1)))) @
% 99.25/13.47 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl517])).
% 99.25/13.47 thf(zip_derived_cl537, plain,
% 99.25/13.47 (~ (((quantDeMorgan1) =>
% 99.25/13.47 (((quantDeMorgan2) =>
% 99.25/13.47 (((quantDeMorgan3) =>
% 99.25/13.47 (((quantDeMorgan4) =>
% 99.25/13.47 (((prop2setI) =>
% 99.25/13.47 (((prop2set2propI) =>
% 99.25/13.47 (((notdexE) =>
% 99.25/13.47 (((notdallE) =>
% 99.25/13.47 (((exuI1) =>
% 99.25/13.47 (((exuI3) =>
% 99.25/13.47 (((exuI2) =>
% 99.25/13.47 (((inCongP) =>
% 99.25/13.47 (((in__Cong) =>
% 99.25/13.47 (((exuE3u) =>
% 99.25/13.47 (((exu__Cong) =>
% 99.25/13.47 (((setadjoin__Cong) =>
% 99.25/13.47 (((powerset__Cong) =>
% 99.25/13.47 (((setunion__Cong) =>
% 99.25/13.47 (((exuEu) =>
% 99.25/13.47 (((descr__Cong) =>
% 99.25/13.47 (((dsetconstr__Cong) =>
% 99.25/13.47 (((subsetI1) =>
% 99.25/13.47 (((eqimpsubset2) =>
% 99.25/13.47 (((eqimpsubset1) =>
% 99.25/13.47 (((subsetI2) =>
% 99.25/13.47 (((emptysetsubset) =>
% 99.25/13.47 (((subsetE) =>
% 99.25/13.47 (((subsetE2) =>
% 99.25/13.47 (((notsubsetI) =>
% 99.25/13.47 (((notequalI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (notequalI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetRefl) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetTrans) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setadjoinSub2) =>
% 99.25/13.47 ((
% 99.25/13.47 (subset2powerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (setextsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (subsetemptysetimpeq) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetE1) =>
% 99.25/13.47 ((
% 99.25/13.47 (inPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (powersetsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepInPowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (sepSubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2IR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionEcases) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionE) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binunionRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectI) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset5) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset3) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectER) =>
% 99.25/13.47 ((
% 99.25/13.47 (disjointsetsI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectRsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset4) =>
% 99.25/13.47 ((
% 99.25/13.47 (binintersectSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (bs114d) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusI) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusER) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusERneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusELneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusILneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusIRneg) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusLsub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setminusSubset1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffE) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffI2) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg1) =>
% 99.25/13.47 ((
% 99.25/13.47 (symdiffIneg2) =>
% 99.25/13.47 ((
% 99.25/13.47 (secondinupair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairIR) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairiskpair) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairp) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsubset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowerset) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletoninpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairset2E) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairsubunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairinpowunion) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem2) =>
% 99.25/13.47 ((
% 99.25/13.47 (ubforcartprodlem3) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair1) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempair) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionE2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton1) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setunionsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1E1) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I) =>
% 99.25/13.47 ((
% 99.25/13.47 (ex1I2) =>
% 99.25/13.47 ((
% 99.25/13.47 (singletonsuniq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (theprop) =>
% 99.25/13.47 ((
% 99.25/13.47 (kfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstin) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjL) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR11) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR12) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR1) =>
% 99.25/13.47 ((
% 99.25/13.47 (upairequniteq) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR2) =>
% 99.25/13.47 ((
% 99.25/13.47 (setukpairinjR) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndsingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (ksndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (kpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndin) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemEL) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairmemER) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodmempaircEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodfstpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodsndpairEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (cartprodpairsurjEq) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrI) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrSub) =>
% 99.25/13.47 ((
% 99.25/13.47 (setOfPairsIsBReln) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrERa) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL1) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrEL2) =>
% 99.25/13.47 ((
% 99.25/13.47 (dpsetconstrER) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcImageSingleton) =>
% 99.25/13.47 ((
% 99.25/13.47 (apProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (app) =>
% 99.25/13.47 ((
% 99.25/13.47 (infuncsetfunc) =>
% 99.25/13.47 ((
% 99.25/13.47 (ap2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (funcinfuncset) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamProp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lamp) =>
% 99.25/13.47 ((
% 99.25/13.47 (lam2p) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall1) =>
% 99.25/13.47 ((
% 99.25/13.47 (brelnall2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1E2) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp3) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcextLem) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp4) =>
% 99.25/13.48 ((
% 99.25/13.48 (subbreln) =>
% 99.25/13.48 ((
% 99.25/13.48 (eqbreln) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcext) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcext2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ap2apEq1) =>
% 99.25/13.48 ((
% 99.25/13.48 (ap2apEq2) =>
% 99.25/13.48 ((
% 99.25/13.48 (beta1) =>
% 99.25/13.48 ((
% 99.25/13.48 (eta1) =>
% 99.25/13.48 ((
% 99.25/13.48 (lam2lamEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (beta2) =>
% 99.25/13.48 ((
% 99.25/13.48 (eta2) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalseProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalseProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ifSingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (ifp) =>
% 99.25/13.48 ((
% 99.25/13.48 (theeq) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrue) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalse) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueorfalse) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (setextT) =>
% 99.25/13.48 ((
% 99.25/13.48 (subsetTI) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetTI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetTE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectTELcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectTERcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT1) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT2) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT3) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementSub1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementSub2) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTnotintersectT) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementImpComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementSubsetComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementInPowersetComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (contraSubsetComplement) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTcontraSubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTILcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTIRcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInUnion) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInUnion2) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInIntersectUnions) =>
% 99.25/13.48 ((
% 99.25/13.48 (intersectInPowersetIntersectUnions) =>
% 99.25/13.48 ((
% 99.25/13.48 (inComplementUnionImpNotIn1) =>
% 99.25/13.48 ((
% 99.25/13.48 (inComplementUnionImpInComplement1) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTE) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTEcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementUnionInPowersetComplement) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a2) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1a) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1b) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2b2) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2b) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule0) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule1) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule3) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule4) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_1) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_3) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_4) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_5) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1all2) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1SetBreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (choice2fnsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (setOfPairsIsBReln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1all1) =>
% 99.25/13.48 ((
% 99.25/13.48 (subbreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (eqbreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invI) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invE) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compI) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compE) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compEex) =>
% 99.25/13.48 ((
% 99.25/13.48 (!!) @ (
% 99.25/13.48 (('#B') @ (
% 99.25/13.48 !!) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#S') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#S') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 =>))) @
% 99.25/13.48 breln1)))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 !!))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#S') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#S') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 =>))) @
% 99.25/13.48 breln1)))))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#C') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 breln1)))) @
% 99.25/13.48 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl528])).
% 99.25/13.48 thf(zip_derived_cl546, plain,
% 99.25/13.48 (~ (((quantDeMorgan2) =>
% 99.25/13.48 (((quantDeMorgan3) =>
% 99.25/13.48 (((quantDeMorgan4) =>
% 99.25/13.48 (((prop2setI) =>
% 99.25/13.48 (((prop2set2propI) =>
% 99.25/13.48 (((notdexE) =>
% 99.25/13.48 (((notdallE) =>
% 99.25/13.48 (((exuI1) =>
% 99.25/13.48 (((exuI3) =>
% 99.25/13.48 (((exuI2) =>
% 99.25/13.48 (((inCongP) =>
% 99.25/13.48 (((in__Cong) =>
% 99.25/13.48 (((exuE3u) =>
% 99.25/13.48 (((exu__Cong) =>
% 99.25/13.48 (((setadjoin__Cong) =>
% 99.25/13.48 (((powerset__Cong) =>
% 99.25/13.48 (((setunion__Cong) =>
% 99.25/13.48 (((exuEu) =>
% 99.25/13.48 (((descr__Cong) =>
% 99.25/13.48 (((dsetconstr__Cong) =>
% 99.25/13.48 (((subsetI1) =>
% 99.25/13.48 (((eqimpsubset2) =>
% 99.25/13.48 (((eqimpsubset1) =>
% 99.25/13.48 (((subsetI2) =>
% 99.25/13.48 (((emptysetsubset) =>
% 99.25/13.48 (((subsetE) =>
% 99.25/13.48 (((subsetE2) =>
% 99.25/13.48 (((notsubsetI) =>
% 99.25/13.48 (((notequalI1) =>
% 99.25/13.48 (((notequalI2) =>
% 99.25/13.48 ((
% 99.25/13.48 (subsetRefl) =>
% 99.25/13.48 ((
% 99.25/13.48 (subsetTrans) =>
% 99.25/13.48 ((
% 99.25/13.48 (setadjoinSub) =>
% 99.25/13.48 ((
% 99.25/13.48 (setadjoinSub2) =>
% 99.25/13.48 ((
% 99.25/13.48 (subset2powerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (setextsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (subsetemptysetimpeq) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (inPowerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetsubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (sepInPowerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (sepSubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionIL) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairset2IR) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionIR) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionEcases) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionE) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionLsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionRsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectI) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset5) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectEL) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectLsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset2) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset3) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectER) =>
% 99.25/13.48 ((
% 99.25/13.48 (disjointsetsI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectRsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset4) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset1) =>
% 99.25/13.48 ((
% 99.25/13.48 (bs114d) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusI) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusEL) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusER) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusSubset2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusERneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusELneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusILneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusIRneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusLsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusSubset1) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffE) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffI2) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffIneg1) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffIneg2) =>
% 99.25/13.48 ((
% 99.25/13.48 (secondinupair) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairIL) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairIR) =>
% 99.25/13.48 ((
% 99.25/13.48 (kpairiskpair) =>
% 99.25/13.48 ((
% 99.25/13.48 (kpairp) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletonsubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletoninpowerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletoninpowunion) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairset2E) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairsubunion) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairinpowunion) =>
% 99.25/13.48 ((
% 99.25/13.48 (ubforcartprodlem1) =>
% 99.25/13.48 ((
% 99.25/13.48 (ubforcartprodlem2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ubforcartprodlem3) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairin) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodmempair1) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodmempair) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionE2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionsingleton1) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionsingleton2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletonprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1E1) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1I) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1I2) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletonsuniq) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjL1) =>
% 99.25/13.48 ((
% 99.25/13.48 (kfstsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (theprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (kfstpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodfstin) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjL2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjL) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR11) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR12) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR1) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairequniteq) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR) =>
% 99.25/13.48 ((
% 99.25/13.48 (ksndsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (ksndpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (kpairsurjEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodsndin) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairmemEL) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairmemER) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodmempaircEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodfstpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodsndpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairsurjEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrI) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrSub) =>
% 99.25/13.48 ((
% 99.25/13.48 (setOfPairsIsBReln) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrERa) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrEL1) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrEL2) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrER) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcImageSingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (apProp) =>
% 99.25/13.48 ((
% 99.25/13.48 (app) =>
% 99.25/13.48 ((
% 99.25/13.48 (infuncsetfunc) =>
% 99.25/13.48 ((
% 99.25/13.48 (ap2p) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcinfuncset) =>
% 99.25/13.48 ((
% 99.25/13.48 (lamProp) =>
% 99.25/13.48 ((
% 99.25/13.48 (lamp) =>
% 99.25/13.48 ((
% 99.25/13.48 (lam2p) =>
% 99.25/13.48 ((
% 99.25/13.48 (brelnall1) =>
% 99.25/13.48 ((
% 99.25/13.48 (brelnall2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1E2) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp3) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcextLem) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp4) =>
% 99.25/13.48 ((
% 99.25/13.48 (subbreln) =>
% 99.25/13.48 ((
% 99.25/13.48 (eqbreln) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcext) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcext2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ap2apEq1) =>
% 99.25/13.48 ((
% 99.25/13.48 (ap2apEq2) =>
% 99.25/13.48 ((
% 99.25/13.48 (beta1) =>
% 99.25/13.48 ((
% 99.25/13.48 (eta1) =>
% 99.25/13.48 ((
% 99.25/13.48 (lam2lamEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (beta2) =>
% 99.25/13.48 ((
% 99.25/13.48 (eta2) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalseProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalseProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ifSingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (ifp) =>
% 99.25/13.48 ((
% 99.25/13.48 (theeq) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrue) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalse) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueorfalse) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (setextT) =>
% 99.25/13.48 ((
% 99.25/13.48 (subsetTI) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetTI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetTE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectTELcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectTERcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT1) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT2) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT3) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementSub1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementSub2) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTnotintersectT) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementImpComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementSubsetComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementInPowersetComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (contraSubsetComplement) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTcontraSubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTILcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTIRcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInUnion) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInUnion2) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInIntersectUnions) =>
% 99.25/13.48 ((
% 99.25/13.48 (intersectInPowersetIntersectUnions) =>
% 99.25/13.48 ((
% 99.25/13.48 (inComplementUnionImpNotIn1) =>
% 99.25/13.48 ((
% 99.25/13.48 (inComplementUnionImpInComplement1) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTE) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTEcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementUnionInPowersetComplement) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a2) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1a) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1b) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2b2) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2b) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule0) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule1) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule3) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule4) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_1) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_3) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_4) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_5) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1all2) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1SetBreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (choice2fnsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (setOfPairsIsBReln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1all1) =>
% 99.25/13.48 ((
% 99.25/13.48 (subbreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (eqbreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invI) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invE) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compI) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compE) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compEex) =>
% 99.25/13.48 ((
% 99.25/13.48 (!!) @ (
% 99.25/13.48 (('#B') @ (
% 99.25/13.48 !!) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#S') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#S') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 =>))) @
% 99.25/13.48 breln1)))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 !!))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#S') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#S') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 =>))) @
% 99.25/13.48 breln1)))))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#C') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 breln1)))) @
% 99.25/13.48 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl537])).
% 99.25/13.48 thf(zip_derived_cl553, plain,
% 99.25/13.48 (~ (((quantDeMorgan3) =>
% 99.25/13.48 (((quantDeMorgan4) =>
% 99.25/13.48 (((prop2setI) =>
% 99.25/13.48 (((prop2set2propI) =>
% 99.25/13.48 (((notdexE) =>
% 99.25/13.48 (((notdallE) =>
% 99.25/13.48 (((exuI1) =>
% 99.25/13.48 (((exuI3) =>
% 99.25/13.48 (((exuI2) =>
% 99.25/13.48 (((inCongP) =>
% 99.25/13.48 (((in__Cong) =>
% 99.25/13.48 (((exuE3u) =>
% 99.25/13.48 (((exu__Cong) =>
% 99.25/13.48 (((setadjoin__Cong) =>
% 99.25/13.48 (((powerset__Cong) =>
% 99.25/13.48 (((setunion__Cong) =>
% 99.25/13.48 (((exuEu) =>
% 99.25/13.48 (((descr__Cong) =>
% 99.25/13.48 (((dsetconstr__Cong) =>
% 99.25/13.48 (((subsetI1) =>
% 99.25/13.48 (((eqimpsubset2) =>
% 99.25/13.48 (((eqimpsubset1) =>
% 99.25/13.48 (((subsetI2) =>
% 99.25/13.48 (((emptysetsubset) =>
% 99.25/13.48 (((subsetE) =>
% 99.25/13.48 (((subsetE2) =>
% 99.25/13.48 (((notsubsetI) =>
% 99.25/13.48 (((notequalI1) =>
% 99.25/13.48 (((notequalI2) =>
% 99.25/13.48 (((subsetRefl) =>
% 99.25/13.48 ((
% 99.25/13.48 (subsetTrans) =>
% 99.25/13.48 ((
% 99.25/13.48 (setadjoinSub) =>
% 99.25/13.48 ((
% 99.25/13.48 (setadjoinSub2) =>
% 99.25/13.48 ((
% 99.25/13.48 (subset2powerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (setextsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (subsetemptysetimpeq) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (inPowerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetsubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (sepInPowerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (sepSubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionIL) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairset2IR) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionIR) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionEcases) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionE) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionLsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionRsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectI) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset5) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectEL) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectLsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset2) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset3) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectER) =>
% 99.25/13.48 ((
% 99.25/13.48 (disjointsetsI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectRsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset4) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset1) =>
% 99.25/13.48 ((
% 99.25/13.48 (bs114d) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusI) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusEL) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusER) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusSubset2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusERneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusELneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusILneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusIRneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusLsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusSubset1) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffE) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffI2) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffIneg1) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffIneg2) =>
% 99.25/13.48 ((
% 99.25/13.48 (secondinupair) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairIL) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairIR) =>
% 99.25/13.48 ((
% 99.25/13.48 (kpairiskpair) =>
% 99.25/13.48 ((
% 99.25/13.48 (kpairp) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletonsubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletoninpowerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletoninpowunion) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairset2E) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairsubunion) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairinpowunion) =>
% 99.25/13.48 ((
% 99.25/13.48 (ubforcartprodlem1) =>
% 99.25/13.48 ((
% 99.25/13.48 (ubforcartprodlem2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ubforcartprodlem3) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairin) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodmempair1) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodmempair) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionE2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionsingleton1) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionsingleton2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletonprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1E1) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1I) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1I2) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletonsuniq) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjL1) =>
% 99.25/13.48 ((
% 99.25/13.48 (kfstsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (theprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (kfstpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodfstin) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjL2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjL) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR11) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR12) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR1) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairequniteq) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR) =>
% 99.25/13.48 ((
% 99.25/13.48 (ksndsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (ksndpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (kpairsurjEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodsndin) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairmemEL) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairmemER) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodmempaircEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodfstpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodsndpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairsurjEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrI) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrSub) =>
% 99.25/13.48 ((
% 99.25/13.48 (setOfPairsIsBReln) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrERa) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrEL1) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrEL2) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrER) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcImageSingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (apProp) =>
% 99.25/13.48 ((
% 99.25/13.48 (app) =>
% 99.25/13.48 ((
% 99.25/13.48 (infuncsetfunc) =>
% 99.25/13.48 ((
% 99.25/13.48 (ap2p) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcinfuncset) =>
% 99.25/13.48 ((
% 99.25/13.48 (lamProp) =>
% 99.25/13.48 ((
% 99.25/13.48 (lamp) =>
% 99.25/13.48 ((
% 99.25/13.48 (lam2p) =>
% 99.25/13.48 ((
% 99.25/13.48 (brelnall1) =>
% 99.25/13.48 ((
% 99.25/13.48 (brelnall2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1E2) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp3) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcextLem) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp4) =>
% 99.25/13.48 ((
% 99.25/13.48 (subbreln) =>
% 99.25/13.48 ((
% 99.25/13.48 (eqbreln) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcext) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcext2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ap2apEq1) =>
% 99.25/13.48 ((
% 99.25/13.48 (ap2apEq2) =>
% 99.25/13.48 ((
% 99.25/13.48 (beta1) =>
% 99.25/13.48 ((
% 99.25/13.48 (eta1) =>
% 99.25/13.48 ((
% 99.25/13.48 (lam2lamEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (beta2) =>
% 99.25/13.48 ((
% 99.25/13.48 (eta2) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalseProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalseProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ifSingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (ifp) =>
% 99.25/13.48 ((
% 99.25/13.48 (theeq) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrue) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalse) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueorfalse) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (setextT) =>
% 99.25/13.48 ((
% 99.25/13.48 (subsetTI) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetTI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetTE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectTELcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectTERcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT1) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT2) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT3) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementSub1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementSub2) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTnotintersectT) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementImpComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementSubsetComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementInPowersetComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (contraSubsetComplement) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTcontraSubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTILcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTIRcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInUnion) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInUnion2) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInIntersectUnions) =>
% 99.25/13.48 ((
% 99.25/13.48 (intersectInPowersetIntersectUnions) =>
% 99.25/13.48 ((
% 99.25/13.48 (inComplementUnionImpNotIn1) =>
% 99.25/13.48 ((
% 99.25/13.48 (inComplementUnionImpInComplement1) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTE) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTEcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementUnionInPowersetComplement) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a2) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1a) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1b) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2b2) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2b) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule0) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule1) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule3) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule4) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_1) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_3) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_4) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_5) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1all2) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1SetBreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (choice2fnsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (setOfPairsIsBReln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1all1) =>
% 99.25/13.48 ((
% 99.25/13.48 (subbreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (eqbreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invI) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invE) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compI) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compE) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compEex) =>
% 99.25/13.48 ((
% 99.25/13.48 (!!) @ (
% 99.25/13.48 (('#B') @ (
% 99.25/13.48 !!) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#S') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#S') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 =>))) @
% 99.25/13.48 breln1)))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 !!))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#S') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#S') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 =>))) @
% 99.25/13.48 breln1)))))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#C') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 breln1)))) @
% 99.25/13.48 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl546])).
% 99.25/13.48 thf(zip_derived_cl561, plain,
% 99.25/13.48 (~ (((quantDeMorgan4) =>
% 99.25/13.48 (((prop2setI) =>
% 99.25/13.48 (((prop2set2propI) =>
% 99.25/13.48 (((notdexE) =>
% 99.25/13.48 (((notdallE) =>
% 99.25/13.48 (((exuI1) =>
% 99.25/13.48 (((exuI3) =>
% 99.25/13.48 (((exuI2) =>
% 99.25/13.48 (((inCongP) =>
% 99.25/13.48 (((in__Cong) =>
% 99.25/13.48 (((exuE3u) =>
% 99.25/13.48 (((exu__Cong) =>
% 99.25/13.48 (((setadjoin__Cong) =>
% 99.25/13.48 (((powerset__Cong) =>
% 99.25/13.48 (((setunion__Cong) =>
% 99.25/13.48 (((exuEu) =>
% 99.25/13.48 (((descr__Cong) =>
% 99.25/13.48 (((dsetconstr__Cong) =>
% 99.25/13.48 (((subsetI1) =>
% 99.25/13.48 (((eqimpsubset2) =>
% 99.25/13.48 (((eqimpsubset1) =>
% 99.25/13.48 (((subsetI2) =>
% 99.25/13.48 (((emptysetsubset) =>
% 99.25/13.48 (((subsetE) =>
% 99.25/13.48 (((subsetE2) =>
% 99.25/13.48 (((notsubsetI) =>
% 99.25/13.48 (((notequalI1) =>
% 99.25/13.48 (((notequalI2) =>
% 99.25/13.48 (((subsetRefl) =>
% 99.25/13.48 (((subsetTrans) =>
% 99.25/13.48 ((
% 99.25/13.48 (setadjoinSub) =>
% 99.25/13.48 ((
% 99.25/13.48 (setadjoinSub2) =>
% 99.25/13.48 ((
% 99.25/13.48 (subset2powerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (setextsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (subsetemptysetimpeq) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (inPowerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetsubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (sepInPowerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (sepSubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionIL) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairset2IR) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionIR) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionEcases) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionE) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionLsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionRsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectI) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset5) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectEL) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectLsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset2) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset3) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectER) =>
% 99.25/13.48 ((
% 99.25/13.48 (disjointsetsI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectRsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset4) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset1) =>
% 99.25/13.48 ((
% 99.25/13.48 (bs114d) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusI) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusEL) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusER) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusSubset2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusERneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusELneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusILneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusIRneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusLsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusSubset1) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffE) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffI2) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffIneg1) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffIneg2) =>
% 99.25/13.48 ((
% 99.25/13.48 (secondinupair) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairIL) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairIR) =>
% 99.25/13.48 ((
% 99.25/13.48 (kpairiskpair) =>
% 99.25/13.48 ((
% 99.25/13.48 (kpairp) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletonsubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletoninpowerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletoninpowunion) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairset2E) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairsubunion) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairinpowunion) =>
% 99.25/13.48 ((
% 99.25/13.48 (ubforcartprodlem1) =>
% 99.25/13.48 ((
% 99.25/13.48 (ubforcartprodlem2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ubforcartprodlem3) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairin) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodmempair1) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodmempair) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionE2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionsingleton1) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionsingleton2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletonprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1E1) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1I) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1I2) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletonsuniq) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjL1) =>
% 99.25/13.48 ((
% 99.25/13.48 (kfstsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (theprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (kfstpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodfstin) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjL2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjL) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR11) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR12) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR1) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairequniteq) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR) =>
% 99.25/13.48 ((
% 99.25/13.48 (ksndsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (ksndpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (kpairsurjEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodsndin) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairmemEL) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairmemER) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodmempaircEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodfstpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodsndpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairsurjEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrI) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrSub) =>
% 99.25/13.48 ((
% 99.25/13.48 (setOfPairsIsBReln) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrERa) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrEL1) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrEL2) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrER) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcImageSingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (apProp) =>
% 99.25/13.48 ((
% 99.25/13.48 (app) =>
% 99.25/13.48 ((
% 99.25/13.48 (infuncsetfunc) =>
% 99.25/13.48 ((
% 99.25/13.48 (ap2p) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcinfuncset) =>
% 99.25/13.48 ((
% 99.25/13.48 (lamProp) =>
% 99.25/13.48 ((
% 99.25/13.48 (lamp) =>
% 99.25/13.48 ((
% 99.25/13.48 (lam2p) =>
% 99.25/13.48 ((
% 99.25/13.48 (brelnall1) =>
% 99.25/13.48 ((
% 99.25/13.48 (brelnall2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1E2) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp3) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcextLem) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp4) =>
% 99.25/13.48 ((
% 99.25/13.48 (subbreln) =>
% 99.25/13.48 ((
% 99.25/13.48 (eqbreln) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcext) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcext2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ap2apEq1) =>
% 99.25/13.48 ((
% 99.25/13.48 (ap2apEq2) =>
% 99.25/13.48 ((
% 99.25/13.48 (beta1) =>
% 99.25/13.48 ((
% 99.25/13.48 (eta1) =>
% 99.25/13.48 ((
% 99.25/13.48 (lam2lamEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (beta2) =>
% 99.25/13.48 ((
% 99.25/13.48 (eta2) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalseProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalseProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ifSingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (ifp) =>
% 99.25/13.48 ((
% 99.25/13.48 (theeq) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrue) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalse) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueorfalse) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (setextT) =>
% 99.25/13.48 ((
% 99.25/13.48 (subsetTI) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetTI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetTE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectTELcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectTERcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT1) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT2) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT3) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementSub1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementSub2) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTnotintersectT) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementImpComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementSubsetComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementInPowersetComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (contraSubsetComplement) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTcontraSubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTILcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTIRcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInUnion) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInUnion2) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInIntersectUnions) =>
% 99.25/13.48 ((
% 99.25/13.48 (intersectInPowersetIntersectUnions) =>
% 99.25/13.48 ((
% 99.25/13.48 (inComplementUnionImpNotIn1) =>
% 99.25/13.48 ((
% 99.25/13.48 (inComplementUnionImpInComplement1) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTE) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTEcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementUnionInPowersetComplement) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a2) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1a) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1b) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2b2) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2b) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule0) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule1) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule3) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule4) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_1) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_3) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_4) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_5) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1all2) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1SetBreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (choice2fnsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (setOfPairsIsBReln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1all1) =>
% 99.25/13.48 ((
% 99.25/13.48 (subbreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (eqbreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invI) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invE) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compI) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compE) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compEex) =>
% 99.25/13.48 ((
% 99.25/13.48 (!!) @ (
% 99.25/13.48 (('#B') @ (
% 99.25/13.48 !!) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#S') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#S') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 =>))) @
% 99.25/13.48 breln1)))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 !!))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#S') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#S') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 =>))) @
% 99.25/13.48 breln1)))))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#C') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 breln1)))) @
% 99.25/13.48 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl553])).
% 99.25/13.48 thf(zip_derived_cl570, plain,
% 99.25/13.48 (~ (((prop2setI) =>
% 99.25/13.48 (((prop2set2propI) =>
% 99.25/13.48 (((notdexE) =>
% 99.25/13.48 (((notdallE) =>
% 99.25/13.48 (((exuI1) =>
% 99.25/13.48 (((exuI3) =>
% 99.25/13.48 (((exuI2) =>
% 99.25/13.48 (((inCongP) =>
% 99.25/13.48 (((in__Cong) =>
% 99.25/13.48 (((exuE3u) =>
% 99.25/13.48 (((exu__Cong) =>
% 99.25/13.48 (((setadjoin__Cong) =>
% 99.25/13.48 (((powerset__Cong) =>
% 99.25/13.48 (((setunion__Cong) =>
% 99.25/13.48 (((exuEu) =>
% 99.25/13.48 (((descr__Cong) =>
% 99.25/13.48 (((dsetconstr__Cong) =>
% 99.25/13.48 (((subsetI1) =>
% 99.25/13.48 (((eqimpsubset2) =>
% 99.25/13.48 (((eqimpsubset1) =>
% 99.25/13.48 (((subsetI2) =>
% 99.25/13.48 (((emptysetsubset) =>
% 99.25/13.48 (((subsetE) =>
% 99.25/13.48 (((subsetE2) =>
% 99.25/13.48 (((notsubsetI) =>
% 99.25/13.48 (((notequalI1) =>
% 99.25/13.48 (((notequalI2) =>
% 99.25/13.48 (((subsetRefl) =>
% 99.25/13.48 (((subsetTrans) =>
% 99.25/13.48 (((setadjoinSub) =>
% 99.25/13.48 ((
% 99.25/13.48 (setadjoinSub2) =>
% 99.25/13.48 ((
% 99.25/13.48 (subset2powerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (setextsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (subsetemptysetimpeq) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (inPowerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetsubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (sepInPowerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (sepSubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionIL) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairset2IR) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionIR) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionEcases) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionE) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionLsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionRsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectI) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset5) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectEL) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectLsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset2) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset3) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectER) =>
% 99.25/13.48 ((
% 99.25/13.48 (disjointsetsI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectRsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset4) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset1) =>
% 99.25/13.48 ((
% 99.25/13.48 (bs114d) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusI) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusEL) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusER) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusSubset2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusERneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusELneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusILneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusIRneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusLsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusSubset1) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffE) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffI2) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffIneg1) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffIneg2) =>
% 99.25/13.48 ((
% 99.25/13.48 (secondinupair) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairIL) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairIR) =>
% 99.25/13.48 ((
% 99.25/13.48 (kpairiskpair) =>
% 99.25/13.48 ((
% 99.25/13.48 (kpairp) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletonsubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletoninpowerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletoninpowunion) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairset2E) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairsubunion) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairinpowunion) =>
% 99.25/13.48 ((
% 99.25/13.48 (ubforcartprodlem1) =>
% 99.25/13.48 ((
% 99.25/13.48 (ubforcartprodlem2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ubforcartprodlem3) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairin) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodmempair1) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodmempair) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionE2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionsingleton1) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionsingleton2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletonprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1E1) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1I) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1I2) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletonsuniq) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjL1) =>
% 99.25/13.48 ((
% 99.25/13.48 (kfstsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (theprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (kfstpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodfstin) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjL2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjL) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR11) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR12) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR1) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairequniteq) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR) =>
% 99.25/13.48 ((
% 99.25/13.48 (ksndsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (ksndpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (kpairsurjEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodsndin) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairmemEL) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairmemER) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodmempaircEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodfstpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodsndpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairsurjEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrI) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrSub) =>
% 99.25/13.48 ((
% 99.25/13.48 (setOfPairsIsBReln) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrERa) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrEL1) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrEL2) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrER) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcImageSingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (apProp) =>
% 99.25/13.48 ((
% 99.25/13.48 (app) =>
% 99.25/13.48 ((
% 99.25/13.48 (infuncsetfunc) =>
% 99.25/13.48 ((
% 99.25/13.48 (ap2p) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcinfuncset) =>
% 99.25/13.48 ((
% 99.25/13.48 (lamProp) =>
% 99.25/13.48 ((
% 99.25/13.48 (lamp) =>
% 99.25/13.48 ((
% 99.25/13.48 (lam2p) =>
% 99.25/13.48 ((
% 99.25/13.48 (brelnall1) =>
% 99.25/13.48 ((
% 99.25/13.48 (brelnall2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1E2) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp3) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcextLem) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp4) =>
% 99.25/13.48 ((
% 99.25/13.48 (subbreln) =>
% 99.25/13.48 ((
% 99.25/13.48 (eqbreln) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcext) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcext2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ap2apEq1) =>
% 99.25/13.48 ((
% 99.25/13.48 (ap2apEq2) =>
% 99.25/13.48 ((
% 99.25/13.48 (beta1) =>
% 99.25/13.48 ((
% 99.25/13.48 (eta1) =>
% 99.25/13.48 ((
% 99.25/13.48 (lam2lamEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (beta2) =>
% 99.25/13.48 ((
% 99.25/13.48 (eta2) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalseProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalseProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ifSingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (ifp) =>
% 99.25/13.48 ((
% 99.25/13.48 (theeq) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrue) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalse) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueorfalse) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (setextT) =>
% 99.25/13.48 ((
% 99.25/13.48 (subsetTI) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetTI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetTE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectTELcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectTERcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT1) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT2) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT3) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementSub1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementSub2) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTnotintersectT) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementImpComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementSubsetComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementInPowersetComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (contraSubsetComplement) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTcontraSubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTILcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTIRcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInUnion) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInUnion2) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInIntersectUnions) =>
% 99.25/13.48 ((
% 99.25/13.48 (intersectInPowersetIntersectUnions) =>
% 99.25/13.48 ((
% 99.25/13.48 (inComplementUnionImpNotIn1) =>
% 99.25/13.48 ((
% 99.25/13.48 (inComplementUnionImpInComplement1) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTE) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTEcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementUnionInPowersetComplement) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a2) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1a) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1b) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2b2) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2b) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule0) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule1) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule3) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule4) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_1) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_3) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_4) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_5) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1all2) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1SetBreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (choice2fnsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (setOfPairsIsBReln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1all1) =>
% 99.25/13.48 ((
% 99.25/13.48 (subbreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (eqbreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invI) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invE) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compI) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compE) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compEex) =>
% 99.25/13.48 ((
% 99.25/13.48 (!!) @ (
% 99.25/13.48 (('#B') @ (
% 99.25/13.48 !!) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#S') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#S') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 =>))) @
% 99.25/13.48 breln1)))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 !!))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#S') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#S') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 =>))) @
% 99.25/13.48 breln1)))))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#C') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 breln1)))) @
% 99.25/13.48 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl561])).
% 99.25/13.48 thf(zip_derived_cl578, plain,
% 99.25/13.48 (~ (((prop2set2propI) =>
% 99.25/13.48 (((notdexE) =>
% 99.25/13.48 (((notdallE) =>
% 99.25/13.48 (((exuI1) =>
% 99.25/13.48 (((exuI3) =>
% 99.25/13.48 (((exuI2) =>
% 99.25/13.48 (((inCongP) =>
% 99.25/13.48 (((in__Cong) =>
% 99.25/13.48 (((exuE3u) =>
% 99.25/13.48 (((exu__Cong) =>
% 99.25/13.48 (((setadjoin__Cong) =>
% 99.25/13.48 (((powerset__Cong) =>
% 99.25/13.48 (((setunion__Cong) =>
% 99.25/13.48 (((exuEu) =>
% 99.25/13.48 (((descr__Cong) =>
% 99.25/13.48 (((dsetconstr__Cong) =>
% 99.25/13.48 (((subsetI1) =>
% 99.25/13.48 (((eqimpsubset2) =>
% 99.25/13.48 (((eqimpsubset1) =>
% 99.25/13.48 (((subsetI2) =>
% 99.25/13.48 (((emptysetsubset) =>
% 99.25/13.48 (((subsetE) =>
% 99.25/13.48 (((subsetE2) =>
% 99.25/13.48 (((notsubsetI) =>
% 99.25/13.48 (((notequalI1) =>
% 99.25/13.48 (((notequalI2) =>
% 99.25/13.48 (((subsetRefl) =>
% 99.25/13.48 (((subsetTrans) =>
% 99.25/13.48 (((setadjoinSub) =>
% 99.25/13.48 (((setadjoinSub2) =>
% 99.25/13.48 ((
% 99.25/13.48 (subset2powerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (setextsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (subsetemptysetimpeq) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (inPowerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetsubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (sepInPowerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (sepSubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionIL) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairset2IR) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionIR) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionEcases) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionE) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionLsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionRsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectI) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset5) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectEL) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectLsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset2) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset3) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectER) =>
% 99.25/13.48 ((
% 99.25/13.48 (disjointsetsI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectRsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset4) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset1) =>
% 99.25/13.48 ((
% 99.25/13.48 (bs114d) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusI) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusEL) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusER) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusSubset2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusERneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusELneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusILneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusIRneg) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusLsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusSubset1) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffE) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffI2) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffIneg1) =>
% 99.25/13.48 ((
% 99.25/13.48 (symdiffIneg2) =>
% 99.25/13.48 ((
% 99.25/13.48 (secondinupair) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairIL) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairIR) =>
% 99.25/13.48 ((
% 99.25/13.48 (kpairiskpair) =>
% 99.25/13.48 ((
% 99.25/13.48 (kpairp) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletonsubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletoninpowerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletoninpowunion) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairset2E) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairsubunion) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairinpowunion) =>
% 99.25/13.48 ((
% 99.25/13.48 (ubforcartprodlem1) =>
% 99.25/13.48 ((
% 99.25/13.48 (ubforcartprodlem2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ubforcartprodlem3) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairin) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodmempair1) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodmempair) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionE2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionsingleton1) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionsingleton2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setunionsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletonprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1E1) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1I) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1I2) =>
% 99.25/13.48 ((
% 99.25/13.48 (singletonsuniq) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjL1) =>
% 99.25/13.48 ((
% 99.25/13.48 (kfstsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (theprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (kfstpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodfstin) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjL2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjL) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR11) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR12) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR1) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairequniteq) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR2) =>
% 99.25/13.48 ((
% 99.25/13.48 (setukpairinjR) =>
% 99.25/13.48 ((
% 99.25/13.48 (ksndsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (ksndpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (kpairsurjEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodsndin) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairmemEL) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairmemER) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodmempaircEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodfstpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodsndpairEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (cartprodpairsurjEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrI) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrSub) =>
% 99.25/13.48 ((
% 99.25/13.48 (setOfPairsIsBReln) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrERa) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrEL1) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrEL2) =>
% 99.25/13.48 ((
% 99.25/13.48 (dpsetconstrER) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcImageSingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (apProp) =>
% 99.25/13.48 ((
% 99.25/13.48 (app) =>
% 99.25/13.48 ((
% 99.25/13.48 (infuncsetfunc) =>
% 99.25/13.48 ((
% 99.25/13.48 (ap2p) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcinfuncset) =>
% 99.25/13.48 ((
% 99.25/13.48 (lamProp) =>
% 99.25/13.48 ((
% 99.25/13.48 (lamp) =>
% 99.25/13.48 ((
% 99.25/13.48 (lam2p) =>
% 99.25/13.48 ((
% 99.25/13.48 (brelnall1) =>
% 99.25/13.48 ((
% 99.25/13.48 (brelnall2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ex1E2) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp3) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcextLem) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcGraphProp4) =>
% 99.25/13.48 ((
% 99.25/13.48 (subbreln) =>
% 99.25/13.48 ((
% 99.25/13.48 (eqbreln) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcext) =>
% 99.25/13.48 ((
% 99.25/13.48 (funcext2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ap2apEq1) =>
% 99.25/13.48 ((
% 99.25/13.48 (ap2apEq2) =>
% 99.25/13.48 ((
% 99.25/13.48 (beta1) =>
% 99.25/13.48 ((
% 99.25/13.48 (eta1) =>
% 99.25/13.48 ((
% 99.25/13.48 (lam2lamEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (beta2) =>
% 99.25/13.48 ((
% 99.25/13.48 (eta2) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalseProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalseProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueProp1) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueProp2) =>
% 99.25/13.48 ((
% 99.25/13.48 (ifSingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (ifp) =>
% 99.25/13.48 ((
% 99.25/13.48 (theeq) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrue) =>
% 99.25/13.48 ((
% 99.25/13.48 (iffalse) =>
% 99.25/13.48 ((
% 99.25/13.48 (iftrueorfalse) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (setminusT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementT_lem) =>
% 99.25/13.48 ((
% 99.25/13.48 (setextT) =>
% 99.25/13.48 ((
% 99.25/13.48 (subsetTI) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetTI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetTE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectTELcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectTERcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT1) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT2) =>
% 99.25/13.48 ((
% 99.25/13.48 (contrasubsetT3) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementSub1) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementSub2) =>
% 99.25/13.48 ((
% 99.25/13.48 (doubleComplementEq) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTnotintersectT) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementImpComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementSubsetComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementInPowersetComplementIntersect) =>
% 99.25/13.48 ((
% 99.25/13.48 (contraSubsetComplement) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementTcontraSubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTILcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTIRcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInUnion) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInUnion2) =>
% 99.25/13.48 ((
% 99.25/13.48 (inIntersectImpInIntersectUnions) =>
% 99.25/13.48 ((
% 99.25/13.48 (intersectInPowersetIntersectUnions) =>
% 99.25/13.48 ((
% 99.25/13.48 (inComplementUnionImpNotIn1) =>
% 99.25/13.48 ((
% 99.25/13.48 (inComplementUnionImpInComplement1) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTE) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionTEcontra) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a1) =>
% 99.25/13.48 ((
% 99.25/13.48 (complementUnionInPowersetComplement) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a2) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1a) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1b) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan1) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2a) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2b2) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2b) =>
% 99.25/13.48 ((
% 99.25/13.48 (demorgan2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule0) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule1) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule3) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz13rule4) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_1) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_2) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_3) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_4) =>
% 99.25/13.48 ((
% 99.25/13.48 (woz1_5) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1all2) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1SetBreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (choice2fnsingleton) =>
% 99.25/13.48 ((
% 99.25/13.48 (setOfPairsIsBReln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1all1) =>
% 99.25/13.48 ((
% 99.25/13.48 (subbreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (eqbreln1) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invI) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1invE) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compprop) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compI) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compE) =>
% 99.25/13.48 ((
% 99.25/13.48 (breln1compEex) =>
% 99.25/13.48 ((
% 99.25/13.48 (!!) @ (
% 99.25/13.48 (('#B') @ (
% 99.25/13.48 !!) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#S') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#S') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 =>))) @
% 99.25/13.48 breln1)))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 !!))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#S') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#S') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 =>))) @
% 99.25/13.48 breln1)))))) @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#C') @ (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 (
% 99.25/13.48 (
% 99.25/13.48 ('#B') @ (
% 99.25/13.48 '#B') @
% 99.25/13.48 breln1)))) @
% 99.25/13.48 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.25/13.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl570])).
% 99.25/13.48 thf(zip_derived_cl586, plain,
% 99.25/13.48 (~ (((notdexE) =>
% 99.25/13.48 (((notdallE) =>
% 99.25/13.48 (((exuI1) =>
% 99.25/13.48 (((exuI3) =>
% 99.25/13.48 (((exuI2) =>
% 99.25/13.48 (((inCongP) =>
% 99.25/13.48 (((in__Cong) =>
% 99.25/13.48 (((exuE3u) =>
% 99.25/13.48 (((exu__Cong) =>
% 99.25/13.48 (((setadjoin__Cong) =>
% 99.25/13.48 (((powerset__Cong) =>
% 99.25/13.48 (((setunion__Cong) =>
% 99.25/13.48 (((exuEu) =>
% 99.25/13.48 (((descr__Cong) =>
% 99.25/13.48 (((dsetconstr__Cong) =>
% 99.25/13.48 (((subsetI1) =>
% 99.25/13.48 (((eqimpsubset2) =>
% 99.25/13.48 (((eqimpsubset1) =>
% 99.25/13.48 (((subsetI2) =>
% 99.25/13.48 (((emptysetsubset) =>
% 99.25/13.48 (((subsetE) =>
% 99.25/13.48 (((subsetE2) =>
% 99.25/13.48 (((notsubsetI) =>
% 99.25/13.48 (((notequalI1) =>
% 99.25/13.48 (((notequalI2) =>
% 99.25/13.48 (((subsetRefl) =>
% 99.25/13.48 (((subsetTrans) =>
% 99.25/13.48 (((setadjoinSub) =>
% 99.25/13.48 (((setadjoinSub2) =>
% 99.25/13.48 (((subset2powerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (setextsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (subsetemptysetimpeq) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetI1) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetE1) =>
% 99.25/13.48 ((
% 99.25/13.48 (inPowerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (powersetsubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (sepInPowerset) =>
% 99.25/13.48 ((
% 99.25/13.48 (sepSubset) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionIL) =>
% 99.25/13.48 ((
% 99.25/13.48 (upairset2IR) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionIR) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionEcases) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionE) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionLsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binunionRsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectI) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset5) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectEL) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectLsub) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset2) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectSubset3) =>
% 99.25/13.48 ((
% 99.25/13.48 (binintersectER) =>
% 99.66/13.48 ((
% 99.66/13.48 (disjointsetsI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectRsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset4) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset1) =>
% 99.66/13.48 ((
% 99.66/13.48 (bs114d) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusI) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusEL) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusER) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusSubset2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusERneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusELneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusILneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusIRneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusLsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusSubset1) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffE) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffI2) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffIneg1) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffIneg2) =>
% 99.66/13.48 ((
% 99.66/13.48 (secondinupair) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairIL) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairIR) =>
% 99.66/13.48 ((
% 99.66/13.48 (kpairiskpair) =>
% 99.66/13.48 ((
% 99.66/13.48 (kpairp) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletonsubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletoninpowerset) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletoninpowunion) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairset2E) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairsubunion) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairinpowunion) =>
% 99.66/13.48 ((
% 99.66/13.48 (ubforcartprodlem1) =>
% 99.66/13.48 ((
% 99.66/13.48 (ubforcartprodlem2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ubforcartprodlem3) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairin) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodmempair1) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodmempair) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionE2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionsingleton1) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionsingleton2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletonprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1E1) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1I) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1I2) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletonsuniq) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjL1) =>
% 99.66/13.48 ((
% 99.66/13.48 (kfstsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (theprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (kfstpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodfstin) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjL2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjL) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR11) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR12) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR1) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairequniteq) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR) =>
% 99.66/13.48 ((
% 99.66/13.48 (ksndsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (ksndpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (kpairsurjEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodsndin) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairmemEL) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairmemER) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodmempaircEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodfstpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodsndpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairsurjEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrI) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrSub) =>
% 99.66/13.48 ((
% 99.66/13.48 (setOfPairsIsBReln) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrERa) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrEL1) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrEL2) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrER) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcImageSingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (apProp) =>
% 99.66/13.48 ((
% 99.66/13.48 (app) =>
% 99.66/13.48 ((
% 99.66/13.48 (infuncsetfunc) =>
% 99.66/13.48 ((
% 99.66/13.48 (ap2p) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcinfuncset) =>
% 99.66/13.48 ((
% 99.66/13.48 (lamProp) =>
% 99.66/13.48 ((
% 99.66/13.48 (lamp) =>
% 99.66/13.48 ((
% 99.66/13.48 (lam2p) =>
% 99.66/13.48 ((
% 99.66/13.48 (brelnall1) =>
% 99.66/13.48 ((
% 99.66/13.48 (brelnall2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1E2) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp1) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp3) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp2) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcextLem) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp4) =>
% 99.66/13.48 ((
% 99.66/13.48 (subbreln) =>
% 99.66/13.48 ((
% 99.66/13.48 (eqbreln) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcext) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcext2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ap2apEq1) =>
% 99.66/13.48 ((
% 99.66/13.48 (ap2apEq2) =>
% 99.66/13.48 ((
% 99.66/13.48 (beta1) =>
% 99.66/13.48 ((
% 99.66/13.48 (eta1) =>
% 99.66/13.48 ((
% 99.66/13.48 (lam2lamEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (beta2) =>
% 99.66/13.48 ((
% 99.66/13.48 (eta2) =>
% 99.66/13.48 ((
% 99.66/13.48 (iffalseProp1) =>
% 99.66/13.48 ((
% 99.66/13.48 (iffalseProp2) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrueProp1) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrueProp2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ifSingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (ifp) =>
% 99.66/13.48 ((
% 99.66/13.48 (theeq) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrue) =>
% 99.66/13.48 ((
% 99.66/13.48 (iffalse) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrueorfalse) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (setextT) =>
% 99.66/13.48 ((
% 99.66/13.48 (subsetTI) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetTI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetTE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectTELcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectTERcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT1) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT2) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT3) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementSub1) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementSub2) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTnotintersectT) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementImpComplementIntersect) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementSubsetComplementIntersect) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementInPowersetComplementIntersect) =>
% 99.66/13.48 ((
% 99.66/13.48 (contraSubsetComplement) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTcontraSubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTILcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTIRcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (inIntersectImpInUnion) =>
% 99.66/13.48 ((
% 99.66/13.48 (inIntersectImpInUnion2) =>
% 99.66/13.48 ((
% 99.66/13.48 (inIntersectImpInIntersectUnions) =>
% 99.66/13.48 ((
% 99.66/13.48 (intersectInPowersetIntersectUnions) =>
% 99.66/13.48 ((
% 99.66/13.48 (inComplementUnionImpNotIn1) =>
% 99.66/13.48 ((
% 99.66/13.48 (inComplementUnionImpInComplement1) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTE) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTEcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2a1) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementUnionInPowersetComplement) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2a2) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan1a) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan1b) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan1) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2a) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2b2) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2b) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule0) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule1) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule2) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule3) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule4) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_1) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_2) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_3) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_4) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_5) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1all2) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1SetBreln1) =>
% 99.66/13.48 ((
% 99.66/13.48 (choice2fnsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (setOfPairsIsBReln1) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1all1) =>
% 99.66/13.48 ((
% 99.66/13.48 (subbreln1) =>
% 99.66/13.48 ((
% 99.66/13.48 (eqbreln1) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1invprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1invI) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1invE) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1compprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1compI) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1compE) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1compEex) =>
% 99.66/13.48 ((
% 99.66/13.48 (!!) @ (
% 99.66/13.48 (('#B') @ (
% 99.66/13.48 !!) @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#S') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#S') @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 =>))) @
% 99.66/13.48 breln1)))) @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 !!))) @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#S') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#B') @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#S') @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 =>))) @
% 99.66/13.48 breln1)))))) @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#C') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#B') @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#B') @
% 99.66/13.48 breln1)))) @
% 99.66/13.48 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
% 99.66/13.48 thf(zip_derived_cl595, plain,
% 99.66/13.48 (~ (((notdallE) =>
% 99.66/13.48 (((exuI1) =>
% 99.66/13.48 (((exuI3) =>
% 99.66/13.48 (((exuI2) =>
% 99.66/13.48 (((inCongP) =>
% 99.66/13.48 (((in__Cong) =>
% 99.66/13.48 (((exuE3u) =>
% 99.66/13.48 (((exu__Cong) =>
% 99.66/13.48 (((setadjoin__Cong) =>
% 99.66/13.48 (((powerset__Cong) =>
% 99.66/13.48 (((setunion__Cong) =>
% 99.66/13.48 (((exuEu) =>
% 99.66/13.48 (((descr__Cong) =>
% 99.66/13.48 (((dsetconstr__Cong) =>
% 99.66/13.48 (((subsetI1) =>
% 99.66/13.48 (((eqimpsubset2) =>
% 99.66/13.48 (((eqimpsubset1) =>
% 99.66/13.48 (((subsetI2) =>
% 99.66/13.48 (((emptysetsubset) =>
% 99.66/13.48 (((subsetE) =>
% 99.66/13.48 (((subsetE2) =>
% 99.66/13.48 (((notsubsetI) =>
% 99.66/13.48 (((notequalI1) =>
% 99.66/13.48 (((notequalI2) =>
% 99.66/13.48 (((subsetRefl) =>
% 99.66/13.48 (((subsetTrans) =>
% 99.66/13.48 (((setadjoinSub) =>
% 99.66/13.48 (((setadjoinSub2) =>
% 99.66/13.48 (((subset2powerset) =>
% 99.66/13.48 (((setextsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (subsetemptysetimpeq) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (inPowerset) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetsubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (sepInPowerset) =>
% 99.66/13.48 ((
% 99.66/13.48 (sepSubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionIL) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairset2IR) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionIR) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionEcases) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionE) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionLsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionRsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectI) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset5) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectEL) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectLsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset2) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset3) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectER) =>
% 99.66/13.48 ((
% 99.66/13.48 (disjointsetsI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectRsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset4) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset1) =>
% 99.66/13.48 ((
% 99.66/13.48 (bs114d) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusI) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusEL) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusER) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusSubset2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusERneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusELneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusILneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusIRneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusLsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusSubset1) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffE) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffI2) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffIneg1) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffIneg2) =>
% 99.66/13.48 ((
% 99.66/13.48 (secondinupair) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairIL) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairIR) =>
% 99.66/13.48 ((
% 99.66/13.48 (kpairiskpair) =>
% 99.66/13.48 ((
% 99.66/13.48 (kpairp) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletonsubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletoninpowerset) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletoninpowunion) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairset2E) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairsubunion) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairinpowunion) =>
% 99.66/13.48 ((
% 99.66/13.48 (ubforcartprodlem1) =>
% 99.66/13.48 ((
% 99.66/13.48 (ubforcartprodlem2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ubforcartprodlem3) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairin) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodmempair1) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodmempair) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionE2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionsingleton1) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionsingleton2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletonprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1E1) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1I) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1I2) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletonsuniq) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjL1) =>
% 99.66/13.48 ((
% 99.66/13.48 (kfstsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (theprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (kfstpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodfstin) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjL2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjL) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR11) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR12) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR1) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairequniteq) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR) =>
% 99.66/13.48 ((
% 99.66/13.48 (ksndsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (ksndpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (kpairsurjEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodsndin) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairmemEL) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairmemER) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodmempaircEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodfstpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodsndpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairsurjEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrI) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrSub) =>
% 99.66/13.48 ((
% 99.66/13.48 (setOfPairsIsBReln) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrERa) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrEL1) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrEL2) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrER) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcImageSingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (apProp) =>
% 99.66/13.48 ((
% 99.66/13.48 (app) =>
% 99.66/13.48 ((
% 99.66/13.48 (infuncsetfunc) =>
% 99.66/13.48 ((
% 99.66/13.48 (ap2p) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcinfuncset) =>
% 99.66/13.48 ((
% 99.66/13.48 (lamProp) =>
% 99.66/13.48 ((
% 99.66/13.48 (lamp) =>
% 99.66/13.48 ((
% 99.66/13.48 (lam2p) =>
% 99.66/13.48 ((
% 99.66/13.48 (brelnall1) =>
% 99.66/13.48 ((
% 99.66/13.48 (brelnall2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1E2) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp1) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp3) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp2) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcextLem) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp4) =>
% 99.66/13.48 ((
% 99.66/13.48 (subbreln) =>
% 99.66/13.48 ((
% 99.66/13.48 (eqbreln) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcext) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcext2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ap2apEq1) =>
% 99.66/13.48 ((
% 99.66/13.48 (ap2apEq2) =>
% 99.66/13.48 ((
% 99.66/13.48 (beta1) =>
% 99.66/13.48 ((
% 99.66/13.48 (eta1) =>
% 99.66/13.48 ((
% 99.66/13.48 (lam2lamEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (beta2) =>
% 99.66/13.48 ((
% 99.66/13.48 (eta2) =>
% 99.66/13.48 ((
% 99.66/13.48 (iffalseProp1) =>
% 99.66/13.48 ((
% 99.66/13.48 (iffalseProp2) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrueProp1) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrueProp2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ifSingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (ifp) =>
% 99.66/13.48 ((
% 99.66/13.48 (theeq) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrue) =>
% 99.66/13.48 ((
% 99.66/13.48 (iffalse) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrueorfalse) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (setextT) =>
% 99.66/13.48 ((
% 99.66/13.48 (subsetTI) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetTI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetTE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectTELcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectTERcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT1) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT2) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT3) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementSub1) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementSub2) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTnotintersectT) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementImpComplementIntersect) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementSubsetComplementIntersect) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementInPowersetComplementIntersect) =>
% 99.66/13.48 ((
% 99.66/13.48 (contraSubsetComplement) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTcontraSubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTILcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTIRcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (inIntersectImpInUnion) =>
% 99.66/13.48 ((
% 99.66/13.48 (inIntersectImpInUnion2) =>
% 99.66/13.48 ((
% 99.66/13.48 (inIntersectImpInIntersectUnions) =>
% 99.66/13.48 ((
% 99.66/13.48 (intersectInPowersetIntersectUnions) =>
% 99.66/13.48 ((
% 99.66/13.48 (inComplementUnionImpNotIn1) =>
% 99.66/13.48 ((
% 99.66/13.48 (inComplementUnionImpInComplement1) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTE) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTEcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2a1) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementUnionInPowersetComplement) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2a2) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan1a) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan1b) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan1) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2a) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2b2) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2b) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule0) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule1) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule2) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule3) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule4) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_1) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_2) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_3) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_4) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_5) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1all2) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1SetBreln1) =>
% 99.66/13.48 ((
% 99.66/13.48 (choice2fnsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (setOfPairsIsBReln1) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1all1) =>
% 99.66/13.48 ((
% 99.66/13.48 (subbreln1) =>
% 99.66/13.48 ((
% 99.66/13.48 (eqbreln1) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1invprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1invI) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1invE) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1compprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1compI) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1compE) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1compEex) =>
% 99.66/13.48 ((
% 99.66/13.48 (!!) @ (
% 99.66/13.48 (('#B') @ (
% 99.66/13.48 !!) @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#S') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#S') @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 =>))) @
% 99.66/13.48 breln1)))) @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 !!))) @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#S') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#B') @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#S') @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 =>))) @
% 99.66/13.48 breln1)))))) @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#C') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#B') @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#B') @
% 99.66/13.48 breln1)))) @
% 99.66/13.48 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl586])).
% 99.66/13.48 thf(zip_derived_cl606, plain,
% 99.66/13.48 (~ (((exuI1) =>
% 99.66/13.48 (((exuI3) =>
% 99.66/13.48 (((exuI2) =>
% 99.66/13.48 (((inCongP) =>
% 99.66/13.48 (((in__Cong) =>
% 99.66/13.48 (((exuE3u) =>
% 99.66/13.48 (((exu__Cong) =>
% 99.66/13.48 (((setadjoin__Cong) =>
% 99.66/13.48 (((powerset__Cong) =>
% 99.66/13.48 (((setunion__Cong) =>
% 99.66/13.48 (((exuEu) =>
% 99.66/13.48 (((descr__Cong) =>
% 99.66/13.48 (((dsetconstr__Cong) =>
% 99.66/13.48 (((subsetI1) =>
% 99.66/13.48 (((eqimpsubset2) =>
% 99.66/13.48 (((eqimpsubset1) =>
% 99.66/13.48 (((subsetI2) =>
% 99.66/13.48 (((emptysetsubset) =>
% 99.66/13.48 (((subsetE) =>
% 99.66/13.48 (((subsetE2) =>
% 99.66/13.48 (((notsubsetI) =>
% 99.66/13.48 (((notequalI1) =>
% 99.66/13.48 (((notequalI2) =>
% 99.66/13.48 (((subsetRefl) =>
% 99.66/13.48 (((subsetTrans) =>
% 99.66/13.48 (((setadjoinSub) =>
% 99.66/13.48 (((setadjoinSub2) =>
% 99.66/13.48 (((subset2powerset) =>
% 99.66/13.48 (((setextsub) =>
% 99.66/13.48 (((subsetemptysetimpeq) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (inPowerset) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetsubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (sepInPowerset) =>
% 99.66/13.48 ((
% 99.66/13.48 (sepSubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionIL) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairset2IR) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionIR) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionEcases) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionE) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionLsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionRsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectI) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset5) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectEL) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectLsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset2) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset3) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectER) =>
% 99.66/13.48 ((
% 99.66/13.48 (disjointsetsI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectRsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset4) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset1) =>
% 99.66/13.48 ((
% 99.66/13.48 (bs114d) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusI) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusEL) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusER) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusSubset2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusERneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusELneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusILneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusIRneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusLsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusSubset1) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffE) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffI2) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffIneg1) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffIneg2) =>
% 99.66/13.48 ((
% 99.66/13.48 (secondinupair) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairIL) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairIR) =>
% 99.66/13.48 ((
% 99.66/13.48 (kpairiskpair) =>
% 99.66/13.48 ((
% 99.66/13.48 (kpairp) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletonsubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletoninpowerset) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletoninpowunion) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairset2E) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairsubunion) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairinpowunion) =>
% 99.66/13.48 ((
% 99.66/13.48 (ubforcartprodlem1) =>
% 99.66/13.48 ((
% 99.66/13.48 (ubforcartprodlem2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ubforcartprodlem3) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairin) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodmempair1) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodmempair) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionE2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionsingleton1) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionsingleton2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletonprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1E1) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1I) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1I2) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletonsuniq) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjL1) =>
% 99.66/13.48 ((
% 99.66/13.48 (kfstsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (theprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (kfstpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodfstin) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjL2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjL) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR11) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR12) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR1) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairequniteq) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR) =>
% 99.66/13.48 ((
% 99.66/13.48 (ksndsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (ksndpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (kpairsurjEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodsndin) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairmemEL) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairmemER) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodmempaircEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodfstpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodsndpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairsurjEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrI) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrSub) =>
% 99.66/13.48 ((
% 99.66/13.48 (setOfPairsIsBReln) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrERa) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrEL1) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrEL2) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrER) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcImageSingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (apProp) =>
% 99.66/13.48 ((
% 99.66/13.48 (app) =>
% 99.66/13.48 ((
% 99.66/13.48 (infuncsetfunc) =>
% 99.66/13.48 ((
% 99.66/13.48 (ap2p) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcinfuncset) =>
% 99.66/13.48 ((
% 99.66/13.48 (lamProp) =>
% 99.66/13.48 ((
% 99.66/13.48 (lamp) =>
% 99.66/13.48 ((
% 99.66/13.48 (lam2p) =>
% 99.66/13.48 ((
% 99.66/13.48 (brelnall1) =>
% 99.66/13.48 ((
% 99.66/13.48 (brelnall2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1E2) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp1) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp3) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp2) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcextLem) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp4) =>
% 99.66/13.48 ((
% 99.66/13.48 (subbreln) =>
% 99.66/13.48 ((
% 99.66/13.48 (eqbreln) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcext) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcext2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ap2apEq1) =>
% 99.66/13.48 ((
% 99.66/13.48 (ap2apEq2) =>
% 99.66/13.48 ((
% 99.66/13.48 (beta1) =>
% 99.66/13.48 ((
% 99.66/13.48 (eta1) =>
% 99.66/13.48 ((
% 99.66/13.48 (lam2lamEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (beta2) =>
% 99.66/13.48 ((
% 99.66/13.48 (eta2) =>
% 99.66/13.48 ((
% 99.66/13.48 (iffalseProp1) =>
% 99.66/13.48 ((
% 99.66/13.48 (iffalseProp2) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrueProp1) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrueProp2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ifSingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (ifp) =>
% 99.66/13.48 ((
% 99.66/13.48 (theeq) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrue) =>
% 99.66/13.48 ((
% 99.66/13.48 (iffalse) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrueorfalse) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (setextT) =>
% 99.66/13.48 ((
% 99.66/13.48 (subsetTI) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetTI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetTE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectTELcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectTERcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT1) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT2) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT3) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementSub1) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementSub2) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTnotintersectT) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementImpComplementIntersect) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementSubsetComplementIntersect) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementInPowersetComplementIntersect) =>
% 99.66/13.48 ((
% 99.66/13.48 (contraSubsetComplement) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTcontraSubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTILcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTIRcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (inIntersectImpInUnion) =>
% 99.66/13.48 ((
% 99.66/13.48 (inIntersectImpInUnion2) =>
% 99.66/13.48 ((
% 99.66/13.48 (inIntersectImpInIntersectUnions) =>
% 99.66/13.48 ((
% 99.66/13.48 (intersectInPowersetIntersectUnions) =>
% 99.66/13.48 ((
% 99.66/13.48 (inComplementUnionImpNotIn1) =>
% 99.66/13.48 ((
% 99.66/13.48 (inComplementUnionImpInComplement1) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTE) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTEcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2a1) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementUnionInPowersetComplement) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2a2) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan1a) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan1b) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan1) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2a) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2b2) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2b) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule0) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule1) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule2) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule3) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule4) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_1) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_2) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_3) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_4) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_5) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1all2) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1SetBreln1) =>
% 99.66/13.48 ((
% 99.66/13.48 (choice2fnsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (setOfPairsIsBReln1) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1all1) =>
% 99.66/13.48 ((
% 99.66/13.48 (subbreln1) =>
% 99.66/13.48 ((
% 99.66/13.48 (eqbreln1) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1invprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1invI) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1invE) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1compprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1compI) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1compE) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1compEex) =>
% 99.66/13.48 ((
% 99.66/13.48 (!!) @ (
% 99.66/13.48 (('#B') @ (
% 99.66/13.48 !!) @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#S') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#S') @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 =>))) @
% 99.66/13.48 breln1)))) @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 !!))) @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#S') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#B') @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#S') @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 =>))) @
% 99.66/13.48 breln1)))))) @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#C') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#B') @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#B') @
% 99.66/13.48 breln1)))) @
% 99.66/13.48 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl595])).
% 99.66/13.48 thf(zip_derived_cl619, plain,
% 99.66/13.48 (~ (((exuI3) =>
% 99.66/13.48 (((exuI2) =>
% 99.66/13.48 (((inCongP) =>
% 99.66/13.48 (((in__Cong) =>
% 99.66/13.48 (((exuE3u) =>
% 99.66/13.48 (((exu__Cong) =>
% 99.66/13.48 (((setadjoin__Cong) =>
% 99.66/13.48 (((powerset__Cong) =>
% 99.66/13.48 (((setunion__Cong) =>
% 99.66/13.48 (((exuEu) =>
% 99.66/13.48 (((descr__Cong) =>
% 99.66/13.48 (((dsetconstr__Cong) =>
% 99.66/13.48 (((subsetI1) =>
% 99.66/13.48 (((eqimpsubset2) =>
% 99.66/13.48 (((eqimpsubset1) =>
% 99.66/13.48 (((subsetI2) =>
% 99.66/13.48 (((emptysetsubset) =>
% 99.66/13.48 (((subsetE) =>
% 99.66/13.48 (((subsetE2) =>
% 99.66/13.48 (((notsubsetI) =>
% 99.66/13.48 (((notequalI1) =>
% 99.66/13.48 (((notequalI2) =>
% 99.66/13.48 (((subsetRefl) =>
% 99.66/13.48 (((subsetTrans) =>
% 99.66/13.48 (((setadjoinSub) =>
% 99.66/13.48 (((setadjoinSub2) =>
% 99.66/13.48 (((subset2powerset) =>
% 99.66/13.48 (((setextsub) =>
% 99.66/13.48 (((subsetemptysetimpeq) =>
% 99.66/13.48 (((powersetI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (inPowerset) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetsubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (sepInPowerset) =>
% 99.66/13.48 ((
% 99.66/13.48 (sepSubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionIL) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairset2IR) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionIR) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionEcases) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionE) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionLsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionRsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectI) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset5) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectEL) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectLsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset2) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset3) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectER) =>
% 99.66/13.48 ((
% 99.66/13.48 (disjointsetsI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectRsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset4) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset1) =>
% 99.66/13.48 ((
% 99.66/13.48 (bs114d) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusI) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusEL) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusER) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusSubset2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusERneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusELneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusILneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusIRneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusLsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusSubset1) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffE) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffI2) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffIneg1) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffIneg2) =>
% 99.66/13.48 ((
% 99.66/13.48 (secondinupair) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairIL) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairIR) =>
% 99.66/13.48 ((
% 99.66/13.48 (kpairiskpair) =>
% 99.66/13.48 ((
% 99.66/13.48 (kpairp) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletonsubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletoninpowerset) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletoninpowunion) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairset2E) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairsubunion) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairinpowunion) =>
% 99.66/13.48 ((
% 99.66/13.48 (ubforcartprodlem1) =>
% 99.66/13.48 ((
% 99.66/13.48 (ubforcartprodlem2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ubforcartprodlem3) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairin) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodmempair1) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodmempair) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionE2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionsingleton1) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionsingleton2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletonprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1E1) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1I) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1I2) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletonsuniq) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjL1) =>
% 99.66/13.48 ((
% 99.66/13.48 (kfstsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (theprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (kfstpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodfstin) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjL2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjL) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR11) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR12) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR1) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairequniteq) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR) =>
% 99.66/13.48 ((
% 99.66/13.48 (ksndsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (ksndpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (kpairsurjEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodsndin) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairmemEL) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairmemER) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodmempaircEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodfstpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodsndpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairsurjEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrI) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrSub) =>
% 99.66/13.48 ((
% 99.66/13.48 (setOfPairsIsBReln) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrERa) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrEL1) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrEL2) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrER) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcImageSingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (apProp) =>
% 99.66/13.48 ((
% 99.66/13.48 (app) =>
% 99.66/13.48 ((
% 99.66/13.48 (infuncsetfunc) =>
% 99.66/13.48 ((
% 99.66/13.48 (ap2p) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcinfuncset) =>
% 99.66/13.48 ((
% 99.66/13.48 (lamProp) =>
% 99.66/13.48 ((
% 99.66/13.48 (lamp) =>
% 99.66/13.48 ((
% 99.66/13.48 (lam2p) =>
% 99.66/13.48 ((
% 99.66/13.48 (brelnall1) =>
% 99.66/13.48 ((
% 99.66/13.48 (brelnall2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1E2) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp1) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp3) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp2) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcextLem) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp4) =>
% 99.66/13.48 ((
% 99.66/13.48 (subbreln) =>
% 99.66/13.48 ((
% 99.66/13.48 (eqbreln) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcext) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcext2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ap2apEq1) =>
% 99.66/13.48 ((
% 99.66/13.48 (ap2apEq2) =>
% 99.66/13.48 ((
% 99.66/13.48 (beta1) =>
% 99.66/13.48 ((
% 99.66/13.48 (eta1) =>
% 99.66/13.48 ((
% 99.66/13.48 (lam2lamEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (beta2) =>
% 99.66/13.48 ((
% 99.66/13.48 (eta2) =>
% 99.66/13.48 ((
% 99.66/13.48 (iffalseProp1) =>
% 99.66/13.48 ((
% 99.66/13.48 (iffalseProp2) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrueProp1) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrueProp2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ifSingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (ifp) =>
% 99.66/13.48 ((
% 99.66/13.48 (theeq) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrue) =>
% 99.66/13.48 ((
% 99.66/13.48 (iffalse) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrueorfalse) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (setextT) =>
% 99.66/13.48 ((
% 99.66/13.48 (subsetTI) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetTI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetTE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectTELcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectTERcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT1) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT2) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT3) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementSub1) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementSub2) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTnotintersectT) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementImpComplementIntersect) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementSubsetComplementIntersect) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementInPowersetComplementIntersect) =>
% 99.66/13.48 ((
% 99.66/13.48 (contraSubsetComplement) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTcontraSubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTILcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTIRcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (inIntersectImpInUnion) =>
% 99.66/13.48 ((
% 99.66/13.48 (inIntersectImpInUnion2) =>
% 99.66/13.48 ((
% 99.66/13.48 (inIntersectImpInIntersectUnions) =>
% 99.66/13.48 ((
% 99.66/13.48 (intersectInPowersetIntersectUnions) =>
% 99.66/13.48 ((
% 99.66/13.48 (inComplementUnionImpNotIn1) =>
% 99.66/13.48 ((
% 99.66/13.48 (inComplementUnionImpInComplement1) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTE) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTEcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2a1) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementUnionInPowersetComplement) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2a2) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan1a) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan1b) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan1) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2a) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2b2) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2b) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule0) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule1) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule2) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule3) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule4) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_1) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_2) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_3) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_4) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_5) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1all2) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1SetBreln1) =>
% 99.66/13.48 ((
% 99.66/13.48 (choice2fnsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (setOfPairsIsBReln1) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1all1) =>
% 99.66/13.48 ((
% 99.66/13.48 (subbreln1) =>
% 99.66/13.48 ((
% 99.66/13.48 (eqbreln1) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1invprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1invI) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1invE) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1compprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1compI) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1compE) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1compEex) =>
% 99.66/13.48 ((
% 99.66/13.48 (!!) @ (
% 99.66/13.48 (('#B') @ (
% 99.66/13.48 !!) @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#S') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#S') @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 =>))) @
% 99.66/13.48 breln1)))) @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 !!))) @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#S') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#B') @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#S') @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 =>))) @
% 99.66/13.48 breln1)))))) @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#C') @ (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#B') @
% 99.66/13.48 (
% 99.66/13.48 (
% 99.66/13.48 ('#B') @ (
% 99.66/13.48 '#B') @
% 99.66/13.48 breln1)))) @
% 99.66/13.48 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl606])).
% 99.66/13.48 thf(zip_derived_cl630, plain,
% 99.66/13.48 (~ (((exuI2) =>
% 99.66/13.48 (((inCongP) =>
% 99.66/13.48 (((in__Cong) =>
% 99.66/13.48 (((exuE3u) =>
% 99.66/13.48 (((exu__Cong) =>
% 99.66/13.48 (((setadjoin__Cong) =>
% 99.66/13.48 (((powerset__Cong) =>
% 99.66/13.48 (((setunion__Cong) =>
% 99.66/13.48 (((exuEu) =>
% 99.66/13.48 (((descr__Cong) =>
% 99.66/13.48 (((dsetconstr__Cong) =>
% 99.66/13.48 (((subsetI1) =>
% 99.66/13.48 (((eqimpsubset2) =>
% 99.66/13.48 (((eqimpsubset1) =>
% 99.66/13.48 (((subsetI2) =>
% 99.66/13.48 (((emptysetsubset) =>
% 99.66/13.48 (((subsetE) =>
% 99.66/13.48 (((subsetE2) =>
% 99.66/13.48 (((notsubsetI) =>
% 99.66/13.48 (((notequalI1) =>
% 99.66/13.48 (((notequalI2) =>
% 99.66/13.48 (((subsetRefl) =>
% 99.66/13.48 (((subsetTrans) =>
% 99.66/13.48 (((setadjoinSub) =>
% 99.66/13.48 (((setadjoinSub2) =>
% 99.66/13.48 (((subset2powerset) =>
% 99.66/13.48 (((setextsub) =>
% 99.66/13.48 (((subsetemptysetimpeq) =>
% 99.66/13.48 (((powersetI1) =>
% 99.66/13.48 (((powersetE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (inPowerset) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetsubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (sepInPowerset) =>
% 99.66/13.48 ((
% 99.66/13.48 (sepSubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionIL) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairset2IR) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionIR) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionEcases) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionE) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionLsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionRsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectI) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset5) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectEL) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectLsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset2) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset3) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectER) =>
% 99.66/13.48 ((
% 99.66/13.48 (disjointsetsI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectRsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset4) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectSubset1) =>
% 99.66/13.48 ((
% 99.66/13.48 (bs114d) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusI) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusEL) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusER) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusSubset2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusERneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusELneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusILneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusIRneg) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusLsub) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusSubset1) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffE) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffI2) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffIneg1) =>
% 99.66/13.48 ((
% 99.66/13.48 (symdiffIneg2) =>
% 99.66/13.48 ((
% 99.66/13.48 (secondinupair) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairIL) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairIR) =>
% 99.66/13.48 ((
% 99.66/13.48 (kpairiskpair) =>
% 99.66/13.48 ((
% 99.66/13.48 (kpairp) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletonsubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletoninpowerset) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletoninpowunion) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairset2E) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairsubunion) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairinpowunion) =>
% 99.66/13.48 ((
% 99.66/13.48 (ubforcartprodlem1) =>
% 99.66/13.48 ((
% 99.66/13.48 (ubforcartprodlem2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ubforcartprodlem3) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairin) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodmempair1) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodmempair) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionE2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionsingleton1) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionsingleton2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setunionsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletonprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1E1) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1I) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1I2) =>
% 99.66/13.48 ((
% 99.66/13.48 (singletonsuniq) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjL1) =>
% 99.66/13.48 ((
% 99.66/13.48 (kfstsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (theprop) =>
% 99.66/13.48 ((
% 99.66/13.48 (kfstpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodfstin) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjL2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjL) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR11) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR12) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR1) =>
% 99.66/13.48 ((
% 99.66/13.48 (upairequniteq) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR2) =>
% 99.66/13.48 ((
% 99.66/13.48 (setukpairinjR) =>
% 99.66/13.48 ((
% 99.66/13.48 (ksndsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (ksndpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (kpairsurjEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodsndin) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairmemEL) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairmemER) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodmempaircEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodfstpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodsndpairEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (cartprodpairsurjEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrI) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrSub) =>
% 99.66/13.48 ((
% 99.66/13.48 (setOfPairsIsBReln) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrERa) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrEL1) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrEL2) =>
% 99.66/13.48 ((
% 99.66/13.48 (dpsetconstrER) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcImageSingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (apProp) =>
% 99.66/13.48 ((
% 99.66/13.48 (app) =>
% 99.66/13.48 ((
% 99.66/13.48 (infuncsetfunc) =>
% 99.66/13.48 ((
% 99.66/13.48 (ap2p) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcinfuncset) =>
% 99.66/13.48 ((
% 99.66/13.48 (lamProp) =>
% 99.66/13.48 ((
% 99.66/13.48 (lamp) =>
% 99.66/13.48 ((
% 99.66/13.48 (lam2p) =>
% 99.66/13.48 ((
% 99.66/13.48 (brelnall1) =>
% 99.66/13.48 ((
% 99.66/13.48 (brelnall2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ex1E2) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp1) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp3) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp2) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcextLem) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcGraphProp4) =>
% 99.66/13.48 ((
% 99.66/13.48 (subbreln) =>
% 99.66/13.48 ((
% 99.66/13.48 (eqbreln) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcext) =>
% 99.66/13.48 ((
% 99.66/13.48 (funcext2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ap2apEq1) =>
% 99.66/13.48 ((
% 99.66/13.48 (ap2apEq2) =>
% 99.66/13.48 ((
% 99.66/13.48 (beta1) =>
% 99.66/13.48 ((
% 99.66/13.48 (eta1) =>
% 99.66/13.48 ((
% 99.66/13.48 (lam2lamEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (beta2) =>
% 99.66/13.48 ((
% 99.66/13.48 (eta2) =>
% 99.66/13.48 ((
% 99.66/13.48 (iffalseProp1) =>
% 99.66/13.48 ((
% 99.66/13.48 (iffalseProp2) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrueProp1) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrueProp2) =>
% 99.66/13.48 ((
% 99.66/13.48 (ifSingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (ifp) =>
% 99.66/13.48 ((
% 99.66/13.48 (theeq) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrue) =>
% 99.66/13.48 ((
% 99.66/13.48 (iffalse) =>
% 99.66/13.48 ((
% 99.66/13.48 (iftrueorfalse) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (setminusT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementT_lem) =>
% 99.66/13.48 ((
% 99.66/13.48 (setextT) =>
% 99.66/13.48 ((
% 99.66/13.48 (subsetTI) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetTI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (powersetTE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectTELcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (binintersectTERcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT1) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT2) =>
% 99.66/13.48 ((
% 99.66/13.48 (contrasubsetT3) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementI1) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementE1) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementSub1) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementSub2) =>
% 99.66/13.48 ((
% 99.66/13.48 (doubleComplementEq) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTnotintersectT) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementImpComplementIntersect) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementSubsetComplementIntersect) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementInPowersetComplementIntersect) =>
% 99.66/13.48 ((
% 99.66/13.48 (contraSubsetComplement) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementTcontraSubset) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTILcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTIRcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (inIntersectImpInUnion) =>
% 99.66/13.48 ((
% 99.66/13.48 (inIntersectImpInUnion2) =>
% 99.66/13.48 ((
% 99.66/13.48 (inIntersectImpInIntersectUnions) =>
% 99.66/13.48 ((
% 99.66/13.48 (intersectInPowersetIntersectUnions) =>
% 99.66/13.48 ((
% 99.66/13.48 (inComplementUnionImpNotIn1) =>
% 99.66/13.48 ((
% 99.66/13.48 (inComplementUnionImpInComplement1) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTE) =>
% 99.66/13.48 ((
% 99.66/13.48 (binunionTEcontra) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2a1) =>
% 99.66/13.48 ((
% 99.66/13.48 (complementUnionInPowersetComplement) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2a2) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan1a) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan1b) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan1) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2a) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2b2) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2b) =>
% 99.66/13.48 ((
% 99.66/13.48 (demorgan2) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule0) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule1) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule2) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule3) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz13rule4) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_1) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_2) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_3) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_4) =>
% 99.66/13.48 ((
% 99.66/13.48 (woz1_5) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1all2) =>
% 99.66/13.48 ((
% 99.66/13.48 (breln1SetBreln1) =>
% 99.66/13.48 ((
% 99.66/13.48 (choice2fnsingleton) =>
% 99.66/13.48 ((
% 99.66/13.48 (setOfPairsIsBReln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all1) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compEex) =>
% 99.66/13.49 ((
% 99.66/13.49 (!!) @ (
% 99.66/13.49 (('#B') @ (
% 99.66/13.49 !!) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 !!))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#C') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl619])).
% 99.66/13.49 thf(zip_derived_cl640, plain,
% 99.66/13.49 (~ (((inCongP) =>
% 99.66/13.49 (((in__Cong) =>
% 99.66/13.49 (((exuE3u) =>
% 99.66/13.49 (((exu__Cong) =>
% 99.66/13.49 (((setadjoin__Cong) =>
% 99.66/13.49 (((powerset__Cong) =>
% 99.66/13.49 (((setunion__Cong) =>
% 99.66/13.49 (((exuEu) =>
% 99.66/13.49 (((descr__Cong) =>
% 99.66/13.49 (((dsetconstr__Cong) =>
% 99.66/13.49 (((subsetI1) =>
% 99.66/13.49 (((eqimpsubset2) =>
% 99.66/13.49 (((eqimpsubset1) =>
% 99.66/13.49 (((subsetI2) =>
% 99.66/13.49 (((emptysetsubset) =>
% 99.66/13.49 (((subsetE) =>
% 99.66/13.49 (((subsetE2) =>
% 99.66/13.49 (((notsubsetI) =>
% 99.66/13.49 (((notequalI1) =>
% 99.66/13.49 (((notequalI2) =>
% 99.66/13.49 (((subsetRefl) =>
% 99.66/13.49 (((subsetTrans) =>
% 99.66/13.49 (((setadjoinSub) =>
% 99.66/13.49 (((setadjoinSub2) =>
% 99.66/13.49 (((subset2powerset) =>
% 99.66/13.49 (((setextsub) =>
% 99.66/13.49 (((subsetemptysetimpeq) =>
% 99.66/13.49 (((powersetI1) =>
% 99.66/13.49 (((powersetE1) =>
% 99.66/13.49 (((inPowerset) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetsubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (sepInPowerset) =>
% 99.66/13.49 ((
% 99.66/13.49 (sepSubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionIL) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairset2IR) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionEcases) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectI) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset5) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset3) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectER) =>
% 99.66/13.49 ((
% 99.66/13.49 (disjointsetsI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset4) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (bs114d) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusI) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusER) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusERneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusELneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusILneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusIRneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffE) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI2) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg2) =>
% 99.66/13.49 ((
% 99.66/13.49 (secondinupair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairiskpair) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairp) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowerset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairset2E) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairsubunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairinpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem3) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair1) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionE2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton1) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I2) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsuniq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (theprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstin) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR11) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR12) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR1) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairequniteq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemER) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempaircEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrI) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrSub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrERa) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrER) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcImageSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (apProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (app) =>
% 99.66/13.49 ((
% 99.66/13.49 (infuncsetfunc) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcinfuncset) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall1) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp3) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcextLem) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp4) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq2) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2lamEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifp) =>
% 99.66/13.49 ((
% 99.66/13.49 (theeq) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrue) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueorfalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setextT) =>
% 99.66/13.49 ((
% 99.66/13.49 (subsetTI) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTELcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTERcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT1) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT2) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT3) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub2) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTnotintersectT) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementImpComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementSubsetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementInPowersetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (contraSubsetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTcontraSubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTILcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTIRcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion2) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (intersectInPowersetIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpNotIn1) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpInComplement1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTEcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementUnionInPowersetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule0) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_5) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all2) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1SetBreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (choice2fnsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all1) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compEex) =>
% 99.66/13.49 ((
% 99.66/13.49 (!!) @ (
% 99.66/13.49 (('#B') @ (
% 99.66/13.49 !!) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 !!))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#C') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl630])).
% 99.66/13.49 thf(zip_derived_cl650, plain,
% 99.66/13.49 (~ (((in__Cong) =>
% 99.66/13.49 (((exuE3u) =>
% 99.66/13.49 (((exu__Cong) =>
% 99.66/13.49 (((setadjoin__Cong) =>
% 99.66/13.49 (((powerset__Cong) =>
% 99.66/13.49 (((setunion__Cong) =>
% 99.66/13.49 (((exuEu) =>
% 99.66/13.49 (((descr__Cong) =>
% 99.66/13.49 (((dsetconstr__Cong) =>
% 99.66/13.49 (((subsetI1) =>
% 99.66/13.49 (((eqimpsubset2) =>
% 99.66/13.49 (((eqimpsubset1) =>
% 99.66/13.49 (((subsetI2) =>
% 99.66/13.49 (((emptysetsubset) =>
% 99.66/13.49 (((subsetE) =>
% 99.66/13.49 (((subsetE2) =>
% 99.66/13.49 (((notsubsetI) =>
% 99.66/13.49 (((notequalI1) =>
% 99.66/13.49 (((notequalI2) =>
% 99.66/13.49 (((subsetRefl) =>
% 99.66/13.49 (((subsetTrans) =>
% 99.66/13.49 (((setadjoinSub) =>
% 99.66/13.49 (((setadjoinSub2) =>
% 99.66/13.49 (((subset2powerset) =>
% 99.66/13.49 (((setextsub) =>
% 99.66/13.49 (((subsetemptysetimpeq) =>
% 99.66/13.49 (((powersetI1) =>
% 99.66/13.49 (((powersetE1) =>
% 99.66/13.49 (((inPowerset) =>
% 99.66/13.49 (((powersetsubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (sepInPowerset) =>
% 99.66/13.49 ((
% 99.66/13.49 (sepSubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionIL) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairset2IR) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionEcases) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectI) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset5) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset3) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectER) =>
% 99.66/13.49 ((
% 99.66/13.49 (disjointsetsI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset4) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (bs114d) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusI) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusER) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusERneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusELneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusILneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusIRneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffE) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI2) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg2) =>
% 99.66/13.49 ((
% 99.66/13.49 (secondinupair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairiskpair) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairp) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowerset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairset2E) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairsubunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairinpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem3) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair1) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionE2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton1) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I2) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsuniq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (theprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstin) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR11) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR12) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR1) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairequniteq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemER) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempaircEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrI) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrSub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrERa) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrER) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcImageSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (apProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (app) =>
% 99.66/13.49 ((
% 99.66/13.49 (infuncsetfunc) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcinfuncset) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall1) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp3) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcextLem) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp4) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq2) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2lamEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifp) =>
% 99.66/13.49 ((
% 99.66/13.49 (theeq) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrue) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueorfalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setextT) =>
% 99.66/13.49 ((
% 99.66/13.49 (subsetTI) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTELcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTERcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT1) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT2) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT3) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub2) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTnotintersectT) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementImpComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementSubsetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementInPowersetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (contraSubsetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTcontraSubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTILcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTIRcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion2) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (intersectInPowersetIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpNotIn1) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpInComplement1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTEcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementUnionInPowersetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule0) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_5) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all2) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1SetBreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (choice2fnsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all1) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compEex) =>
% 99.66/13.49 ((
% 99.66/13.49 (!!) @ (
% 99.66/13.49 (('#B') @ (
% 99.66/13.49 !!) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 !!))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#C') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl640])).
% 99.66/13.49 thf(zip_derived_cl660, plain,
% 99.66/13.49 (~ (((exuE3u) =>
% 99.66/13.49 (((exu__Cong) =>
% 99.66/13.49 (((setadjoin__Cong) =>
% 99.66/13.49 (((powerset__Cong) =>
% 99.66/13.49 (((setunion__Cong) =>
% 99.66/13.49 (((exuEu) =>
% 99.66/13.49 (((descr__Cong) =>
% 99.66/13.49 (((dsetconstr__Cong) =>
% 99.66/13.49 (((subsetI1) =>
% 99.66/13.49 (((eqimpsubset2) =>
% 99.66/13.49 (((eqimpsubset1) =>
% 99.66/13.49 (((subsetI2) =>
% 99.66/13.49 (((emptysetsubset) =>
% 99.66/13.49 (((subsetE) =>
% 99.66/13.49 (((subsetE2) =>
% 99.66/13.49 (((notsubsetI) =>
% 99.66/13.49 (((notequalI1) =>
% 99.66/13.49 (((notequalI2) =>
% 99.66/13.49 (((subsetRefl) =>
% 99.66/13.49 (((subsetTrans) =>
% 99.66/13.49 (((setadjoinSub) =>
% 99.66/13.49 (((setadjoinSub2) =>
% 99.66/13.49 (((subset2powerset) =>
% 99.66/13.49 (((setextsub) =>
% 99.66/13.49 (((subsetemptysetimpeq) =>
% 99.66/13.49 (((powersetI1) =>
% 99.66/13.49 (((powersetE1) =>
% 99.66/13.49 (((inPowerset) =>
% 99.66/13.49 (((powersetsubset) =>
% 99.66/13.49 (((sepInPowerset) =>
% 99.66/13.49 ((
% 99.66/13.49 (sepSubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionIL) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairset2IR) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionEcases) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectI) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset5) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset3) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectER) =>
% 99.66/13.49 ((
% 99.66/13.49 (disjointsetsI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset4) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (bs114d) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusI) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusER) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusERneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusELneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusILneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusIRneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffE) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI2) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg2) =>
% 99.66/13.49 ((
% 99.66/13.49 (secondinupair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairiskpair) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairp) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowerset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairset2E) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairsubunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairinpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem3) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair1) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionE2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton1) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I2) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsuniq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (theprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstin) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR11) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR12) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR1) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairequniteq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemER) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempaircEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrI) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrSub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrERa) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrER) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcImageSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (apProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (app) =>
% 99.66/13.49 ((
% 99.66/13.49 (infuncsetfunc) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcinfuncset) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall1) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp3) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcextLem) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp4) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq2) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2lamEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifp) =>
% 99.66/13.49 ((
% 99.66/13.49 (theeq) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrue) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueorfalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setextT) =>
% 99.66/13.49 ((
% 99.66/13.49 (subsetTI) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTELcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTERcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT1) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT2) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT3) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub2) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTnotintersectT) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementImpComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementSubsetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementInPowersetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (contraSubsetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTcontraSubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTILcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTIRcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion2) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (intersectInPowersetIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpNotIn1) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpInComplement1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTEcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementUnionInPowersetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule0) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_5) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all2) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1SetBreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (choice2fnsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all1) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compEex) =>
% 99.66/13.49 ((
% 99.66/13.49 (!!) @ (
% 99.66/13.49 (('#B') @ (
% 99.66/13.49 !!) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 !!))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#C') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl650])).
% 99.66/13.49 thf(zip_derived_cl672, plain,
% 99.66/13.49 (~ (((exu__Cong) =>
% 99.66/13.49 (((setadjoin__Cong) =>
% 99.66/13.49 (((powerset__Cong) =>
% 99.66/13.49 (((setunion__Cong) =>
% 99.66/13.49 (((exuEu) =>
% 99.66/13.49 (((descr__Cong) =>
% 99.66/13.49 (((dsetconstr__Cong) =>
% 99.66/13.49 (((subsetI1) =>
% 99.66/13.49 (((eqimpsubset2) =>
% 99.66/13.49 (((eqimpsubset1) =>
% 99.66/13.49 (((subsetI2) =>
% 99.66/13.49 (((emptysetsubset) =>
% 99.66/13.49 (((subsetE) =>
% 99.66/13.49 (((subsetE2) =>
% 99.66/13.49 (((notsubsetI) =>
% 99.66/13.49 (((notequalI1) =>
% 99.66/13.49 (((notequalI2) =>
% 99.66/13.49 (((subsetRefl) =>
% 99.66/13.49 (((subsetTrans) =>
% 99.66/13.49 (((setadjoinSub) =>
% 99.66/13.49 (((setadjoinSub2) =>
% 99.66/13.49 (((subset2powerset) =>
% 99.66/13.49 (((setextsub) =>
% 99.66/13.49 (((subsetemptysetimpeq) =>
% 99.66/13.49 (((powersetI1) =>
% 99.66/13.49 (((powersetE1) =>
% 99.66/13.49 (((inPowerset) =>
% 99.66/13.49 (((powersetsubset) =>
% 99.66/13.49 (((sepInPowerset) =>
% 99.66/13.49 (((sepSubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionIL) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairset2IR) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionEcases) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectI) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset5) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset3) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectER) =>
% 99.66/13.49 ((
% 99.66/13.49 (disjointsetsI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset4) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (bs114d) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusI) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusER) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusERneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusELneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusILneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusIRneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffE) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI2) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg2) =>
% 99.66/13.49 ((
% 99.66/13.49 (secondinupair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairiskpair) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairp) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowerset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairset2E) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairsubunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairinpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem3) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair1) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionE2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton1) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I2) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsuniq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (theprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstin) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR11) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR12) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR1) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairequniteq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemER) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempaircEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrI) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrSub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrERa) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrER) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcImageSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (apProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (app) =>
% 99.66/13.49 ((
% 99.66/13.49 (infuncsetfunc) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcinfuncset) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall1) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp3) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcextLem) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp4) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq2) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2lamEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifp) =>
% 99.66/13.49 ((
% 99.66/13.49 (theeq) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrue) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueorfalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setextT) =>
% 99.66/13.49 ((
% 99.66/13.49 (subsetTI) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTELcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTERcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT1) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT2) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT3) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub2) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTnotintersectT) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementImpComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementSubsetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementInPowersetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (contraSubsetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTcontraSubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTILcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTIRcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion2) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (intersectInPowersetIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpNotIn1) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpInComplement1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTEcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementUnionInPowersetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule0) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_5) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all2) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1SetBreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (choice2fnsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all1) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compEex) =>
% 99.66/13.49 ((
% 99.66/13.49 (!!) @ (
% 99.66/13.49 (('#B') @ (
% 99.66/13.49 !!) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 !!))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#C') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl660])).
% 99.66/13.49 thf(zip_derived_cl685, plain,
% 99.66/13.49 (~ (((setadjoin__Cong) =>
% 99.66/13.49 (((powerset__Cong) =>
% 99.66/13.49 (((setunion__Cong) =>
% 99.66/13.49 (((exuEu) =>
% 99.66/13.49 (((descr__Cong) =>
% 99.66/13.49 (((dsetconstr__Cong) =>
% 99.66/13.49 (((subsetI1) =>
% 99.66/13.49 (((eqimpsubset2) =>
% 99.66/13.49 (((eqimpsubset1) =>
% 99.66/13.49 (((subsetI2) =>
% 99.66/13.49 (((emptysetsubset) =>
% 99.66/13.49 (((subsetE) =>
% 99.66/13.49 (((subsetE2) =>
% 99.66/13.49 (((notsubsetI) =>
% 99.66/13.49 (((notequalI1) =>
% 99.66/13.49 (((notequalI2) =>
% 99.66/13.49 (((subsetRefl) =>
% 99.66/13.49 (((subsetTrans) =>
% 99.66/13.49 (((setadjoinSub) =>
% 99.66/13.49 (((setadjoinSub2) =>
% 99.66/13.49 (((subset2powerset) =>
% 99.66/13.49 (((setextsub) =>
% 99.66/13.49 (((subsetemptysetimpeq) =>
% 99.66/13.49 (((powersetI1) =>
% 99.66/13.49 (((powersetE1) =>
% 99.66/13.49 (((inPowerset) =>
% 99.66/13.49 (((powersetsubset) =>
% 99.66/13.49 (((sepInPowerset) =>
% 99.66/13.49 (((sepSubset) =>
% 99.66/13.49 (((binunionIL) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairset2IR) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionEcases) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectI) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset5) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset3) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectER) =>
% 99.66/13.49 ((
% 99.66/13.49 (disjointsetsI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset4) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (bs114d) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusI) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusER) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusERneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusELneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusILneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusIRneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffE) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI2) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg2) =>
% 99.66/13.49 ((
% 99.66/13.49 (secondinupair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairiskpair) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairp) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowerset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairset2E) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairsubunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairinpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem3) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair1) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionE2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton1) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I2) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsuniq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (theprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstin) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR11) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR12) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR1) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairequniteq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemER) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempaircEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrI) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrSub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrERa) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrER) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcImageSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (apProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (app) =>
% 99.66/13.49 ((
% 99.66/13.49 (infuncsetfunc) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcinfuncset) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall1) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp3) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcextLem) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp4) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq2) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2lamEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifp) =>
% 99.66/13.49 ((
% 99.66/13.49 (theeq) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrue) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueorfalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setextT) =>
% 99.66/13.49 ((
% 99.66/13.49 (subsetTI) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTELcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTERcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT1) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT2) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT3) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub2) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTnotintersectT) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementImpComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementSubsetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementInPowersetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (contraSubsetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTcontraSubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTILcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTIRcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion2) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (intersectInPowersetIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpNotIn1) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpInComplement1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTEcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementUnionInPowersetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule0) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_5) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all2) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1SetBreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (choice2fnsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all1) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compEex) =>
% 99.66/13.49 ((
% 99.66/13.49 (!!) @ (
% 99.66/13.49 (('#B') @ (
% 99.66/13.49 !!) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 !!))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#C') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl672])).
% 99.66/13.49 thf(zip_derived_cl699, plain,
% 99.66/13.49 (~ (((powerset__Cong) =>
% 99.66/13.49 (((setunion__Cong) =>
% 99.66/13.49 (((exuEu) =>
% 99.66/13.49 (((descr__Cong) =>
% 99.66/13.49 (((dsetconstr__Cong) =>
% 99.66/13.49 (((subsetI1) =>
% 99.66/13.49 (((eqimpsubset2) =>
% 99.66/13.49 (((eqimpsubset1) =>
% 99.66/13.49 (((subsetI2) =>
% 99.66/13.49 (((emptysetsubset) =>
% 99.66/13.49 (((subsetE) =>
% 99.66/13.49 (((subsetE2) =>
% 99.66/13.49 (((notsubsetI) =>
% 99.66/13.49 (((notequalI1) =>
% 99.66/13.49 (((notequalI2) =>
% 99.66/13.49 (((subsetRefl) =>
% 99.66/13.49 (((subsetTrans) =>
% 99.66/13.49 (((setadjoinSub) =>
% 99.66/13.49 (((setadjoinSub2) =>
% 99.66/13.49 (((subset2powerset) =>
% 99.66/13.49 (((setextsub) =>
% 99.66/13.49 (((subsetemptysetimpeq) =>
% 99.66/13.49 (((powersetI1) =>
% 99.66/13.49 (((powersetE1) =>
% 99.66/13.49 (((inPowerset) =>
% 99.66/13.49 (((powersetsubset) =>
% 99.66/13.49 (((sepInPowerset) =>
% 99.66/13.49 (((sepSubset) =>
% 99.66/13.49 (((binunionIL) =>
% 99.66/13.49 (((upairset2IR) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionEcases) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectI) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset5) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset3) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectER) =>
% 99.66/13.49 ((
% 99.66/13.49 (disjointsetsI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset4) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (bs114d) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusI) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusER) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusERneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusELneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusILneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusIRneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffE) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI2) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg2) =>
% 99.66/13.49 ((
% 99.66/13.49 (secondinupair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairiskpair) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairp) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowerset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairset2E) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairsubunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairinpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem3) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair1) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionE2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton1) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I2) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsuniq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (theprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstin) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR11) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR12) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR1) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairequniteq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemER) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempaircEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrI) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrSub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrERa) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrER) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcImageSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (apProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (app) =>
% 99.66/13.49 ((
% 99.66/13.49 (infuncsetfunc) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcinfuncset) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall1) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp3) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcextLem) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp4) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq2) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2lamEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifp) =>
% 99.66/13.49 ((
% 99.66/13.49 (theeq) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrue) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueorfalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setextT) =>
% 99.66/13.49 ((
% 99.66/13.49 (subsetTI) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTELcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTERcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT1) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT2) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT3) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub2) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTnotintersectT) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementImpComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementSubsetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementInPowersetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (contraSubsetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTcontraSubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTILcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTIRcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion2) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (intersectInPowersetIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpNotIn1) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpInComplement1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTEcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementUnionInPowersetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule0) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_5) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all2) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1SetBreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (choice2fnsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all1) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compEex) =>
% 99.66/13.49 ((
% 99.66/13.49 (!!) @ (
% 99.66/13.49 (('#B') @ (
% 99.66/13.49 !!) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 !!))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#C') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl685])).
% 99.66/13.49 thf(zip_derived_cl714, plain,
% 99.66/13.49 (~ (((setunion__Cong) =>
% 99.66/13.49 (((exuEu) =>
% 99.66/13.49 (((descr__Cong) =>
% 99.66/13.49 (((dsetconstr__Cong) =>
% 99.66/13.49 (((subsetI1) =>
% 99.66/13.49 (((eqimpsubset2) =>
% 99.66/13.49 (((eqimpsubset1) =>
% 99.66/13.49 (((subsetI2) =>
% 99.66/13.49 (((emptysetsubset) =>
% 99.66/13.49 (((subsetE) =>
% 99.66/13.49 (((subsetE2) =>
% 99.66/13.49 (((notsubsetI) =>
% 99.66/13.49 (((notequalI1) =>
% 99.66/13.49 (((notequalI2) =>
% 99.66/13.49 (((subsetRefl) =>
% 99.66/13.49 (((subsetTrans) =>
% 99.66/13.49 (((setadjoinSub) =>
% 99.66/13.49 (((setadjoinSub2) =>
% 99.66/13.49 (((subset2powerset) =>
% 99.66/13.49 (((setextsub) =>
% 99.66/13.49 (((subsetemptysetimpeq) =>
% 99.66/13.49 (((powersetI1) =>
% 99.66/13.49 (((powersetE1) =>
% 99.66/13.49 (((inPowerset) =>
% 99.66/13.49 (((powersetsubset) =>
% 99.66/13.49 (((sepInPowerset) =>
% 99.66/13.49 (((sepSubset) =>
% 99.66/13.49 (((binunionIL) =>
% 99.66/13.49 (((upairset2IR) =>
% 99.66/13.49 (((binunionIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionEcases) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectI) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset5) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset3) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectER) =>
% 99.66/13.49 ((
% 99.66/13.49 (disjointsetsI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset4) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (bs114d) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusI) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusER) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusERneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusELneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusILneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusIRneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffE) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI2) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg2) =>
% 99.66/13.49 ((
% 99.66/13.49 (secondinupair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairiskpair) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairp) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowerset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairset2E) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairsubunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairinpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem3) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair1) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionE2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton1) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I2) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsuniq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (theprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstin) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR11) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR12) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR1) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairequniteq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemER) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempaircEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrI) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrSub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrERa) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrER) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcImageSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (apProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (app) =>
% 99.66/13.49 ((
% 99.66/13.49 (infuncsetfunc) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcinfuncset) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall1) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp3) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcextLem) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp4) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq2) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2lamEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifp) =>
% 99.66/13.49 ((
% 99.66/13.49 (theeq) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrue) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueorfalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setextT) =>
% 99.66/13.49 ((
% 99.66/13.49 (subsetTI) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTELcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTERcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT1) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT2) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT3) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub2) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTnotintersectT) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementImpComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementSubsetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementInPowersetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (contraSubsetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTcontraSubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTILcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTIRcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion2) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (intersectInPowersetIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpNotIn1) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpInComplement1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTEcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementUnionInPowersetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule0) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_5) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all2) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1SetBreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (choice2fnsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all1) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compEex) =>
% 99.66/13.49 ((
% 99.66/13.49 (!!) @ (
% 99.66/13.49 (('#B') @ (
% 99.66/13.49 !!) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 !!))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#C') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl699])).
% 99.66/13.49 thf(zip_derived_cl731, plain,
% 99.66/13.49 (~ (((exuEu) =>
% 99.66/13.49 (((descr__Cong) =>
% 99.66/13.49 (((dsetconstr__Cong) =>
% 99.66/13.49 (((subsetI1) =>
% 99.66/13.49 (((eqimpsubset2) =>
% 99.66/13.49 (((eqimpsubset1) =>
% 99.66/13.49 (((subsetI2) =>
% 99.66/13.49 (((emptysetsubset) =>
% 99.66/13.49 (((subsetE) =>
% 99.66/13.49 (((subsetE2) =>
% 99.66/13.49 (((notsubsetI) =>
% 99.66/13.49 (((notequalI1) =>
% 99.66/13.49 (((notequalI2) =>
% 99.66/13.49 (((subsetRefl) =>
% 99.66/13.49 (((subsetTrans) =>
% 99.66/13.49 (((setadjoinSub) =>
% 99.66/13.49 (((setadjoinSub2) =>
% 99.66/13.49 (((subset2powerset) =>
% 99.66/13.49 (((setextsub) =>
% 99.66/13.49 (((subsetemptysetimpeq) =>
% 99.66/13.49 (((powersetI1) =>
% 99.66/13.49 (((powersetE1) =>
% 99.66/13.49 (((inPowerset) =>
% 99.66/13.49 (((powersetsubset) =>
% 99.66/13.49 (((sepInPowerset) =>
% 99.66/13.49 (((sepSubset) =>
% 99.66/13.49 (((binunionIL) =>
% 99.66/13.49 (((upairset2IR) =>
% 99.66/13.49 (((binunionIR) =>
% 99.66/13.49 (((binunionEcases) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectI) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset5) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset3) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectER) =>
% 99.66/13.49 ((
% 99.66/13.49 (disjointsetsI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset4) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (bs114d) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusI) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusER) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusERneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusELneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusILneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusIRneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffE) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI2) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg2) =>
% 99.66/13.49 ((
% 99.66/13.49 (secondinupair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairiskpair) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairp) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowerset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairset2E) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairsubunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairinpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem3) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair1) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionE2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton1) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I2) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsuniq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (theprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstin) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR11) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR12) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR1) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairequniteq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemER) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempaircEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrI) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrSub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrERa) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrER) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcImageSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (apProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (app) =>
% 99.66/13.49 ((
% 99.66/13.49 (infuncsetfunc) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcinfuncset) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall1) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp3) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcextLem) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp4) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq2) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2lamEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifp) =>
% 99.66/13.49 ((
% 99.66/13.49 (theeq) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrue) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueorfalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setextT) =>
% 99.66/13.49 ((
% 99.66/13.49 (subsetTI) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTELcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTERcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT1) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT2) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT3) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub2) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTnotintersectT) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementImpComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementSubsetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementInPowersetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (contraSubsetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTcontraSubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTILcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTIRcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion2) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (intersectInPowersetIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpNotIn1) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpInComplement1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTEcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementUnionInPowersetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule0) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_5) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all2) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1SetBreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (choice2fnsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all1) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compEex) =>
% 99.66/13.49 ((
% 99.66/13.49 (!!) @ (
% 99.66/13.49 (('#B') @ (
% 99.66/13.49 !!) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 !!))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#C') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl714])).
% 99.66/13.49 thf(zip_derived_cl749, plain,
% 99.66/13.49 (~ (((descr__Cong) =>
% 99.66/13.49 (((dsetconstr__Cong) =>
% 99.66/13.49 (((subsetI1) =>
% 99.66/13.49 (((eqimpsubset2) =>
% 99.66/13.49 (((eqimpsubset1) =>
% 99.66/13.49 (((subsetI2) =>
% 99.66/13.49 (((emptysetsubset) =>
% 99.66/13.49 (((subsetE) =>
% 99.66/13.49 (((subsetE2) =>
% 99.66/13.49 (((notsubsetI) =>
% 99.66/13.49 (((notequalI1) =>
% 99.66/13.49 (((notequalI2) =>
% 99.66/13.49 (((subsetRefl) =>
% 99.66/13.49 (((subsetTrans) =>
% 99.66/13.49 (((setadjoinSub) =>
% 99.66/13.49 (((setadjoinSub2) =>
% 99.66/13.49 (((subset2powerset) =>
% 99.66/13.49 (((setextsub) =>
% 99.66/13.49 (((subsetemptysetimpeq) =>
% 99.66/13.49 (((powersetI1) =>
% 99.66/13.49 (((powersetE1) =>
% 99.66/13.49 (((inPowerset) =>
% 99.66/13.49 (((powersetsubset) =>
% 99.66/13.49 (((sepInPowerset) =>
% 99.66/13.49 (((sepSubset) =>
% 99.66/13.49 (((binunionIL) =>
% 99.66/13.49 (((upairset2IR) =>
% 99.66/13.49 (((binunionIR) =>
% 99.66/13.49 (((binunionEcases) =>
% 99.66/13.49 (((binunionE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectI) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset5) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset3) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectER) =>
% 99.66/13.49 ((
% 99.66/13.49 (disjointsetsI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset4) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (bs114d) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusI) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusER) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusERneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusELneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusILneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusIRneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffE) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI2) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg2) =>
% 99.66/13.49 ((
% 99.66/13.49 (secondinupair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairiskpair) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairp) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowerset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairset2E) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairsubunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairinpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem3) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair1) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionE2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton1) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I2) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsuniq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (theprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstin) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR11) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR12) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR1) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairequniteq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemER) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempaircEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrI) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrSub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrERa) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrER) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcImageSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (apProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (app) =>
% 99.66/13.49 ((
% 99.66/13.49 (infuncsetfunc) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcinfuncset) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall1) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp3) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcextLem) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp4) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq2) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2lamEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifp) =>
% 99.66/13.49 ((
% 99.66/13.49 (theeq) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrue) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueorfalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setextT) =>
% 99.66/13.49 ((
% 99.66/13.49 (subsetTI) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTELcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTERcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT1) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT2) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT3) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub2) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTnotintersectT) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementImpComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementSubsetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementInPowersetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (contraSubsetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTcontraSubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTILcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTIRcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion2) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (intersectInPowersetIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpNotIn1) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpInComplement1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTEcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementUnionInPowersetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule0) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_5) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all2) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1SetBreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (choice2fnsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all1) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compEex) =>
% 99.66/13.49 ((
% 99.66/13.49 (!!) @ (
% 99.66/13.49 (('#B') @ (
% 99.66/13.49 !!) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 !!))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#C') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl731])).
% 99.66/13.49 thf(zip_derived_cl769, plain,
% 99.66/13.49 (~ (((dsetconstr__Cong) =>
% 99.66/13.49 (((subsetI1) =>
% 99.66/13.49 (((eqimpsubset2) =>
% 99.66/13.49 (((eqimpsubset1) =>
% 99.66/13.49 (((subsetI2) =>
% 99.66/13.49 (((emptysetsubset) =>
% 99.66/13.49 (((subsetE) =>
% 99.66/13.49 (((subsetE2) =>
% 99.66/13.49 (((notsubsetI) =>
% 99.66/13.49 (((notequalI1) =>
% 99.66/13.49 (((notequalI2) =>
% 99.66/13.49 (((subsetRefl) =>
% 99.66/13.49 (((subsetTrans) =>
% 99.66/13.49 (((setadjoinSub) =>
% 99.66/13.49 (((setadjoinSub2) =>
% 99.66/13.49 (((subset2powerset) =>
% 99.66/13.49 (((setextsub) =>
% 99.66/13.49 (((subsetemptysetimpeq) =>
% 99.66/13.49 (((powersetI1) =>
% 99.66/13.49 (((powersetE1) =>
% 99.66/13.49 (((inPowerset) =>
% 99.66/13.49 (((powersetsubset) =>
% 99.66/13.49 (((sepInPowerset) =>
% 99.66/13.49 (((sepSubset) =>
% 99.66/13.49 (((binunionIL) =>
% 99.66/13.49 (((upairset2IR) =>
% 99.66/13.49 (((binunionIR) =>
% 99.66/13.49 (((binunionEcases) =>
% 99.66/13.49 (((binunionE) =>
% 99.66/13.49 (((binunionLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectI) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset5) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset3) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectER) =>
% 99.66/13.49 ((
% 99.66/13.49 (disjointsetsI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset4) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (bs114d) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusI) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusER) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusERneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusELneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusILneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusIRneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffE) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI2) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg2) =>
% 99.66/13.49 ((
% 99.66/13.49 (secondinupair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairiskpair) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairp) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowerset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairset2E) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairsubunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairinpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem3) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair1) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionE2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton1) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I2) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsuniq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (theprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstin) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR11) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR12) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR1) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairequniteq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemER) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempaircEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrI) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrSub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrERa) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrER) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcImageSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (apProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (app) =>
% 99.66/13.49 ((
% 99.66/13.49 (infuncsetfunc) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcinfuncset) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall1) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp3) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcextLem) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp4) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq2) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2lamEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifp) =>
% 99.66/13.49 ((
% 99.66/13.49 (theeq) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrue) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueorfalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setextT) =>
% 99.66/13.49 ((
% 99.66/13.49 (subsetTI) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTELcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTERcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT1) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT2) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT3) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub2) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTnotintersectT) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementImpComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementSubsetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementInPowersetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (contraSubsetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTcontraSubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTILcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTIRcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInUnion2) =>
% 99.66/13.49 ((
% 99.66/13.49 (inIntersectImpInIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (intersectInPowersetIntersectUnions) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpNotIn1) =>
% 99.66/13.49 ((
% 99.66/13.49 (inComplementUnionImpInComplement1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTE) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTEcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementUnionInPowersetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan1) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2a) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b2) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2b) =>
% 99.66/13.49 ((
% 99.66/13.49 (demorgan2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule0) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz13rule4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_1) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_2) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_3) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_4) =>
% 99.66/13.49 ((
% 99.66/13.49 (woz1_5) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all2) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1SetBreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (choice2fnsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1all1) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln1) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1invE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compI) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compE) =>
% 99.66/13.49 ((
% 99.66/13.49 (breln1compEex) =>
% 99.66/13.49 ((
% 99.66/13.49 (!!) @ (
% 99.66/13.49 (('#B') @ (
% 99.66/13.49 !!) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 !!))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#S') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#S') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 =>))) @
% 99.66/13.49 breln1)))))) @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#C') @ (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 (
% 99.66/13.49 (
% 99.66/13.49 ('#B') @ (
% 99.66/13.49 '#B') @
% 99.66/13.49 breln1)))) @
% 99.66/13.49 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl749])).
% 99.66/13.49 thf(zip_derived_cl789, plain,
% 99.66/13.49 (~ (((subsetI1) =>
% 99.66/13.49 (((eqimpsubset2) =>
% 99.66/13.49 (((eqimpsubset1) =>
% 99.66/13.49 (((subsetI2) =>
% 99.66/13.49 (((emptysetsubset) =>
% 99.66/13.49 (((subsetE) =>
% 99.66/13.49 (((subsetE2) =>
% 99.66/13.49 (((notsubsetI) =>
% 99.66/13.49 (((notequalI1) =>
% 99.66/13.49 (((notequalI2) =>
% 99.66/13.49 (((subsetRefl) =>
% 99.66/13.49 (((subsetTrans) =>
% 99.66/13.49 (((setadjoinSub) =>
% 99.66/13.49 (((setadjoinSub2) =>
% 99.66/13.49 (((subset2powerset) =>
% 99.66/13.49 (((setextsub) =>
% 99.66/13.49 (((subsetemptysetimpeq) =>
% 99.66/13.49 (((powersetI1) =>
% 99.66/13.49 (((powersetE1) =>
% 99.66/13.49 (((inPowerset) =>
% 99.66/13.49 (((powersetsubset) =>
% 99.66/13.49 (((sepInPowerset) =>
% 99.66/13.49 (((sepSubset) =>
% 99.66/13.49 (((binunionIL) =>
% 99.66/13.49 (((upairset2IR) =>
% 99.66/13.49 (((binunionIR) =>
% 99.66/13.49 (((binunionEcases) =>
% 99.66/13.49 (((binunionE) =>
% 99.66/13.49 (((binunionLsub) =>
% 99.66/13.49 (((binunionRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectI) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset5) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset3) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectER) =>
% 99.66/13.49 ((
% 99.66/13.49 (disjointsetsI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectRsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset4) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (bs114d) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusI) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusER) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusERneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusELneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusILneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusIRneg) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusLsub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusSubset1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffE) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffI2) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg1) =>
% 99.66/13.49 ((
% 99.66/13.49 (symdiffIneg2) =>
% 99.66/13.49 ((
% 99.66/13.49 (secondinupair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairIR) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairiskpair) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairp) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowerset) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletoninpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairset2E) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairsubunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairinpowunion) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ubforcartprodlem3) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair1) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempair) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionE2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton1) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setunionsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1I2) =>
% 99.66/13.49 ((
% 99.66/13.49 (singletonsuniq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (theprop) =>
% 99.66/13.49 ((
% 99.66/13.49 (kfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstin) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjL) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR11) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR12) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR1) =>
% 99.66/13.49 ((
% 99.66/13.49 (upairequniteq) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR2) =>
% 99.66/13.49 ((
% 99.66/13.49 (setukpairinjR) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndsingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ksndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (kpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndin) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemEL) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairmemER) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodmempaircEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodfstpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodsndpairEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (cartprodpairsurjEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrI) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrSub) =>
% 99.66/13.49 ((
% 99.66/13.49 (setOfPairsIsBReln) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrERa) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL1) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrEL2) =>
% 99.66/13.49 ((
% 99.66/13.49 (dpsetconstrER) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcImageSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (apProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (app) =>
% 99.66/13.49 ((
% 99.66/13.49 (infuncsetfunc) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcinfuncset) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamProp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lamp) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2p) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall1) =>
% 99.66/13.49 ((
% 99.66/13.49 (brelnall2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ex1E2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp3) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcextLem) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcGraphProp4) =>
% 99.66/13.49 ((
% 99.66/13.49 (subbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (eqbreln) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext) =>
% 99.66/13.49 ((
% 99.66/13.49 (funcext2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq1) =>
% 99.66/13.49 ((
% 99.66/13.49 (ap2apEq2) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta1) =>
% 99.66/13.49 ((
% 99.66/13.49 (lam2lamEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (beta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (eta2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalseProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp1) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueProp2) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifSingleton) =>
% 99.66/13.49 ((
% 99.66/13.49 (ifp) =>
% 99.66/13.49 ((
% 99.66/13.49 (theeq) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrue) =>
% 99.66/13.49 ((
% 99.66/13.49 (iffalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (iftrueorfalse) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setminusT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementT_lem) =>
% 99.66/13.49 ((
% 99.66/13.49 (setextT) =>
% 99.66/13.49 ((
% 99.66/13.49 (subsetTI) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (powersetTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTELcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binintersectTERcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT1) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT2) =>
% 99.66/13.49 ((
% 99.66/13.49 (contrasubsetT3) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementI1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementE1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub1) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementSub2) =>
% 99.66/13.49 ((
% 99.66/13.49 (doubleComplementEq) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTnotintersectT) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementImpComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementSubsetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementInPowersetComplementIntersect) =>
% 99.66/13.49 ((
% 99.66/13.49 (contraSubsetComplement) =>
% 99.66/13.49 ((
% 99.66/13.49 (complementTcontraSubset) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTILcontra) =>
% 99.66/13.49 ((
% 99.66/13.49 (binunionTIRcontra) =>
% 99.66/13.49 ((
% 99.66/13.50 (inIntersectImpInUnion) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion2) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (intersectInPowersetIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpNotIn1) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpInComplement1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTE) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTEcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementUnionInPowersetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule0) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_5) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all2) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1SetBreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (choice2fnsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all1) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compEex) =>
% 99.66/13.50 ((
% 99.66/13.50 (!!) @ (
% 99.66/13.50 (('#B') @ (
% 99.66/13.50 !!) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 !!))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#C') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl769])).
% 99.66/13.50 thf(zip_derived_cl807, plain,
% 99.66/13.50 (~ (((eqimpsubset2) =>
% 99.66/13.50 (((eqimpsubset1) =>
% 99.66/13.50 (((subsetI2) =>
% 99.66/13.50 (((emptysetsubset) =>
% 99.66/13.50 (((subsetE) =>
% 99.66/13.50 (((subsetE2) =>
% 99.66/13.50 (((notsubsetI) =>
% 99.66/13.50 (((notequalI1) =>
% 99.66/13.50 (((notequalI2) =>
% 99.66/13.50 (((subsetRefl) =>
% 99.66/13.50 (((subsetTrans) =>
% 99.66/13.50 (((setadjoinSub) =>
% 99.66/13.50 (((setadjoinSub2) =>
% 99.66/13.50 (((subset2powerset) =>
% 99.66/13.50 (((setextsub) =>
% 99.66/13.50 (((subsetemptysetimpeq) =>
% 99.66/13.50 (((powersetI1) =>
% 99.66/13.50 (((powersetE1) =>
% 99.66/13.50 (((inPowerset) =>
% 99.66/13.50 (((powersetsubset) =>
% 99.66/13.50 (((sepInPowerset) =>
% 99.66/13.50 (((sepSubset) =>
% 99.66/13.50 (((binunionIL) =>
% 99.66/13.50 (((upairset2IR) =>
% 99.66/13.50 (((binunionIR) =>
% 99.66/13.50 (((binunionEcases) =>
% 99.66/13.50 (((binunionE) =>
% 99.66/13.50 (((binunionLsub) =>
% 99.66/13.50 (((binunionRsub) =>
% 99.66/13.50 (((binintersectI) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset5) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectLsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset2) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset3) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectER) =>
% 99.66/13.50 ((
% 99.66/13.50 (disjointsetsI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectRsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset4) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (bs114d) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusI) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusER) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusERneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusELneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusILneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusIRneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusLsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffE) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI2) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg2) =>
% 99.66/13.50 ((
% 99.66/13.50 (secondinupair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIR) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairiskpair) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairp) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowerset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairset2E) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairsubunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairinpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem3) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair1) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionE2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton1) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I2) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsuniq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (theprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstin) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR11) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR12) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR1) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairequniteq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemER) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempaircEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrI) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrSub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrERa) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrER) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcImageSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (apProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (app) =>
% 99.66/13.50 ((
% 99.66/13.50 (infuncsetfunc) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcinfuncset) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall1) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp3) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcextLem) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp4) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq2) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2lamEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifp) =>
% 99.66/13.50 ((
% 99.66/13.50 (theeq) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrue) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueorfalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setextT) =>
% 99.66/13.50 ((
% 99.66/13.50 (subsetTI) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTELcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTERcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT1) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT2) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT3) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub2) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTnotintersectT) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementImpComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementSubsetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementInPowersetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (contraSubsetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTcontraSubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTILcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTIRcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion2) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (intersectInPowersetIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpNotIn1) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpInComplement1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTE) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTEcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementUnionInPowersetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule0) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_5) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all2) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1SetBreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (choice2fnsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all1) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compEex) =>
% 99.66/13.50 ((
% 99.66/13.50 (!!) @ (
% 99.66/13.50 (('#B') @ (
% 99.66/13.50 !!) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 !!))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#C') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl789])).
% 99.66/13.50 thf(zip_derived_cl824, plain,
% 99.66/13.50 (~ (((eqimpsubset1) =>
% 99.66/13.50 (((subsetI2) =>
% 99.66/13.50 (((emptysetsubset) =>
% 99.66/13.50 (((subsetE) =>
% 99.66/13.50 (((subsetE2) =>
% 99.66/13.50 (((notsubsetI) =>
% 99.66/13.50 (((notequalI1) =>
% 99.66/13.50 (((notequalI2) =>
% 99.66/13.50 (((subsetRefl) =>
% 99.66/13.50 (((subsetTrans) =>
% 99.66/13.50 (((setadjoinSub) =>
% 99.66/13.50 (((setadjoinSub2) =>
% 99.66/13.50 (((subset2powerset) =>
% 99.66/13.50 (((setextsub) =>
% 99.66/13.50 (((subsetemptysetimpeq) =>
% 99.66/13.50 (((powersetI1) =>
% 99.66/13.50 (((powersetE1) =>
% 99.66/13.50 (((inPowerset) =>
% 99.66/13.50 (((powersetsubset) =>
% 99.66/13.50 (((sepInPowerset) =>
% 99.66/13.50 (((sepSubset) =>
% 99.66/13.50 (((binunionIL) =>
% 99.66/13.50 (((upairset2IR) =>
% 99.66/13.50 (((binunionIR) =>
% 99.66/13.50 (((binunionEcases) =>
% 99.66/13.50 (((binunionE) =>
% 99.66/13.50 (((binunionLsub) =>
% 99.66/13.50 (((binunionRsub) =>
% 99.66/13.50 (((binintersectI) =>
% 99.66/13.50 (((binintersectSubset5) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectLsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset2) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset3) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectER) =>
% 99.66/13.50 ((
% 99.66/13.50 (disjointsetsI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectRsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset4) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (bs114d) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusI) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusER) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusERneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusELneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusILneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusIRneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusLsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffE) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI2) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg2) =>
% 99.66/13.50 ((
% 99.66/13.50 (secondinupair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIR) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairiskpair) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairp) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowerset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairset2E) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairsubunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairinpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem3) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair1) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionE2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton1) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I2) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsuniq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (theprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstin) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR11) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR12) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR1) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairequniteq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemER) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempaircEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrI) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrSub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrERa) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrER) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcImageSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (apProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (app) =>
% 99.66/13.50 ((
% 99.66/13.50 (infuncsetfunc) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcinfuncset) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall1) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp3) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcextLem) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp4) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq2) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2lamEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifp) =>
% 99.66/13.50 ((
% 99.66/13.50 (theeq) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrue) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueorfalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setextT) =>
% 99.66/13.50 ((
% 99.66/13.50 (subsetTI) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTELcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTERcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT1) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT2) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT3) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub2) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTnotintersectT) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementImpComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementSubsetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementInPowersetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (contraSubsetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTcontraSubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTILcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTIRcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion2) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (intersectInPowersetIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpNotIn1) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpInComplement1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTE) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTEcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementUnionInPowersetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule0) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_5) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all2) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1SetBreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (choice2fnsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all1) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compEex) =>
% 99.66/13.50 ((
% 99.66/13.50 (!!) @ (
% 99.66/13.50 (('#B') @ (
% 99.66/13.50 !!) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 !!))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#C') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl807])).
% 99.66/13.50 thf(zip_derived_cl838, plain,
% 99.66/13.50 (~ (((subsetI2) =>
% 99.66/13.50 (((emptysetsubset) =>
% 99.66/13.50 (((subsetE) =>
% 99.66/13.50 (((subsetE2) =>
% 99.66/13.50 (((notsubsetI) =>
% 99.66/13.50 (((notequalI1) =>
% 99.66/13.50 (((notequalI2) =>
% 99.66/13.50 (((subsetRefl) =>
% 99.66/13.50 (((subsetTrans) =>
% 99.66/13.50 (((setadjoinSub) =>
% 99.66/13.50 (((setadjoinSub2) =>
% 99.66/13.50 (((subset2powerset) =>
% 99.66/13.50 (((setextsub) =>
% 99.66/13.50 (((subsetemptysetimpeq) =>
% 99.66/13.50 (((powersetI1) =>
% 99.66/13.50 (((powersetE1) =>
% 99.66/13.50 (((inPowerset) =>
% 99.66/13.50 (((powersetsubset) =>
% 99.66/13.50 (((sepInPowerset) =>
% 99.66/13.50 (((sepSubset) =>
% 99.66/13.50 (((binunionIL) =>
% 99.66/13.50 (((upairset2IR) =>
% 99.66/13.50 (((binunionIR) =>
% 99.66/13.50 (((binunionEcases) =>
% 99.66/13.50 (((binunionE) =>
% 99.66/13.50 (((binunionLsub) =>
% 99.66/13.50 (((binunionRsub) =>
% 99.66/13.50 (((binintersectI) =>
% 99.66/13.50 (((binintersectSubset5) =>
% 99.66/13.50 (((binintersectEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectLsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset2) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset3) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectER) =>
% 99.66/13.50 ((
% 99.66/13.50 (disjointsetsI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectRsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset4) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (bs114d) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusI) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusER) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusERneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusELneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusILneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusIRneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusLsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffE) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI2) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg2) =>
% 99.66/13.50 ((
% 99.66/13.50 (secondinupair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIR) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairiskpair) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairp) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowerset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairset2E) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairsubunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairinpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem3) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair1) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionE2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton1) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I2) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsuniq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (theprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstin) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR11) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR12) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR1) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairequniteq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemER) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempaircEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrI) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrSub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrERa) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrER) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcImageSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (apProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (app) =>
% 99.66/13.50 ((
% 99.66/13.50 (infuncsetfunc) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcinfuncset) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall1) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp3) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcextLem) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp4) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq2) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2lamEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifp) =>
% 99.66/13.50 ((
% 99.66/13.50 (theeq) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrue) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueorfalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setextT) =>
% 99.66/13.50 ((
% 99.66/13.50 (subsetTI) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTELcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTERcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT1) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT2) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT3) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub2) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTnotintersectT) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementImpComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementSubsetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementInPowersetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (contraSubsetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTcontraSubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTILcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTIRcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion2) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (intersectInPowersetIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpNotIn1) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpInComplement1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTE) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTEcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementUnionInPowersetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule0) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_5) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all2) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1SetBreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (choice2fnsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all1) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compEex) =>
% 99.66/13.50 ((
% 99.66/13.50 (!!) @ (
% 99.66/13.50 (('#B') @ (
% 99.66/13.50 !!) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 !!))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#C') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl824])).
% 99.66/13.50 thf(zip_derived_cl850, plain,
% 99.66/13.50 (~ (((emptysetsubset) =>
% 99.66/13.50 (((subsetE) =>
% 99.66/13.50 (((subsetE2) =>
% 99.66/13.50 (((notsubsetI) =>
% 99.66/13.50 (((notequalI1) =>
% 99.66/13.50 (((notequalI2) =>
% 99.66/13.50 (((subsetRefl) =>
% 99.66/13.50 (((subsetTrans) =>
% 99.66/13.50 (((setadjoinSub) =>
% 99.66/13.50 (((setadjoinSub2) =>
% 99.66/13.50 (((subset2powerset) =>
% 99.66/13.50 (((setextsub) =>
% 99.66/13.50 (((subsetemptysetimpeq) =>
% 99.66/13.50 (((powersetI1) =>
% 99.66/13.50 (((powersetE1) =>
% 99.66/13.50 (((inPowerset) =>
% 99.66/13.50 (((powersetsubset) =>
% 99.66/13.50 (((sepInPowerset) =>
% 99.66/13.50 (((sepSubset) =>
% 99.66/13.50 (((binunionIL) =>
% 99.66/13.50 (((upairset2IR) =>
% 99.66/13.50 (((binunionIR) =>
% 99.66/13.50 (((binunionEcases) =>
% 99.66/13.50 (((binunionE) =>
% 99.66/13.50 (((binunionLsub) =>
% 99.66/13.50 (((binunionRsub) =>
% 99.66/13.50 (((binintersectI) =>
% 99.66/13.50 (((binintersectSubset5) =>
% 99.66/13.50 (((binintersectEL) =>
% 99.66/13.50 (((binintersectLsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset2) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset3) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectER) =>
% 99.66/13.50 ((
% 99.66/13.50 (disjointsetsI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectRsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset4) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (bs114d) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusI) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusER) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusERneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusELneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusILneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusIRneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusLsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffE) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI2) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg2) =>
% 99.66/13.50 ((
% 99.66/13.50 (secondinupair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIR) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairiskpair) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairp) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowerset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairset2E) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairsubunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairinpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem3) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair1) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionE2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton1) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I2) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsuniq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (theprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstin) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR11) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR12) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR1) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairequniteq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemER) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempaircEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrI) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrSub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrERa) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrER) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcImageSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (apProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (app) =>
% 99.66/13.50 ((
% 99.66/13.50 (infuncsetfunc) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcinfuncset) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall1) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp3) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcextLem) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp4) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq2) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2lamEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifp) =>
% 99.66/13.50 ((
% 99.66/13.50 (theeq) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrue) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueorfalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setextT) =>
% 99.66/13.50 ((
% 99.66/13.50 (subsetTI) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTELcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTERcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT1) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT2) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT3) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub2) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTnotintersectT) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementImpComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementSubsetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementInPowersetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (contraSubsetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTcontraSubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTILcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTIRcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion2) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (intersectInPowersetIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpNotIn1) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpInComplement1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTE) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTEcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementUnionInPowersetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule0) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_5) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all2) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1SetBreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (choice2fnsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all1) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compEex) =>
% 99.66/13.50 ((
% 99.66/13.50 (!!) @ (
% 99.66/13.50 (('#B') @ (
% 99.66/13.50 !!) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 !!))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#C') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl838])).
% 99.66/13.50 thf(zip_derived_cl863, plain,
% 99.66/13.50 (~ (((subsetE) =>
% 99.66/13.50 (((subsetE2) =>
% 99.66/13.50 (((notsubsetI) =>
% 99.66/13.50 (((notequalI1) =>
% 99.66/13.50 (((notequalI2) =>
% 99.66/13.50 (((subsetRefl) =>
% 99.66/13.50 (((subsetTrans) =>
% 99.66/13.50 (((setadjoinSub) =>
% 99.66/13.50 (((setadjoinSub2) =>
% 99.66/13.50 (((subset2powerset) =>
% 99.66/13.50 (((setextsub) =>
% 99.66/13.50 (((subsetemptysetimpeq) =>
% 99.66/13.50 (((powersetI1) =>
% 99.66/13.50 (((powersetE1) =>
% 99.66/13.50 (((inPowerset) =>
% 99.66/13.50 (((powersetsubset) =>
% 99.66/13.50 (((sepInPowerset) =>
% 99.66/13.50 (((sepSubset) =>
% 99.66/13.50 (((binunionIL) =>
% 99.66/13.50 (((upairset2IR) =>
% 99.66/13.50 (((binunionIR) =>
% 99.66/13.50 (((binunionEcases) =>
% 99.66/13.50 (((binunionE) =>
% 99.66/13.50 (((binunionLsub) =>
% 99.66/13.50 (((binunionRsub) =>
% 99.66/13.50 (((binintersectI) =>
% 99.66/13.50 (((binintersectSubset5) =>
% 99.66/13.50 (((binintersectEL) =>
% 99.66/13.50 (((binintersectLsub) =>
% 99.66/13.50 (((binintersectSubset2) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset3) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectER) =>
% 99.66/13.50 ((
% 99.66/13.50 (disjointsetsI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectRsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset4) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (bs114d) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusI) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusER) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusERneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusELneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusILneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusIRneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusLsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffE) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI2) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg2) =>
% 99.66/13.50 ((
% 99.66/13.50 (secondinupair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIR) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairiskpair) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairp) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowerset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairset2E) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairsubunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairinpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem3) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair1) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionE2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton1) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I2) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsuniq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (theprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstin) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR11) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR12) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR1) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairequniteq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemER) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempaircEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrI) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrSub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrERa) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrER) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcImageSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (apProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (app) =>
% 99.66/13.50 ((
% 99.66/13.50 (infuncsetfunc) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcinfuncset) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall1) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp3) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcextLem) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp4) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq2) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2lamEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifp) =>
% 99.66/13.50 ((
% 99.66/13.50 (theeq) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrue) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueorfalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setextT) =>
% 99.66/13.50 ((
% 99.66/13.50 (subsetTI) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTELcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTERcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT1) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT2) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT3) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub2) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTnotintersectT) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementImpComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementSubsetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementInPowersetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (contraSubsetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTcontraSubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTILcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTIRcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion2) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (intersectInPowersetIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpNotIn1) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpInComplement1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTE) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTEcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementUnionInPowersetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule0) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_5) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all2) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1SetBreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (choice2fnsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all1) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compEex) =>
% 99.66/13.50 ((
% 99.66/13.50 (!!) @ (
% 99.66/13.50 (('#B') @ (
% 99.66/13.50 !!) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 !!))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#C') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl850])).
% 99.66/13.50 thf(zip_derived_cl878, plain,
% 99.66/13.50 (~ (((subsetE2) =>
% 99.66/13.50 (((notsubsetI) =>
% 99.66/13.50 (((notequalI1) =>
% 99.66/13.50 (((notequalI2) =>
% 99.66/13.50 (((subsetRefl) =>
% 99.66/13.50 (((subsetTrans) =>
% 99.66/13.50 (((setadjoinSub) =>
% 99.66/13.50 (((setadjoinSub2) =>
% 99.66/13.50 (((subset2powerset) =>
% 99.66/13.50 (((setextsub) =>
% 99.66/13.50 (((subsetemptysetimpeq) =>
% 99.66/13.50 (((powersetI1) =>
% 99.66/13.50 (((powersetE1) =>
% 99.66/13.50 (((inPowerset) =>
% 99.66/13.50 (((powersetsubset) =>
% 99.66/13.50 (((sepInPowerset) =>
% 99.66/13.50 (((sepSubset) =>
% 99.66/13.50 (((binunionIL) =>
% 99.66/13.50 (((upairset2IR) =>
% 99.66/13.50 (((binunionIR) =>
% 99.66/13.50 (((binunionEcases) =>
% 99.66/13.50 (((binunionE) =>
% 99.66/13.50 (((binunionLsub) =>
% 99.66/13.50 (((binunionRsub) =>
% 99.66/13.50 (((binintersectI) =>
% 99.66/13.50 (((binintersectSubset5) =>
% 99.66/13.50 (((binintersectEL) =>
% 99.66/13.50 (((binintersectLsub) =>
% 99.66/13.50 (((binintersectSubset2) =>
% 99.66/13.50 (((binintersectSubset3) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectER) =>
% 99.66/13.50 ((
% 99.66/13.50 (disjointsetsI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectRsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset4) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (bs114d) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusI) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusER) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusERneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusELneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusILneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusIRneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusLsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffE) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI2) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg2) =>
% 99.66/13.50 ((
% 99.66/13.50 (secondinupair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIR) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairiskpair) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairp) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowerset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairset2E) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairsubunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairinpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem3) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair1) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionE2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton1) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I2) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsuniq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (theprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstin) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR11) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR12) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR1) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairequniteq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemER) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempaircEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrI) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrSub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrERa) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrER) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcImageSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (apProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (app) =>
% 99.66/13.50 ((
% 99.66/13.50 (infuncsetfunc) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcinfuncset) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall1) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp3) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcextLem) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp4) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq2) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2lamEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifp) =>
% 99.66/13.50 ((
% 99.66/13.50 (theeq) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrue) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueorfalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setextT) =>
% 99.66/13.50 ((
% 99.66/13.50 (subsetTI) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTELcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTERcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT1) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT2) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT3) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub2) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTnotintersectT) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementImpComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementSubsetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementInPowersetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (contraSubsetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTcontraSubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTILcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTIRcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion2) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (intersectInPowersetIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpNotIn1) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpInComplement1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTE) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTEcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementUnionInPowersetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule0) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_5) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all2) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1SetBreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (choice2fnsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all1) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compEex) =>
% 99.66/13.50 ((
% 99.66/13.50 (!!) @ (
% 99.66/13.50 (('#B') @ (
% 99.66/13.50 !!) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 !!))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#C') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl863])).
% 99.66/13.50 thf(zip_derived_cl896, plain,
% 99.66/13.50 (~ (((notsubsetI) =>
% 99.66/13.50 (((notequalI1) =>
% 99.66/13.50 (((notequalI2) =>
% 99.66/13.50 (((subsetRefl) =>
% 99.66/13.50 (((subsetTrans) =>
% 99.66/13.50 (((setadjoinSub) =>
% 99.66/13.50 (((setadjoinSub2) =>
% 99.66/13.50 (((subset2powerset) =>
% 99.66/13.50 (((setextsub) =>
% 99.66/13.50 (((subsetemptysetimpeq) =>
% 99.66/13.50 (((powersetI1) =>
% 99.66/13.50 (((powersetE1) =>
% 99.66/13.50 (((inPowerset) =>
% 99.66/13.50 (((powersetsubset) =>
% 99.66/13.50 (((sepInPowerset) =>
% 99.66/13.50 (((sepSubset) =>
% 99.66/13.50 (((binunionIL) =>
% 99.66/13.50 (((upairset2IR) =>
% 99.66/13.50 (((binunionIR) =>
% 99.66/13.50 (((binunionEcases) =>
% 99.66/13.50 (((binunionE) =>
% 99.66/13.50 (((binunionLsub) =>
% 99.66/13.50 (((binunionRsub) =>
% 99.66/13.50 (((binintersectI) =>
% 99.66/13.50 (((binintersectSubset5) =>
% 99.66/13.50 (((binintersectEL) =>
% 99.66/13.50 (((binintersectLsub) =>
% 99.66/13.50 (((binintersectSubset2) =>
% 99.66/13.50 (((binintersectSubset3) =>
% 99.66/13.50 (((binintersectER) =>
% 99.66/13.50 ((
% 99.66/13.50 (disjointsetsI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectRsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset4) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (bs114d) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusI) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusER) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusERneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusELneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusILneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusIRneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusLsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffE) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI2) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg2) =>
% 99.66/13.50 ((
% 99.66/13.50 (secondinupair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIR) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairiskpair) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairp) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowerset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairset2E) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairsubunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairinpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem3) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair1) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionE2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton1) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I2) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsuniq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (theprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstin) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR11) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR12) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR1) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairequniteq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemER) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempaircEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrI) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrSub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrERa) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrER) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcImageSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (apProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (app) =>
% 99.66/13.50 ((
% 99.66/13.50 (infuncsetfunc) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcinfuncset) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall1) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp3) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcextLem) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp4) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq2) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2lamEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifp) =>
% 99.66/13.50 ((
% 99.66/13.50 (theeq) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrue) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueorfalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setextT) =>
% 99.66/13.50 ((
% 99.66/13.50 (subsetTI) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTELcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTERcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT1) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT2) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT3) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub2) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTnotintersectT) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementImpComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementSubsetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementInPowersetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (contraSubsetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTcontraSubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTILcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTIRcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion2) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (intersectInPowersetIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpNotIn1) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpInComplement1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTE) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTEcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementUnionInPowersetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule0) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_5) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all2) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1SetBreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (choice2fnsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all1) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compEex) =>
% 99.66/13.50 ((
% 99.66/13.50 (!!) @ (
% 99.66/13.50 (('#B') @ (
% 99.66/13.50 !!) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 !!))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#C') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl878])).
% 99.66/13.50 thf(zip_derived_cl909, plain,
% 99.66/13.50 (~ (((notequalI1) =>
% 99.66/13.50 (((notequalI2) =>
% 99.66/13.50 (((subsetRefl) =>
% 99.66/13.50 (((subsetTrans) =>
% 99.66/13.50 (((setadjoinSub) =>
% 99.66/13.50 (((setadjoinSub2) =>
% 99.66/13.50 (((subset2powerset) =>
% 99.66/13.50 (((setextsub) =>
% 99.66/13.50 (((subsetemptysetimpeq) =>
% 99.66/13.50 (((powersetI1) =>
% 99.66/13.50 (((powersetE1) =>
% 99.66/13.50 (((inPowerset) =>
% 99.66/13.50 (((powersetsubset) =>
% 99.66/13.50 (((sepInPowerset) =>
% 99.66/13.50 (((sepSubset) =>
% 99.66/13.50 (((binunionIL) =>
% 99.66/13.50 (((upairset2IR) =>
% 99.66/13.50 (((binunionIR) =>
% 99.66/13.50 (((binunionEcases) =>
% 99.66/13.50 (((binunionE) =>
% 99.66/13.50 (((binunionLsub) =>
% 99.66/13.50 (((binunionRsub) =>
% 99.66/13.50 (((binintersectI) =>
% 99.66/13.50 (((binintersectSubset5) =>
% 99.66/13.50 (((binintersectEL) =>
% 99.66/13.50 (((binintersectLsub) =>
% 99.66/13.50 (((binintersectSubset2) =>
% 99.66/13.50 (((binintersectSubset3) =>
% 99.66/13.50 (((binintersectER) =>
% 99.66/13.50 (((disjointsetsI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectRsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset4) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (bs114d) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusI) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusER) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusERneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusELneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusILneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusIRneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusLsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffE) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI2) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg2) =>
% 99.66/13.50 ((
% 99.66/13.50 (secondinupair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIR) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairiskpair) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairp) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowerset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairset2E) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairsubunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairinpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem3) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair1) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionE2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton1) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I2) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsuniq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (theprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstin) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR11) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR12) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR1) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairequniteq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemER) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempaircEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrI) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrSub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrERa) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrER) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcImageSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (apProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (app) =>
% 99.66/13.50 ((
% 99.66/13.50 (infuncsetfunc) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcinfuncset) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall1) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp3) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcextLem) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp4) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq2) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2lamEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifp) =>
% 99.66/13.50 ((
% 99.66/13.50 (theeq) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrue) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueorfalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setextT) =>
% 99.66/13.50 ((
% 99.66/13.50 (subsetTI) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTELcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTERcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT1) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT2) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT3) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub2) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTnotintersectT) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementImpComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementSubsetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementInPowersetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (contraSubsetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTcontraSubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTILcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTIRcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion2) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (intersectInPowersetIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpNotIn1) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpInComplement1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTE) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTEcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementUnionInPowersetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule0) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_5) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all2) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1SetBreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (choice2fnsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all1) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compEex) =>
% 99.66/13.50 ((
% 99.66/13.50 (!!) @ (
% 99.66/13.50 (('#B') @ (
% 99.66/13.50 !!) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 !!))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#C') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl896])).
% 99.66/13.50 thf(zip_derived_cl924, plain,
% 99.66/13.50 (~ (((notequalI2) =>
% 99.66/13.50 (((subsetRefl) =>
% 99.66/13.50 (((subsetTrans) =>
% 99.66/13.50 (((setadjoinSub) =>
% 99.66/13.50 (((setadjoinSub2) =>
% 99.66/13.50 (((subset2powerset) =>
% 99.66/13.50 (((setextsub) =>
% 99.66/13.50 (((subsetemptysetimpeq) =>
% 99.66/13.50 (((powersetI1) =>
% 99.66/13.50 (((powersetE1) =>
% 99.66/13.50 (((inPowerset) =>
% 99.66/13.50 (((powersetsubset) =>
% 99.66/13.50 (((sepInPowerset) =>
% 99.66/13.50 (((sepSubset) =>
% 99.66/13.50 (((binunionIL) =>
% 99.66/13.50 (((upairset2IR) =>
% 99.66/13.50 (((binunionIR) =>
% 99.66/13.50 (((binunionEcases) =>
% 99.66/13.50 (((binunionE) =>
% 99.66/13.50 (((binunionLsub) =>
% 99.66/13.50 (((binunionRsub) =>
% 99.66/13.50 (((binintersectI) =>
% 99.66/13.50 (((binintersectSubset5) =>
% 99.66/13.50 (((binintersectEL) =>
% 99.66/13.50 (((binintersectLsub) =>
% 99.66/13.50 (((binintersectSubset2) =>
% 99.66/13.50 (((binintersectSubset3) =>
% 99.66/13.50 (((binintersectER) =>
% 99.66/13.50 (((disjointsetsI1) =>
% 99.66/13.50 (((binintersectRsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset4) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (bs114d) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusI) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusER) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusERneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusELneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusILneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusIRneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusLsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffE) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI2) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg2) =>
% 99.66/13.50 ((
% 99.66/13.50 (secondinupair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIR) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairiskpair) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairp) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowerset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairset2E) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairsubunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairinpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem3) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair1) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionE2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton1) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I2) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsuniq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (theprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstin) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR11) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR12) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR1) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairequniteq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemER) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempaircEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrI) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrSub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrERa) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrER) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcImageSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (apProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (app) =>
% 99.66/13.50 ((
% 99.66/13.50 (infuncsetfunc) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcinfuncset) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall1) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp3) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcextLem) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp4) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq2) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2lamEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifp) =>
% 99.66/13.50 ((
% 99.66/13.50 (theeq) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrue) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueorfalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setextT) =>
% 99.66/13.50 ((
% 99.66/13.50 (subsetTI) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTELcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTERcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT1) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT2) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT3) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub2) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTnotintersectT) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementImpComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementSubsetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementInPowersetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (contraSubsetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTcontraSubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTILcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTIRcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion2) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (intersectInPowersetIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpNotIn1) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpInComplement1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTE) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTEcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementUnionInPowersetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule0) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_5) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all2) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1SetBreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (choice2fnsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all1) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compEex) =>
% 99.66/13.50 ((
% 99.66/13.50 (!!) @ (
% 99.66/13.50 (('#B') @ (
% 99.66/13.50 !!) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 !!))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#C') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl909])).
% 99.66/13.50 thf(zip_derived_cl938, plain,
% 99.66/13.50 (~ (((subsetRefl) =>
% 99.66/13.50 (((subsetTrans) =>
% 99.66/13.50 (((setadjoinSub) =>
% 99.66/13.50 (((setadjoinSub2) =>
% 99.66/13.50 (((subset2powerset) =>
% 99.66/13.50 (((setextsub) =>
% 99.66/13.50 (((subsetemptysetimpeq) =>
% 99.66/13.50 (((powersetI1) =>
% 99.66/13.50 (((powersetE1) =>
% 99.66/13.50 (((inPowerset) =>
% 99.66/13.50 (((powersetsubset) =>
% 99.66/13.50 (((sepInPowerset) =>
% 99.66/13.50 (((sepSubset) =>
% 99.66/13.50 (((binunionIL) =>
% 99.66/13.50 (((upairset2IR) =>
% 99.66/13.50 (((binunionIR) =>
% 99.66/13.50 (((binunionEcases) =>
% 99.66/13.50 (((binunionE) =>
% 99.66/13.50 (((binunionLsub) =>
% 99.66/13.50 (((binunionRsub) =>
% 99.66/13.50 (((binintersectI) =>
% 99.66/13.50 (((binintersectSubset5) =>
% 99.66/13.50 (((binintersectEL) =>
% 99.66/13.50 (((binintersectLsub) =>
% 99.66/13.50 (((binintersectSubset2) =>
% 99.66/13.50 (((binintersectSubset3) =>
% 99.66/13.50 (((binintersectER) =>
% 99.66/13.50 (((disjointsetsI1) =>
% 99.66/13.50 (((binintersectRsub) =>
% 99.66/13.50 (((binintersectSubset4) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (bs114d) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusI) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusER) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusERneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusELneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusILneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusIRneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusLsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffE) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI2) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg2) =>
% 99.66/13.50 ((
% 99.66/13.50 (secondinupair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIR) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairiskpair) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairp) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowerset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairset2E) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairsubunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairinpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem3) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair1) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionE2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton1) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I2) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsuniq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (theprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstin) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR11) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR12) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR1) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairequniteq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemER) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempaircEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrI) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrSub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrERa) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrER) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcImageSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (apProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (app) =>
% 99.66/13.50 ((
% 99.66/13.50 (infuncsetfunc) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcinfuncset) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall1) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp3) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcextLem) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp4) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq2) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2lamEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifp) =>
% 99.66/13.50 ((
% 99.66/13.50 (theeq) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrue) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueorfalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setextT) =>
% 99.66/13.50 ((
% 99.66/13.50 (subsetTI) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTELcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTERcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT1) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT2) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT3) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub2) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTnotintersectT) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementImpComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementSubsetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementInPowersetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (contraSubsetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTcontraSubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTILcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTIRcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion2) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (intersectInPowersetIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpNotIn1) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpInComplement1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTE) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTEcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementUnionInPowersetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule0) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_5) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all2) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1SetBreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (choice2fnsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all1) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compEex) =>
% 99.66/13.50 ((
% 99.66/13.50 (!!) @ (
% 99.66/13.50 (('#B') @ (
% 99.66/13.50 !!) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 !!))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#C') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl924])).
% 99.66/13.50 thf(zip_derived_cl952, plain,
% 99.66/13.50 (~ (((subsetTrans) =>
% 99.66/13.50 (((setadjoinSub) =>
% 99.66/13.50 (((setadjoinSub2) =>
% 99.66/13.50 (((subset2powerset) =>
% 99.66/13.50 (((setextsub) =>
% 99.66/13.50 (((subsetemptysetimpeq) =>
% 99.66/13.50 (((powersetI1) =>
% 99.66/13.50 (((powersetE1) =>
% 99.66/13.50 (((inPowerset) =>
% 99.66/13.50 (((powersetsubset) =>
% 99.66/13.50 (((sepInPowerset) =>
% 99.66/13.50 (((sepSubset) =>
% 99.66/13.50 (((binunionIL) =>
% 99.66/13.50 (((upairset2IR) =>
% 99.66/13.50 (((binunionIR) =>
% 99.66/13.50 (((binunionEcases) =>
% 99.66/13.50 (((binunionE) =>
% 99.66/13.50 (((binunionLsub) =>
% 99.66/13.50 (((binunionRsub) =>
% 99.66/13.50 (((binintersectI) =>
% 99.66/13.50 (((binintersectSubset5) =>
% 99.66/13.50 (((binintersectEL) =>
% 99.66/13.50 (((binintersectLsub) =>
% 99.66/13.50 (((binintersectSubset2) =>
% 99.66/13.50 (((binintersectSubset3) =>
% 99.66/13.50 (((binintersectER) =>
% 99.66/13.50 (((disjointsetsI1) =>
% 99.66/13.50 (((binintersectRsub) =>
% 99.66/13.50 (((binintersectSubset4) =>
% 99.66/13.50 (((binintersectSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (bs114d) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusI) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusER) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusERneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusELneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusILneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusIRneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusLsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffE) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI2) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg2) =>
% 99.66/13.50 ((
% 99.66/13.50 (secondinupair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIR) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairiskpair) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairp) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowerset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairset2E) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairsubunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairinpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem3) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair1) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionE2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton1) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I2) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsuniq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (theprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (kfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstin) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR11) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR12) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR1) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairequniteq) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairinjR) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ksndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairmemER) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempaircEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodfstpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodsndpairEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairsurjEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrI) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrSub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrERa) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL1) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrEL2) =>
% 99.66/13.50 ((
% 99.66/13.50 (dpsetconstrER) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcImageSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (apProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (app) =>
% 99.66/13.50 ((
% 99.66/13.50 (infuncsetfunc) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcinfuncset) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamProp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lamp) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2p) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall1) =>
% 99.66/13.50 ((
% 99.66/13.50 (brelnall2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp3) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcextLem) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcGraphProp4) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext) =>
% 99.66/13.50 ((
% 99.66/13.50 (funcext2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ap2apEq2) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta1) =>
% 99.66/13.50 ((
% 99.66/13.50 (lam2lamEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (beta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (eta2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalseProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp1) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueProp2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifSingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (ifp) =>
% 99.66/13.50 ((
% 99.66/13.50 (theeq) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrue) =>
% 99.66/13.50 ((
% 99.66/13.50 (iffalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (iftrueorfalse) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementT_lem) =>
% 99.66/13.50 ((
% 99.66/13.50 (setextT) =>
% 99.66/13.50 ((
% 99.66/13.50 (subsetTI) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (powersetTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTELcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binintersectTERcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT1) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT2) =>
% 99.66/13.50 ((
% 99.66/13.50 (contrasubsetT3) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementE1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub1) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementSub2) =>
% 99.66/13.50 ((
% 99.66/13.50 (doubleComplementEq) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTnotintersectT) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementImpComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementSubsetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementInPowersetComplementIntersect) =>
% 99.66/13.50 ((
% 99.66/13.50 (contraSubsetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementTcontraSubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTILcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTIRcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInUnion2) =>
% 99.66/13.50 ((
% 99.66/13.50 (inIntersectImpInIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (intersectInPowersetIntersectUnions) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpNotIn1) =>
% 99.66/13.50 ((
% 99.66/13.50 (inComplementUnionImpInComplement1) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTE) =>
% 99.66/13.50 ((
% 99.66/13.50 (binunionTEcontra) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a1) =>
% 99.66/13.50 ((
% 99.66/13.50 (complementUnionInPowersetComplement) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan1) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2a) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b2) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2b) =>
% 99.66/13.50 ((
% 99.66/13.50 (demorgan2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule0) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz13rule4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_1) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_2) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_3) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_4) =>
% 99.66/13.50 ((
% 99.66/13.50 (woz1_5) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all2) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1SetBreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (choice2fnsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (setOfPairsIsBReln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1all1) =>
% 99.66/13.50 ((
% 99.66/13.50 (subbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (eqbreln1) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1invE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compI) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compE) =>
% 99.66/13.50 ((
% 99.66/13.50 (breln1compEex) =>
% 99.66/13.50 ((
% 99.66/13.50 (!!) @ (
% 99.66/13.50 (('#B') @ (
% 99.66/13.50 !!) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 !!))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#S') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#S') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 =>))) @
% 99.66/13.50 breln1)))))) @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#C') @ (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 (
% 99.66/13.50 (
% 99.66/13.50 ('#B') @ (
% 99.66/13.50 '#B') @
% 99.66/13.50 breln1)))) @
% 99.66/13.50 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl938])).
% 99.66/13.50 thf(zip_derived_cl967, plain,
% 99.66/13.50 (~ (((setadjoinSub) =>
% 99.66/13.50 (((setadjoinSub2) =>
% 99.66/13.50 (((subset2powerset) =>
% 99.66/13.50 (((setextsub) =>
% 99.66/13.50 (((subsetemptysetimpeq) =>
% 99.66/13.50 (((powersetI1) =>
% 99.66/13.50 (((powersetE1) =>
% 99.66/13.50 (((inPowerset) =>
% 99.66/13.50 (((powersetsubset) =>
% 99.66/13.50 (((sepInPowerset) =>
% 99.66/13.50 (((sepSubset) =>
% 99.66/13.50 (((binunionIL) =>
% 99.66/13.50 (((upairset2IR) =>
% 99.66/13.50 (((binunionIR) =>
% 99.66/13.50 (((binunionEcases) =>
% 99.66/13.50 (((binunionE) =>
% 99.66/13.50 (((binunionLsub) =>
% 99.66/13.50 (((binunionRsub) =>
% 99.66/13.50 (((binintersectI) =>
% 99.66/13.50 (((binintersectSubset5) =>
% 99.66/13.50 (((binintersectEL) =>
% 99.66/13.50 (((binintersectLsub) =>
% 99.66/13.50 (((binintersectSubset2) =>
% 99.66/13.50 (((binintersectSubset3) =>
% 99.66/13.50 (((binintersectER) =>
% 99.66/13.50 (((disjointsetsI1) =>
% 99.66/13.50 (((binintersectRsub) =>
% 99.66/13.50 (((binintersectSubset4) =>
% 99.66/13.50 (((binintersectSubset1) =>
% 99.66/13.50 (((bs114d) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusI) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusEL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusER) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusERneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusELneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusILneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusIRneg) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusLsub) =>
% 99.66/13.50 ((
% 99.66/13.50 (setminusSubset1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffE) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffI2) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg1) =>
% 99.66/13.50 ((
% 99.66/13.50 (symdiffIneg2) =>
% 99.66/13.50 ((
% 99.66/13.50 (secondinupair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIL) =>
% 99.66/13.50 ((
% 99.66/13.50 (setukpairIR) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairiskpair) =>
% 99.66/13.50 ((
% 99.66/13.50 (kpairp) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsubset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowerset) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletoninpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairset2E) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairsubunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (upairinpowunion) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem2) =>
% 99.66/13.50 ((
% 99.66/13.50 (ubforcartprodlem3) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodpairin) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair1) =>
% 99.66/13.50 ((
% 99.66/13.50 (cartprodmempair) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionE2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton1) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton2) =>
% 99.66/13.50 ((
% 99.66/13.50 (setunionsingleton) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonprop) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1E1) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I) =>
% 99.66/13.50 ((
% 99.66/13.50 (ex1I2) =>
% 99.66/13.50 ((
% 99.66/13.50 (singletonsuniq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (theprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstin) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR11) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR12) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR1) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairequniteq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemEL) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemER) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempaircEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrI) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrSub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrERa) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrER) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcImageSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (apProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (app) =>
% 99.66/13.51 ((
% 99.66/13.51 (infuncsetfunc) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcinfuncset) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall1) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp3) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcextLem) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp4) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq2) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2lamEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifp) =>
% 99.66/13.51 ((
% 99.66/13.51 (theeq) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrue) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueorfalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setextT) =>
% 99.66/13.51 ((
% 99.66/13.51 (subsetTI) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTELcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTERcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT1) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT2) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT3) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub2) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTnotintersectT) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementImpComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementSubsetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementInPowersetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (contraSubsetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTcontraSubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTILcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTIRcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion2) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (intersectInPowersetIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpNotIn1) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpInComplement1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTE) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTEcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementUnionInPowersetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule0) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_5) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all2) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1SetBreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (choice2fnsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all1) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compEex) =>
% 99.66/13.51 ((
% 99.66/13.51 (!!) @ (
% 99.66/13.51 (('#B') @ (
% 99.66/13.51 !!) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 !!))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#C') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl952])).
% 99.66/13.51 thf(zip_derived_cl984, plain,
% 99.66/13.51 (~ (((setadjoinSub2) =>
% 99.66/13.51 (((subset2powerset) =>
% 99.66/13.51 (((setextsub) =>
% 99.66/13.51 (((subsetemptysetimpeq) =>
% 99.66/13.51 (((powersetI1) =>
% 99.66/13.51 (((powersetE1) =>
% 99.66/13.51 (((inPowerset) =>
% 99.66/13.51 (((powersetsubset) =>
% 99.66/13.51 (((sepInPowerset) =>
% 99.66/13.51 (((sepSubset) =>
% 99.66/13.51 (((binunionIL) =>
% 99.66/13.51 (((upairset2IR) =>
% 99.66/13.51 (((binunionIR) =>
% 99.66/13.51 (((binunionEcases) =>
% 99.66/13.51 (((binunionE) =>
% 99.66/13.51 (((binunionLsub) =>
% 99.66/13.51 (((binunionRsub) =>
% 99.66/13.51 (((binintersectI) =>
% 99.66/13.51 (((binintersectSubset5) =>
% 99.66/13.51 (((binintersectEL) =>
% 99.66/13.51 (((binintersectLsub) =>
% 99.66/13.51 (((binintersectSubset2) =>
% 99.66/13.51 (((binintersectSubset3) =>
% 99.66/13.51 (((binintersectER) =>
% 99.66/13.51 (((disjointsetsI1) =>
% 99.66/13.51 (((binintersectRsub) =>
% 99.66/13.51 (((binintersectSubset4) =>
% 99.66/13.51 (((binintersectSubset1) =>
% 99.66/13.51 (((bs114d) =>
% 99.66/13.51 (((setminusI) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusEL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusER) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusSubset2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusERneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusELneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusILneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusIRneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusLsub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusSubset1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffE) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI2) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg2) =>
% 99.66/13.51 ((
% 99.66/13.51 (secondinupair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIR) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairiskpair) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairp) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowerset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairset2E) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairsubunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairinpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem3) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair1) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionE2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton1) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I2) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsuniq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (theprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstin) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR11) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR12) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR1) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairequniteq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemEL) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemER) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempaircEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrI) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrSub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrERa) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrER) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcImageSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (apProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (app) =>
% 99.66/13.51 ((
% 99.66/13.51 (infuncsetfunc) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcinfuncset) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall1) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp3) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcextLem) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp4) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq2) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2lamEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifp) =>
% 99.66/13.51 ((
% 99.66/13.51 (theeq) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrue) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueorfalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setextT) =>
% 99.66/13.51 ((
% 99.66/13.51 (subsetTI) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTELcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTERcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT1) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT2) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT3) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub2) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTnotintersectT) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementImpComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementSubsetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementInPowersetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (contraSubsetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTcontraSubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTILcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTIRcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion2) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (intersectInPowersetIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpNotIn1) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpInComplement1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTE) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTEcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementUnionInPowersetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule0) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_5) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all2) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1SetBreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (choice2fnsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all1) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compEex) =>
% 99.66/13.51 ((
% 99.66/13.51 (!!) @ (
% 99.66/13.51 (('#B') @ (
% 99.66/13.51 !!) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 !!))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#C') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl967])).
% 99.66/13.51 thf(zip_derived_cl1000, plain,
% 99.66/13.51 (~ (((subset2powerset) =>
% 99.66/13.51 (((setextsub) =>
% 99.66/13.51 (((subsetemptysetimpeq) =>
% 99.66/13.51 (((powersetI1) =>
% 99.66/13.51 (((powersetE1) =>
% 99.66/13.51 (((inPowerset) =>
% 99.66/13.51 (((powersetsubset) =>
% 99.66/13.51 (((sepInPowerset) =>
% 99.66/13.51 (((sepSubset) =>
% 99.66/13.51 (((binunionIL) =>
% 99.66/13.51 (((upairset2IR) =>
% 99.66/13.51 (((binunionIR) =>
% 99.66/13.51 (((binunionEcases) =>
% 99.66/13.51 (((binunionE) =>
% 99.66/13.51 (((binunionLsub) =>
% 99.66/13.51 (((binunionRsub) =>
% 99.66/13.51 (((binintersectI) =>
% 99.66/13.51 (((binintersectSubset5) =>
% 99.66/13.51 (((binintersectEL) =>
% 99.66/13.51 (((binintersectLsub) =>
% 99.66/13.51 (((binintersectSubset2) =>
% 99.66/13.51 (((binintersectSubset3) =>
% 99.66/13.51 (((binintersectER) =>
% 99.66/13.51 (((disjointsetsI1) =>
% 99.66/13.51 (((binintersectRsub) =>
% 99.66/13.51 (((binintersectSubset4) =>
% 99.66/13.51 (((binintersectSubset1) =>
% 99.66/13.51 (((bs114d) =>
% 99.66/13.51 (((setminusI) =>
% 99.66/13.51 (((setminusEL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusER) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusSubset2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusERneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusELneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusILneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusIRneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusLsub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusSubset1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffE) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI2) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg2) =>
% 99.66/13.51 ((
% 99.66/13.51 (secondinupair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIR) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairiskpair) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairp) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowerset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairset2E) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairsubunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairinpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem3) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair1) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionE2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton1) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I2) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsuniq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (theprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstin) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR11) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR12) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR1) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairequniteq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemEL) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemER) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempaircEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrI) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrSub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrERa) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrER) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcImageSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (apProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (app) =>
% 99.66/13.51 ((
% 99.66/13.51 (infuncsetfunc) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcinfuncset) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall1) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp3) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcextLem) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp4) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq2) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2lamEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifp) =>
% 99.66/13.51 ((
% 99.66/13.51 (theeq) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrue) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueorfalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setextT) =>
% 99.66/13.51 ((
% 99.66/13.51 (subsetTI) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTELcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTERcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT1) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT2) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT3) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub2) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTnotintersectT) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementImpComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementSubsetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementInPowersetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (contraSubsetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTcontraSubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTILcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTIRcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion2) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (intersectInPowersetIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpNotIn1) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpInComplement1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTE) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTEcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementUnionInPowersetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule0) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_5) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all2) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1SetBreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (choice2fnsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all1) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compEex) =>
% 99.66/13.51 ((
% 99.66/13.51 (!!) @ (
% 99.66/13.51 (('#B') @ (
% 99.66/13.51 !!) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 !!))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#C') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl984])).
% 99.66/13.51 thf(zip_derived_cl1015, plain,
% 99.66/13.51 (~ (((setextsub) =>
% 99.66/13.51 (((subsetemptysetimpeq) =>
% 99.66/13.51 (((powersetI1) =>
% 99.66/13.51 (((powersetE1) =>
% 99.66/13.51 (((inPowerset) =>
% 99.66/13.51 (((powersetsubset) =>
% 99.66/13.51 (((sepInPowerset) =>
% 99.66/13.51 (((sepSubset) =>
% 99.66/13.51 (((binunionIL) =>
% 99.66/13.51 (((upairset2IR) =>
% 99.66/13.51 (((binunionIR) =>
% 99.66/13.51 (((binunionEcases) =>
% 99.66/13.51 (((binunionE) =>
% 99.66/13.51 (((binunionLsub) =>
% 99.66/13.51 (((binunionRsub) =>
% 99.66/13.51 (((binintersectI) =>
% 99.66/13.51 (((binintersectSubset5) =>
% 99.66/13.51 (((binintersectEL) =>
% 99.66/13.51 (((binintersectLsub) =>
% 99.66/13.51 (((binintersectSubset2) =>
% 99.66/13.51 (((binintersectSubset3) =>
% 99.66/13.51 (((binintersectER) =>
% 99.66/13.51 (((disjointsetsI1) =>
% 99.66/13.51 (((binintersectRsub) =>
% 99.66/13.51 (((binintersectSubset4) =>
% 99.66/13.51 (((binintersectSubset1) =>
% 99.66/13.51 (((bs114d) =>
% 99.66/13.51 (((setminusI) =>
% 99.66/13.51 (((setminusEL) =>
% 99.66/13.51 (((setminusER) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusSubset2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusERneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusELneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusILneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusIRneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusLsub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusSubset1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffE) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI2) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg2) =>
% 99.66/13.51 ((
% 99.66/13.51 (secondinupair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIR) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairiskpair) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairp) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowerset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairset2E) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairsubunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairinpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem3) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair1) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionE2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton1) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I2) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsuniq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (theprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstin) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR11) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR12) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR1) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairequniteq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemEL) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemER) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempaircEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrI) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrSub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrERa) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrER) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcImageSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (apProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (app) =>
% 99.66/13.51 ((
% 99.66/13.51 (infuncsetfunc) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcinfuncset) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall1) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp3) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcextLem) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp4) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq2) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2lamEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifp) =>
% 99.66/13.51 ((
% 99.66/13.51 (theeq) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrue) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueorfalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setextT) =>
% 99.66/13.51 ((
% 99.66/13.51 (subsetTI) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTELcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTERcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT1) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT2) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT3) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub2) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTnotintersectT) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementImpComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementSubsetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementInPowersetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (contraSubsetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTcontraSubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTILcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTIRcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion2) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (intersectInPowersetIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpNotIn1) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpInComplement1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTE) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTEcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementUnionInPowersetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule0) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_5) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all2) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1SetBreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (choice2fnsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all1) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compEex) =>
% 99.66/13.51 ((
% 99.66/13.51 (!!) @ (
% 99.66/13.51 (('#B') @ (
% 99.66/13.51 !!) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 !!))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#C') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1000])).
% 99.66/13.51 thf(zip_derived_cl1027, plain,
% 99.66/13.51 (~ (((subsetemptysetimpeq) =>
% 99.66/13.51 (((powersetI1) =>
% 99.66/13.51 (((powersetE1) =>
% 99.66/13.51 (((inPowerset) =>
% 99.66/13.51 (((powersetsubset) =>
% 99.66/13.51 (((sepInPowerset) =>
% 99.66/13.51 (((sepSubset) =>
% 99.66/13.51 (((binunionIL) =>
% 99.66/13.51 (((upairset2IR) =>
% 99.66/13.51 (((binunionIR) =>
% 99.66/13.51 (((binunionEcases) =>
% 99.66/13.51 (((binunionE) =>
% 99.66/13.51 (((binunionLsub) =>
% 99.66/13.51 (((binunionRsub) =>
% 99.66/13.51 (((binintersectI) =>
% 99.66/13.51 (((binintersectSubset5) =>
% 99.66/13.51 (((binintersectEL) =>
% 99.66/13.51 (((binintersectLsub) =>
% 99.66/13.51 (((binintersectSubset2) =>
% 99.66/13.51 (((binintersectSubset3) =>
% 99.66/13.51 (((binintersectER) =>
% 99.66/13.51 (((disjointsetsI1) =>
% 99.66/13.51 (((binintersectRsub) =>
% 99.66/13.51 (((binintersectSubset4) =>
% 99.66/13.51 (((binintersectSubset1) =>
% 99.66/13.51 (((bs114d) =>
% 99.66/13.51 (((setminusI) =>
% 99.66/13.51 (((setminusEL) =>
% 99.66/13.51 (((setminusER) =>
% 99.66/13.51 (((setminusSubset2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusERneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusELneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusILneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusIRneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusLsub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusSubset1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffE) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI2) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg2) =>
% 99.66/13.51 ((
% 99.66/13.51 (secondinupair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIR) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairiskpair) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairp) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowerset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairset2E) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairsubunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairinpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem3) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair1) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionE2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton1) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I2) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsuniq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (theprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstin) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR11) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR12) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR1) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairequniteq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemEL) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemER) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempaircEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrI) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrSub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrERa) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrER) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcImageSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (apProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (app) =>
% 99.66/13.51 ((
% 99.66/13.51 (infuncsetfunc) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcinfuncset) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall1) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp3) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcextLem) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp4) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq2) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2lamEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifp) =>
% 99.66/13.51 ((
% 99.66/13.51 (theeq) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrue) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueorfalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setextT) =>
% 99.66/13.51 ((
% 99.66/13.51 (subsetTI) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTELcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTERcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT1) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT2) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT3) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub2) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTnotintersectT) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementImpComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementSubsetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementInPowersetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (contraSubsetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTcontraSubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTILcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTIRcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion2) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (intersectInPowersetIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpNotIn1) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpInComplement1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTE) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTEcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementUnionInPowersetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule0) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_5) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all2) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1SetBreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (choice2fnsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all1) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compEex) =>
% 99.66/13.51 ((
% 99.66/13.51 (!!) @ (
% 99.66/13.51 (('#B') @ (
% 99.66/13.51 !!) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 !!))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#C') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1015])).
% 99.66/13.51 thf(zip_derived_cl1039, plain,
% 99.66/13.51 (~ (((powersetI1) =>
% 99.66/13.51 (((powersetE1) =>
% 99.66/13.51 (((inPowerset) =>
% 99.66/13.51 (((powersetsubset) =>
% 99.66/13.51 (((sepInPowerset) =>
% 99.66/13.51 (((sepSubset) =>
% 99.66/13.51 (((binunionIL) =>
% 99.66/13.51 (((upairset2IR) =>
% 99.66/13.51 (((binunionIR) =>
% 99.66/13.51 (((binunionEcases) =>
% 99.66/13.51 (((binunionE) =>
% 99.66/13.51 (((binunionLsub) =>
% 99.66/13.51 (((binunionRsub) =>
% 99.66/13.51 (((binintersectI) =>
% 99.66/13.51 (((binintersectSubset5) =>
% 99.66/13.51 (((binintersectEL) =>
% 99.66/13.51 (((binintersectLsub) =>
% 99.66/13.51 (((binintersectSubset2) =>
% 99.66/13.51 (((binintersectSubset3) =>
% 99.66/13.51 (((binintersectER) =>
% 99.66/13.51 (((disjointsetsI1) =>
% 99.66/13.51 (((binintersectRsub) =>
% 99.66/13.51 (((binintersectSubset4) =>
% 99.66/13.51 (((binintersectSubset1) =>
% 99.66/13.51 (((bs114d) =>
% 99.66/13.51 (((setminusI) =>
% 99.66/13.51 (((setminusEL) =>
% 99.66/13.51 (((setminusER) =>
% 99.66/13.51 (((setminusSubset2) =>
% 99.66/13.51 (((setminusERneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusELneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusILneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusIRneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusLsub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusSubset1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffE) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI2) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg2) =>
% 99.66/13.51 ((
% 99.66/13.51 (secondinupair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIR) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairiskpair) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairp) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowerset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairset2E) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairsubunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairinpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem3) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair1) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionE2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton1) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I2) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsuniq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (theprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstin) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR11) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR12) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR1) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairequniteq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemEL) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemER) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempaircEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrI) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrSub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrERa) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrER) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcImageSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (apProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (app) =>
% 99.66/13.51 ((
% 99.66/13.51 (infuncsetfunc) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcinfuncset) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall1) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp3) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcextLem) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp4) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq2) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2lamEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifp) =>
% 99.66/13.51 ((
% 99.66/13.51 (theeq) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrue) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueorfalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setextT) =>
% 99.66/13.51 ((
% 99.66/13.51 (subsetTI) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTELcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTERcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT1) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT2) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT3) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub2) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTnotintersectT) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementImpComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementSubsetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementInPowersetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (contraSubsetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTcontraSubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTILcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTIRcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion2) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (intersectInPowersetIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpNotIn1) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpInComplement1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTE) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTEcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementUnionInPowersetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule0) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_5) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all2) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1SetBreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (choice2fnsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all1) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compEex) =>
% 99.66/13.51 ((
% 99.66/13.51 (!!) @ (
% 99.66/13.51 (('#B') @ (
% 99.66/13.51 !!) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 !!))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#C') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1027])).
% 99.66/13.51 thf(zip_derived_cl1055, plain,
% 99.66/13.51 (~ (((powersetE1) =>
% 99.66/13.51 (((inPowerset) =>
% 99.66/13.51 (((powersetsubset) =>
% 99.66/13.51 (((sepInPowerset) =>
% 99.66/13.51 (((sepSubset) =>
% 99.66/13.51 (((binunionIL) =>
% 99.66/13.51 (((upairset2IR) =>
% 99.66/13.51 (((binunionIR) =>
% 99.66/13.51 (((binunionEcases) =>
% 99.66/13.51 (((binunionE) =>
% 99.66/13.51 (((binunionLsub) =>
% 99.66/13.51 (((binunionRsub) =>
% 99.66/13.51 (((binintersectI) =>
% 99.66/13.51 (((binintersectSubset5) =>
% 99.66/13.51 (((binintersectEL) =>
% 99.66/13.51 (((binintersectLsub) =>
% 99.66/13.51 (((binintersectSubset2) =>
% 99.66/13.51 (((binintersectSubset3) =>
% 99.66/13.51 (((binintersectER) =>
% 99.66/13.51 (((disjointsetsI1) =>
% 99.66/13.51 (((binintersectRsub) =>
% 99.66/13.51 (((binintersectSubset4) =>
% 99.66/13.51 (((binintersectSubset1) =>
% 99.66/13.51 (((bs114d) =>
% 99.66/13.51 (((setminusI) =>
% 99.66/13.51 (((setminusEL) =>
% 99.66/13.51 (((setminusER) =>
% 99.66/13.51 (((setminusSubset2) =>
% 99.66/13.51 (((setminusERneg) =>
% 99.66/13.51 (((setminusELneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusILneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusIRneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusLsub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusSubset1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffE) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI2) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg2) =>
% 99.66/13.51 ((
% 99.66/13.51 (secondinupair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIR) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairiskpair) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairp) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowerset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairset2E) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairsubunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairinpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem3) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair1) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionE2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton1) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I2) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsuniq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (theprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstin) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR11) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR12) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR1) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairequniteq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemEL) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemER) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempaircEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrI) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrSub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrERa) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrER) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcImageSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (apProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (app) =>
% 99.66/13.51 ((
% 99.66/13.51 (infuncsetfunc) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcinfuncset) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall1) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp3) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcextLem) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp4) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq2) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2lamEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifp) =>
% 99.66/13.51 ((
% 99.66/13.51 (theeq) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrue) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueorfalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setextT) =>
% 99.66/13.51 ((
% 99.66/13.51 (subsetTI) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTELcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTERcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT1) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT2) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT3) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub2) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTnotintersectT) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementImpComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementSubsetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementInPowersetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (contraSubsetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTcontraSubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTILcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTIRcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion2) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (intersectInPowersetIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpNotIn1) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpInComplement1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTE) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTEcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementUnionInPowersetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule0) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_5) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all2) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1SetBreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (choice2fnsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all1) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compEex) =>
% 99.66/13.51 ((
% 99.66/13.51 (!!) @ (
% 99.66/13.51 (('#B') @ (
% 99.66/13.51 !!) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 !!))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#C') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1039])).
% 99.66/13.51 thf(zip_derived_cl1067, plain,
% 99.66/13.51 (~ (((inPowerset) =>
% 99.66/13.51 (((powersetsubset) =>
% 99.66/13.51 (((sepInPowerset) =>
% 99.66/13.51 (((sepSubset) =>
% 99.66/13.51 (((binunionIL) =>
% 99.66/13.51 (((upairset2IR) =>
% 99.66/13.51 (((binunionIR) =>
% 99.66/13.51 (((binunionEcases) =>
% 99.66/13.51 (((binunionE) =>
% 99.66/13.51 (((binunionLsub) =>
% 99.66/13.51 (((binunionRsub) =>
% 99.66/13.51 (((binintersectI) =>
% 99.66/13.51 (((binintersectSubset5) =>
% 99.66/13.51 (((binintersectEL) =>
% 99.66/13.51 (((binintersectLsub) =>
% 99.66/13.51 (((binintersectSubset2) =>
% 99.66/13.51 (((binintersectSubset3) =>
% 99.66/13.51 (((binintersectER) =>
% 99.66/13.51 (((disjointsetsI1) =>
% 99.66/13.51 (((binintersectRsub) =>
% 99.66/13.51 (((binintersectSubset4) =>
% 99.66/13.51 (((binintersectSubset1) =>
% 99.66/13.51 (((bs114d) =>
% 99.66/13.51 (((setminusI) =>
% 99.66/13.51 (((setminusEL) =>
% 99.66/13.51 (((setminusER) =>
% 99.66/13.51 (((setminusSubset2) =>
% 99.66/13.51 (((setminusERneg) =>
% 99.66/13.51 (((setminusELneg) =>
% 99.66/13.51 (((setminusILneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusIRneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusLsub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusSubset1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffE) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI2) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg2) =>
% 99.66/13.51 ((
% 99.66/13.51 (secondinupair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIR) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairiskpair) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairp) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowerset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairset2E) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairsubunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairinpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem3) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair1) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionE2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton1) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I2) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsuniq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (theprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstin) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR11) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR12) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR1) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairequniteq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemEL) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemER) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempaircEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrI) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrSub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrERa) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrER) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcImageSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (apProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (app) =>
% 99.66/13.51 ((
% 99.66/13.51 (infuncsetfunc) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcinfuncset) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall1) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp3) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcextLem) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp4) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq2) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2lamEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifp) =>
% 99.66/13.51 ((
% 99.66/13.51 (theeq) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrue) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueorfalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setextT) =>
% 99.66/13.51 ((
% 99.66/13.51 (subsetTI) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTELcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTERcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT1) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT2) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT3) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub2) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTnotintersectT) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementImpComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementSubsetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementInPowersetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (contraSubsetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTcontraSubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTILcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTIRcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion2) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (intersectInPowersetIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpNotIn1) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpInComplement1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTE) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTEcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementUnionInPowersetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule0) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_5) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all2) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1SetBreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (choice2fnsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all1) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compEex) =>
% 99.66/13.51 ((
% 99.66/13.51 (!!) @ (
% 99.66/13.51 (('#B') @ (
% 99.66/13.51 !!) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 !!))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#C') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1055])).
% 99.66/13.51 thf(zip_derived_cl1074, plain,
% 99.66/13.51 (~ (((powersetsubset) =>
% 99.66/13.51 (((sepInPowerset) =>
% 99.66/13.51 (((sepSubset) =>
% 99.66/13.51 (((binunionIL) =>
% 99.66/13.51 (((upairset2IR) =>
% 99.66/13.51 (((binunionIR) =>
% 99.66/13.51 (((binunionEcases) =>
% 99.66/13.51 (((binunionE) =>
% 99.66/13.51 (((binunionLsub) =>
% 99.66/13.51 (((binunionRsub) =>
% 99.66/13.51 (((binintersectI) =>
% 99.66/13.51 (((binintersectSubset5) =>
% 99.66/13.51 (((binintersectEL) =>
% 99.66/13.51 (((binintersectLsub) =>
% 99.66/13.51 (((binintersectSubset2) =>
% 99.66/13.51 (((binintersectSubset3) =>
% 99.66/13.51 (((binintersectER) =>
% 99.66/13.51 (((disjointsetsI1) =>
% 99.66/13.51 (((binintersectRsub) =>
% 99.66/13.51 (((binintersectSubset4) =>
% 99.66/13.51 (((binintersectSubset1) =>
% 99.66/13.51 (((bs114d) =>
% 99.66/13.51 (((setminusI) =>
% 99.66/13.51 (((setminusEL) =>
% 99.66/13.51 (((setminusER) =>
% 99.66/13.51 (((setminusSubset2) =>
% 99.66/13.51 (((setminusERneg) =>
% 99.66/13.51 (((setminusELneg) =>
% 99.66/13.51 (((setminusILneg) =>
% 99.66/13.51 (((setminusIRneg) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusLsub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusSubset1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffE) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI2) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg2) =>
% 99.66/13.51 ((
% 99.66/13.51 (secondinupair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIR) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairiskpair) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairp) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowerset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairset2E) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairsubunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairinpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem3) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair1) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionE2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton1) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I2) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsuniq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (theprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstin) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR11) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR12) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR1) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairequniteq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemEL) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemER) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempaircEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrI) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrSub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrERa) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrER) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcImageSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (apProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (app) =>
% 99.66/13.51 ((
% 99.66/13.51 (infuncsetfunc) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcinfuncset) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall1) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp3) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcextLem) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp4) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq2) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2lamEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifp) =>
% 99.66/13.51 ((
% 99.66/13.51 (theeq) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrue) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueorfalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setextT) =>
% 99.66/13.51 ((
% 99.66/13.51 (subsetTI) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTELcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTERcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT1) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT2) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT3) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub2) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTnotintersectT) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementImpComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementSubsetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementInPowersetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (contraSubsetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTcontraSubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTILcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTIRcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion2) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (intersectInPowersetIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpNotIn1) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpInComplement1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTE) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTEcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementUnionInPowersetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule0) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_5) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all2) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1SetBreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (choice2fnsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all1) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compEex) =>
% 99.66/13.51 ((
% 99.66/13.51 (!!) @ (
% 99.66/13.51 (('#B') @ (
% 99.66/13.51 !!) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 !!))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#C') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1067])).
% 99.66/13.51 thf(zip_derived_cl1082, plain,
% 99.66/13.51 (~ (((sepInPowerset) =>
% 99.66/13.51 (((sepSubset) =>
% 99.66/13.51 (((binunionIL) =>
% 99.66/13.51 (((upairset2IR) =>
% 99.66/13.51 (((binunionIR) =>
% 99.66/13.51 (((binunionEcases) =>
% 99.66/13.51 (((binunionE) =>
% 99.66/13.51 (((binunionLsub) =>
% 99.66/13.51 (((binunionRsub) =>
% 99.66/13.51 (((binintersectI) =>
% 99.66/13.51 (((binintersectSubset5) =>
% 99.66/13.51 (((binintersectEL) =>
% 99.66/13.51 (((binintersectLsub) =>
% 99.66/13.51 (((binintersectSubset2) =>
% 99.66/13.51 (((binintersectSubset3) =>
% 99.66/13.51 (((binintersectER) =>
% 99.66/13.51 (((disjointsetsI1) =>
% 99.66/13.51 (((binintersectRsub) =>
% 99.66/13.51 (((binintersectSubset4) =>
% 99.66/13.51 (((binintersectSubset1) =>
% 99.66/13.51 (((bs114d) =>
% 99.66/13.51 (((setminusI) =>
% 99.66/13.51 (((setminusEL) =>
% 99.66/13.51 (((setminusER) =>
% 99.66/13.51 (((setminusSubset2) =>
% 99.66/13.51 (((setminusERneg) =>
% 99.66/13.51 (((setminusELneg) =>
% 99.66/13.51 (((setminusILneg) =>
% 99.66/13.51 (((setminusIRneg) =>
% 99.66/13.51 (((setminusLsub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusSubset1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffE) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI2) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg2) =>
% 99.66/13.51 ((
% 99.66/13.51 (secondinupair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIR) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairiskpair) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairp) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowerset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairset2E) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairsubunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairinpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem3) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair1) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionE2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton1) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I2) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsuniq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (theprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstin) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR11) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR12) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR1) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairequniteq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemEL) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemER) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempaircEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrI) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrSub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrERa) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrER) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcImageSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (apProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (app) =>
% 99.66/13.51 ((
% 99.66/13.51 (infuncsetfunc) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcinfuncset) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall1) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp3) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcextLem) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp4) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq2) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2lamEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifp) =>
% 99.66/13.51 ((
% 99.66/13.51 (theeq) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrue) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueorfalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setextT) =>
% 99.66/13.51 ((
% 99.66/13.51 (subsetTI) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTELcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTERcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT1) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT2) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT3) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub2) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTnotintersectT) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementImpComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementSubsetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementInPowersetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (contraSubsetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTcontraSubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTILcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTIRcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion2) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (intersectInPowersetIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpNotIn1) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpInComplement1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTE) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTEcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementUnionInPowersetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule0) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_5) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all2) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1SetBreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (choice2fnsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all1) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compEex) =>
% 99.66/13.51 ((
% 99.66/13.51 (!!) @ (
% 99.66/13.51 (('#B') @ (
% 99.66/13.51 !!) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 !!))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#C') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1074])).
% 99.66/13.51 thf(zip_derived_cl1090, plain,
% 99.66/13.51 (~ (((sepSubset) =>
% 99.66/13.51 (((binunionIL) =>
% 99.66/13.51 (((upairset2IR) =>
% 99.66/13.51 (((binunionIR) =>
% 99.66/13.51 (((binunionEcases) =>
% 99.66/13.51 (((binunionE) =>
% 99.66/13.51 (((binunionLsub) =>
% 99.66/13.51 (((binunionRsub) =>
% 99.66/13.51 (((binintersectI) =>
% 99.66/13.51 (((binintersectSubset5) =>
% 99.66/13.51 (((binintersectEL) =>
% 99.66/13.51 (((binintersectLsub) =>
% 99.66/13.51 (((binintersectSubset2) =>
% 99.66/13.51 (((binintersectSubset3) =>
% 99.66/13.51 (((binintersectER) =>
% 99.66/13.51 (((disjointsetsI1) =>
% 99.66/13.51 (((binintersectRsub) =>
% 99.66/13.51 (((binintersectSubset4) =>
% 99.66/13.51 (((binintersectSubset1) =>
% 99.66/13.51 (((bs114d) =>
% 99.66/13.51 (((setminusI) =>
% 99.66/13.51 (((setminusEL) =>
% 99.66/13.51 (((setminusER) =>
% 99.66/13.51 (((setminusSubset2) =>
% 99.66/13.51 (((setminusERneg) =>
% 99.66/13.51 (((setminusELneg) =>
% 99.66/13.51 (((setminusILneg) =>
% 99.66/13.51 (((setminusIRneg) =>
% 99.66/13.51 (((setminusLsub) =>
% 99.66/13.51 (((setminusSubset1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffE) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI2) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg2) =>
% 99.66/13.51 ((
% 99.66/13.51 (secondinupair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIR) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairiskpair) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairp) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowerset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairset2E) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairsubunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairinpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem3) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair1) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionE2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton1) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I2) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsuniq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (theprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstin) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR11) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR12) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR1) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairequniteq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemEL) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemER) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempaircEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrI) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrSub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrERa) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrER) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcImageSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (apProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (app) =>
% 99.66/13.51 ((
% 99.66/13.51 (infuncsetfunc) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcinfuncset) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall1) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp3) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcextLem) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp4) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq2) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2lamEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifp) =>
% 99.66/13.51 ((
% 99.66/13.51 (theeq) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrue) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueorfalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setextT) =>
% 99.66/13.51 ((
% 99.66/13.51 (subsetTI) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTELcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTERcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT1) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT2) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT3) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub2) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTnotintersectT) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementImpComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementSubsetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementInPowersetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (contraSubsetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTcontraSubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTILcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTIRcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion2) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (intersectInPowersetIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpNotIn1) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpInComplement1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTE) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTEcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementUnionInPowersetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule0) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_5) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all2) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1SetBreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (choice2fnsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all1) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compEex) =>
% 99.66/13.51 ((
% 99.66/13.51 (!!) @ (
% 99.66/13.51 (('#B') @ (
% 99.66/13.51 !!) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 !!))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#C') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1082])).
% 99.66/13.51 thf(zip_derived_cl1096, plain,
% 99.66/13.51 (~ (((binunionIL) =>
% 99.66/13.51 (((upairset2IR) =>
% 99.66/13.51 (((binunionIR) =>
% 99.66/13.51 (((binunionEcases) =>
% 99.66/13.51 (((binunionE) =>
% 99.66/13.51 (((binunionLsub) =>
% 99.66/13.51 (((binunionRsub) =>
% 99.66/13.51 (((binintersectI) =>
% 99.66/13.51 (((binintersectSubset5) =>
% 99.66/13.51 (((binintersectEL) =>
% 99.66/13.51 (((binintersectLsub) =>
% 99.66/13.51 (((binintersectSubset2) =>
% 99.66/13.51 (((binintersectSubset3) =>
% 99.66/13.51 (((binintersectER) =>
% 99.66/13.51 (((disjointsetsI1) =>
% 99.66/13.51 (((binintersectRsub) =>
% 99.66/13.51 (((binintersectSubset4) =>
% 99.66/13.51 (((binintersectSubset1) =>
% 99.66/13.51 (((bs114d) =>
% 99.66/13.51 (((setminusI) =>
% 99.66/13.51 (((setminusEL) =>
% 99.66/13.51 (((setminusER) =>
% 99.66/13.51 (((setminusSubset2) =>
% 99.66/13.51 (((setminusERneg) =>
% 99.66/13.51 (((setminusELneg) =>
% 99.66/13.51 (((setminusILneg) =>
% 99.66/13.51 (((setminusIRneg) =>
% 99.66/13.51 (((setminusLsub) =>
% 99.66/13.51 (((setminusSubset1) =>
% 99.66/13.51 (((symdiffE) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI2) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg2) =>
% 99.66/13.51 ((
% 99.66/13.51 (secondinupair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIR) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairiskpair) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairp) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowerset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairset2E) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairsubunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairinpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem3) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair1) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionE2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton1) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I2) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsuniq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (theprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstin) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR11) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR12) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR1) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairequniteq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemEL) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemER) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempaircEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrI) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrSub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrERa) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrER) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcImageSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (apProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (app) =>
% 99.66/13.51 ((
% 99.66/13.51 (infuncsetfunc) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcinfuncset) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall1) =>
% 99.66/13.51 ((
% 99.66/13.51 (brelnall2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp3) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcextLem) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcGraphProp4) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcext2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2apEq2) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta1) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2lamEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (beta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (eta2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalseProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp1) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueProp2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ifp) =>
% 99.66/13.51 ((
% 99.66/13.51 (theeq) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrue) =>
% 99.66/13.51 ((
% 99.66/13.51 (iffalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (iftrueorfalse) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setminusT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementT_lem) =>
% 99.66/13.51 ((
% 99.66/13.51 (setextT) =>
% 99.66/13.51 ((
% 99.66/13.51 (subsetTI) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (powersetTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTELcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binintersectTERcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT1) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT2) =>
% 99.66/13.51 ((
% 99.66/13.51 (contrasubsetT3) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementE1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub1) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementSub2) =>
% 99.66/13.51 ((
% 99.66/13.51 (doubleComplementEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTnotintersectT) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementImpComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementSubsetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementInPowersetComplementIntersect) =>
% 99.66/13.51 ((
% 99.66/13.51 (contraSubsetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementTcontraSubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTILcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTIRcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInUnion2) =>
% 99.66/13.51 ((
% 99.66/13.51 (inIntersectImpInIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (intersectInPowersetIntersectUnions) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpNotIn1) =>
% 99.66/13.51 ((
% 99.66/13.51 (inComplementUnionImpInComplement1) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTE) =>
% 99.66/13.51 ((
% 99.66/13.51 (binunionTEcontra) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a1) =>
% 99.66/13.51 ((
% 99.66/13.51 (complementUnionInPowersetComplement) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan1) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2a) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b2) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2b) =>
% 99.66/13.51 ((
% 99.66/13.51 (demorgan2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule0) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz13rule4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_1) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_2) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_3) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_4) =>
% 99.66/13.51 ((
% 99.66/13.51 (woz1_5) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all2) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1SetBreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (choice2fnsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1all1) =>
% 99.66/13.51 ((
% 99.66/13.51 (subbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (eqbreln1) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1invE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compI) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compE) =>
% 99.66/13.51 ((
% 99.66/13.51 (breln1compEex) =>
% 99.66/13.51 ((
% 99.66/13.51 (!!) @ (
% 99.66/13.51 (('#B') @ (
% 99.66/13.51 !!) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 !!))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#S') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#S') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 =>))) @
% 99.66/13.51 breln1)))))) @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#C') @ (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 (
% 99.66/13.51 (
% 99.66/13.51 ('#B') @ (
% 99.66/13.51 '#B') @
% 99.66/13.51 breln1)))) @
% 99.66/13.51 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1090])).
% 99.66/13.51 thf(zip_derived_cl1102, plain,
% 99.66/13.51 (~ (((upairset2IR) =>
% 99.66/13.51 (((binunionIR) =>
% 99.66/13.51 (((binunionEcases) =>
% 99.66/13.51 (((binunionE) =>
% 99.66/13.51 (((binunionLsub) =>
% 99.66/13.51 (((binunionRsub) =>
% 99.66/13.51 (((binintersectI) =>
% 99.66/13.51 (((binintersectSubset5) =>
% 99.66/13.51 (((binintersectEL) =>
% 99.66/13.51 (((binintersectLsub) =>
% 99.66/13.51 (((binintersectSubset2) =>
% 99.66/13.51 (((binintersectSubset3) =>
% 99.66/13.51 (((binintersectER) =>
% 99.66/13.51 (((disjointsetsI1) =>
% 99.66/13.51 (((binintersectRsub) =>
% 99.66/13.51 (((binintersectSubset4) =>
% 99.66/13.51 (((binintersectSubset1) =>
% 99.66/13.51 (((bs114d) =>
% 99.66/13.51 (((setminusI) =>
% 99.66/13.51 (((setminusEL) =>
% 99.66/13.51 (((setminusER) =>
% 99.66/13.51 (((setminusSubset2) =>
% 99.66/13.51 (((setminusERneg) =>
% 99.66/13.51 (((setminusELneg) =>
% 99.66/13.51 (((setminusILneg) =>
% 99.66/13.51 (((setminusIRneg) =>
% 99.66/13.51 (((setminusLsub) =>
% 99.66/13.51 (((setminusSubset1) =>
% 99.66/13.51 (((symdiffE) =>
% 99.66/13.51 (((symdiffI1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffI2) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg1) =>
% 99.66/13.51 ((
% 99.66/13.51 (symdiffIneg2) =>
% 99.66/13.51 ((
% 99.66/13.51 (secondinupair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairIR) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairiskpair) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairp) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsubset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowerset) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletoninpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairset2E) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairsubunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairinpowunion) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem2) =>
% 99.66/13.51 ((
% 99.66/13.51 (ubforcartprodlem3) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair1) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempair) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionE2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton1) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setunionsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1E1) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I) =>
% 99.66/13.51 ((
% 99.66/13.51 (ex1I2) =>
% 99.66/13.51 ((
% 99.66/13.51 (singletonsuniq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (theprop) =>
% 99.66/13.51 ((
% 99.66/13.51 (kfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstin) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjL) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR11) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR12) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR1) =>
% 99.66/13.51 ((
% 99.66/13.51 (upairequniteq) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR2) =>
% 99.66/13.51 ((
% 99.66/13.51 (setukpairinjR) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndsingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (ksndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (kpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndin) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemEL) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairmemER) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodmempaircEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodfstpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodsndpairEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (cartprodpairsurjEq) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrI) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrSub) =>
% 99.66/13.51 ((
% 99.66/13.51 (setOfPairsIsBReln) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrERa) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL1) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrEL2) =>
% 99.66/13.51 ((
% 99.66/13.51 (dpsetconstrER) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcImageSingleton) =>
% 99.66/13.51 ((
% 99.66/13.51 (apProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (app) =>
% 99.66/13.51 ((
% 99.66/13.51 (infuncsetfunc) =>
% 99.66/13.51 ((
% 99.66/13.51 (ap2p) =>
% 99.66/13.51 ((
% 99.66/13.51 (funcinfuncset) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamProp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lamp) =>
% 99.66/13.51 ((
% 99.66/13.51 (lam2p) =>
% 99.66/13.51 ((
% 99.66/13.52 (brelnall1) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp3) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcextLem) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp4) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq2) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2lamEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifp) =>
% 99.66/13.52 ((
% 99.66/13.52 (theeq) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrue) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueorfalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setminusT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setextT) =>
% 99.66/13.52 ((
% 99.66/13.52 (subsetTI) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTELcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTERcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT1) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT2) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT3) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub2) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTnotintersectT) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementImpComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementSubsetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementInPowersetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (contraSubsetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTcontraSubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTILcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTIRcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion2) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (intersectInPowersetIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpNotIn1) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpInComplement1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTE) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTEcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementUnionInPowersetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule0) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_5) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all2) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1SetBreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (choice2fnsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all1) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compEex) =>
% 99.66/13.52 ((
% 99.66/13.52 (!!) @ (
% 99.66/13.52 (('#B') @ (
% 99.66/13.52 !!) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 !!))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#C') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1096])).
% 99.66/13.52 thf(zip_derived_cl1109, plain,
% 99.66/13.52 (~ (((binunionIR) =>
% 99.66/13.52 (((binunionEcases) =>
% 99.66/13.52 (((binunionE) =>
% 99.66/13.52 (((binunionLsub) =>
% 99.66/13.52 (((binunionRsub) =>
% 99.66/13.52 (((binintersectI) =>
% 99.66/13.52 (((binintersectSubset5) =>
% 99.66/13.52 (((binintersectEL) =>
% 99.66/13.52 (((binintersectLsub) =>
% 99.66/13.52 (((binintersectSubset2) =>
% 99.66/13.52 (((binintersectSubset3) =>
% 99.66/13.52 (((binintersectER) =>
% 99.66/13.52 (((disjointsetsI1) =>
% 99.66/13.52 (((binintersectRsub) =>
% 99.66/13.52 (((binintersectSubset4) =>
% 99.66/13.52 (((binintersectSubset1) =>
% 99.66/13.52 (((bs114d) =>
% 99.66/13.52 (((setminusI) =>
% 99.66/13.52 (((setminusEL) =>
% 99.66/13.52 (((setminusER) =>
% 99.66/13.52 (((setminusSubset2) =>
% 99.66/13.52 (((setminusERneg) =>
% 99.66/13.52 (((setminusELneg) =>
% 99.66/13.52 (((setminusILneg) =>
% 99.66/13.52 (((setminusIRneg) =>
% 99.66/13.52 (((setminusLsub) =>
% 99.66/13.52 (((setminusSubset1) =>
% 99.66/13.52 (((symdiffE) =>
% 99.66/13.52 (((symdiffI1) =>
% 99.66/13.52 (((symdiffI2) =>
% 99.66/13.52 ((
% 99.66/13.52 (symdiffIneg1) =>
% 99.66/13.52 ((
% 99.66/13.52 (symdiffIneg2) =>
% 99.66/13.52 ((
% 99.66/13.52 (secondinupair) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairIL) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairIR) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairiskpair) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairp) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowerset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairset2E) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairsubunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairinpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem3) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair1) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionE2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton1) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I2) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsuniq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (theprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstin) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR11) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR12) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR1) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairequniteq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemEL) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemER) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempaircEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrI) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrSub) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrERa) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrER) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcImageSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (apProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (app) =>
% 99.66/13.52 ((
% 99.66/13.52 (infuncsetfunc) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcinfuncset) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall1) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp3) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcextLem) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp4) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq2) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2lamEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifp) =>
% 99.66/13.52 ((
% 99.66/13.52 (theeq) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrue) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueorfalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setminusT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setextT) =>
% 99.66/13.52 ((
% 99.66/13.52 (subsetTI) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTELcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTERcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT1) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT2) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT3) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub2) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTnotintersectT) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementImpComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementSubsetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementInPowersetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (contraSubsetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTcontraSubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTILcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTIRcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion2) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (intersectInPowersetIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpNotIn1) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpInComplement1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTE) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTEcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementUnionInPowersetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule0) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_5) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all2) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1SetBreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (choice2fnsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all1) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compEex) =>
% 99.66/13.52 ((
% 99.66/13.52 (!!) @ (
% 99.66/13.52 (('#B') @ (
% 99.66/13.52 !!) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 !!))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#C') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1102])).
% 99.66/13.52 thf(zip_derived_cl1115, plain,
% 99.66/13.52 (~ (((binunionEcases) =>
% 99.66/13.52 (((binunionE) =>
% 99.66/13.52 (((binunionLsub) =>
% 99.66/13.52 (((binunionRsub) =>
% 99.66/13.52 (((binintersectI) =>
% 99.66/13.52 (((binintersectSubset5) =>
% 99.66/13.52 (((binintersectEL) =>
% 99.66/13.52 (((binintersectLsub) =>
% 99.66/13.52 (((binintersectSubset2) =>
% 99.66/13.52 (((binintersectSubset3) =>
% 99.66/13.52 (((binintersectER) =>
% 99.66/13.52 (((disjointsetsI1) =>
% 99.66/13.52 (((binintersectRsub) =>
% 99.66/13.52 (((binintersectSubset4) =>
% 99.66/13.52 (((binintersectSubset1) =>
% 99.66/13.52 (((bs114d) =>
% 99.66/13.52 (((setminusI) =>
% 99.66/13.52 (((setminusEL) =>
% 99.66/13.52 (((setminusER) =>
% 99.66/13.52 (((setminusSubset2) =>
% 99.66/13.52 (((setminusERneg) =>
% 99.66/13.52 (((setminusELneg) =>
% 99.66/13.52 (((setminusILneg) =>
% 99.66/13.52 (((setminusIRneg) =>
% 99.66/13.52 (((setminusLsub) =>
% 99.66/13.52 (((setminusSubset1) =>
% 99.66/13.52 (((symdiffE) =>
% 99.66/13.52 (((symdiffI1) =>
% 99.66/13.52 (((symdiffI2) =>
% 99.66/13.52 (((symdiffIneg1) =>
% 99.66/13.52 ((
% 99.66/13.52 (symdiffIneg2) =>
% 99.66/13.52 ((
% 99.66/13.52 (secondinupair) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairIL) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairIR) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairiskpair) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairp) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowerset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairset2E) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairsubunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairinpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem3) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair1) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionE2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton1) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I2) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsuniq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (theprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstin) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR11) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR12) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR1) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairequniteq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemEL) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemER) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempaircEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrI) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrSub) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrERa) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrER) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcImageSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (apProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (app) =>
% 99.66/13.52 ((
% 99.66/13.52 (infuncsetfunc) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcinfuncset) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall1) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp3) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcextLem) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp4) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq2) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2lamEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifp) =>
% 99.66/13.52 ((
% 99.66/13.52 (theeq) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrue) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueorfalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setminusT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setextT) =>
% 99.66/13.52 ((
% 99.66/13.52 (subsetTI) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTELcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTERcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT1) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT2) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT3) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub2) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTnotintersectT) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementImpComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementSubsetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementInPowersetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (contraSubsetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTcontraSubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTILcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTIRcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion2) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (intersectInPowersetIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpNotIn1) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpInComplement1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTE) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTEcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementUnionInPowersetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule0) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_5) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all2) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1SetBreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (choice2fnsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all1) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compEex) =>
% 99.66/13.52 ((
% 99.66/13.52 (!!) @ (
% 99.66/13.52 (('#B') @ (
% 99.66/13.52 !!) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 !!))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#C') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1109])).
% 99.66/13.52 thf(zip_derived_cl1121, plain,
% 99.66/13.52 (~ (((binunionE) =>
% 99.66/13.52 (((binunionLsub) =>
% 99.66/13.52 (((binunionRsub) =>
% 99.66/13.52 (((binintersectI) =>
% 99.66/13.52 (((binintersectSubset5) =>
% 99.66/13.52 (((binintersectEL) =>
% 99.66/13.52 (((binintersectLsub) =>
% 99.66/13.52 (((binintersectSubset2) =>
% 99.66/13.52 (((binintersectSubset3) =>
% 99.66/13.52 (((binintersectER) =>
% 99.66/13.52 (((disjointsetsI1) =>
% 99.66/13.52 (((binintersectRsub) =>
% 99.66/13.52 (((binintersectSubset4) =>
% 99.66/13.52 (((binintersectSubset1) =>
% 99.66/13.52 (((bs114d) =>
% 99.66/13.52 (((setminusI) =>
% 99.66/13.52 (((setminusEL) =>
% 99.66/13.52 (((setminusER) =>
% 99.66/13.52 (((setminusSubset2) =>
% 99.66/13.52 (((setminusERneg) =>
% 99.66/13.52 (((setminusELneg) =>
% 99.66/13.52 (((setminusILneg) =>
% 99.66/13.52 (((setminusIRneg) =>
% 99.66/13.52 (((setminusLsub) =>
% 99.66/13.52 (((setminusSubset1) =>
% 99.66/13.52 (((symdiffE) =>
% 99.66/13.52 (((symdiffI1) =>
% 99.66/13.52 (((symdiffI2) =>
% 99.66/13.52 (((symdiffIneg1) =>
% 99.66/13.52 (((symdiffIneg2) =>
% 99.66/13.52 ((
% 99.66/13.52 (secondinupair) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairIL) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairIR) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairiskpair) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairp) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowerset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairset2E) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairsubunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairinpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem3) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair1) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionE2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton1) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I2) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsuniq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (theprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstin) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR11) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR12) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR1) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairequniteq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemEL) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemER) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempaircEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrI) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrSub) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrERa) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrER) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcImageSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (apProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (app) =>
% 99.66/13.52 ((
% 99.66/13.52 (infuncsetfunc) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcinfuncset) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall1) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp3) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcextLem) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp4) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq2) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2lamEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifp) =>
% 99.66/13.52 ((
% 99.66/13.52 (theeq) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrue) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueorfalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setminusT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setextT) =>
% 99.66/13.52 ((
% 99.66/13.52 (subsetTI) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTELcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTERcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT1) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT2) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT3) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub2) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTnotintersectT) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementImpComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementSubsetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementInPowersetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (contraSubsetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTcontraSubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTILcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTIRcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion2) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (intersectInPowersetIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpNotIn1) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpInComplement1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTE) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTEcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementUnionInPowersetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule0) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_5) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all2) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1SetBreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (choice2fnsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all1) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compEex) =>
% 99.66/13.52 ((
% 99.66/13.52 (!!) @ (
% 99.66/13.52 (('#B') @ (
% 99.66/13.52 !!) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 !!))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#C') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1115])).
% 99.66/13.52 thf(zip_derived_cl1128, plain,
% 99.66/13.52 (~ (((binunionLsub) =>
% 99.66/13.52 (((binunionRsub) =>
% 99.66/13.52 (((binintersectI) =>
% 99.66/13.52 (((binintersectSubset5) =>
% 99.66/13.52 (((binintersectEL) =>
% 99.66/13.52 (((binintersectLsub) =>
% 99.66/13.52 (((binintersectSubset2) =>
% 99.66/13.52 (((binintersectSubset3) =>
% 99.66/13.52 (((binintersectER) =>
% 99.66/13.52 (((disjointsetsI1) =>
% 99.66/13.52 (((binintersectRsub) =>
% 99.66/13.52 (((binintersectSubset4) =>
% 99.66/13.52 (((binintersectSubset1) =>
% 99.66/13.52 (((bs114d) =>
% 99.66/13.52 (((setminusI) =>
% 99.66/13.52 (((setminusEL) =>
% 99.66/13.52 (((setminusER) =>
% 99.66/13.52 (((setminusSubset2) =>
% 99.66/13.52 (((setminusERneg) =>
% 99.66/13.52 (((setminusELneg) =>
% 99.66/13.52 (((setminusILneg) =>
% 99.66/13.52 (((setminusIRneg) =>
% 99.66/13.52 (((setminusLsub) =>
% 99.66/13.52 (((setminusSubset1) =>
% 99.66/13.52 (((symdiffE) =>
% 99.66/13.52 (((symdiffI1) =>
% 99.66/13.52 (((symdiffI2) =>
% 99.66/13.52 (((symdiffIneg1) =>
% 99.66/13.52 (((symdiffIneg2) =>
% 99.66/13.52 (((secondinupair) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairIL) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairIR) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairiskpair) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairp) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowerset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairset2E) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairsubunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairinpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem3) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair1) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionE2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton1) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I2) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsuniq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (theprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstin) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR11) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR12) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR1) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairequniteq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemEL) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemER) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempaircEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrI) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrSub) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrERa) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrER) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcImageSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (apProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (app) =>
% 99.66/13.52 ((
% 99.66/13.52 (infuncsetfunc) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcinfuncset) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall1) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp3) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcextLem) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp4) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq2) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2lamEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifp) =>
% 99.66/13.52 ((
% 99.66/13.52 (theeq) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrue) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueorfalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setminusT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setextT) =>
% 99.66/13.52 ((
% 99.66/13.52 (subsetTI) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTELcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTERcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT1) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT2) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT3) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub2) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTnotintersectT) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementImpComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementSubsetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementInPowersetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (contraSubsetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTcontraSubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTILcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTIRcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion2) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (intersectInPowersetIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpNotIn1) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpInComplement1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTE) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTEcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementUnionInPowersetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule0) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_5) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all2) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1SetBreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (choice2fnsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all1) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compEex) =>
% 99.66/13.52 ((
% 99.66/13.52 (!!) @ (
% 99.66/13.52 (('#B') @ (
% 99.66/13.52 !!) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 !!))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#C') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1121])).
% 99.66/13.52 thf(zip_derived_cl1135, plain,
% 99.66/13.52 (~ (((binunionRsub) =>
% 99.66/13.52 (((binintersectI) =>
% 99.66/13.52 (((binintersectSubset5) =>
% 99.66/13.52 (((binintersectEL) =>
% 99.66/13.52 (((binintersectLsub) =>
% 99.66/13.52 (((binintersectSubset2) =>
% 99.66/13.52 (((binintersectSubset3) =>
% 99.66/13.52 (((binintersectER) =>
% 99.66/13.52 (((disjointsetsI1) =>
% 99.66/13.52 (((binintersectRsub) =>
% 99.66/13.52 (((binintersectSubset4) =>
% 99.66/13.52 (((binintersectSubset1) =>
% 99.66/13.52 (((bs114d) =>
% 99.66/13.52 (((setminusI) =>
% 99.66/13.52 (((setminusEL) =>
% 99.66/13.52 (((setminusER) =>
% 99.66/13.52 (((setminusSubset2) =>
% 99.66/13.52 (((setminusERneg) =>
% 99.66/13.52 (((setminusELneg) =>
% 99.66/13.52 (((setminusILneg) =>
% 99.66/13.52 (((setminusIRneg) =>
% 99.66/13.52 (((setminusLsub) =>
% 99.66/13.52 (((setminusSubset1) =>
% 99.66/13.52 (((symdiffE) =>
% 99.66/13.52 (((symdiffI1) =>
% 99.66/13.52 (((symdiffI2) =>
% 99.66/13.52 (((symdiffIneg1) =>
% 99.66/13.52 (((symdiffIneg2) =>
% 99.66/13.52 (((secondinupair) =>
% 99.66/13.52 (((setukpairIL) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairIR) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairiskpair) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairp) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowerset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairset2E) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairsubunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairinpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem3) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair1) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionE2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton1) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I2) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsuniq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (theprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstin) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR11) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR12) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR1) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairequniteq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemEL) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemER) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempaircEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrI) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrSub) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrERa) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrER) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcImageSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (apProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (app) =>
% 99.66/13.52 ((
% 99.66/13.52 (infuncsetfunc) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcinfuncset) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall1) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp3) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcextLem) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp4) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq2) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2lamEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifp) =>
% 99.66/13.52 ((
% 99.66/13.52 (theeq) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrue) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueorfalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setminusT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setextT) =>
% 99.66/13.52 ((
% 99.66/13.52 (subsetTI) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTELcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTERcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT1) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT2) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT3) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub2) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTnotintersectT) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementImpComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementSubsetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementInPowersetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (contraSubsetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTcontraSubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTILcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTIRcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion2) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (intersectInPowersetIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpNotIn1) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpInComplement1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTE) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTEcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementUnionInPowersetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule0) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_5) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all2) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1SetBreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (choice2fnsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all1) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compEex) =>
% 99.66/13.52 ((
% 99.66/13.52 (!!) @ (
% 99.66/13.52 (('#B') @ (
% 99.66/13.52 !!) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 !!))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#C') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1128])).
% 99.66/13.52 thf(zip_derived_cl1142, plain,
% 99.66/13.52 (~ (((binintersectI) =>
% 99.66/13.52 (((binintersectSubset5) =>
% 99.66/13.52 (((binintersectEL) =>
% 99.66/13.52 (((binintersectLsub) =>
% 99.66/13.52 (((binintersectSubset2) =>
% 99.66/13.52 (((binintersectSubset3) =>
% 99.66/13.52 (((binintersectER) =>
% 99.66/13.52 (((disjointsetsI1) =>
% 99.66/13.52 (((binintersectRsub) =>
% 99.66/13.52 (((binintersectSubset4) =>
% 99.66/13.52 (((binintersectSubset1) =>
% 99.66/13.52 (((bs114d) =>
% 99.66/13.52 (((setminusI) =>
% 99.66/13.52 (((setminusEL) =>
% 99.66/13.52 (((setminusER) =>
% 99.66/13.52 (((setminusSubset2) =>
% 99.66/13.52 (((setminusERneg) =>
% 99.66/13.52 (((setminusELneg) =>
% 99.66/13.52 (((setminusILneg) =>
% 99.66/13.52 (((setminusIRneg) =>
% 99.66/13.52 (((setminusLsub) =>
% 99.66/13.52 (((setminusSubset1) =>
% 99.66/13.52 (((symdiffE) =>
% 99.66/13.52 (((symdiffI1) =>
% 99.66/13.52 (((symdiffI2) =>
% 99.66/13.52 (((symdiffIneg1) =>
% 99.66/13.52 (((symdiffIneg2) =>
% 99.66/13.52 (((secondinupair) =>
% 99.66/13.52 (((setukpairIL) =>
% 99.66/13.52 (((setukpairIR) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairiskpair) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairp) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowerset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairset2E) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairsubunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairinpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem3) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair1) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionE2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton1) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I2) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsuniq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (theprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstin) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR11) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR12) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR1) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairequniteq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemEL) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemER) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempaircEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrI) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrSub) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrERa) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrER) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcImageSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (apProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (app) =>
% 99.66/13.52 ((
% 99.66/13.52 (infuncsetfunc) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcinfuncset) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall1) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp3) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcextLem) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp4) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq2) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2lamEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifp) =>
% 99.66/13.52 ((
% 99.66/13.52 (theeq) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrue) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueorfalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setminusT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setextT) =>
% 99.66/13.52 ((
% 99.66/13.52 (subsetTI) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTELcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTERcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT1) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT2) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT3) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub2) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTnotintersectT) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementImpComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementSubsetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementInPowersetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (contraSubsetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTcontraSubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTILcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTIRcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion2) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (intersectInPowersetIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpNotIn1) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpInComplement1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTE) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTEcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementUnionInPowersetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule0) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_5) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all2) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1SetBreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (choice2fnsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all1) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compEex) =>
% 99.66/13.52 ((
% 99.66/13.52 (!!) @ (
% 99.66/13.52 (('#B') @ (
% 99.66/13.52 !!) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 !!))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#C') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1135])).
% 99.66/13.52 thf(zip_derived_cl1150, plain,
% 99.66/13.52 (~ (((binintersectSubset5) =>
% 99.66/13.52 (((binintersectEL) =>
% 99.66/13.52 (((binintersectLsub) =>
% 99.66/13.52 (((binintersectSubset2) =>
% 99.66/13.52 (((binintersectSubset3) =>
% 99.66/13.52 (((binintersectER) =>
% 99.66/13.52 (((disjointsetsI1) =>
% 99.66/13.52 (((binintersectRsub) =>
% 99.66/13.52 (((binintersectSubset4) =>
% 99.66/13.52 (((binintersectSubset1) =>
% 99.66/13.52 (((bs114d) =>
% 99.66/13.52 (((setminusI) =>
% 99.66/13.52 (((setminusEL) =>
% 99.66/13.52 (((setminusER) =>
% 99.66/13.52 (((setminusSubset2) =>
% 99.66/13.52 (((setminusERneg) =>
% 99.66/13.52 (((setminusELneg) =>
% 99.66/13.52 (((setminusILneg) =>
% 99.66/13.52 (((setminusIRneg) =>
% 99.66/13.52 (((setminusLsub) =>
% 99.66/13.52 (((setminusSubset1) =>
% 99.66/13.52 (((symdiffE) =>
% 99.66/13.52 (((symdiffI1) =>
% 99.66/13.52 (((symdiffI2) =>
% 99.66/13.52 (((symdiffIneg1) =>
% 99.66/13.52 (((symdiffIneg2) =>
% 99.66/13.52 (((secondinupair) =>
% 99.66/13.52 (((setukpairIL) =>
% 99.66/13.52 (((setukpairIR) =>
% 99.66/13.52 (((kpairiskpair) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairp) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowerset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairset2E) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairsubunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairinpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem3) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair1) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionE2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton1) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I2) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsuniq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (theprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstin) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR11) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR12) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR1) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairequniteq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemEL) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemER) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempaircEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrI) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrSub) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrERa) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrER) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcImageSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (apProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (app) =>
% 99.66/13.52 ((
% 99.66/13.52 (infuncsetfunc) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcinfuncset) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall1) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp3) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcextLem) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp4) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq2) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2lamEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifp) =>
% 99.66/13.52 ((
% 99.66/13.52 (theeq) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrue) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueorfalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setminusT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setextT) =>
% 99.66/13.52 ((
% 99.66/13.52 (subsetTI) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTELcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTERcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT1) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT2) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT3) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub2) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTnotintersectT) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementImpComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementSubsetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementInPowersetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (contraSubsetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTcontraSubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTILcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTIRcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion2) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (intersectInPowersetIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpNotIn1) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpInComplement1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTE) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTEcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementUnionInPowersetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule0) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_5) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all2) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1SetBreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (choice2fnsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all1) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compEex) =>
% 99.66/13.52 ((
% 99.66/13.52 (!!) @ (
% 99.66/13.52 (('#B') @ (
% 99.66/13.52 !!) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 !!))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#C') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1142])).
% 99.66/13.52 thf(zip_derived_cl1158, plain,
% 99.66/13.52 (~ (((binintersectEL) =>
% 99.66/13.52 (((binintersectLsub) =>
% 99.66/13.52 (((binintersectSubset2) =>
% 99.66/13.52 (((binintersectSubset3) =>
% 99.66/13.52 (((binintersectER) =>
% 99.66/13.52 (((disjointsetsI1) =>
% 99.66/13.52 (((binintersectRsub) =>
% 99.66/13.52 (((binintersectSubset4) =>
% 99.66/13.52 (((binintersectSubset1) =>
% 99.66/13.52 (((bs114d) =>
% 99.66/13.52 (((setminusI) =>
% 99.66/13.52 (((setminusEL) =>
% 99.66/13.52 (((setminusER) =>
% 99.66/13.52 (((setminusSubset2) =>
% 99.66/13.52 (((setminusERneg) =>
% 99.66/13.52 (((setminusELneg) =>
% 99.66/13.52 (((setminusILneg) =>
% 99.66/13.52 (((setminusIRneg) =>
% 99.66/13.52 (((setminusLsub) =>
% 99.66/13.52 (((setminusSubset1) =>
% 99.66/13.52 (((symdiffE) =>
% 99.66/13.52 (((symdiffI1) =>
% 99.66/13.52 (((symdiffI2) =>
% 99.66/13.52 (((symdiffIneg1) =>
% 99.66/13.52 (((symdiffIneg2) =>
% 99.66/13.52 (((secondinupair) =>
% 99.66/13.52 (((setukpairIL) =>
% 99.66/13.52 (((setukpairIR) =>
% 99.66/13.52 (((kpairiskpair) =>
% 99.66/13.52 (((kpairp) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowerset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairset2E) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairsubunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairinpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem3) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair1) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionE2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton1) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I2) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsuniq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (theprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstin) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR11) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR12) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR1) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairequniteq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemEL) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemER) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempaircEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrI) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrSub) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrERa) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrER) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcImageSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (apProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (app) =>
% 99.66/13.52 ((
% 99.66/13.52 (infuncsetfunc) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcinfuncset) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall1) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp3) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcextLem) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp4) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq2) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2lamEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifp) =>
% 99.66/13.52 ((
% 99.66/13.52 (theeq) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrue) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueorfalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setminusT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setextT) =>
% 99.66/13.52 ((
% 99.66/13.52 (subsetTI) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTELcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTERcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT1) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT2) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT3) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub2) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTnotintersectT) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementImpComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementSubsetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementInPowersetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (contraSubsetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTcontraSubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTILcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTIRcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion2) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (intersectInPowersetIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpNotIn1) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpInComplement1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTE) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTEcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementUnionInPowersetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule0) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_5) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all2) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1SetBreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (choice2fnsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all1) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compEex) =>
% 99.66/13.52 ((
% 99.66/13.52 (!!) @ (
% 99.66/13.52 (('#B') @ (
% 99.66/13.52 !!) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 !!))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#C') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1150])).
% 99.66/13.52 thf(zip_derived_cl1166, plain,
% 99.66/13.52 (~ (((binintersectLsub) =>
% 99.66/13.52 (((binintersectSubset2) =>
% 99.66/13.52 (((binintersectSubset3) =>
% 99.66/13.52 (((binintersectER) =>
% 99.66/13.52 (((disjointsetsI1) =>
% 99.66/13.52 (((binintersectRsub) =>
% 99.66/13.52 (((binintersectSubset4) =>
% 99.66/13.52 (((binintersectSubset1) =>
% 99.66/13.52 (((bs114d) =>
% 99.66/13.52 (((setminusI) =>
% 99.66/13.52 (((setminusEL) =>
% 99.66/13.52 (((setminusER) =>
% 99.66/13.52 (((setminusSubset2) =>
% 99.66/13.52 (((setminusERneg) =>
% 99.66/13.52 (((setminusELneg) =>
% 99.66/13.52 (((setminusILneg) =>
% 99.66/13.52 (((setminusIRneg) =>
% 99.66/13.52 (((setminusLsub) =>
% 99.66/13.52 (((setminusSubset1) =>
% 99.66/13.52 (((symdiffE) =>
% 99.66/13.52 (((symdiffI1) =>
% 99.66/13.52 (((symdiffI2) =>
% 99.66/13.52 (((symdiffIneg1) =>
% 99.66/13.52 (((symdiffIneg2) =>
% 99.66/13.52 (((secondinupair) =>
% 99.66/13.52 (((setukpairIL) =>
% 99.66/13.52 (((setukpairIR) =>
% 99.66/13.52 (((kpairiskpair) =>
% 99.66/13.52 (((kpairp) =>
% 99.66/13.52 (((singletonsubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowerset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairset2E) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairsubunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairinpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem3) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair1) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionE2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton1) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I2) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsuniq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (theprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstin) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR11) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR12) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR1) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairequniteq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemEL) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemER) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempaircEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrI) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrSub) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrERa) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrER) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcImageSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (apProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (app) =>
% 99.66/13.52 ((
% 99.66/13.52 (infuncsetfunc) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcinfuncset) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall1) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp3) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcextLem) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp4) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq2) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2lamEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifp) =>
% 99.66/13.52 ((
% 99.66/13.52 (theeq) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrue) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueorfalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setminusT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setextT) =>
% 99.66/13.52 ((
% 99.66/13.52 (subsetTI) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTELcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTERcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT1) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT2) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT3) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub2) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTnotintersectT) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementImpComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementSubsetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementInPowersetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (contraSubsetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTcontraSubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTILcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTIRcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion2) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (intersectInPowersetIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpNotIn1) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpInComplement1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTE) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTEcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementUnionInPowersetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule0) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_5) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all2) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1SetBreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (choice2fnsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all1) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compEex) =>
% 99.66/13.52 ((
% 99.66/13.52 (!!) @ (
% 99.66/13.52 (('#B') @ (
% 99.66/13.52 !!) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 !!))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#C') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1158])).
% 99.66/13.52 thf(zip_derived_cl1174, plain,
% 99.66/13.52 (~ (((binintersectSubset2) =>
% 99.66/13.52 (((binintersectSubset3) =>
% 99.66/13.52 (((binintersectER) =>
% 99.66/13.52 (((disjointsetsI1) =>
% 99.66/13.52 (((binintersectRsub) =>
% 99.66/13.52 (((binintersectSubset4) =>
% 99.66/13.52 (((binintersectSubset1) =>
% 99.66/13.52 (((bs114d) =>
% 99.66/13.52 (((setminusI) =>
% 99.66/13.52 (((setminusEL) =>
% 99.66/13.52 (((setminusER) =>
% 99.66/13.52 (((setminusSubset2) =>
% 99.66/13.52 (((setminusERneg) =>
% 99.66/13.52 (((setminusELneg) =>
% 99.66/13.52 (((setminusILneg) =>
% 99.66/13.52 (((setminusIRneg) =>
% 99.66/13.52 (((setminusLsub) =>
% 99.66/13.52 (((setminusSubset1) =>
% 99.66/13.52 (((symdiffE) =>
% 99.66/13.52 (((symdiffI1) =>
% 99.66/13.52 (((symdiffI2) =>
% 99.66/13.52 (((symdiffIneg1) =>
% 99.66/13.52 (((symdiffIneg2) =>
% 99.66/13.52 (((secondinupair) =>
% 99.66/13.52 (((setukpairIL) =>
% 99.66/13.52 (((setukpairIR) =>
% 99.66/13.52 (((kpairiskpair) =>
% 99.66/13.52 (((kpairp) =>
% 99.66/13.52 (((singletonsubset) =>
% 99.66/13.52 (((singletoninpowerset) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletoninpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairset2E) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairsubunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairinpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem3) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair1) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionE2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton1) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I2) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsuniq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (theprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstin) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR11) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR12) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR1) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairequniteq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjR) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ksndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (kpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemEL) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairmemER) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempaircEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodsndpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairsurjEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrI) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrSub) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrERa) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrEL2) =>
% 99.66/13.52 ((
% 99.66/13.52 (dpsetconstrER) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcImageSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (apProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (app) =>
% 99.66/13.52 ((
% 99.66/13.52 (infuncsetfunc) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcinfuncset) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamProp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lamp) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2p) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall1) =>
% 99.66/13.52 ((
% 99.66/13.52 (brelnall2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp3) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcextLem) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcGraphProp4) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext) =>
% 99.66/13.52 ((
% 99.66/13.52 (funcext2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ap2apEq2) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta1) =>
% 99.66/13.52 ((
% 99.66/13.52 (lam2lamEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (beta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (eta2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalseProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp1) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueProp2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifSingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (ifp) =>
% 99.66/13.52 ((
% 99.66/13.52 (theeq) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrue) =>
% 99.66/13.52 ((
% 99.66/13.52 (iffalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (iftrueorfalse) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setminusT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementT_lem) =>
% 99.66/13.52 ((
% 99.66/13.52 (setextT) =>
% 99.66/13.52 ((
% 99.66/13.52 (subsetTI) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (powersetTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTELcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binintersectTERcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT1) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT2) =>
% 99.66/13.52 ((
% 99.66/13.52 (contrasubsetT3) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementI1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementE1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub1) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementSub2) =>
% 99.66/13.52 ((
% 99.66/13.52 (doubleComplementEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTnotintersectT) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementImpComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementSubsetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementInPowersetComplementIntersect) =>
% 99.66/13.52 ((
% 99.66/13.52 (contraSubsetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementTcontraSubset) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTILcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTIRcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInUnion2) =>
% 99.66/13.52 ((
% 99.66/13.52 (inIntersectImpInIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (intersectInPowersetIntersectUnions) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpNotIn1) =>
% 99.66/13.52 ((
% 99.66/13.52 (inComplementUnionImpInComplement1) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTE) =>
% 99.66/13.52 ((
% 99.66/13.52 (binunionTEcontra) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a1) =>
% 99.66/13.52 ((
% 99.66/13.52 (complementUnionInPowersetComplement) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan1) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2a) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b2) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2b) =>
% 99.66/13.52 ((
% 99.66/13.52 (demorgan2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule0) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz13rule4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_1) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_2) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_3) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_4) =>
% 99.66/13.52 ((
% 99.66/13.52 (woz1_5) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all2) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1SetBreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (choice2fnsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (setOfPairsIsBReln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1all1) =>
% 99.66/13.52 ((
% 99.66/13.52 (subbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (eqbreln1) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1invE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compI) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compE) =>
% 99.66/13.52 ((
% 99.66/13.52 (breln1compEex) =>
% 99.66/13.52 ((
% 99.66/13.52 (!!) @ (
% 99.66/13.52 (('#B') @ (
% 99.66/13.52 !!) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 !!))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#S') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#S') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 =>))) @
% 99.66/13.52 breln1)))))) @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#C') @ (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 (
% 99.66/13.52 (
% 99.66/13.52 ('#B') @ (
% 99.66/13.52 '#B') @
% 99.66/13.52 breln1)))) @
% 99.66/13.52 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1166])).
% 99.66/13.52 thf(zip_derived_cl1183, plain,
% 99.66/13.52 (~ (((binintersectSubset3) =>
% 99.66/13.52 (((binintersectER) =>
% 99.66/13.52 (((disjointsetsI1) =>
% 99.66/13.52 (((binintersectRsub) =>
% 99.66/13.52 (((binintersectSubset4) =>
% 99.66/13.52 (((binintersectSubset1) =>
% 99.66/13.52 (((bs114d) =>
% 99.66/13.52 (((setminusI) =>
% 99.66/13.52 (((setminusEL) =>
% 99.66/13.52 (((setminusER) =>
% 99.66/13.52 (((setminusSubset2) =>
% 99.66/13.52 (((setminusERneg) =>
% 99.66/13.52 (((setminusELneg) =>
% 99.66/13.52 (((setminusILneg) =>
% 99.66/13.52 (((setminusIRneg) =>
% 99.66/13.52 (((setminusLsub) =>
% 99.66/13.52 (((setminusSubset1) =>
% 99.66/13.52 (((symdiffE) =>
% 99.66/13.52 (((symdiffI1) =>
% 99.66/13.52 (((symdiffI2) =>
% 99.66/13.52 (((symdiffIneg1) =>
% 99.66/13.52 (((symdiffIneg2) =>
% 99.66/13.52 (((secondinupair) =>
% 99.66/13.52 (((setukpairIL) =>
% 99.66/13.52 (((setukpairIR) =>
% 99.66/13.52 (((kpairiskpair) =>
% 99.66/13.52 (((kpairp) =>
% 99.66/13.52 (((singletonsubset) =>
% 99.66/13.52 (((singletoninpowerset) =>
% 99.66/13.52 (((singletoninpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairset2E) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairsubunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (upairinpowunion) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem2) =>
% 99.66/13.52 ((
% 99.66/13.52 (ubforcartprodlem3) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodpairin) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair1) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodmempair) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionE2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton1) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton2) =>
% 99.66/13.52 ((
% 99.66/13.52 (setunionsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1E1) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I) =>
% 99.66/13.52 ((
% 99.66/13.52 (ex1I2) =>
% 99.66/13.52 ((
% 99.66/13.52 (singletonsuniq) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL1) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstsingleton) =>
% 99.66/13.52 ((
% 99.66/13.52 (theprop) =>
% 99.66/13.52 ((
% 99.66/13.52 (kfstpairEq) =>
% 99.66/13.52 ((
% 99.66/13.52 (cartprodfstin) =>
% 99.66/13.52 ((
% 99.66/13.52 (setukpairinjL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR11) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR12) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR1) =>
% 99.66/13.53 ((
% 99.66/13.53 (upairequniteq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (kpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndin) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemEL) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemER) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempaircEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrI) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrSub) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrERa) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrER) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcImageSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (apProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (app) =>
% 99.66/13.53 ((
% 99.66/13.53 (infuncsetfunc) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcinfuncset) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall1) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp3) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcextLem) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp4) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq2) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2lamEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifp) =>
% 99.66/13.53 ((
% 99.66/13.53 (theeq) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrue) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueorfalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setminusT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setextT) =>
% 99.66/13.53 ((
% 99.66/13.53 (subsetTI) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTELcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTERcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT1) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT2) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT3) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub2) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTnotintersectT) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementImpComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementSubsetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementInPowersetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (contraSubsetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTcontraSubset) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTILcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTIRcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion2) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (intersectInPowersetIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpNotIn1) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpInComplement1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTE) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTEcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementUnionInPowersetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule0) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_5) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all2) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1SetBreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (choice2fnsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all1) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compEex) =>
% 99.66/13.53 ((
% 99.66/13.53 (!!) @ (
% 99.66/13.53 (('#B') @ (
% 99.66/13.53 !!) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 !!))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#C') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1174])).
% 99.66/13.53 thf(zip_derived_cl1193, plain,
% 99.66/13.53 (~ (((binintersectER) =>
% 99.66/13.53 (((disjointsetsI1) =>
% 99.66/13.53 (((binintersectRsub) =>
% 99.66/13.53 (((binintersectSubset4) =>
% 99.66/13.53 (((binintersectSubset1) =>
% 99.66/13.53 (((bs114d) =>
% 99.66/13.53 (((setminusI) =>
% 99.66/13.53 (((setminusEL) =>
% 99.66/13.53 (((setminusER) =>
% 99.66/13.53 (((setminusSubset2) =>
% 99.66/13.53 (((setminusERneg) =>
% 99.66/13.53 (((setminusELneg) =>
% 99.66/13.53 (((setminusILneg) =>
% 99.66/13.53 (((setminusIRneg) =>
% 99.66/13.53 (((setminusLsub) =>
% 99.66/13.53 (((setminusSubset1) =>
% 99.66/13.53 (((symdiffE) =>
% 99.66/13.53 (((symdiffI1) =>
% 99.66/13.53 (((symdiffI2) =>
% 99.66/13.53 (((symdiffIneg1) =>
% 99.66/13.53 (((symdiffIneg2) =>
% 99.66/13.53 (((secondinupair) =>
% 99.66/13.53 (((setukpairIL) =>
% 99.66/13.53 (((setukpairIR) =>
% 99.66/13.53 (((kpairiskpair) =>
% 99.66/13.53 (((kpairp) =>
% 99.66/13.53 (((singletonsubset) =>
% 99.66/13.53 (((singletoninpowerset) =>
% 99.66/13.53 (((singletoninpowunion) =>
% 99.66/13.53 (((upairset2E) =>
% 99.66/13.53 ((
% 99.66/13.53 (upairsubunion) =>
% 99.66/13.53 ((
% 99.66/13.53 (upairinpowunion) =>
% 99.66/13.53 ((
% 99.66/13.53 (ubforcartprodlem1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ubforcartprodlem2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ubforcartprodlem3) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairin) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempair1) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempair) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionE2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton1) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I2) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonsuniq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (theprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstin) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR11) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR12) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR1) =>
% 99.66/13.53 ((
% 99.66/13.53 (upairequniteq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (kpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndin) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemEL) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemER) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempaircEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrI) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrSub) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrERa) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrER) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcImageSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (apProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (app) =>
% 99.66/13.53 ((
% 99.66/13.53 (infuncsetfunc) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcinfuncset) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall1) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp3) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcextLem) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp4) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq2) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2lamEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifp) =>
% 99.66/13.53 ((
% 99.66/13.53 (theeq) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrue) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueorfalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setminusT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setextT) =>
% 99.66/13.53 ((
% 99.66/13.53 (subsetTI) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTELcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTERcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT1) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT2) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT3) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub2) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTnotintersectT) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementImpComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementSubsetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementInPowersetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (contraSubsetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTcontraSubset) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTILcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTIRcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion2) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (intersectInPowersetIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpNotIn1) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpInComplement1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTE) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTEcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementUnionInPowersetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule0) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_5) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all2) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1SetBreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (choice2fnsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all1) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compEex) =>
% 99.66/13.53 ((
% 99.66/13.53 (!!) @ (
% 99.66/13.53 (('#B') @ (
% 99.66/13.53 !!) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 !!))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#C') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1183])).
% 99.66/13.53 thf(zip_derived_cl1206, plain,
% 99.66/13.53 (~ (((disjointsetsI1) =>
% 99.66/13.53 (((binintersectRsub) =>
% 99.66/13.53 (((binintersectSubset4) =>
% 99.66/13.53 (((binintersectSubset1) =>
% 99.66/13.53 (((bs114d) =>
% 99.66/13.53 (((setminusI) =>
% 99.66/13.53 (((setminusEL) =>
% 99.66/13.53 (((setminusER) =>
% 99.66/13.53 (((setminusSubset2) =>
% 99.66/13.53 (((setminusERneg) =>
% 99.66/13.53 (((setminusELneg) =>
% 99.66/13.53 (((setminusILneg) =>
% 99.66/13.53 (((setminusIRneg) =>
% 99.66/13.53 (((setminusLsub) =>
% 99.66/13.53 (((setminusSubset1) =>
% 99.66/13.53 (((symdiffE) =>
% 99.66/13.53 (((symdiffI1) =>
% 99.66/13.53 (((symdiffI2) =>
% 99.66/13.53 (((symdiffIneg1) =>
% 99.66/13.53 (((symdiffIneg2) =>
% 99.66/13.53 (((secondinupair) =>
% 99.66/13.53 (((setukpairIL) =>
% 99.66/13.53 (((setukpairIR) =>
% 99.66/13.53 (((kpairiskpair) =>
% 99.66/13.53 (((kpairp) =>
% 99.66/13.53 (((singletonsubset) =>
% 99.66/13.53 (((singletoninpowerset) =>
% 99.66/13.53 (((singletoninpowunion) =>
% 99.66/13.53 (((upairset2E) =>
% 99.66/13.53 (((upairsubunion) =>
% 99.66/13.53 ((
% 99.66/13.53 (upairinpowunion) =>
% 99.66/13.53 ((
% 99.66/13.53 (ubforcartprodlem1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ubforcartprodlem2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ubforcartprodlem3) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairin) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempair1) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempair) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionE2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton1) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I2) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonsuniq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (theprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstin) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR11) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR12) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR1) =>
% 99.66/13.53 ((
% 99.66/13.53 (upairequniteq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (kpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndin) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemEL) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemER) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempaircEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrI) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrSub) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrERa) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrER) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcImageSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (apProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (app) =>
% 99.66/13.53 ((
% 99.66/13.53 (infuncsetfunc) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcinfuncset) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall1) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp3) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcextLem) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp4) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq2) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2lamEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifp) =>
% 99.66/13.53 ((
% 99.66/13.53 (theeq) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrue) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueorfalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setminusT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setextT) =>
% 99.66/13.53 ((
% 99.66/13.53 (subsetTI) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTELcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTERcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT1) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT2) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT3) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub2) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTnotintersectT) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementImpComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementSubsetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementInPowersetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (contraSubsetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTcontraSubset) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTILcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTIRcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion2) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (intersectInPowersetIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpNotIn1) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpInComplement1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTE) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTEcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementUnionInPowersetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule0) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_5) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all2) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1SetBreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (choice2fnsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all1) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compEex) =>
% 99.66/13.53 ((
% 99.66/13.53 (!!) @ (
% 99.66/13.53 (('#B') @ (
% 99.66/13.53 !!) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 !!))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#C') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1193])).
% 99.66/13.53 thf(zip_derived_cl1216, plain,
% 99.66/13.53 (~ (((binintersectRsub) =>
% 99.66/13.53 (((binintersectSubset4) =>
% 99.66/13.53 (((binintersectSubset1) =>
% 99.66/13.53 (((bs114d) =>
% 99.66/13.53 (((setminusI) =>
% 99.66/13.53 (((setminusEL) =>
% 99.66/13.53 (((setminusER) =>
% 99.66/13.53 (((setminusSubset2) =>
% 99.66/13.53 (((setminusERneg) =>
% 99.66/13.53 (((setminusELneg) =>
% 99.66/13.53 (((setminusILneg) =>
% 99.66/13.53 (((setminusIRneg) =>
% 99.66/13.53 (((setminusLsub) =>
% 99.66/13.53 (((setminusSubset1) =>
% 99.66/13.53 (((symdiffE) =>
% 99.66/13.53 (((symdiffI1) =>
% 99.66/13.53 (((symdiffI2) =>
% 99.66/13.53 (((symdiffIneg1) =>
% 99.66/13.53 (((symdiffIneg2) =>
% 99.66/13.53 (((secondinupair) =>
% 99.66/13.53 (((setukpairIL) =>
% 99.66/13.53 (((setukpairIR) =>
% 99.66/13.53 (((kpairiskpair) =>
% 99.66/13.53 (((kpairp) =>
% 99.66/13.53 (((singletonsubset) =>
% 99.66/13.53 (((singletoninpowerset) =>
% 99.66/13.53 (((singletoninpowunion) =>
% 99.66/13.53 (((upairset2E) =>
% 99.66/13.53 (((upairsubunion) =>
% 99.66/13.53 (((upairinpowunion) =>
% 99.66/13.53 ((
% 99.66/13.53 (ubforcartprodlem1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ubforcartprodlem2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ubforcartprodlem3) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairin) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempair1) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempair) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionE2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton1) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I2) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonsuniq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (theprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstin) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR11) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR12) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR1) =>
% 99.66/13.53 ((
% 99.66/13.53 (upairequniteq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (kpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndin) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemEL) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemER) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempaircEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrI) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrSub) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrERa) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrER) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcImageSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (apProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (app) =>
% 99.66/13.53 ((
% 99.66/13.53 (infuncsetfunc) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcinfuncset) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall1) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp3) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcextLem) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp4) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq2) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2lamEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifp) =>
% 99.66/13.53 ((
% 99.66/13.53 (theeq) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrue) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueorfalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setminusT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setextT) =>
% 99.66/13.53 ((
% 99.66/13.53 (subsetTI) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTELcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTERcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT1) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT2) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT3) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub2) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTnotintersectT) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementImpComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementSubsetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementInPowersetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (contraSubsetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTcontraSubset) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTILcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTIRcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion2) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (intersectInPowersetIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpNotIn1) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpInComplement1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTE) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTEcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementUnionInPowersetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule0) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_5) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all2) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1SetBreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (choice2fnsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all1) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compEex) =>
% 99.66/13.53 ((
% 99.66/13.53 (!!) @ (
% 99.66/13.53 (('#B') @ (
% 99.66/13.53 !!) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 !!))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#C') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1206])).
% 99.66/13.53 thf(zip_derived_cl1223, plain,
% 99.66/13.53 (~ (((binintersectSubset4) =>
% 99.66/13.53 (((binintersectSubset1) =>
% 99.66/13.53 (((bs114d) =>
% 99.66/13.53 (((setminusI) =>
% 99.66/13.53 (((setminusEL) =>
% 99.66/13.53 (((setminusER) =>
% 99.66/13.53 (((setminusSubset2) =>
% 99.66/13.53 (((setminusERneg) =>
% 99.66/13.53 (((setminusELneg) =>
% 99.66/13.53 (((setminusILneg) =>
% 99.66/13.53 (((setminusIRneg) =>
% 99.66/13.53 (((setminusLsub) =>
% 99.66/13.53 (((setminusSubset1) =>
% 99.66/13.53 (((symdiffE) =>
% 99.66/13.53 (((symdiffI1) =>
% 99.66/13.53 (((symdiffI2) =>
% 99.66/13.53 (((symdiffIneg1) =>
% 99.66/13.53 (((symdiffIneg2) =>
% 99.66/13.53 (((secondinupair) =>
% 99.66/13.53 (((setukpairIL) =>
% 99.66/13.53 (((setukpairIR) =>
% 99.66/13.53 (((kpairiskpair) =>
% 99.66/13.53 (((kpairp) =>
% 99.66/13.53 (((singletonsubset) =>
% 99.66/13.53 (((singletoninpowerset) =>
% 99.66/13.53 (((singletoninpowunion) =>
% 99.66/13.53 (((upairset2E) =>
% 99.66/13.53 (((upairsubunion) =>
% 99.66/13.53 (((upairinpowunion) =>
% 99.66/13.53 (((ubforcartprodlem1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ubforcartprodlem2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ubforcartprodlem3) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairin) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempair1) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempair) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionE2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton1) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I2) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonsuniq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (theprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstin) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR11) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR12) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR1) =>
% 99.66/13.53 ((
% 99.66/13.53 (upairequniteq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (kpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndin) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemEL) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemER) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempaircEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrI) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrSub) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrERa) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrER) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcImageSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (apProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (app) =>
% 99.66/13.53 ((
% 99.66/13.53 (infuncsetfunc) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcinfuncset) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall1) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp3) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcextLem) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp4) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq2) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2lamEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifp) =>
% 99.66/13.53 ((
% 99.66/13.53 (theeq) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrue) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueorfalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setminusT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setextT) =>
% 99.66/13.53 ((
% 99.66/13.53 (subsetTI) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTELcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTERcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT1) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT2) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT3) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub2) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTnotintersectT) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementImpComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementSubsetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementInPowersetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (contraSubsetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTcontraSubset) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTILcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTIRcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion2) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (intersectInPowersetIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpNotIn1) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpInComplement1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTE) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTEcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementUnionInPowersetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule0) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_5) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all2) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1SetBreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (choice2fnsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all1) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compEex) =>
% 99.66/13.53 ((
% 99.66/13.53 (!!) @ (
% 99.66/13.53 (('#B') @ (
% 99.66/13.53 !!) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 !!))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#C') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1216])).
% 99.66/13.53 thf(zip_derived_cl1231, plain,
% 99.66/13.53 (~ (((binintersectSubset1) =>
% 99.66/13.53 (((bs114d) =>
% 99.66/13.53 (((setminusI) =>
% 99.66/13.53 (((setminusEL) =>
% 99.66/13.53 (((setminusER) =>
% 99.66/13.53 (((setminusSubset2) =>
% 99.66/13.53 (((setminusERneg) =>
% 99.66/13.53 (((setminusELneg) =>
% 99.66/13.53 (((setminusILneg) =>
% 99.66/13.53 (((setminusIRneg) =>
% 99.66/13.53 (((setminusLsub) =>
% 99.66/13.53 (((setminusSubset1) =>
% 99.66/13.53 (((symdiffE) =>
% 99.66/13.53 (((symdiffI1) =>
% 99.66/13.53 (((symdiffI2) =>
% 99.66/13.53 (((symdiffIneg1) =>
% 99.66/13.53 (((symdiffIneg2) =>
% 99.66/13.53 (((secondinupair) =>
% 99.66/13.53 (((setukpairIL) =>
% 99.66/13.53 (((setukpairIR) =>
% 99.66/13.53 (((kpairiskpair) =>
% 99.66/13.53 (((kpairp) =>
% 99.66/13.53 (((singletonsubset) =>
% 99.66/13.53 (((singletoninpowerset) =>
% 99.66/13.53 (((singletoninpowunion) =>
% 99.66/13.53 (((upairset2E) =>
% 99.66/13.53 (((upairsubunion) =>
% 99.66/13.53 (((upairinpowunion) =>
% 99.66/13.53 (((ubforcartprodlem1) =>
% 99.66/13.53 (((ubforcartprodlem2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ubforcartprodlem3) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairin) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempair1) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempair) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionE2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton1) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I2) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonsuniq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (theprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstin) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR11) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR12) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR1) =>
% 99.66/13.53 ((
% 99.66/13.53 (upairequniteq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (kpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndin) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemEL) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemER) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempaircEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrI) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrSub) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrERa) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrER) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcImageSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (apProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (app) =>
% 99.66/13.53 ((
% 99.66/13.53 (infuncsetfunc) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcinfuncset) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall1) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp3) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcextLem) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp4) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq2) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2lamEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifp) =>
% 99.66/13.53 ((
% 99.66/13.53 (theeq) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrue) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueorfalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setminusT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setextT) =>
% 99.66/13.53 ((
% 99.66/13.53 (subsetTI) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTELcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTERcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT1) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT2) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT3) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub2) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTnotintersectT) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementImpComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementSubsetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementInPowersetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (contraSubsetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTcontraSubset) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTILcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTIRcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion2) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (intersectInPowersetIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpNotIn1) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpInComplement1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTE) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTEcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementUnionInPowersetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule0) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_5) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all2) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1SetBreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (choice2fnsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all1) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compEex) =>
% 99.66/13.53 ((
% 99.66/13.53 (!!) @ (
% 99.66/13.53 (('#B') @ (
% 99.66/13.53 !!) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 !!))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#C') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1223])).
% 99.66/13.53 thf(zip_derived_cl1239, plain,
% 99.66/13.53 (~ (((bs114d) =>
% 99.66/13.53 (((setminusI) =>
% 99.66/13.53 (((setminusEL) =>
% 99.66/13.53 (((setminusER) =>
% 99.66/13.53 (((setminusSubset2) =>
% 99.66/13.53 (((setminusERneg) =>
% 99.66/13.53 (((setminusELneg) =>
% 99.66/13.53 (((setminusILneg) =>
% 99.66/13.53 (((setminusIRneg) =>
% 99.66/13.53 (((setminusLsub) =>
% 99.66/13.53 (((setminusSubset1) =>
% 99.66/13.53 (((symdiffE) =>
% 99.66/13.53 (((symdiffI1) =>
% 99.66/13.53 (((symdiffI2) =>
% 99.66/13.53 (((symdiffIneg1) =>
% 99.66/13.53 (((symdiffIneg2) =>
% 99.66/13.53 (((secondinupair) =>
% 99.66/13.53 (((setukpairIL) =>
% 99.66/13.53 (((setukpairIR) =>
% 99.66/13.53 (((kpairiskpair) =>
% 99.66/13.53 (((kpairp) =>
% 99.66/13.53 (((singletonsubset) =>
% 99.66/13.53 (((singletoninpowerset) =>
% 99.66/13.53 (((singletoninpowunion) =>
% 99.66/13.53 (((upairset2E) =>
% 99.66/13.53 (((upairsubunion) =>
% 99.66/13.53 (((upairinpowunion) =>
% 99.66/13.53 (((ubforcartprodlem1) =>
% 99.66/13.53 (((ubforcartprodlem2) =>
% 99.66/13.53 (((ubforcartprodlem3) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairin) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempair1) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempair) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionE2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton1) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I2) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonsuniq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (theprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstin) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR11) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR12) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR1) =>
% 99.66/13.53 ((
% 99.66/13.53 (upairequniteq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (kpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndin) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemEL) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemER) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempaircEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrI) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrSub) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrERa) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrER) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcImageSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (apProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (app) =>
% 99.66/13.53 ((
% 99.66/13.53 (infuncsetfunc) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcinfuncset) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall1) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp3) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcextLem) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp4) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq2) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2lamEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifp) =>
% 99.66/13.53 ((
% 99.66/13.53 (theeq) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrue) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueorfalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setminusT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setextT) =>
% 99.66/13.53 ((
% 99.66/13.53 (subsetTI) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTELcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTERcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT1) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT2) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT3) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub2) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTnotintersectT) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementImpComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementSubsetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementInPowersetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (contraSubsetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTcontraSubset) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTILcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTIRcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion2) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (intersectInPowersetIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpNotIn1) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpInComplement1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTE) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTEcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementUnionInPowersetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule0) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_5) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all2) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1SetBreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (choice2fnsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all1) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compEex) =>
% 99.66/13.53 ((
% 99.66/13.53 (!!) @ (
% 99.66/13.53 (('#B') @ (
% 99.66/13.53 !!) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 !!))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#C') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1231])).
% 99.66/13.53 thf(zip_derived_cl1247, plain,
% 99.66/13.53 (~ (((setminusI) =>
% 99.66/13.53 (((setminusEL) =>
% 99.66/13.53 (((setminusER) =>
% 99.66/13.53 (((setminusSubset2) =>
% 99.66/13.53 (((setminusERneg) =>
% 99.66/13.53 (((setminusELneg) =>
% 99.66/13.53 (((setminusILneg) =>
% 99.66/13.53 (((setminusIRneg) =>
% 99.66/13.53 (((setminusLsub) =>
% 99.66/13.53 (((setminusSubset1) =>
% 99.66/13.53 (((symdiffE) =>
% 99.66/13.53 (((symdiffI1) =>
% 99.66/13.53 (((symdiffI2) =>
% 99.66/13.53 (((symdiffIneg1) =>
% 99.66/13.53 (((symdiffIneg2) =>
% 99.66/13.53 (((secondinupair) =>
% 99.66/13.53 (((setukpairIL) =>
% 99.66/13.53 (((setukpairIR) =>
% 99.66/13.53 (((kpairiskpair) =>
% 99.66/13.53 (((kpairp) =>
% 99.66/13.53 (((singletonsubset) =>
% 99.66/13.53 (((singletoninpowerset) =>
% 99.66/13.53 (((singletoninpowunion) =>
% 99.66/13.53 (((upairset2E) =>
% 99.66/13.53 (((upairsubunion) =>
% 99.66/13.53 (((upairinpowunion) =>
% 99.66/13.53 (((ubforcartprodlem1) =>
% 99.66/13.53 (((ubforcartprodlem2) =>
% 99.66/13.53 (((ubforcartprodlem3) =>
% 99.66/13.53 (((cartprodpairin) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempair1) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempair) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionE2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton1) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I2) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonsuniq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (theprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstin) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR11) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR12) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR1) =>
% 99.66/13.53 ((
% 99.66/13.53 (upairequniteq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (kpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndin) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemEL) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemER) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempaircEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrI) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrSub) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrERa) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrER) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcImageSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (apProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (app) =>
% 99.66/13.53 ((
% 99.66/13.53 (infuncsetfunc) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcinfuncset) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall1) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp3) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcextLem) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp4) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq2) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2lamEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifp) =>
% 99.66/13.53 ((
% 99.66/13.53 (theeq) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrue) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueorfalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setminusT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setextT) =>
% 99.66/13.53 ((
% 99.66/13.53 (subsetTI) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTELcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTERcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT1) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT2) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT3) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub2) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTnotintersectT) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementImpComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementSubsetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementInPowersetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (contraSubsetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTcontraSubset) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTILcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTIRcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion2) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (intersectInPowersetIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpNotIn1) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpInComplement1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTE) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTEcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementUnionInPowersetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule0) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_5) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all2) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1SetBreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (choice2fnsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all1) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compEex) =>
% 99.66/13.53 ((
% 99.66/13.53 (!!) @ (
% 99.66/13.53 (('#B') @ (
% 99.66/13.53 !!) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 !!))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#C') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1239])).
% 99.66/13.53 thf(zip_derived_cl1255, plain,
% 99.66/13.53 (~ (((setminusEL) =>
% 99.66/13.53 (((setminusER) =>
% 99.66/13.53 (((setminusSubset2) =>
% 99.66/13.53 (((setminusERneg) =>
% 99.66/13.53 (((setminusELneg) =>
% 99.66/13.53 (((setminusILneg) =>
% 99.66/13.53 (((setminusIRneg) =>
% 99.66/13.53 (((setminusLsub) =>
% 99.66/13.53 (((setminusSubset1) =>
% 99.66/13.53 (((symdiffE) =>
% 99.66/13.53 (((symdiffI1) =>
% 99.66/13.53 (((symdiffI2) =>
% 99.66/13.53 (((symdiffIneg1) =>
% 99.66/13.53 (((symdiffIneg2) =>
% 99.66/13.53 (((secondinupair) =>
% 99.66/13.53 (((setukpairIL) =>
% 99.66/13.53 (((setukpairIR) =>
% 99.66/13.53 (((kpairiskpair) =>
% 99.66/13.53 (((kpairp) =>
% 99.66/13.53 (((singletonsubset) =>
% 99.66/13.53 (((singletoninpowerset) =>
% 99.66/13.53 (((singletoninpowunion) =>
% 99.66/13.53 (((upairset2E) =>
% 99.66/13.53 (((upairsubunion) =>
% 99.66/13.53 (((upairinpowunion) =>
% 99.66/13.53 (((ubforcartprodlem1) =>
% 99.66/13.53 (((ubforcartprodlem2) =>
% 99.66/13.53 (((ubforcartprodlem3) =>
% 99.66/13.53 (((cartprodpairin) =>
% 99.66/13.53 (((cartprodmempair1) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempair) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionE2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton1) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I2) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonsuniq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (theprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstin) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR11) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR12) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR1) =>
% 99.66/13.53 ((
% 99.66/13.53 (upairequniteq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (kpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndin) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemEL) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemER) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempaircEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrI) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrSub) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrERa) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrER) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcImageSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (apProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (app) =>
% 99.66/13.53 ((
% 99.66/13.53 (infuncsetfunc) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcinfuncset) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall1) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp3) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcextLem) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp4) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq2) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2lamEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifp) =>
% 99.66/13.53 ((
% 99.66/13.53 (theeq) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrue) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueorfalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setminusT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setextT) =>
% 99.66/13.53 ((
% 99.66/13.53 (subsetTI) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTELcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTERcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT1) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT2) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT3) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub2) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTnotintersectT) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementImpComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementSubsetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementInPowersetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (contraSubsetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTcontraSubset) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTILcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTIRcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInUnion2) =>
% 99.66/13.53 ((
% 99.66/13.53 (inIntersectImpInIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (intersectInPowersetIntersectUnions) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpNotIn1) =>
% 99.66/13.53 ((
% 99.66/13.53 (inComplementUnionImpInComplement1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTE) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionTEcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementUnionInPowersetComplement) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan1) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2a) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b2) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2b) =>
% 99.66/13.53 ((
% 99.66/13.53 (demorgan2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule0) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz13rule4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_1) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_2) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_3) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_4) =>
% 99.66/13.53 ((
% 99.66/13.53 (woz1_5) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all2) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1SetBreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (choice2fnsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1all1) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln1) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1invE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compI) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compE) =>
% 99.66/13.53 ((
% 99.66/13.53 (breln1compEex) =>
% 99.66/13.53 ((
% 99.66/13.53 (!!) @ (
% 99.66/13.53 (('#B') @ (
% 99.66/13.53 !!) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 !!))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#S') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#S') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 =>))) @
% 99.66/13.53 breln1)))))) @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#C') @ (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 (
% 99.66/13.53 (
% 99.66/13.53 ('#B') @ (
% 99.66/13.53 '#B') @
% 99.66/13.53 breln1)))) @
% 99.66/13.53 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1247])).
% 99.66/13.53 thf(zip_derived_cl1264, plain,
% 99.66/13.53 (~ (((setminusER) =>
% 99.66/13.53 (((setminusSubset2) =>
% 99.66/13.53 (((setminusERneg) =>
% 99.66/13.53 (((setminusELneg) =>
% 99.66/13.53 (((setminusILneg) =>
% 99.66/13.53 (((setminusIRneg) =>
% 99.66/13.53 (((setminusLsub) =>
% 99.66/13.53 (((setminusSubset1) =>
% 99.66/13.53 (((symdiffE) =>
% 99.66/13.53 (((symdiffI1) =>
% 99.66/13.53 (((symdiffI2) =>
% 99.66/13.53 (((symdiffIneg1) =>
% 99.66/13.53 (((symdiffIneg2) =>
% 99.66/13.53 (((secondinupair) =>
% 99.66/13.53 (((setukpairIL) =>
% 99.66/13.53 (((setukpairIR) =>
% 99.66/13.53 (((kpairiskpair) =>
% 99.66/13.53 (((kpairp) =>
% 99.66/13.53 (((singletonsubset) =>
% 99.66/13.53 (((singletoninpowerset) =>
% 99.66/13.53 (((singletoninpowunion) =>
% 99.66/13.53 (((upairset2E) =>
% 99.66/13.53 (((upairsubunion) =>
% 99.66/13.53 (((upairinpowunion) =>
% 99.66/13.53 (((ubforcartprodlem1) =>
% 99.66/13.53 (((ubforcartprodlem2) =>
% 99.66/13.53 (((ubforcartprodlem3) =>
% 99.66/13.53 (((cartprodpairin) =>
% 99.66/13.53 (((cartprodmempair1) =>
% 99.66/13.53 (((cartprodmempair) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionE2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton1) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setunionsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1I2) =>
% 99.66/13.53 ((
% 99.66/13.53 (singletonsuniq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (theprop) =>
% 99.66/13.53 ((
% 99.66/13.53 (kfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstin) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjL) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR11) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR12) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR1) =>
% 99.66/13.53 ((
% 99.66/13.53 (upairequniteq) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR2) =>
% 99.66/13.53 ((
% 99.66/13.53 (setukpairinjR) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndsingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ksndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (kpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndin) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemEL) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairmemER) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodmempaircEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodfstpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodsndpairEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (cartprodpairsurjEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrI) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrSub) =>
% 99.66/13.53 ((
% 99.66/13.53 (setOfPairsIsBReln) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrERa) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL1) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrEL2) =>
% 99.66/13.53 ((
% 99.66/13.53 (dpsetconstrER) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcImageSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (apProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (app) =>
% 99.66/13.53 ((
% 99.66/13.53 (infuncsetfunc) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcinfuncset) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamProp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lamp) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2p) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall1) =>
% 99.66/13.53 ((
% 99.66/13.53 (brelnall2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ex1E2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp3) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcextLem) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcGraphProp4) =>
% 99.66/13.53 ((
% 99.66/13.53 (subbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (eqbreln) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext) =>
% 99.66/13.53 ((
% 99.66/13.53 (funcext2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq1) =>
% 99.66/13.53 ((
% 99.66/13.53 (ap2apEq2) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta1) =>
% 99.66/13.53 ((
% 99.66/13.53 (lam2lamEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (beta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (eta2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalseProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp1) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueProp2) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifSingleton) =>
% 99.66/13.53 ((
% 99.66/13.53 (ifp) =>
% 99.66/13.53 ((
% 99.66/13.53 (theeq) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrue) =>
% 99.66/13.53 ((
% 99.66/13.53 (iffalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (iftrueorfalse) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (binunionT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setminusT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementT_lem) =>
% 99.66/13.53 ((
% 99.66/13.53 (setextT) =>
% 99.66/13.53 ((
% 99.66/13.53 (subsetTI) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (powersetTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTELcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (binintersectTERcontra) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT1) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT2) =>
% 99.66/13.53 ((
% 99.66/13.53 (contrasubsetT3) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementI1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementE1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub1) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementSub2) =>
% 99.66/13.53 ((
% 99.66/13.53 (doubleComplementEq) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementTnotintersectT) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementImpComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementSubsetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (complementInPowersetComplementIntersect) =>
% 99.66/13.53 ((
% 99.66/13.53 (contraSubsetComplement) =>
% 99.66/13.53 ((
% 99.66/13.54 (complementTcontraSubset) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTILcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTIRcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion2) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (intersectInPowersetIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpNotIn1) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpInComplement1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTE) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTEcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementUnionInPowersetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule0) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_5) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all2) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1SetBreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (choice2fnsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all1) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compEex) =>
% 99.66/13.54 ((
% 99.66/13.54 (!!) @ (
% 99.66/13.54 (('#B') @ (
% 99.66/13.54 !!) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 !!))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#C') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1255])).
% 99.66/13.54 thf(zip_derived_cl1272, plain,
% 99.66/13.54 (~ (((setminusSubset2) =>
% 99.66/13.54 (((setminusERneg) =>
% 99.66/13.54 (((setminusELneg) =>
% 99.66/13.54 (((setminusILneg) =>
% 99.66/13.54 (((setminusIRneg) =>
% 99.66/13.54 (((setminusLsub) =>
% 99.66/13.54 (((setminusSubset1) =>
% 99.66/13.54 (((symdiffE) =>
% 99.66/13.54 (((symdiffI1) =>
% 99.66/13.54 (((symdiffI2) =>
% 99.66/13.54 (((symdiffIneg1) =>
% 99.66/13.54 (((symdiffIneg2) =>
% 99.66/13.54 (((secondinupair) =>
% 99.66/13.54 (((setukpairIL) =>
% 99.66/13.54 (((setukpairIR) =>
% 99.66/13.54 (((kpairiskpair) =>
% 99.66/13.54 (((kpairp) =>
% 99.66/13.54 (((singletonsubset) =>
% 99.66/13.54 (((singletoninpowerset) =>
% 99.66/13.54 (((singletoninpowunion) =>
% 99.66/13.54 (((upairset2E) =>
% 99.66/13.54 (((upairsubunion) =>
% 99.66/13.54 (((upairinpowunion) =>
% 99.66/13.54 (((ubforcartprodlem1) =>
% 99.66/13.54 (((ubforcartprodlem2) =>
% 99.66/13.54 (((ubforcartprodlem3) =>
% 99.66/13.54 (((cartprodpairin) =>
% 99.66/13.54 (((cartprodmempair1) =>
% 99.66/13.54 (((cartprodmempair) =>
% 99.66/13.54 (((setunionE2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setunionsingleton1) =>
% 99.66/13.54 ((
% 99.66/13.54 (setunionsingleton2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setunionsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (singletonprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1I) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1I2) =>
% 99.66/13.54 ((
% 99.66/13.54 (singletonsuniq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (theprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstin) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR11) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR12) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR1) =>
% 99.66/13.54 ((
% 99.66/13.54 (upairequniteq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (kpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndin) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemEL) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemER) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodmempaircEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrI) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrSub) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrERa) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrER) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcImageSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (apProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (app) =>
% 99.66/13.54 ((
% 99.66/13.54 (infuncsetfunc) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcinfuncset) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall1) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp3) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcextLem) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp4) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq2) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2lamEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifp) =>
% 99.66/13.54 ((
% 99.66/13.54 (theeq) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrue) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueorfalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setminusT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setextT) =>
% 99.66/13.54 ((
% 99.66/13.54 (subsetTI) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTELcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTERcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT1) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT2) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT3) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub2) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTnotintersectT) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementImpComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementSubsetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementInPowersetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (contraSubsetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTcontraSubset) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTILcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTIRcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion2) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (intersectInPowersetIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpNotIn1) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpInComplement1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTE) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTEcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementUnionInPowersetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule0) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_5) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all2) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1SetBreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (choice2fnsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all1) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compEex) =>
% 99.66/13.54 ((
% 99.66/13.54 (!!) @ (
% 99.66/13.54 (('#B') @ (
% 99.66/13.54 !!) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 !!))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#C') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1264])).
% 99.66/13.54 thf(zip_derived_cl1280, plain,
% 99.66/13.54 (~ (((setminusERneg) =>
% 99.66/13.54 (((setminusELneg) =>
% 99.66/13.54 (((setminusILneg) =>
% 99.66/13.54 (((setminusIRneg) =>
% 99.66/13.54 (((setminusLsub) =>
% 99.66/13.54 (((setminusSubset1) =>
% 99.66/13.54 (((symdiffE) =>
% 99.66/13.54 (((symdiffI1) =>
% 99.66/13.54 (((symdiffI2) =>
% 99.66/13.54 (((symdiffIneg1) =>
% 99.66/13.54 (((symdiffIneg2) =>
% 99.66/13.54 (((secondinupair) =>
% 99.66/13.54 (((setukpairIL) =>
% 99.66/13.54 (((setukpairIR) =>
% 99.66/13.54 (((kpairiskpair) =>
% 99.66/13.54 (((kpairp) =>
% 99.66/13.54 (((singletonsubset) =>
% 99.66/13.54 (((singletoninpowerset) =>
% 99.66/13.54 (((singletoninpowunion) =>
% 99.66/13.54 (((upairset2E) =>
% 99.66/13.54 (((upairsubunion) =>
% 99.66/13.54 (((upairinpowunion) =>
% 99.66/13.54 (((ubforcartprodlem1) =>
% 99.66/13.54 (((ubforcartprodlem2) =>
% 99.66/13.54 (((ubforcartprodlem3) =>
% 99.66/13.54 (((cartprodpairin) =>
% 99.66/13.54 (((cartprodmempair1) =>
% 99.66/13.54 (((cartprodmempair) =>
% 99.66/13.54 (((setunionE2) =>
% 99.66/13.54 (((setunionsingleton1) =>
% 99.66/13.54 ((
% 99.66/13.54 (setunionsingleton2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setunionsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (singletonprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1I) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1I2) =>
% 99.66/13.54 ((
% 99.66/13.54 (singletonsuniq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (theprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstin) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR11) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR12) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR1) =>
% 99.66/13.54 ((
% 99.66/13.54 (upairequniteq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (kpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndin) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemEL) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemER) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodmempaircEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrI) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrSub) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrERa) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrER) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcImageSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (apProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (app) =>
% 99.66/13.54 ((
% 99.66/13.54 (infuncsetfunc) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcinfuncset) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall1) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp3) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcextLem) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp4) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq2) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2lamEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifp) =>
% 99.66/13.54 ((
% 99.66/13.54 (theeq) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrue) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueorfalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setminusT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setextT) =>
% 99.66/13.54 ((
% 99.66/13.54 (subsetTI) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTELcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTERcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT1) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT2) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT3) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub2) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTnotintersectT) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementImpComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementSubsetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementInPowersetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (contraSubsetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTcontraSubset) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTILcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTIRcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion2) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (intersectInPowersetIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpNotIn1) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpInComplement1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTE) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTEcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementUnionInPowersetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule0) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_5) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all2) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1SetBreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (choice2fnsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all1) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compEex) =>
% 99.66/13.54 ((
% 99.66/13.54 (!!) @ (
% 99.66/13.54 (('#B') @ (
% 99.66/13.54 !!) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 !!))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#C') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1272])).
% 99.66/13.54 thf(zip_derived_cl1288, plain,
% 99.66/13.54 (~ (((setminusELneg) =>
% 99.66/13.54 (((setminusILneg) =>
% 99.66/13.54 (((setminusIRneg) =>
% 99.66/13.54 (((setminusLsub) =>
% 99.66/13.54 (((setminusSubset1) =>
% 99.66/13.54 (((symdiffE) =>
% 99.66/13.54 (((symdiffI1) =>
% 99.66/13.54 (((symdiffI2) =>
% 99.66/13.54 (((symdiffIneg1) =>
% 99.66/13.54 (((symdiffIneg2) =>
% 99.66/13.54 (((secondinupair) =>
% 99.66/13.54 (((setukpairIL) =>
% 99.66/13.54 (((setukpairIR) =>
% 99.66/13.54 (((kpairiskpair) =>
% 99.66/13.54 (((kpairp) =>
% 99.66/13.54 (((singletonsubset) =>
% 99.66/13.54 (((singletoninpowerset) =>
% 99.66/13.54 (((singletoninpowunion) =>
% 99.66/13.54 (((upairset2E) =>
% 99.66/13.54 (((upairsubunion) =>
% 99.66/13.54 (((upairinpowunion) =>
% 99.66/13.54 (((ubforcartprodlem1) =>
% 99.66/13.54 (((ubforcartprodlem2) =>
% 99.66/13.54 (((ubforcartprodlem3) =>
% 99.66/13.54 (((cartprodpairin) =>
% 99.66/13.54 (((cartprodmempair1) =>
% 99.66/13.54 (((cartprodmempair) =>
% 99.66/13.54 (((setunionE2) =>
% 99.66/13.54 (((setunionsingleton1) =>
% 99.66/13.54 (((setunionsingleton2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setunionsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (singletonprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1I) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1I2) =>
% 99.66/13.54 ((
% 99.66/13.54 (singletonsuniq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (theprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstin) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR11) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR12) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR1) =>
% 99.66/13.54 ((
% 99.66/13.54 (upairequniteq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (kpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndin) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemEL) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemER) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodmempaircEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrI) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrSub) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrERa) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrER) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcImageSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (apProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (app) =>
% 99.66/13.54 ((
% 99.66/13.54 (infuncsetfunc) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcinfuncset) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall1) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp3) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcextLem) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp4) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq2) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2lamEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifp) =>
% 99.66/13.54 ((
% 99.66/13.54 (theeq) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrue) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueorfalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setminusT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setextT) =>
% 99.66/13.54 ((
% 99.66/13.54 (subsetTI) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTELcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTERcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT1) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT2) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT3) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub2) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTnotintersectT) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementImpComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementSubsetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementInPowersetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (contraSubsetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTcontraSubset) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTILcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTIRcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion2) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (intersectInPowersetIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpNotIn1) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpInComplement1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTE) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTEcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementUnionInPowersetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule0) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_5) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all2) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1SetBreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (choice2fnsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all1) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compEex) =>
% 99.66/13.54 ((
% 99.66/13.54 (!!) @ (
% 99.66/13.54 (('#B') @ (
% 99.66/13.54 !!) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 !!))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#C') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1280])).
% 99.66/13.54 thf(zip_derived_cl1296, plain,
% 99.66/13.54 (~ (((setminusILneg) =>
% 99.66/13.54 (((setminusIRneg) =>
% 99.66/13.54 (((setminusLsub) =>
% 99.66/13.54 (((setminusSubset1) =>
% 99.66/13.54 (((symdiffE) =>
% 99.66/13.54 (((symdiffI1) =>
% 99.66/13.54 (((symdiffI2) =>
% 99.66/13.54 (((symdiffIneg1) =>
% 99.66/13.54 (((symdiffIneg2) =>
% 99.66/13.54 (((secondinupair) =>
% 99.66/13.54 (((setukpairIL) =>
% 99.66/13.54 (((setukpairIR) =>
% 99.66/13.54 (((kpairiskpair) =>
% 99.66/13.54 (((kpairp) =>
% 99.66/13.54 (((singletonsubset) =>
% 99.66/13.54 (((singletoninpowerset) =>
% 99.66/13.54 (((singletoninpowunion) =>
% 99.66/13.54 (((upairset2E) =>
% 99.66/13.54 (((upairsubunion) =>
% 99.66/13.54 (((upairinpowunion) =>
% 99.66/13.54 (((ubforcartprodlem1) =>
% 99.66/13.54 (((ubforcartprodlem2) =>
% 99.66/13.54 (((ubforcartprodlem3) =>
% 99.66/13.54 (((cartprodpairin) =>
% 99.66/13.54 (((cartprodmempair1) =>
% 99.66/13.54 (((cartprodmempair) =>
% 99.66/13.54 (((setunionE2) =>
% 99.66/13.54 (((setunionsingleton1) =>
% 99.66/13.54 (((setunionsingleton2) =>
% 99.66/13.54 (((setunionsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (singletonprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1I) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1I2) =>
% 99.66/13.54 ((
% 99.66/13.54 (singletonsuniq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (theprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstin) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR11) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR12) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR1) =>
% 99.66/13.54 ((
% 99.66/13.54 (upairequniteq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (kpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndin) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemEL) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemER) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodmempaircEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrI) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrSub) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrERa) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrER) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcImageSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (apProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (app) =>
% 99.66/13.54 ((
% 99.66/13.54 (infuncsetfunc) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcinfuncset) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall1) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp3) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcextLem) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp4) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq2) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2lamEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifp) =>
% 99.66/13.54 ((
% 99.66/13.54 (theeq) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrue) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueorfalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setminusT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setextT) =>
% 99.66/13.54 ((
% 99.66/13.54 (subsetTI) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTELcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTERcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT1) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT2) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT3) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub2) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTnotintersectT) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementImpComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementSubsetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementInPowersetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (contraSubsetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTcontraSubset) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTILcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTIRcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion2) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (intersectInPowersetIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpNotIn1) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpInComplement1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTE) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTEcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementUnionInPowersetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule0) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_5) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all2) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1SetBreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (choice2fnsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all1) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compEex) =>
% 99.66/13.54 ((
% 99.66/13.54 (!!) @ (
% 99.66/13.54 (('#B') @ (
% 99.66/13.54 !!) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 !!))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#C') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1288])).
% 99.66/13.54 thf(zip_derived_cl1305, plain,
% 99.66/13.54 (~ (((setminusIRneg) =>
% 99.66/13.54 (((setminusLsub) =>
% 99.66/13.54 (((setminusSubset1) =>
% 99.66/13.54 (((symdiffE) =>
% 99.66/13.54 (((symdiffI1) =>
% 99.66/13.54 (((symdiffI2) =>
% 99.66/13.54 (((symdiffIneg1) =>
% 99.66/13.54 (((symdiffIneg2) =>
% 99.66/13.54 (((secondinupair) =>
% 99.66/13.54 (((setukpairIL) =>
% 99.66/13.54 (((setukpairIR) =>
% 99.66/13.54 (((kpairiskpair) =>
% 99.66/13.54 (((kpairp) =>
% 99.66/13.54 (((singletonsubset) =>
% 99.66/13.54 (((singletoninpowerset) =>
% 99.66/13.54 (((singletoninpowunion) =>
% 99.66/13.54 (((upairset2E) =>
% 99.66/13.54 (((upairsubunion) =>
% 99.66/13.54 (((upairinpowunion) =>
% 99.66/13.54 (((ubforcartprodlem1) =>
% 99.66/13.54 (((ubforcartprodlem2) =>
% 99.66/13.54 (((ubforcartprodlem3) =>
% 99.66/13.54 (((cartprodpairin) =>
% 99.66/13.54 (((cartprodmempair1) =>
% 99.66/13.54 (((cartprodmempair) =>
% 99.66/13.54 (((setunionE2) =>
% 99.66/13.54 (((setunionsingleton1) =>
% 99.66/13.54 (((setunionsingleton2) =>
% 99.66/13.54 (((setunionsingleton) =>
% 99.66/13.54 (((singletonprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1I) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1I2) =>
% 99.66/13.54 ((
% 99.66/13.54 (singletonsuniq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (theprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstin) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR11) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR12) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR1) =>
% 99.66/13.54 ((
% 99.66/13.54 (upairequniteq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (kpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndin) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemEL) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemER) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodmempaircEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrI) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrSub) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrERa) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrER) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcImageSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (apProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (app) =>
% 99.66/13.54 ((
% 99.66/13.54 (infuncsetfunc) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcinfuncset) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall1) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp3) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcextLem) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp4) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq2) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2lamEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifp) =>
% 99.66/13.54 ((
% 99.66/13.54 (theeq) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrue) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueorfalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setminusT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setextT) =>
% 99.66/13.54 ((
% 99.66/13.54 (subsetTI) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTELcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTERcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT1) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT2) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT3) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub2) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTnotintersectT) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementImpComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementSubsetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementInPowersetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (contraSubsetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTcontraSubset) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTILcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTIRcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion2) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (intersectInPowersetIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpNotIn1) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpInComplement1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTE) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTEcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementUnionInPowersetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule0) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_5) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all2) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1SetBreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (choice2fnsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all1) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compEex) =>
% 99.66/13.54 ((
% 99.66/13.54 (!!) @ (
% 99.66/13.54 (('#B') @ (
% 99.66/13.54 !!) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 !!))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#C') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1296])).
% 99.66/13.54 thf(zip_derived_cl1313, plain,
% 99.66/13.54 (~ (((setminusLsub) =>
% 99.66/13.54 (((setminusSubset1) =>
% 99.66/13.54 (((symdiffE) =>
% 99.66/13.54 (((symdiffI1) =>
% 99.66/13.54 (((symdiffI2) =>
% 99.66/13.54 (((symdiffIneg1) =>
% 99.66/13.54 (((symdiffIneg2) =>
% 99.66/13.54 (((secondinupair) =>
% 99.66/13.54 (((setukpairIL) =>
% 99.66/13.54 (((setukpairIR) =>
% 99.66/13.54 (((kpairiskpair) =>
% 99.66/13.54 (((kpairp) =>
% 99.66/13.54 (((singletonsubset) =>
% 99.66/13.54 (((singletoninpowerset) =>
% 99.66/13.54 (((singletoninpowunion) =>
% 99.66/13.54 (((upairset2E) =>
% 99.66/13.54 (((upairsubunion) =>
% 99.66/13.54 (((upairinpowunion) =>
% 99.66/13.54 (((ubforcartprodlem1) =>
% 99.66/13.54 (((ubforcartprodlem2) =>
% 99.66/13.54 (((ubforcartprodlem3) =>
% 99.66/13.54 (((cartprodpairin) =>
% 99.66/13.54 (((cartprodmempair1) =>
% 99.66/13.54 (((cartprodmempair) =>
% 99.66/13.54 (((setunionE2) =>
% 99.66/13.54 (((setunionsingleton1) =>
% 99.66/13.54 (((setunionsingleton2) =>
% 99.66/13.54 (((setunionsingleton) =>
% 99.66/13.54 (((singletonprop) =>
% 99.66/13.54 (((ex1E1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1I) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1I2) =>
% 99.66/13.54 ((
% 99.66/13.54 (singletonsuniq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (theprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstin) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR11) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR12) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR1) =>
% 99.66/13.54 ((
% 99.66/13.54 (upairequniteq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (kpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndin) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemEL) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemER) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodmempaircEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrI) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrSub) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrERa) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrER) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcImageSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (apProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (app) =>
% 99.66/13.54 ((
% 99.66/13.54 (infuncsetfunc) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcinfuncset) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall1) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp3) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcextLem) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp4) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq2) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2lamEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifp) =>
% 99.66/13.54 ((
% 99.66/13.54 (theeq) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrue) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueorfalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setminusT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setextT) =>
% 99.66/13.54 ((
% 99.66/13.54 (subsetTI) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTELcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTERcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT1) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT2) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT3) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub2) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTnotintersectT) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementImpComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementSubsetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementInPowersetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (contraSubsetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTcontraSubset) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTILcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTIRcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion2) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (intersectInPowersetIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpNotIn1) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpInComplement1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTE) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTEcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementUnionInPowersetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule0) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_5) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all2) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1SetBreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (choice2fnsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all1) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compEex) =>
% 99.66/13.54 ((
% 99.66/13.54 (!!) @ (
% 99.66/13.54 (('#B') @ (
% 99.66/13.54 !!) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 !!))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#C') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1305])).
% 99.66/13.54 thf(zip_derived_cl1321, plain,
% 99.66/13.54 (~ (((setminusSubset1) =>
% 99.66/13.54 (((symdiffE) =>
% 99.66/13.54 (((symdiffI1) =>
% 99.66/13.54 (((symdiffI2) =>
% 99.66/13.54 (((symdiffIneg1) =>
% 99.66/13.54 (((symdiffIneg2) =>
% 99.66/13.54 (((secondinupair) =>
% 99.66/13.54 (((setukpairIL) =>
% 99.66/13.54 (((setukpairIR) =>
% 99.66/13.54 (((kpairiskpair) =>
% 99.66/13.54 (((kpairp) =>
% 99.66/13.54 (((singletonsubset) =>
% 99.66/13.54 (((singletoninpowerset) =>
% 99.66/13.54 (((singletoninpowunion) =>
% 99.66/13.54 (((upairset2E) =>
% 99.66/13.54 (((upairsubunion) =>
% 99.66/13.54 (((upairinpowunion) =>
% 99.66/13.54 (((ubforcartprodlem1) =>
% 99.66/13.54 (((ubforcartprodlem2) =>
% 99.66/13.54 (((ubforcartprodlem3) =>
% 99.66/13.54 (((cartprodpairin) =>
% 99.66/13.54 (((cartprodmempair1) =>
% 99.66/13.54 (((cartprodmempair) =>
% 99.66/13.54 (((setunionE2) =>
% 99.66/13.54 (((setunionsingleton1) =>
% 99.66/13.54 (((setunionsingleton2) =>
% 99.66/13.54 (((setunionsingleton) =>
% 99.66/13.54 (((singletonprop) =>
% 99.66/13.54 (((ex1E1) =>
% 99.66/13.54 (((ex1I) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1I2) =>
% 99.66/13.54 ((
% 99.66/13.54 (singletonsuniq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (theprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstin) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR11) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR12) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR1) =>
% 99.66/13.54 ((
% 99.66/13.54 (upairequniteq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (kpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndin) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemEL) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemER) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodmempaircEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrI) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrSub) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrERa) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrER) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcImageSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (apProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (app) =>
% 99.66/13.54 ((
% 99.66/13.54 (infuncsetfunc) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcinfuncset) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall1) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp3) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcextLem) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp4) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq2) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2lamEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifp) =>
% 99.66/13.54 ((
% 99.66/13.54 (theeq) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrue) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueorfalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setminusT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setextT) =>
% 99.66/13.54 ((
% 99.66/13.54 (subsetTI) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTELcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTERcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT1) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT2) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT3) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub2) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTnotintersectT) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementImpComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementSubsetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementInPowersetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (contraSubsetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTcontraSubset) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTILcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTIRcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion2) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (intersectInPowersetIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpNotIn1) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpInComplement1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTE) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTEcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementUnionInPowersetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule0) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_5) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all2) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1SetBreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (choice2fnsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all1) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compEex) =>
% 99.66/13.54 ((
% 99.66/13.54 (!!) @ (
% 99.66/13.54 (('#B') @ (
% 99.66/13.54 !!) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 !!))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#C') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1313])).
% 99.66/13.54 thf(zip_derived_cl1329, plain,
% 99.66/13.54 (~ (((symdiffE) =>
% 99.66/13.54 (((symdiffI1) =>
% 99.66/13.54 (((symdiffI2) =>
% 99.66/13.54 (((symdiffIneg1) =>
% 99.66/13.54 (((symdiffIneg2) =>
% 99.66/13.54 (((secondinupair) =>
% 99.66/13.54 (((setukpairIL) =>
% 99.66/13.54 (((setukpairIR) =>
% 99.66/13.54 (((kpairiskpair) =>
% 99.66/13.54 (((kpairp) =>
% 99.66/13.54 (((singletonsubset) =>
% 99.66/13.54 (((singletoninpowerset) =>
% 99.66/13.54 (((singletoninpowunion) =>
% 99.66/13.54 (((upairset2E) =>
% 99.66/13.54 (((upairsubunion) =>
% 99.66/13.54 (((upairinpowunion) =>
% 99.66/13.54 (((ubforcartprodlem1) =>
% 99.66/13.54 (((ubforcartprodlem2) =>
% 99.66/13.54 (((ubforcartprodlem3) =>
% 99.66/13.54 (((cartprodpairin) =>
% 99.66/13.54 (((cartprodmempair1) =>
% 99.66/13.54 (((cartprodmempair) =>
% 99.66/13.54 (((setunionE2) =>
% 99.66/13.54 (((setunionsingleton1) =>
% 99.66/13.54 (((setunionsingleton2) =>
% 99.66/13.54 (((setunionsingleton) =>
% 99.66/13.54 (((singletonprop) =>
% 99.66/13.54 (((ex1E1) =>
% 99.66/13.54 (((ex1I) =>
% 99.66/13.54 (((ex1I2) =>
% 99.66/13.54 ((
% 99.66/13.54 (singletonsuniq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (theprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstin) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR11) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR12) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR1) =>
% 99.66/13.54 ((
% 99.66/13.54 (upairequniteq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (kpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndin) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemEL) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemER) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodmempaircEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrI) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrSub) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrERa) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrER) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcImageSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (apProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (app) =>
% 99.66/13.54 ((
% 99.66/13.54 (infuncsetfunc) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcinfuncset) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall1) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp3) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcextLem) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp4) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq2) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2lamEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifp) =>
% 99.66/13.54 ((
% 99.66/13.54 (theeq) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrue) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueorfalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setminusT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setextT) =>
% 99.66/13.54 ((
% 99.66/13.54 (subsetTI) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTELcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTERcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT1) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT2) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT3) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub2) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTnotintersectT) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementImpComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementSubsetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementInPowersetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (contraSubsetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTcontraSubset) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTILcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTIRcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion2) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (intersectInPowersetIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpNotIn1) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpInComplement1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTE) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTEcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementUnionInPowersetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule0) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_5) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all2) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1SetBreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (choice2fnsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all1) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compEex) =>
% 99.66/13.54 ((
% 99.66/13.54 (!!) @ (
% 99.66/13.54 (('#B') @ (
% 99.66/13.54 !!) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 !!))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#C') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1321])).
% 99.66/13.54 thf(zip_derived_cl1338, plain,
% 99.66/13.54 (~ (((symdiffI1) =>
% 99.66/13.54 (((symdiffI2) =>
% 99.66/13.54 (((symdiffIneg1) =>
% 99.66/13.54 (((symdiffIneg2) =>
% 99.66/13.54 (((secondinupair) =>
% 99.66/13.54 (((setukpairIL) =>
% 99.66/13.54 (((setukpairIR) =>
% 99.66/13.54 (((kpairiskpair) =>
% 99.66/13.54 (((kpairp) =>
% 99.66/13.54 (((singletonsubset) =>
% 99.66/13.54 (((singletoninpowerset) =>
% 99.66/13.54 (((singletoninpowunion) =>
% 99.66/13.54 (((upairset2E) =>
% 99.66/13.54 (((upairsubunion) =>
% 99.66/13.54 (((upairinpowunion) =>
% 99.66/13.54 (((ubforcartprodlem1) =>
% 99.66/13.54 (((ubforcartprodlem2) =>
% 99.66/13.54 (((ubforcartprodlem3) =>
% 99.66/13.54 (((cartprodpairin) =>
% 99.66/13.54 (((cartprodmempair1) =>
% 99.66/13.54 (((cartprodmempair) =>
% 99.66/13.54 (((setunionE2) =>
% 99.66/13.54 (((setunionsingleton1) =>
% 99.66/13.54 (((setunionsingleton2) =>
% 99.66/13.54 (((setunionsingleton) =>
% 99.66/13.54 (((singletonprop) =>
% 99.66/13.54 (((ex1E1) =>
% 99.66/13.54 (((ex1I) =>
% 99.66/13.54 (((ex1I2) =>
% 99.66/13.54 (((singletonsuniq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (theprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstin) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR11) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR12) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR1) =>
% 99.66/13.54 ((
% 99.66/13.54 (upairequniteq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (kpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndin) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemEL) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemER) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodmempaircEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrI) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrSub) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrERa) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrER) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcImageSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (apProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (app) =>
% 99.66/13.54 ((
% 99.66/13.54 (infuncsetfunc) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcinfuncset) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall1) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp3) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcextLem) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp4) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq2) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2lamEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifp) =>
% 99.66/13.54 ((
% 99.66/13.54 (theeq) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrue) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueorfalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setminusT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setextT) =>
% 99.66/13.54 ((
% 99.66/13.54 (subsetTI) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTELcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTERcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT1) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT2) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT3) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub2) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTnotintersectT) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementImpComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementSubsetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementInPowersetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (contraSubsetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTcontraSubset) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTILcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTIRcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion2) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (intersectInPowersetIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpNotIn1) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpInComplement1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTE) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTEcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementUnionInPowersetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule0) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_5) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all2) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1SetBreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (choice2fnsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all1) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compEex) =>
% 99.66/13.54 ((
% 99.66/13.54 (!!) @ (
% 99.66/13.54 (('#B') @ (
% 99.66/13.54 !!) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 !!))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#C') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1329])).
% 99.66/13.54 thf(zip_derived_cl1347, plain,
% 99.66/13.54 (~ (((symdiffI2) =>
% 99.66/13.54 (((symdiffIneg1) =>
% 99.66/13.54 (((symdiffIneg2) =>
% 99.66/13.54 (((secondinupair) =>
% 99.66/13.54 (((setukpairIL) =>
% 99.66/13.54 (((setukpairIR) =>
% 99.66/13.54 (((kpairiskpair) =>
% 99.66/13.54 (((kpairp) =>
% 99.66/13.54 (((singletonsubset) =>
% 99.66/13.54 (((singletoninpowerset) =>
% 99.66/13.54 (((singletoninpowunion) =>
% 99.66/13.54 (((upairset2E) =>
% 99.66/13.54 (((upairsubunion) =>
% 99.66/13.54 (((upairinpowunion) =>
% 99.66/13.54 (((ubforcartprodlem1) =>
% 99.66/13.54 (((ubforcartprodlem2) =>
% 99.66/13.54 (((ubforcartprodlem3) =>
% 99.66/13.54 (((cartprodpairin) =>
% 99.66/13.54 (((cartprodmempair1) =>
% 99.66/13.54 (((cartprodmempair) =>
% 99.66/13.54 (((setunionE2) =>
% 99.66/13.54 (((setunionsingleton1) =>
% 99.66/13.54 (((setunionsingleton2) =>
% 99.66/13.54 (((setunionsingleton) =>
% 99.66/13.54 (((singletonprop) =>
% 99.66/13.54 (((ex1E1) =>
% 99.66/13.54 (((ex1I) =>
% 99.66/13.54 (((ex1I2) =>
% 99.66/13.54 (((singletonsuniq) =>
% 99.66/13.54 (((setukpairinjL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (theprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstin) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR11) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR12) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR1) =>
% 99.66/13.54 ((
% 99.66/13.54 (upairequniteq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (kpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndin) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemEL) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemER) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodmempaircEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrI) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrSub) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrERa) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrER) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcImageSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (apProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (app) =>
% 99.66/13.54 ((
% 99.66/13.54 (infuncsetfunc) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcinfuncset) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall1) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp3) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcextLem) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp4) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq2) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2lamEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifp) =>
% 99.66/13.54 ((
% 99.66/13.54 (theeq) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrue) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueorfalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setminusT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setextT) =>
% 99.66/13.54 ((
% 99.66/13.54 (subsetTI) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTELcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTERcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT1) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT2) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT3) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub2) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTnotintersectT) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementImpComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementSubsetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementInPowersetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (contraSubsetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTcontraSubset) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTILcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTIRcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion2) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (intersectInPowersetIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpNotIn1) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpInComplement1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTE) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTEcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementUnionInPowersetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule0) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_5) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all2) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1SetBreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (choice2fnsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all1) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compEex) =>
% 99.66/13.54 ((
% 99.66/13.54 (!!) @ (
% 99.66/13.54 (('#B') @ (
% 99.66/13.54 !!) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 !!))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#C') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1338])).
% 99.66/13.54 thf(zip_derived_cl1354, plain,
% 99.66/13.54 (~ (((symdiffIneg1) =>
% 99.66/13.54 (((symdiffIneg2) =>
% 99.66/13.54 (((secondinupair) =>
% 99.66/13.54 (((setukpairIL) =>
% 99.66/13.54 (((setukpairIR) =>
% 99.66/13.54 (((kpairiskpair) =>
% 99.66/13.54 (((kpairp) =>
% 99.66/13.54 (((singletonsubset) =>
% 99.66/13.54 (((singletoninpowerset) =>
% 99.66/13.54 (((singletoninpowunion) =>
% 99.66/13.54 (((upairset2E) =>
% 99.66/13.54 (((upairsubunion) =>
% 99.66/13.54 (((upairinpowunion) =>
% 99.66/13.54 (((ubforcartprodlem1) =>
% 99.66/13.54 (((ubforcartprodlem2) =>
% 99.66/13.54 (((ubforcartprodlem3) =>
% 99.66/13.54 (((cartprodpairin) =>
% 99.66/13.54 (((cartprodmempair1) =>
% 99.66/13.54 (((cartprodmempair) =>
% 99.66/13.54 (((setunionE2) =>
% 99.66/13.54 (((setunionsingleton1) =>
% 99.66/13.54 (((setunionsingleton2) =>
% 99.66/13.54 (((setunionsingleton) =>
% 99.66/13.54 (((singletonprop) =>
% 99.66/13.54 (((ex1E1) =>
% 99.66/13.54 (((ex1I) =>
% 99.66/13.54 (((ex1I2) =>
% 99.66/13.54 (((singletonsuniq) =>
% 99.66/13.54 (((setukpairinjL1) =>
% 99.66/13.54 (((kfstsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (theprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstin) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR11) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR12) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR1) =>
% 99.66/13.54 ((
% 99.66/13.54 (upairequniteq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (kpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndin) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemEL) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemER) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodmempaircEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrI) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrSub) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrERa) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrER) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcImageSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (apProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (app) =>
% 99.66/13.54 ((
% 99.66/13.54 (infuncsetfunc) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcinfuncset) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall1) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp3) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcextLem) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp4) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq2) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2lamEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifp) =>
% 99.66/13.54 ((
% 99.66/13.54 (theeq) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrue) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueorfalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setminusT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setextT) =>
% 99.66/13.54 ((
% 99.66/13.54 (subsetTI) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTELcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTERcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT1) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT2) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT3) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub2) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTnotintersectT) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementImpComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementSubsetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementInPowersetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (contraSubsetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTcontraSubset) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTILcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTIRcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion2) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (intersectInPowersetIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpNotIn1) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpInComplement1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTE) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTEcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementUnionInPowersetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule0) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_5) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all2) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1SetBreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (choice2fnsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all1) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compEex) =>
% 99.66/13.54 ((
% 99.66/13.54 (!!) @ (
% 99.66/13.54 (('#B') @ (
% 99.66/13.54 !!) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 !!))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#C') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1347])).
% 99.66/13.54 thf(zip_derived_cl1361, plain,
% 99.66/13.54 (~ (((symdiffIneg2) =>
% 99.66/13.54 (((secondinupair) =>
% 99.66/13.54 (((setukpairIL) =>
% 99.66/13.54 (((setukpairIR) =>
% 99.66/13.54 (((kpairiskpair) =>
% 99.66/13.54 (((kpairp) =>
% 99.66/13.54 (((singletonsubset) =>
% 99.66/13.54 (((singletoninpowerset) =>
% 99.66/13.54 (((singletoninpowunion) =>
% 99.66/13.54 (((upairset2E) =>
% 99.66/13.54 (((upairsubunion) =>
% 99.66/13.54 (((upairinpowunion) =>
% 99.66/13.54 (((ubforcartprodlem1) =>
% 99.66/13.54 (((ubforcartprodlem2) =>
% 99.66/13.54 (((ubforcartprodlem3) =>
% 99.66/13.54 (((cartprodpairin) =>
% 99.66/13.54 (((cartprodmempair1) =>
% 99.66/13.54 (((cartprodmempair) =>
% 99.66/13.54 (((setunionE2) =>
% 99.66/13.54 (((setunionsingleton1) =>
% 99.66/13.54 (((setunionsingleton2) =>
% 99.66/13.54 (((setunionsingleton) =>
% 99.66/13.54 (((singletonprop) =>
% 99.66/13.54 (((ex1E1) =>
% 99.66/13.54 (((ex1I) =>
% 99.66/13.54 (((ex1I2) =>
% 99.66/13.54 (((singletonsuniq) =>
% 99.66/13.54 (((setukpairinjL1) =>
% 99.66/13.54 (((kfstsingleton) =>
% 99.66/13.54 (((theprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (kfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstin) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR11) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR12) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR1) =>
% 99.66/13.54 ((
% 99.66/13.54 (upairequniteq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (kpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndin) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemEL) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemER) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodmempaircEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrI) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrSub) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrERa) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrER) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcImageSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (apProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (app) =>
% 99.66/13.54 ((
% 99.66/13.54 (infuncsetfunc) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcinfuncset) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall1) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp3) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcextLem) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp4) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq2) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2lamEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifp) =>
% 99.66/13.54 ((
% 99.66/13.54 (theeq) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrue) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueorfalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setminusT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setextT) =>
% 99.66/13.54 ((
% 99.66/13.54 (subsetTI) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTELcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTERcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT1) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT2) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT3) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub2) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTnotintersectT) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementImpComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementSubsetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementInPowersetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (contraSubsetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTcontraSubset) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTILcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTIRcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion2) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (intersectInPowersetIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpNotIn1) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpInComplement1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTE) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTEcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementUnionInPowersetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule0) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_5) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all2) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1SetBreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (choice2fnsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all1) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compEex) =>
% 99.66/13.54 ((
% 99.66/13.54 (!!) @ (
% 99.66/13.54 (('#B') @ (
% 99.66/13.54 !!) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 !!))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#C') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1354])).
% 99.66/13.54 thf(zip_derived_cl1369, plain,
% 99.66/13.54 (~ (((secondinupair) =>
% 99.66/13.54 (((setukpairIL) =>
% 99.66/13.54 (((setukpairIR) =>
% 99.66/13.54 (((kpairiskpair) =>
% 99.66/13.54 (((kpairp) =>
% 99.66/13.54 (((singletonsubset) =>
% 99.66/13.54 (((singletoninpowerset) =>
% 99.66/13.54 (((singletoninpowunion) =>
% 99.66/13.54 (((upairset2E) =>
% 99.66/13.54 (((upairsubunion) =>
% 99.66/13.54 (((upairinpowunion) =>
% 99.66/13.54 (((ubforcartprodlem1) =>
% 99.66/13.54 (((ubforcartprodlem2) =>
% 99.66/13.54 (((ubforcartprodlem3) =>
% 99.66/13.54 (((cartprodpairin) =>
% 99.66/13.54 (((cartprodmempair1) =>
% 99.66/13.54 (((cartprodmempair) =>
% 99.66/13.54 (((setunionE2) =>
% 99.66/13.54 (((setunionsingleton1) =>
% 99.66/13.54 (((setunionsingleton2) =>
% 99.66/13.54 (((setunionsingleton) =>
% 99.66/13.54 (((singletonprop) =>
% 99.66/13.54 (((ex1E1) =>
% 99.66/13.54 (((ex1I) =>
% 99.66/13.54 (((ex1I2) =>
% 99.66/13.54 (((singletonsuniq) =>
% 99.66/13.54 (((setukpairinjL1) =>
% 99.66/13.54 (((kfstsingleton) =>
% 99.66/13.54 (((theprop) =>
% 99.66/13.54 (((kfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstin) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR11) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR12) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR1) =>
% 99.66/13.54 ((
% 99.66/13.54 (upairequniteq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (kpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndin) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemEL) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemER) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodmempaircEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrI) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrSub) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrERa) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrER) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcImageSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (apProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (app) =>
% 99.66/13.54 ((
% 99.66/13.54 (infuncsetfunc) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcinfuncset) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall1) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp3) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcextLem) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp4) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq2) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2lamEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifp) =>
% 99.66/13.54 ((
% 99.66/13.54 (theeq) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrue) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueorfalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setminusT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (setextT) =>
% 99.66/13.54 ((
% 99.66/13.54 (subsetTI) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (powersetTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTELcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectTERcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT1) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT2) =>
% 99.66/13.54 ((
% 99.66/13.54 (contrasubsetT3) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementI1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementE1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub1) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementSub2) =>
% 99.66/13.54 ((
% 99.66/13.54 (doubleComplementEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTnotintersectT) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementImpComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementSubsetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementInPowersetComplementIntersect) =>
% 99.66/13.54 ((
% 99.66/13.54 (contraSubsetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementTcontraSubset) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTILcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTIRcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInUnion2) =>
% 99.66/13.54 ((
% 99.66/13.54 (inIntersectImpInIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (intersectInPowersetIntersectUnions) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpNotIn1) =>
% 99.66/13.54 ((
% 99.66/13.54 (inComplementUnionImpInComplement1) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTE) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionTEcontra) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a1) =>
% 99.66/13.54 ((
% 99.66/13.54 (complementUnionInPowersetComplement) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan1) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2a) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b2) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2b) =>
% 99.66/13.54 ((
% 99.66/13.54 (demorgan2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule0) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz13rule4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_1) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_2) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_3) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_4) =>
% 99.66/13.54 ((
% 99.66/13.54 (woz1_5) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all2) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1SetBreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (choice2fnsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1all1) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln1) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1invE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compprop) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compI) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compE) =>
% 99.66/13.54 ((
% 99.66/13.54 (breln1compEex) =>
% 99.66/13.54 ((
% 99.66/13.54 (!!) @ (
% 99.66/13.54 (('#B') @ (
% 99.66/13.54 !!) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 !!))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#S') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#S') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 =>))) @
% 99.66/13.54 breln1)))))) @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#C') @ (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 (
% 99.66/13.54 (
% 99.66/13.54 ('#B') @ (
% 99.66/13.54 '#B') @
% 99.66/13.54 breln1)))) @
% 99.66/13.54 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])).
% 99.66/13.54 thf(zip_derived_cl1377, plain,
% 99.66/13.54 (~ (((setukpairIL) =>
% 99.66/13.54 (((setukpairIR) =>
% 99.66/13.54 (((kpairiskpair) =>
% 99.66/13.54 (((kpairp) =>
% 99.66/13.54 (((singletonsubset) =>
% 99.66/13.54 (((singletoninpowerset) =>
% 99.66/13.54 (((singletoninpowunion) =>
% 99.66/13.54 (((upairset2E) =>
% 99.66/13.54 (((upairsubunion) =>
% 99.66/13.54 (((upairinpowunion) =>
% 99.66/13.54 (((ubforcartprodlem1) =>
% 99.66/13.54 (((ubforcartprodlem2) =>
% 99.66/13.54 (((ubforcartprodlem3) =>
% 99.66/13.54 (((cartprodpairin) =>
% 99.66/13.54 (((cartprodmempair1) =>
% 99.66/13.54 (((cartprodmempair) =>
% 99.66/13.54 (((setunionE2) =>
% 99.66/13.54 (((setunionsingleton1) =>
% 99.66/13.54 (((setunionsingleton2) =>
% 99.66/13.54 (((setunionsingleton) =>
% 99.66/13.54 (((singletonprop) =>
% 99.66/13.54 (((ex1E1) =>
% 99.66/13.54 (((ex1I) =>
% 99.66/13.54 (((ex1I2) =>
% 99.66/13.54 (((singletonsuniq) =>
% 99.66/13.54 (((setukpairinjL1) =>
% 99.66/13.54 (((kfstsingleton) =>
% 99.66/13.54 (((theprop) =>
% 99.66/13.54 (((kfstpairEq) =>
% 99.66/13.54 (((cartprodfstin) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjL) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR11) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR12) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR1) =>
% 99.66/13.54 ((
% 99.66/13.54 (upairequniteq) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR2) =>
% 99.66/13.54 ((
% 99.66/13.54 (setukpairinjR) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndsingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ksndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (kpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndin) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemEL) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairmemER) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodmempaircEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodfstpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodsndpairEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (cartprodpairsurjEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrI) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrSub) =>
% 99.66/13.54 ((
% 99.66/13.54 (setOfPairsIsBReln) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrERa) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL1) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrEL2) =>
% 99.66/13.54 ((
% 99.66/13.54 (dpsetconstrER) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcImageSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (apProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (app) =>
% 99.66/13.54 ((
% 99.66/13.54 (infuncsetfunc) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcinfuncset) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamProp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lamp) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2p) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall1) =>
% 99.66/13.54 ((
% 99.66/13.54 (brelnall2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ex1E2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp3) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcextLem) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcGraphProp4) =>
% 99.66/13.54 ((
% 99.66/13.54 (subbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (eqbreln) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext) =>
% 99.66/13.54 ((
% 99.66/13.54 (funcext2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq1) =>
% 99.66/13.54 ((
% 99.66/13.54 (ap2apEq2) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta1) =>
% 99.66/13.54 ((
% 99.66/13.54 (lam2lamEq) =>
% 99.66/13.54 ((
% 99.66/13.54 (beta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (eta2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalseProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp1) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueProp2) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifSingleton) =>
% 99.66/13.54 ((
% 99.66/13.54 (ifp) =>
% 99.66/13.54 ((
% 99.66/13.54 (theeq) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrue) =>
% 99.66/13.54 ((
% 99.66/13.54 (iffalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (iftrueorfalse) =>
% 99.66/13.54 ((
% 99.66/13.54 (binintersectT_lem) =>
% 99.66/13.54 ((
% 99.66/13.54 (binunionT_lem) =>
% 99.66/13.54 ((
% 99.66/13.55 (powersetT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setminusT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setextT) =>
% 99.66/13.55 ((
% 99.66/13.55 (subsetTI) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTELcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTERcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT1) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT2) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT3) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub2) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTnotintersectT) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementImpComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementSubsetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementInPowersetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (contraSubsetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTcontraSubset) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTILcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTIRcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion2) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (intersectInPowersetIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpNotIn1) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpInComplement1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTE) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTEcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementUnionInPowersetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule0) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_5) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all2) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1SetBreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (choice2fnsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all1) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compEex) =>
% 99.66/13.55 ((
% 99.66/13.55 (!!) @ (
% 99.66/13.55 (('#B') @ (
% 99.66/13.55 !!) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 !!))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#C') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1369])).
% 99.66/13.55 thf(zip_derived_cl1386, plain,
% 99.66/13.55 (~ (((setukpairIR) =>
% 99.66/13.55 (((kpairiskpair) =>
% 99.66/13.55 (((kpairp) =>
% 99.66/13.55 (((singletonsubset) =>
% 99.66/13.55 (((singletoninpowerset) =>
% 99.66/13.55 (((singletoninpowunion) =>
% 99.66/13.55 (((upairset2E) =>
% 99.66/13.55 (((upairsubunion) =>
% 99.66/13.55 (((upairinpowunion) =>
% 99.66/13.55 (((ubforcartprodlem1) =>
% 99.66/13.55 (((ubforcartprodlem2) =>
% 99.66/13.55 (((ubforcartprodlem3) =>
% 99.66/13.55 (((cartprodpairin) =>
% 99.66/13.55 (((cartprodmempair1) =>
% 99.66/13.55 (((cartprodmempair) =>
% 99.66/13.55 (((setunionE2) =>
% 99.66/13.55 (((setunionsingleton1) =>
% 99.66/13.55 (((setunionsingleton2) =>
% 99.66/13.55 (((setunionsingleton) =>
% 99.66/13.55 (((singletonprop) =>
% 99.66/13.55 (((ex1E1) =>
% 99.66/13.55 (((ex1I) =>
% 99.66/13.55 (((ex1I2) =>
% 99.66/13.55 (((singletonsuniq) =>
% 99.66/13.55 (((setukpairinjL1) =>
% 99.66/13.55 (((kfstsingleton) =>
% 99.66/13.55 (((theprop) =>
% 99.66/13.55 (((kfstpairEq) =>
% 99.66/13.55 (((cartprodfstin) =>
% 99.66/13.55 (((setukpairinjL2) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjL) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR11) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR12) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR1) =>
% 99.66/13.55 ((
% 99.66/13.55 (upairequniteq) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR2) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR) =>
% 99.66/13.55 ((
% 99.66/13.55 (ksndsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ksndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (kpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndin) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemEL) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemER) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodmempaircEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodfstpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrI) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrSub) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrERa) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL1) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL2) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrER) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcImageSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (apProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (app) =>
% 99.66/13.55 ((
% 99.66/13.55 (infuncsetfunc) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcinfuncset) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall1) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ex1E2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp3) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcextLem) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp4) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq1) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq2) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2lamEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifp) =>
% 99.66/13.55 ((
% 99.66/13.55 (theeq) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrue) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueorfalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setminusT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setextT) =>
% 99.66/13.55 ((
% 99.66/13.55 (subsetTI) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTELcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTERcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT1) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT2) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT3) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub2) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTnotintersectT) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementImpComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementSubsetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementInPowersetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (contraSubsetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTcontraSubset) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTILcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTIRcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion2) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (intersectInPowersetIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpNotIn1) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpInComplement1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTE) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTEcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementUnionInPowersetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule0) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_5) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all2) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1SetBreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (choice2fnsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all1) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compEex) =>
% 99.66/13.55 ((
% 99.66/13.55 (!!) @ (
% 99.66/13.55 (('#B') @ (
% 99.66/13.55 !!) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 !!))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#C') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1377])).
% 99.66/13.55 thf(zip_derived_cl1396, plain,
% 99.66/13.55 (~ (((kpairiskpair) =>
% 99.66/13.55 (((kpairp) =>
% 99.66/13.55 (((singletonsubset) =>
% 99.66/13.55 (((singletoninpowerset) =>
% 99.66/13.55 (((singletoninpowunion) =>
% 99.66/13.55 (((upairset2E) =>
% 99.66/13.55 (((upairsubunion) =>
% 99.66/13.55 (((upairinpowunion) =>
% 99.66/13.55 (((ubforcartprodlem1) =>
% 99.66/13.55 (((ubforcartprodlem2) =>
% 99.66/13.55 (((ubforcartprodlem3) =>
% 99.66/13.55 (((cartprodpairin) =>
% 99.66/13.55 (((cartprodmempair1) =>
% 99.66/13.55 (((cartprodmempair) =>
% 99.66/13.55 (((setunionE2) =>
% 99.66/13.55 (((setunionsingleton1) =>
% 99.66/13.55 (((setunionsingleton2) =>
% 99.66/13.55 (((setunionsingleton) =>
% 99.66/13.55 (((singletonprop) =>
% 99.66/13.55 (((ex1E1) =>
% 99.66/13.55 (((ex1I) =>
% 99.66/13.55 (((ex1I2) =>
% 99.66/13.55 (((singletonsuniq) =>
% 99.66/13.55 (((setukpairinjL1) =>
% 99.66/13.55 (((kfstsingleton) =>
% 99.66/13.55 (((theprop) =>
% 99.66/13.55 (((kfstpairEq) =>
% 99.66/13.55 (((cartprodfstin) =>
% 99.66/13.55 (((setukpairinjL2) =>
% 99.66/13.55 (((setukpairinjL) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR11) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR12) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR1) =>
% 99.66/13.55 ((
% 99.66/13.55 (upairequniteq) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR2) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR) =>
% 99.66/13.55 ((
% 99.66/13.55 (ksndsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ksndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (kpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndin) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemEL) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemER) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodmempaircEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodfstpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrI) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrSub) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrERa) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL1) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL2) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrER) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcImageSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (apProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (app) =>
% 99.66/13.55 ((
% 99.66/13.55 (infuncsetfunc) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcinfuncset) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall1) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ex1E2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp3) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcextLem) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp4) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq1) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq2) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2lamEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifp) =>
% 99.66/13.55 ((
% 99.66/13.55 (theeq) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrue) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueorfalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setminusT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setextT) =>
% 99.66/13.55 ((
% 99.66/13.55 (subsetTI) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTELcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTERcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT1) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT2) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT3) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub2) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTnotintersectT) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementImpComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementSubsetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementInPowersetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (contraSubsetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTcontraSubset) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTILcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTIRcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion2) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (intersectInPowersetIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpNotIn1) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpInComplement1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTE) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTEcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementUnionInPowersetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule0) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_5) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all2) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1SetBreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (choice2fnsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all1) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compEex) =>
% 99.66/13.55 ((
% 99.66/13.55 (!!) @ (
% 99.66/13.55 (('#B') @ (
% 99.66/13.55 !!) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 !!))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#C') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1386])).
% 99.66/13.55 thf(zip_derived_cl1407, plain,
% 99.66/13.55 (~ (((kpairp) =>
% 99.66/13.55 (((singletonsubset) =>
% 99.66/13.55 (((singletoninpowerset) =>
% 99.66/13.55 (((singletoninpowunion) =>
% 99.66/13.55 (((upairset2E) =>
% 99.66/13.55 (((upairsubunion) =>
% 99.66/13.55 (((upairinpowunion) =>
% 99.66/13.55 (((ubforcartprodlem1) =>
% 99.66/13.55 (((ubforcartprodlem2) =>
% 99.66/13.55 (((ubforcartprodlem3) =>
% 99.66/13.55 (((cartprodpairin) =>
% 99.66/13.55 (((cartprodmempair1) =>
% 99.66/13.55 (((cartprodmempair) =>
% 99.66/13.55 (((setunionE2) =>
% 99.66/13.55 (((setunionsingleton1) =>
% 99.66/13.55 (((setunionsingleton2) =>
% 99.66/13.55 (((setunionsingleton) =>
% 99.66/13.55 (((singletonprop) =>
% 99.66/13.55 (((ex1E1) =>
% 99.66/13.55 (((ex1I) =>
% 99.66/13.55 (((ex1I2) =>
% 99.66/13.55 (((singletonsuniq) =>
% 99.66/13.55 (((setukpairinjL1) =>
% 99.66/13.55 (((kfstsingleton) =>
% 99.66/13.55 (((theprop) =>
% 99.66/13.55 (((kfstpairEq) =>
% 99.66/13.55 (((cartprodfstin) =>
% 99.66/13.55 (((setukpairinjL2) =>
% 99.66/13.55 (((setukpairinjL) =>
% 99.66/13.55 (((setukpairinjR11) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR12) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR1) =>
% 99.66/13.55 ((
% 99.66/13.55 (upairequniteq) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR2) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR) =>
% 99.66/13.55 ((
% 99.66/13.55 (ksndsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ksndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (kpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndin) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemEL) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemER) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodmempaircEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodfstpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrI) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrSub) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrERa) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL1) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL2) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrER) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcImageSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (apProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (app) =>
% 99.66/13.55 ((
% 99.66/13.55 (infuncsetfunc) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcinfuncset) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall1) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ex1E2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp3) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcextLem) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp4) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq1) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq2) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2lamEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifp) =>
% 99.66/13.55 ((
% 99.66/13.55 (theeq) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrue) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueorfalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setminusT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setextT) =>
% 99.66/13.55 ((
% 99.66/13.55 (subsetTI) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTELcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTERcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT1) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT2) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT3) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub2) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTnotintersectT) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementImpComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementSubsetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementInPowersetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (contraSubsetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTcontraSubset) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTILcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTIRcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion2) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (intersectInPowersetIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpNotIn1) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpInComplement1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTE) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTEcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementUnionInPowersetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule0) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_5) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all2) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1SetBreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (choice2fnsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all1) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compEex) =>
% 99.66/13.55 ((
% 99.66/13.55 (!!) @ (
% 99.66/13.55 (('#B') @ (
% 99.66/13.55 !!) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 !!))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#C') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1396])).
% 99.66/13.55 thf(zip_derived_cl1420, plain,
% 99.66/13.55 (~ (((singletonsubset) =>
% 99.66/13.55 (((singletoninpowerset) =>
% 99.66/13.55 (((singletoninpowunion) =>
% 99.66/13.55 (((upairset2E) =>
% 99.66/13.55 (((upairsubunion) =>
% 99.66/13.55 (((upairinpowunion) =>
% 99.66/13.55 (((ubforcartprodlem1) =>
% 99.66/13.55 (((ubforcartprodlem2) =>
% 99.66/13.55 (((ubforcartprodlem3) =>
% 99.66/13.55 (((cartprodpairin) =>
% 99.66/13.55 (((cartprodmempair1) =>
% 99.66/13.55 (((cartprodmempair) =>
% 99.66/13.55 (((setunionE2) =>
% 99.66/13.55 (((setunionsingleton1) =>
% 99.66/13.55 (((setunionsingleton2) =>
% 99.66/13.55 (((setunionsingleton) =>
% 99.66/13.55 (((singletonprop) =>
% 99.66/13.55 (((ex1E1) =>
% 99.66/13.55 (((ex1I) =>
% 99.66/13.55 (((ex1I2) =>
% 99.66/13.55 (((singletonsuniq) =>
% 99.66/13.55 (((setukpairinjL1) =>
% 99.66/13.55 (((kfstsingleton) =>
% 99.66/13.55 (((theprop) =>
% 99.66/13.55 (((kfstpairEq) =>
% 99.66/13.55 (((cartprodfstin) =>
% 99.66/13.55 (((setukpairinjL2) =>
% 99.66/13.55 (((setukpairinjL) =>
% 99.66/13.55 (((setukpairinjR11) =>
% 99.66/13.55 (((setukpairinjR12) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR1) =>
% 99.66/13.55 ((
% 99.66/13.55 (upairequniteq) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR2) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR) =>
% 99.66/13.55 ((
% 99.66/13.55 (ksndsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ksndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (kpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndin) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemEL) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemER) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodmempaircEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodfstpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrI) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrSub) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrERa) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL1) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL2) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrER) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcImageSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (apProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (app) =>
% 99.66/13.55 ((
% 99.66/13.55 (infuncsetfunc) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcinfuncset) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall1) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ex1E2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp3) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcextLem) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp4) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq1) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq2) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2lamEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifp) =>
% 99.66/13.55 ((
% 99.66/13.55 (theeq) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrue) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueorfalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setminusT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setextT) =>
% 99.66/13.55 ((
% 99.66/13.55 (subsetTI) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTELcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTERcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT1) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT2) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT3) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub2) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTnotintersectT) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementImpComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementSubsetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementInPowersetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (contraSubsetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTcontraSubset) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTILcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTIRcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion2) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (intersectInPowersetIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpNotIn1) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpInComplement1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTE) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTEcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementUnionInPowersetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule0) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_5) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all2) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1SetBreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (choice2fnsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all1) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compEex) =>
% 99.66/13.55 ((
% 99.66/13.55 (!!) @ (
% 99.66/13.55 (('#B') @ (
% 99.66/13.55 !!) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 !!))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#C') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1407])).
% 99.66/13.55 thf(zip_derived_cl1433, plain,
% 99.66/13.55 (~ (((singletoninpowerset) =>
% 99.66/13.55 (((singletoninpowunion) =>
% 99.66/13.55 (((upairset2E) =>
% 99.66/13.55 (((upairsubunion) =>
% 99.66/13.55 (((upairinpowunion) =>
% 99.66/13.55 (((ubforcartprodlem1) =>
% 99.66/13.55 (((ubforcartprodlem2) =>
% 99.66/13.55 (((ubforcartprodlem3) =>
% 99.66/13.55 (((cartprodpairin) =>
% 99.66/13.55 (((cartprodmempair1) =>
% 99.66/13.55 (((cartprodmempair) =>
% 99.66/13.55 (((setunionE2) =>
% 99.66/13.55 (((setunionsingleton1) =>
% 99.66/13.55 (((setunionsingleton2) =>
% 99.66/13.55 (((setunionsingleton) =>
% 99.66/13.55 (((singletonprop) =>
% 99.66/13.55 (((ex1E1) =>
% 99.66/13.55 (((ex1I) =>
% 99.66/13.55 (((ex1I2) =>
% 99.66/13.55 (((singletonsuniq) =>
% 99.66/13.55 (((setukpairinjL1) =>
% 99.66/13.55 (((kfstsingleton) =>
% 99.66/13.55 (((theprop) =>
% 99.66/13.55 (((kfstpairEq) =>
% 99.66/13.55 (((cartprodfstin) =>
% 99.66/13.55 (((setukpairinjL2) =>
% 99.66/13.55 (((setukpairinjL) =>
% 99.66/13.55 (((setukpairinjR11) =>
% 99.66/13.55 (((setukpairinjR12) =>
% 99.66/13.55 (((setukpairinjR1) =>
% 99.66/13.55 ((
% 99.66/13.55 (upairequniteq) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR2) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR) =>
% 99.66/13.55 ((
% 99.66/13.55 (ksndsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ksndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (kpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndin) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemEL) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemER) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodmempaircEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodfstpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrI) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrSub) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrERa) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL1) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL2) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrER) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcImageSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (apProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (app) =>
% 99.66/13.55 ((
% 99.66/13.55 (infuncsetfunc) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcinfuncset) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall1) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ex1E2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp3) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcextLem) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp4) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq1) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq2) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2lamEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifp) =>
% 99.66/13.55 ((
% 99.66/13.55 (theeq) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrue) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueorfalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setminusT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setextT) =>
% 99.66/13.55 ((
% 99.66/13.55 (subsetTI) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTELcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTERcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT1) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT2) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT3) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub2) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTnotintersectT) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementImpComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementSubsetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementInPowersetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (contraSubsetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTcontraSubset) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTILcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTIRcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion2) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (intersectInPowersetIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpNotIn1) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpInComplement1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTE) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTEcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementUnionInPowersetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule0) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_5) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all2) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1SetBreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (choice2fnsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all1) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compEex) =>
% 99.66/13.55 ((
% 99.66/13.55 (!!) @ (
% 99.66/13.55 (('#B') @ (
% 99.66/13.55 !!) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 !!))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#C') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1420])).
% 99.66/13.55 thf(zip_derived_cl1444, plain,
% 99.66/13.55 (~ (((singletoninpowunion) =>
% 99.66/13.55 (((upairset2E) =>
% 99.66/13.55 (((upairsubunion) =>
% 99.66/13.55 (((upairinpowunion) =>
% 99.66/13.55 (((ubforcartprodlem1) =>
% 99.66/13.55 (((ubforcartprodlem2) =>
% 99.66/13.55 (((ubforcartprodlem3) =>
% 99.66/13.55 (((cartprodpairin) =>
% 99.66/13.55 (((cartprodmempair1) =>
% 99.66/13.55 (((cartprodmempair) =>
% 99.66/13.55 (((setunionE2) =>
% 99.66/13.55 (((setunionsingleton1) =>
% 99.66/13.55 (((setunionsingleton2) =>
% 99.66/13.55 (((setunionsingleton) =>
% 99.66/13.55 (((singletonprop) =>
% 99.66/13.55 (((ex1E1) =>
% 99.66/13.55 (((ex1I) =>
% 99.66/13.55 (((ex1I2) =>
% 99.66/13.55 (((singletonsuniq) =>
% 99.66/13.55 (((setukpairinjL1) =>
% 99.66/13.55 (((kfstsingleton) =>
% 99.66/13.55 (((theprop) =>
% 99.66/13.55 (((kfstpairEq) =>
% 99.66/13.55 (((cartprodfstin) =>
% 99.66/13.55 (((setukpairinjL2) =>
% 99.66/13.55 (((setukpairinjL) =>
% 99.66/13.55 (((setukpairinjR11) =>
% 99.66/13.55 (((setukpairinjR12) =>
% 99.66/13.55 (((setukpairinjR1) =>
% 99.66/13.55 (((upairequniteq) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR2) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR) =>
% 99.66/13.55 ((
% 99.66/13.55 (ksndsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ksndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (kpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndin) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemEL) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemER) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodmempaircEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodfstpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrI) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrSub) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrERa) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL1) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL2) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrER) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcImageSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (apProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (app) =>
% 99.66/13.55 ((
% 99.66/13.55 (infuncsetfunc) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcinfuncset) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall1) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ex1E2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp3) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcextLem) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp4) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq1) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq2) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2lamEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifp) =>
% 99.66/13.55 ((
% 99.66/13.55 (theeq) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrue) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueorfalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setminusT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setextT) =>
% 99.66/13.55 ((
% 99.66/13.55 (subsetTI) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTELcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTERcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT1) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT2) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT3) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub2) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTnotintersectT) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementImpComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementSubsetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementInPowersetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (contraSubsetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTcontraSubset) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTILcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTIRcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion2) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (intersectInPowersetIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpNotIn1) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpInComplement1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTE) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTEcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementUnionInPowersetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule0) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_5) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all2) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1SetBreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (choice2fnsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all1) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compEex) =>
% 99.66/13.55 ((
% 99.66/13.55 (!!) @ (
% 99.66/13.55 (('#B') @ (
% 99.66/13.55 !!) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 !!))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#C') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1433])).
% 99.66/13.55 thf(zip_derived_cl1452, plain,
% 99.66/13.55 (~ (((upairset2E) =>
% 99.66/13.55 (((upairsubunion) =>
% 99.66/13.55 (((upairinpowunion) =>
% 99.66/13.55 (((ubforcartprodlem1) =>
% 99.66/13.55 (((ubforcartprodlem2) =>
% 99.66/13.55 (((ubforcartprodlem3) =>
% 99.66/13.55 (((cartprodpairin) =>
% 99.66/13.55 (((cartprodmempair1) =>
% 99.66/13.55 (((cartprodmempair) =>
% 99.66/13.55 (((setunionE2) =>
% 99.66/13.55 (((setunionsingleton1) =>
% 99.66/13.55 (((setunionsingleton2) =>
% 99.66/13.55 (((setunionsingleton) =>
% 99.66/13.55 (((singletonprop) =>
% 99.66/13.55 (((ex1E1) =>
% 99.66/13.55 (((ex1I) =>
% 99.66/13.55 (((ex1I2) =>
% 99.66/13.55 (((singletonsuniq) =>
% 99.66/13.55 (((setukpairinjL1) =>
% 99.66/13.55 (((kfstsingleton) =>
% 99.66/13.55 (((theprop) =>
% 99.66/13.55 (((kfstpairEq) =>
% 99.66/13.55 (((cartprodfstin) =>
% 99.66/13.55 (((setukpairinjL2) =>
% 99.66/13.55 (((setukpairinjL) =>
% 99.66/13.55 (((setukpairinjR11) =>
% 99.66/13.55 (((setukpairinjR12) =>
% 99.66/13.55 (((setukpairinjR1) =>
% 99.66/13.55 (((upairequniteq) =>
% 99.66/13.55 (((setukpairinjR2) =>
% 99.66/13.55 ((
% 99.66/13.55 (setukpairinjR) =>
% 99.66/13.55 ((
% 99.66/13.55 (ksndsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ksndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (kpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndin) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemEL) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemER) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodmempaircEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodfstpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrI) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrSub) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrERa) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL1) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL2) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrER) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcImageSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (apProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (app) =>
% 99.66/13.55 ((
% 99.66/13.55 (infuncsetfunc) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcinfuncset) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall1) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ex1E2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp3) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcextLem) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp4) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq1) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq2) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2lamEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifp) =>
% 99.66/13.55 ((
% 99.66/13.55 (theeq) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrue) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueorfalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setminusT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setextT) =>
% 99.66/13.55 ((
% 99.66/13.55 (subsetTI) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTELcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTERcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT1) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT2) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT3) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub2) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTnotintersectT) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementImpComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementSubsetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementInPowersetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (contraSubsetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTcontraSubset) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTILcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTIRcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion2) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (intersectInPowersetIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpNotIn1) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpInComplement1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTE) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTEcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementUnionInPowersetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule0) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_5) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all2) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1SetBreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (choice2fnsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all1) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compEex) =>
% 99.66/13.55 ((
% 99.66/13.55 (!!) @ (
% 99.66/13.55 (('#B') @ (
% 99.66/13.55 !!) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 !!))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#C') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1444])).
% 99.66/13.55 thf(zip_derived_cl1459, plain,
% 99.66/13.55 (~ (((upairsubunion) =>
% 99.66/13.55 (((upairinpowunion) =>
% 99.66/13.55 (((ubforcartprodlem1) =>
% 99.66/13.55 (((ubforcartprodlem2) =>
% 99.66/13.55 (((ubforcartprodlem3) =>
% 99.66/13.55 (((cartprodpairin) =>
% 99.66/13.55 (((cartprodmempair1) =>
% 99.66/13.55 (((cartprodmempair) =>
% 99.66/13.55 (((setunionE2) =>
% 99.66/13.55 (((setunionsingleton1) =>
% 99.66/13.55 (((setunionsingleton2) =>
% 99.66/13.55 (((setunionsingleton) =>
% 99.66/13.55 (((singletonprop) =>
% 99.66/13.55 (((ex1E1) =>
% 99.66/13.55 (((ex1I) =>
% 99.66/13.55 (((ex1I2) =>
% 99.66/13.55 (((singletonsuniq) =>
% 99.66/13.55 (((setukpairinjL1) =>
% 99.66/13.55 (((kfstsingleton) =>
% 99.66/13.55 (((theprop) =>
% 99.66/13.55 (((kfstpairEq) =>
% 99.66/13.55 (((cartprodfstin) =>
% 99.66/13.55 (((setukpairinjL2) =>
% 99.66/13.55 (((setukpairinjL) =>
% 99.66/13.55 (((setukpairinjR11) =>
% 99.66/13.55 (((setukpairinjR12) =>
% 99.66/13.55 (((setukpairinjR1) =>
% 99.66/13.55 (((upairequniteq) =>
% 99.66/13.55 (((setukpairinjR2) =>
% 99.66/13.55 (((setukpairinjR) =>
% 99.66/13.55 ((
% 99.66/13.55 (ksndsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ksndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (kpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndin) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemEL) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemER) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodmempaircEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodfstpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrI) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrSub) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrERa) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL1) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL2) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrER) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcImageSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (apProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (app) =>
% 99.66/13.55 ((
% 99.66/13.55 (infuncsetfunc) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcinfuncset) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall1) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ex1E2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp3) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcextLem) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp4) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq1) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq2) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2lamEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifp) =>
% 99.66/13.55 ((
% 99.66/13.55 (theeq) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrue) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueorfalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setminusT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setextT) =>
% 99.66/13.55 ((
% 99.66/13.55 (subsetTI) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTELcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTERcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT1) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT2) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT3) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub2) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTnotintersectT) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementImpComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementSubsetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementInPowersetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (contraSubsetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTcontraSubset) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTILcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTIRcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion2) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (intersectInPowersetIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpNotIn1) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpInComplement1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTE) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTEcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementUnionInPowersetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule0) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_5) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all2) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1SetBreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (choice2fnsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all1) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compEex) =>
% 99.66/13.55 ((
% 99.66/13.55 (!!) @ (
% 99.66/13.55 (('#B') @ (
% 99.66/13.55 !!) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 !!))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#C') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1452])).
% 99.66/13.55 thf(zip_derived_cl1466, plain,
% 99.66/13.55 (~ (((upairinpowunion) =>
% 99.66/13.55 (((ubforcartprodlem1) =>
% 99.66/13.55 (((ubforcartprodlem2) =>
% 99.66/13.55 (((ubforcartprodlem3) =>
% 99.66/13.55 (((cartprodpairin) =>
% 99.66/13.55 (((cartprodmempair1) =>
% 99.66/13.55 (((cartprodmempair) =>
% 99.66/13.55 (((setunionE2) =>
% 99.66/13.55 (((setunionsingleton1) =>
% 99.66/13.55 (((setunionsingleton2) =>
% 99.66/13.55 (((setunionsingleton) =>
% 99.66/13.55 (((singletonprop) =>
% 99.66/13.55 (((ex1E1) =>
% 99.66/13.55 (((ex1I) =>
% 99.66/13.55 (((ex1I2) =>
% 99.66/13.55 (((singletonsuniq) =>
% 99.66/13.55 (((setukpairinjL1) =>
% 99.66/13.55 (((kfstsingleton) =>
% 99.66/13.55 (((theprop) =>
% 99.66/13.55 (((kfstpairEq) =>
% 99.66/13.55 (((cartprodfstin) =>
% 99.66/13.55 (((setukpairinjL2) =>
% 99.66/13.55 (((setukpairinjL) =>
% 99.66/13.55 (((setukpairinjR11) =>
% 99.66/13.55 (((setukpairinjR12) =>
% 99.66/13.55 (((setukpairinjR1) =>
% 99.66/13.55 (((upairequniteq) =>
% 99.66/13.55 (((setukpairinjR2) =>
% 99.66/13.55 (((setukpairinjR) =>
% 99.66/13.55 (((ksndsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ksndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (kpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndin) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemEL) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemER) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodmempaircEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodfstpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrI) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrSub) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrERa) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL1) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL2) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrER) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcImageSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (apProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (app) =>
% 99.66/13.55 ((
% 99.66/13.55 (infuncsetfunc) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcinfuncset) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall1) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ex1E2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp3) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcextLem) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp4) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq1) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq2) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2lamEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifp) =>
% 99.66/13.55 ((
% 99.66/13.55 (theeq) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrue) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueorfalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setminusT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setextT) =>
% 99.66/13.55 ((
% 99.66/13.55 (subsetTI) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTELcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTERcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT1) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT2) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT3) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub2) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTnotintersectT) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementImpComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementSubsetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementInPowersetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (contraSubsetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTcontraSubset) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTILcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTIRcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion2) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (intersectInPowersetIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpNotIn1) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpInComplement1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTE) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTEcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementUnionInPowersetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule0) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_5) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all2) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1SetBreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (choice2fnsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all1) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compEex) =>
% 99.66/13.55 ((
% 99.66/13.55 (!!) @ (
% 99.66/13.55 (('#B') @ (
% 99.66/13.55 !!) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 !!))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#C') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1459])).
% 99.66/13.55 thf(zip_derived_cl1473, plain,
% 99.66/13.55 (~ (((ubforcartprodlem1) =>
% 99.66/13.55 (((ubforcartprodlem2) =>
% 99.66/13.55 (((ubforcartprodlem3) =>
% 99.66/13.55 (((cartprodpairin) =>
% 99.66/13.55 (((cartprodmempair1) =>
% 99.66/13.55 (((cartprodmempair) =>
% 99.66/13.55 (((setunionE2) =>
% 99.66/13.55 (((setunionsingleton1) =>
% 99.66/13.55 (((setunionsingleton2) =>
% 99.66/13.55 (((setunionsingleton) =>
% 99.66/13.55 (((singletonprop) =>
% 99.66/13.55 (((ex1E1) =>
% 99.66/13.55 (((ex1I) =>
% 99.66/13.55 (((ex1I2) =>
% 99.66/13.55 (((singletonsuniq) =>
% 99.66/13.55 (((setukpairinjL1) =>
% 99.66/13.55 (((kfstsingleton) =>
% 99.66/13.55 (((theprop) =>
% 99.66/13.55 (((kfstpairEq) =>
% 99.66/13.55 (((cartprodfstin) =>
% 99.66/13.55 (((setukpairinjL2) =>
% 99.66/13.55 (((setukpairinjL) =>
% 99.66/13.55 (((setukpairinjR11) =>
% 99.66/13.55 (((setukpairinjR12) =>
% 99.66/13.55 (((setukpairinjR1) =>
% 99.66/13.55 (((upairequniteq) =>
% 99.66/13.55 (((setukpairinjR2) =>
% 99.66/13.55 (((setukpairinjR) =>
% 99.66/13.55 (((ksndsingleton) =>
% 99.66/13.55 (((ksndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (kpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndin) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemEL) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemER) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodmempaircEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodfstpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrI) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrSub) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrERa) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL1) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL2) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrER) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcImageSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (apProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (app) =>
% 99.66/13.55 ((
% 99.66/13.55 (infuncsetfunc) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcinfuncset) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall1) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ex1E2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp3) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcextLem) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp4) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq1) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq2) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2lamEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifp) =>
% 99.66/13.55 ((
% 99.66/13.55 (theeq) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrue) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueorfalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setminusT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setextT) =>
% 99.66/13.55 ((
% 99.66/13.55 (subsetTI) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTELcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTERcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT1) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT2) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT3) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub2) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTnotintersectT) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementImpComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementSubsetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementInPowersetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (contraSubsetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTcontraSubset) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTILcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTIRcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion2) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (intersectInPowersetIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpNotIn1) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpInComplement1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTE) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTEcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementUnionInPowersetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule0) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_5) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all2) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1SetBreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (choice2fnsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all1) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compEex) =>
% 99.66/13.55 ((
% 99.66/13.55 (!!) @ (
% 99.66/13.55 (('#B') @ (
% 99.66/13.55 !!) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 !!))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#C') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1466])).
% 99.66/13.55 thf(zip_derived_cl1480, plain,
% 99.66/13.55 (~ (((ubforcartprodlem2) =>
% 99.66/13.55 (((ubforcartprodlem3) =>
% 99.66/13.55 (((cartprodpairin) =>
% 99.66/13.55 (((cartprodmempair1) =>
% 99.66/13.55 (((cartprodmempair) =>
% 99.66/13.55 (((setunionE2) =>
% 99.66/13.55 (((setunionsingleton1) =>
% 99.66/13.55 (((setunionsingleton2) =>
% 99.66/13.55 (((setunionsingleton) =>
% 99.66/13.55 (((singletonprop) =>
% 99.66/13.55 (((ex1E1) =>
% 99.66/13.55 (((ex1I) =>
% 99.66/13.55 (((ex1I2) =>
% 99.66/13.55 (((singletonsuniq) =>
% 99.66/13.55 (((setukpairinjL1) =>
% 99.66/13.55 (((kfstsingleton) =>
% 99.66/13.55 (((theprop) =>
% 99.66/13.55 (((kfstpairEq) =>
% 99.66/13.55 (((cartprodfstin) =>
% 99.66/13.55 (((setukpairinjL2) =>
% 99.66/13.55 (((setukpairinjL) =>
% 99.66/13.55 (((setukpairinjR11) =>
% 99.66/13.55 (((setukpairinjR12) =>
% 99.66/13.55 (((setukpairinjR1) =>
% 99.66/13.55 (((upairequniteq) =>
% 99.66/13.55 (((setukpairinjR2) =>
% 99.66/13.55 (((setukpairinjR) =>
% 99.66/13.55 (((ksndsingleton) =>
% 99.66/13.55 (((ksndpairEq) =>
% 99.66/13.55 (((kpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndin) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemEL) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemER) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodmempaircEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodfstpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrI) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrSub) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrERa) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL1) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL2) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrER) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcImageSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (apProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (app) =>
% 99.66/13.55 ((
% 99.66/13.55 (infuncsetfunc) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcinfuncset) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall1) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ex1E2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp3) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcextLem) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp4) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq1) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq2) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2lamEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifp) =>
% 99.66/13.55 ((
% 99.66/13.55 (theeq) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrue) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueorfalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setminusT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setextT) =>
% 99.66/13.55 ((
% 99.66/13.55 (subsetTI) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTELcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTERcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT1) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT2) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT3) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub2) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTnotintersectT) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementImpComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementSubsetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementInPowersetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (contraSubsetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTcontraSubset) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTILcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTIRcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion2) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (intersectInPowersetIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpNotIn1) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpInComplement1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTE) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTEcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementUnionInPowersetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule0) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_5) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all2) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1SetBreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (choice2fnsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all1) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compEex) =>
% 99.66/13.55 ((
% 99.66/13.55 (!!) @ (
% 99.66/13.55 (('#B') @ (
% 99.66/13.55 !!) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 !!))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#C') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1473])).
% 99.66/13.55 thf(zip_derived_cl1488, plain,
% 99.66/13.55 (~ (((ubforcartprodlem3) =>
% 99.66/13.55 (((cartprodpairin) =>
% 99.66/13.55 (((cartprodmempair1) =>
% 99.66/13.55 (((cartprodmempair) =>
% 99.66/13.55 (((setunionE2) =>
% 99.66/13.55 (((setunionsingleton1) =>
% 99.66/13.55 (((setunionsingleton2) =>
% 99.66/13.55 (((setunionsingleton) =>
% 99.66/13.55 (((singletonprop) =>
% 99.66/13.55 (((ex1E1) =>
% 99.66/13.55 (((ex1I) =>
% 99.66/13.55 (((ex1I2) =>
% 99.66/13.55 (((singletonsuniq) =>
% 99.66/13.55 (((setukpairinjL1) =>
% 99.66/13.55 (((kfstsingleton) =>
% 99.66/13.55 (((theprop) =>
% 99.66/13.55 (((kfstpairEq) =>
% 99.66/13.55 (((cartprodfstin) =>
% 99.66/13.55 (((setukpairinjL2) =>
% 99.66/13.55 (((setukpairinjL) =>
% 99.66/13.55 (((setukpairinjR11) =>
% 99.66/13.55 (((setukpairinjR12) =>
% 99.66/13.55 (((setukpairinjR1) =>
% 99.66/13.55 (((upairequniteq) =>
% 99.66/13.55 (((setukpairinjR2) =>
% 99.66/13.55 (((setukpairinjR) =>
% 99.66/13.55 (((ksndsingleton) =>
% 99.66/13.55 (((ksndpairEq) =>
% 99.66/13.55 (((kpairsurjEq) =>
% 99.66/13.55 (((cartprodsndin) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemEL) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemER) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodmempaircEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodfstpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrI) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrSub) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrERa) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL1) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL2) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrER) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcImageSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (apProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (app) =>
% 99.66/13.55 ((
% 99.66/13.55 (infuncsetfunc) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcinfuncset) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall1) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ex1E2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp3) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcextLem) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp4) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq1) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq2) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2lamEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifp) =>
% 99.66/13.55 ((
% 99.66/13.55 (theeq) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrue) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueorfalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setminusT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setextT) =>
% 99.66/13.55 ((
% 99.66/13.55 (subsetTI) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTELcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTERcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT1) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT2) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT3) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub2) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTnotintersectT) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementImpComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementSubsetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementInPowersetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (contraSubsetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTcontraSubset) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTILcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTIRcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion2) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (intersectInPowersetIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpNotIn1) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpInComplement1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTE) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTEcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementUnionInPowersetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule0) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_5) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all2) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1SetBreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (choice2fnsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all1) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compEex) =>
% 99.66/13.55 ((
% 99.66/13.55 (!!) @ (
% 99.66/13.55 (('#B') @ (
% 99.66/13.55 !!) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 !!))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#C') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1480])).
% 99.66/13.55 thf(zip_derived_cl1496, plain,
% 99.66/13.55 (~ (((cartprodpairin) =>
% 99.66/13.55 (((cartprodmempair1) =>
% 99.66/13.55 (((cartprodmempair) =>
% 99.66/13.55 (((setunionE2) =>
% 99.66/13.55 (((setunionsingleton1) =>
% 99.66/13.55 (((setunionsingleton2) =>
% 99.66/13.55 (((setunionsingleton) =>
% 99.66/13.55 (((singletonprop) =>
% 99.66/13.55 (((ex1E1) =>
% 99.66/13.55 (((ex1I) =>
% 99.66/13.55 (((ex1I2) =>
% 99.66/13.55 (((singletonsuniq) =>
% 99.66/13.55 (((setukpairinjL1) =>
% 99.66/13.55 (((kfstsingleton) =>
% 99.66/13.55 (((theprop) =>
% 99.66/13.55 (((kfstpairEq) =>
% 99.66/13.55 (((cartprodfstin) =>
% 99.66/13.55 (((setukpairinjL2) =>
% 99.66/13.55 (((setukpairinjL) =>
% 99.66/13.55 (((setukpairinjR11) =>
% 99.66/13.55 (((setukpairinjR12) =>
% 99.66/13.55 (((setukpairinjR1) =>
% 99.66/13.55 (((upairequniteq) =>
% 99.66/13.55 (((setukpairinjR2) =>
% 99.66/13.55 (((setukpairinjR) =>
% 99.66/13.55 (((ksndsingleton) =>
% 99.66/13.55 (((ksndpairEq) =>
% 99.66/13.55 (((kpairsurjEq) =>
% 99.66/13.55 (((cartprodsndin) =>
% 99.66/13.55 (((cartprodpairmemEL) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairmemER) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodmempaircEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodfstpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrI) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrSub) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrERa) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL1) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL2) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrER) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcImageSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (apProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (app) =>
% 99.66/13.55 ((
% 99.66/13.55 (infuncsetfunc) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcinfuncset) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall1) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ex1E2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp3) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcextLem) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp4) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq1) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq2) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2lamEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifp) =>
% 99.66/13.55 ((
% 99.66/13.55 (theeq) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrue) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueorfalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setminusT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setextT) =>
% 99.66/13.55 ((
% 99.66/13.55 (subsetTI) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTELcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTERcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT1) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT2) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT3) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub2) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTnotintersectT) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementImpComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementSubsetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementInPowersetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (contraSubsetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTcontraSubset) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTILcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTIRcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion2) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (intersectInPowersetIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpNotIn1) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpInComplement1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTE) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTEcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementUnionInPowersetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule0) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_5) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all2) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1SetBreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (choice2fnsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all1) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compEex) =>
% 99.66/13.55 ((
% 99.66/13.55 (!!) @ (
% 99.66/13.55 (('#B') @ (
% 99.66/13.55 !!) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 !!))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#C') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1488])).
% 99.66/13.55 thf(zip_derived_cl1505, plain,
% 99.66/13.55 (~ (((cartprodmempair1) =>
% 99.66/13.55 (((cartprodmempair) =>
% 99.66/13.55 (((setunionE2) =>
% 99.66/13.55 (((setunionsingleton1) =>
% 99.66/13.55 (((setunionsingleton2) =>
% 99.66/13.55 (((setunionsingleton) =>
% 99.66/13.55 (((singletonprop) =>
% 99.66/13.55 (((ex1E1) =>
% 99.66/13.55 (((ex1I) =>
% 99.66/13.55 (((ex1I2) =>
% 99.66/13.55 (((singletonsuniq) =>
% 99.66/13.55 (((setukpairinjL1) =>
% 99.66/13.55 (((kfstsingleton) =>
% 99.66/13.55 (((theprop) =>
% 99.66/13.55 (((kfstpairEq) =>
% 99.66/13.55 (((cartprodfstin) =>
% 99.66/13.55 (((setukpairinjL2) =>
% 99.66/13.55 (((setukpairinjL) =>
% 99.66/13.55 (((setukpairinjR11) =>
% 99.66/13.55 (((setukpairinjR12) =>
% 99.66/13.55 (((setukpairinjR1) =>
% 99.66/13.55 (((upairequniteq) =>
% 99.66/13.55 (((setukpairinjR2) =>
% 99.66/13.55 (((setukpairinjR) =>
% 99.66/13.55 (((ksndsingleton) =>
% 99.66/13.55 (((ksndpairEq) =>
% 99.66/13.55 (((kpairsurjEq) =>
% 99.66/13.55 (((cartprodsndin) =>
% 99.66/13.55 (((cartprodpairmemEL) =>
% 99.66/13.55 (((cartprodpairmemER) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodmempaircEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodfstpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrI) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrSub) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrERa) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL1) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL2) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrER) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcImageSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (apProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (app) =>
% 99.66/13.55 ((
% 99.66/13.55 (infuncsetfunc) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcinfuncset) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall1) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ex1E2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp3) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcextLem) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp4) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq1) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq2) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2lamEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifp) =>
% 99.66/13.55 ((
% 99.66/13.55 (theeq) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrue) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueorfalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setminusT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setextT) =>
% 99.66/13.55 ((
% 99.66/13.55 (subsetTI) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTELcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTERcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT1) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT2) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT3) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub2) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTnotintersectT) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementImpComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementSubsetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementInPowersetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (contraSubsetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTcontraSubset) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTILcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTIRcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion2) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (intersectInPowersetIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpNotIn1) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpInComplement1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTE) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTEcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementUnionInPowersetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule0) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_5) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all2) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1SetBreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (choice2fnsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all1) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compEex) =>
% 99.66/13.55 ((
% 99.66/13.55 (!!) @ (
% 99.66/13.55 (('#B') @ (
% 99.66/13.55 !!) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 !!))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#C') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1496])).
% 99.66/13.55 thf(zip_derived_cl1515, plain,
% 99.66/13.55 (~ (((cartprodmempair) =>
% 99.66/13.55 (((setunionE2) =>
% 99.66/13.55 (((setunionsingleton1) =>
% 99.66/13.55 (((setunionsingleton2) =>
% 99.66/13.55 (((setunionsingleton) =>
% 99.66/13.55 (((singletonprop) =>
% 99.66/13.55 (((ex1E1) =>
% 99.66/13.55 (((ex1I) =>
% 99.66/13.55 (((ex1I2) =>
% 99.66/13.55 (((singletonsuniq) =>
% 99.66/13.55 (((setukpairinjL1) =>
% 99.66/13.55 (((kfstsingleton) =>
% 99.66/13.55 (((theprop) =>
% 99.66/13.55 (((kfstpairEq) =>
% 99.66/13.55 (((cartprodfstin) =>
% 99.66/13.55 (((setukpairinjL2) =>
% 99.66/13.55 (((setukpairinjL) =>
% 99.66/13.55 (((setukpairinjR11) =>
% 99.66/13.55 (((setukpairinjR12) =>
% 99.66/13.55 (((setukpairinjR1) =>
% 99.66/13.55 (((upairequniteq) =>
% 99.66/13.55 (((setukpairinjR2) =>
% 99.66/13.55 (((setukpairinjR) =>
% 99.66/13.55 (((ksndsingleton) =>
% 99.66/13.55 (((ksndpairEq) =>
% 99.66/13.55 (((kpairsurjEq) =>
% 99.66/13.55 (((cartprodsndin) =>
% 99.66/13.55 (((cartprodpairmemEL) =>
% 99.66/13.55 (((cartprodpairmemER) =>
% 99.66/13.55 (((cartprodmempaircEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodfstpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodsndpairEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (cartprodpairsurjEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrI) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrSub) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrERa) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL1) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrEL2) =>
% 99.66/13.55 ((
% 99.66/13.55 (dpsetconstrER) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcImageSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (apProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (app) =>
% 99.66/13.55 ((
% 99.66/13.55 (infuncsetfunc) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcinfuncset) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamProp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lamp) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2p) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall1) =>
% 99.66/13.55 ((
% 99.66/13.55 (brelnall2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ex1E2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp3) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcextLem) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcGraphProp4) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext) =>
% 99.66/13.55 ((
% 99.66/13.55 (funcext2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq1) =>
% 99.66/13.55 ((
% 99.66/13.55 (ap2apEq2) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta1) =>
% 99.66/13.55 ((
% 99.66/13.55 (lam2lamEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (beta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (eta2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalseProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp1) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueProp2) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifSingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (ifp) =>
% 99.66/13.55 ((
% 99.66/13.55 (theeq) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrue) =>
% 99.66/13.55 ((
% 99.66/13.55 (iffalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (iftrueorfalse) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setminusT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementT_lem) =>
% 99.66/13.55 ((
% 99.66/13.55 (setextT) =>
% 99.66/13.55 ((
% 99.66/13.55 (subsetTI) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (powersetTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTELcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binintersectTERcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT1) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT2) =>
% 99.66/13.55 ((
% 99.66/13.55 (contrasubsetT3) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementI1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementE1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub1) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementSub2) =>
% 99.66/13.55 ((
% 99.66/13.55 (doubleComplementEq) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTnotintersectT) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementImpComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementSubsetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementInPowersetComplementIntersect) =>
% 99.66/13.55 ((
% 99.66/13.55 (contraSubsetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementTcontraSubset) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTILcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTIRcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInUnion2) =>
% 99.66/13.55 ((
% 99.66/13.55 (inIntersectImpInIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (intersectInPowersetIntersectUnions) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpNotIn1) =>
% 99.66/13.55 ((
% 99.66/13.55 (inComplementUnionImpInComplement1) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTE) =>
% 99.66/13.55 ((
% 99.66/13.55 (binunionTEcontra) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a1) =>
% 99.66/13.55 ((
% 99.66/13.55 (complementUnionInPowersetComplement) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan1) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2a) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b2) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2b) =>
% 99.66/13.55 ((
% 99.66/13.55 (demorgan2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule0) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz13rule4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_1) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_2) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_3) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_4) =>
% 99.66/13.55 ((
% 99.66/13.55 (woz1_5) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all2) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1SetBreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (choice2fnsingleton) =>
% 99.66/13.55 ((
% 99.66/13.55 (setOfPairsIsBReln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1all1) =>
% 99.66/13.55 ((
% 99.66/13.55 (subbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (eqbreln1) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1invE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compprop) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compI) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compE) =>
% 99.66/13.55 ((
% 99.66/13.55 (breln1compEex) =>
% 99.66/13.55 ((
% 99.66/13.55 (!!) @ (
% 99.66/13.55 (('#B') @ (
% 99.66/13.55 !!) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#S') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 =>))) @
% 99.66/13.55 breln1)))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 !!))) @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.55 ('#S') @ (
% 99.66/13.55 (
% 99.66/13.55 ('#B') @ (
% 99.66/13.55 '#B') @
% 99.66/13.55 (
% 99.66/13.55 (
% 99.66/13.56 ('#B') @ (
% 99.66/13.56 '#S') @
% 99.66/13.56 (
% 99.66/13.56 (
% 99.66/13.56 ('#B') @ (
% 99.66/13.56 (
% 99.66/13.56 ('#B') @ (
% 99.66/13.56 =>))) @
% 99.66/13.56 breln1)))))) @
% 99.66/13.56 (
% 99.66/13.56 (
% 99.66/13.56 ('#C') @ (
% 99.66/13.56 (
% 99.66/13.56 ('#B') @ (
% 99.66/13.56 '#B') @
% 99.66/13.56 (
% 99.66/13.56 (
% 99.66/13.56 ('#B') @ (
% 99.66/13.56 '#B') @
% 99.66/13.56 breln1)))) @
% 99.66/13.56 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.66/13.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1505])).
% 99.66/13.56 thf(zip_derived_cl1525, plain,
% 99.66/13.56 (~ (((setunionE2) =>
% 99.66/13.56 (((setunionsingleton1) =>
% 99.66/13.56 (((setunionsingleton2) =>
% 99.66/13.56 (((setunionsingleton) =>
% 99.66/13.56 (((singletonprop) =>
% 99.66/13.56 (((ex1E1) =>
% 99.66/13.56 (((ex1I) =>
% 99.66/13.56 (((ex1I2) =>
% 99.66/13.56 (((singletonsuniq) =>
% 99.66/13.56 (((setukpairinjL1) =>
% 99.66/13.56 (((kfstsingleton) =>
% 99.66/13.56 (((theprop) =>
% 99.66/13.56 (((kfstpairEq) =>
% 99.66/13.56 (((cartprodfstin) =>
% 99.66/13.56 (((setukpairinjL2) =>
% 99.66/13.56 (((setukpairinjL) =>
% 99.66/13.56 (((setukpairinjR11) =>
% 99.66/13.56 (((setukpairinjR12) =>
% 99.66/13.56 (((setukpairinjR1) =>
% 99.66/13.56 (((upairequniteq) =>
% 99.66/13.56 (((setukpairinjR2) =>
% 99.66/13.56 (((setukpairinjR) =>
% 99.66/13.56 (((ksndsingleton) =>
% 99.66/13.56 (((ksndpairEq) =>
% 99.66/13.56 (((kpairsurjEq) =>
% 99.66/13.56 (((cartprodsndin) =>
% 99.66/13.56 (((cartprodpairmemEL) =>
% 99.66/13.56 (((cartprodpairmemER) =>
% 99.66/13.56 (((cartprodmempaircEq) =>
% 99.66/13.56 (((cartprodfstpairEq) =>
% 99.66/13.56 ((
% 99.66/13.56 (cartprodsndpairEq) =>
% 99.66/13.56 ((
% 99.66/13.56 (cartprodpairsurjEq) =>
% 99.66/13.56 ((
% 99.66/13.56 (dpsetconstrI) =>
% 99.66/13.56 ((
% 99.66/13.56 (dpsetconstrSub) =>
% 99.66/13.56 ((
% 99.66/13.56 (setOfPairsIsBReln) =>
% 99.66/13.56 ((
% 99.66/13.56 (dpsetconstrERa) =>
% 99.66/13.56 ((
% 99.66/13.56 (dpsetconstrEL1) =>
% 99.66/13.56 ((
% 99.66/13.56 (dpsetconstrEL2) =>
% 99.66/13.56 ((
% 99.66/13.56 (dpsetconstrER) =>
% 99.66/13.56 ((
% 99.66/13.56 (funcImageSingleton) =>
% 99.66/13.56 ((
% 99.66/13.56 (apProp) =>
% 99.66/13.56 ((
% 99.66/13.56 (app) =>
% 99.66/13.56 ((
% 99.66/13.56 (infuncsetfunc) =>
% 99.66/13.56 ((
% 99.66/13.56 (ap2p) =>
% 99.66/13.56 ((
% 99.66/13.56 (funcinfuncset) =>
% 99.66/13.56 ((
% 99.66/13.56 (lamProp) =>
% 99.66/13.56 ((
% 99.66/13.56 (lamp) =>
% 99.66/13.56 ((
% 99.66/13.56 (lam2p) =>
% 99.66/13.56 ((
% 99.66/13.56 (brelnall1) =>
% 99.66/13.56 ((
% 99.66/13.56 (brelnall2) =>
% 99.66/13.56 ((
% 99.66/13.56 (ex1E2) =>
% 99.66/13.56 ((
% 99.66/13.56 (funcGraphProp1) =>
% 99.66/13.56 ((
% 99.66/13.56 (funcGraphProp3) =>
% 99.66/13.56 ((
% 99.66/13.56 (funcGraphProp2) =>
% 99.66/13.56 ((
% 99.66/13.56 (funcextLem) =>
% 99.66/13.56 ((
% 99.66/13.56 (funcGraphProp4) =>
% 99.66/13.56 ((
% 99.66/13.56 (subbreln) =>
% 99.66/13.56 ((
% 99.66/13.56 (eqbreln) =>
% 99.66/13.56 ((
% 99.66/13.56 (funcext) =>
% 99.66/13.56 ((
% 99.66/13.56 (funcext2) =>
% 99.66/13.56 ((
% 99.66/13.56 (ap2apEq1) =>
% 99.66/13.56 ((
% 99.66/13.56 (ap2apEq2) =>
% 99.66/13.56 ((
% 99.66/13.56 (beta1) =>
% 99.66/13.56 ((
% 99.66/13.56 (eta1) =>
% 99.66/13.56 ((
% 99.66/13.56 (lam2lamEq) =>
% 99.66/13.56 ((
% 99.66/13.56 (beta2) =>
% 99.66/13.56 ((
% 99.66/13.56 (eta2) =>
% 99.66/13.56 ((
% 99.66/13.56 (iffalseProp1) =>
% 99.66/13.56 ((
% 99.66/13.56 (iffalseProp2) =>
% 99.66/13.56 ((
% 99.66/13.56 (iftrueProp1) =>
% 99.66/13.56 ((
% 99.66/13.56 (iftrueProp2) =>
% 99.66/13.56 ((
% 99.66/13.56 (ifSingleton) =>
% 99.66/13.56 ((
% 99.66/13.56 (ifp) =>
% 99.66/13.56 ((
% 99.66/13.56 (theeq) =>
% 99.66/13.56 ((
% 99.66/13.56 (iftrue) =>
% 99.66/13.56 ((
% 99.66/13.56 (iffalse) =>
% 99.66/13.56 ((
% 99.66/13.56 (iftrueorfalse) =>
% 99.66/13.56 ((
% 99.66/13.56 (binintersectT_lem) =>
% 99.66/13.56 ((
% 99.66/13.56 (binunionT_lem) =>
% 99.66/13.56 ((
% 99.66/13.56 (powersetT_lem) =>
% 99.66/13.56 ((
% 99.66/13.56 (setminusT_lem) =>
% 99.66/13.56 ((
% 99.66/13.56 (complementT_lem) =>
% 99.66/13.56 ((
% 99.66/13.56 (setextT) =>
% 99.66/13.56 ((
% 99.66/13.56 (subsetTI) =>
% 99.66/13.56 ((
% 99.66/13.56 (powersetTI1) =>
% 99.66/13.56 ((
% 99.66/13.56 (powersetTE1) =>
% 99.66/13.56 ((
% 99.66/13.56 (complementTI1) =>
% 99.66/13.56 ((
% 99.66/13.56 (complementTE1) =>
% 99.66/13.56 ((
% 99.66/13.56 (binintersectTELcontra) =>
% 99.66/13.56 ((
% 99.66/13.56 (binintersectTERcontra) =>
% 99.66/13.56 ((
% 99.66/13.56 (contrasubsetT) =>
% 99.66/13.56 ((
% 99.66/13.56 (contrasubsetT1) =>
% 99.66/13.56 ((
% 99.66/13.56 (contrasubsetT2) =>
% 99.66/13.56 ((
% 99.66/13.56 (contrasubsetT3) =>
% 99.66/13.56 ((
% 99.66/13.56 (doubleComplementI1) =>
% 99.66/13.56 ((
% 99.66/13.56 (doubleComplementE1) =>
% 99.66/13.56 ((
% 99.66/13.56 (doubleComplementSub1) =>
% 99.66/13.56 ((
% 99.66/13.56 (doubleComplementSub2) =>
% 99.66/13.56 ((
% 99.66/13.56 (doubleComplementEq) =>
% 99.66/13.56 ((
% 99.66/13.56 (complementTnotintersectT) =>
% 99.66/13.56 ((
% 99.66/13.56 (complementImpComplementIntersect) =>
% 99.66/13.56 ((
% 99.66/13.56 (complementSubsetComplementIntersect) =>
% 99.66/13.56 ((
% 99.66/13.56 (complementInPowersetComplementIntersect) =>
% 99.66/13.56 ((
% 99.66/13.56 (contraSubsetComplement) =>
% 99.66/13.56 ((
% 99.66/13.56 (complementTcontraSubset) =>
% 99.66/13.56 ((
% 99.66/13.56 (binunionTILcontra) =>
% 99.66/13.56 ((
% 99.66/13.56 (binunionTIRcontra) =>
% 99.66/13.56 ((
% 99.66/13.56 (inIntersectImpInUnion) =>
% 99.66/13.56 ((
% 99.66/13.56 (inIntersectImpInUnion2) =>
% 99.66/13.56 ((
% 99.66/13.56 (inIntersectImpInIntersectUnions) =>
% 99.66/13.56 ((
% 99.66/13.56 (intersectInPowersetIntersectUnions) =>
% 99.66/13.56 ((
% 99.66/13.56 (inComplementUnionImpNotIn1) =>
% 99.66/13.56 ((
% 99.66/13.56 (inComplementUnionImpInComplement1) =>
% 99.66/13.56 ((
% 99.66/13.56 (binunionTE) =>
% 99.66/13.56 ((
% 99.66/13.56 (binunionTEcontra) =>
% 99.66/13.56 ((
% 99.66/13.56 (demorgan2a1) =>
% 99.66/13.56 ((
% 99.66/13.56 (complementUnionInPowersetComplement) =>
% 99.66/13.56 ((
% 99.66/13.56 (demorgan2a2) =>
% 99.66/13.56 ((
% 99.66/13.56 (demorgan1a) =>
% 99.66/13.56 ((
% 99.66/13.56 (demorgan1b) =>
% 99.66/13.56 ((
% 99.66/13.56 (demorgan1) =>
% 99.66/13.56 ((
% 99.66/13.56 (demorgan2a) =>
% 99.66/13.56 ((
% 99.66/13.56 (demorgan2b2) =>
% 99.66/13.56 ((
% 99.66/13.56 (demorgan2b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule0) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_5) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all2) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1SetBreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (choice2fnsingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all1) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compEex) =>
% 100.17/13.56 ((
% 100.17/13.56 (!!) @ (
% 100.17/13.56 (('#B') @ (
% 100.17/13.56 !!) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 !!))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#C') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1515])).
% 100.17/13.56 thf(zip_derived_cl1535, plain,
% 100.17/13.56 (~ (((setunionsingleton1) =>
% 100.17/13.56 (((setunionsingleton2) =>
% 100.17/13.56 (((setunionsingleton) =>
% 100.17/13.56 (((singletonprop) =>
% 100.17/13.56 (((ex1E1) =>
% 100.17/13.56 (((ex1I) =>
% 100.17/13.56 (((ex1I2) =>
% 100.17/13.56 (((singletonsuniq) =>
% 100.17/13.56 (((setukpairinjL1) =>
% 100.17/13.56 (((kfstsingleton) =>
% 100.17/13.56 (((theprop) =>
% 100.17/13.56 (((kfstpairEq) =>
% 100.17/13.56 (((cartprodfstin) =>
% 100.17/13.56 (((setukpairinjL2) =>
% 100.17/13.56 (((setukpairinjL) =>
% 100.17/13.56 (((setukpairinjR11) =>
% 100.17/13.56 (((setukpairinjR12) =>
% 100.17/13.56 (((setukpairinjR1) =>
% 100.17/13.56 (((upairequniteq) =>
% 100.17/13.56 (((setukpairinjR2) =>
% 100.17/13.56 (((setukpairinjR) =>
% 100.17/13.56 (((ksndsingleton) =>
% 100.17/13.56 (((ksndpairEq) =>
% 100.17/13.56 (((kpairsurjEq) =>
% 100.17/13.56 (((cartprodsndin) =>
% 100.17/13.56 (((cartprodpairmemEL) =>
% 100.17/13.56 (((cartprodpairmemER) =>
% 100.17/13.56 (((cartprodmempaircEq) =>
% 100.17/13.56 (((cartprodfstpairEq) =>
% 100.17/13.56 (((cartprodsndpairEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (cartprodpairsurjEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrI) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrSub) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrERa) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrEL1) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrEL2) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrER) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcImageSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (apProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (app) =>
% 100.17/13.56 ((
% 100.17/13.56 (infuncsetfunc) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcinfuncset) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall1) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ex1E2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp3) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcextLem) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp4) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq1) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq2) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2lamEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifp) =>
% 100.17/13.56 ((
% 100.17/13.56 (theeq) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrue) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueorfalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setminusT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setextT) =>
% 100.17/13.56 ((
% 100.17/13.56 (subsetTI) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTELcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTERcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT1) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT2) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT3) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub2) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTnotintersectT) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementImpComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementSubsetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementInPowersetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (contraSubsetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTcontraSubset) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTILcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTIRcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion2) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (intersectInPowersetIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpNotIn1) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpInComplement1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTE) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTEcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementUnionInPowersetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule0) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_5) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all2) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1SetBreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (choice2fnsingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all1) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compEex) =>
% 100.17/13.56 ((
% 100.17/13.56 (!!) @ (
% 100.17/13.56 (('#B') @ (
% 100.17/13.56 !!) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 !!))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#C') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1525])).
% 100.17/13.56 thf(zip_derived_cl1545, plain,
% 100.17/13.56 (~ (((setunionsingleton2) =>
% 100.17/13.56 (((setunionsingleton) =>
% 100.17/13.56 (((singletonprop) =>
% 100.17/13.56 (((ex1E1) =>
% 100.17/13.56 (((ex1I) =>
% 100.17/13.56 (((ex1I2) =>
% 100.17/13.56 (((singletonsuniq) =>
% 100.17/13.56 (((setukpairinjL1) =>
% 100.17/13.56 (((kfstsingleton) =>
% 100.17/13.56 (((theprop) =>
% 100.17/13.56 (((kfstpairEq) =>
% 100.17/13.56 (((cartprodfstin) =>
% 100.17/13.56 (((setukpairinjL2) =>
% 100.17/13.56 (((setukpairinjL) =>
% 100.17/13.56 (((setukpairinjR11) =>
% 100.17/13.56 (((setukpairinjR12) =>
% 100.17/13.56 (((setukpairinjR1) =>
% 100.17/13.56 (((upairequniteq) =>
% 100.17/13.56 (((setukpairinjR2) =>
% 100.17/13.56 (((setukpairinjR) =>
% 100.17/13.56 (((ksndsingleton) =>
% 100.17/13.56 (((ksndpairEq) =>
% 100.17/13.56 (((kpairsurjEq) =>
% 100.17/13.56 (((cartprodsndin) =>
% 100.17/13.56 (((cartprodpairmemEL) =>
% 100.17/13.56 (((cartprodpairmemER) =>
% 100.17/13.56 (((cartprodmempaircEq) =>
% 100.17/13.56 (((cartprodfstpairEq) =>
% 100.17/13.56 (((cartprodsndpairEq) =>
% 100.17/13.56 (((cartprodpairsurjEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrI) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrSub) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrERa) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrEL1) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrEL2) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrER) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcImageSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (apProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (app) =>
% 100.17/13.56 ((
% 100.17/13.56 (infuncsetfunc) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcinfuncset) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall1) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ex1E2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp3) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcextLem) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp4) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq1) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq2) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2lamEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifp) =>
% 100.17/13.56 ((
% 100.17/13.56 (theeq) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrue) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueorfalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setminusT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setextT) =>
% 100.17/13.56 ((
% 100.17/13.56 (subsetTI) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTELcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTERcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT1) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT2) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT3) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub2) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTnotintersectT) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementImpComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementSubsetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementInPowersetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (contraSubsetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTcontraSubset) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTILcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTIRcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion2) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (intersectInPowersetIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpNotIn1) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpInComplement1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTE) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTEcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementUnionInPowersetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule0) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_5) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all2) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1SetBreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (choice2fnsingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all1) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compEex) =>
% 100.17/13.56 ((
% 100.17/13.56 (!!) @ (
% 100.17/13.56 (('#B') @ (
% 100.17/13.56 !!) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 !!))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#C') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1535])).
% 100.17/13.56 thf(zip_derived_cl1555, plain,
% 100.17/13.56 (~ (((setunionsingleton) =>
% 100.17/13.56 (((singletonprop) =>
% 100.17/13.56 (((ex1E1) =>
% 100.17/13.56 (((ex1I) =>
% 100.17/13.56 (((ex1I2) =>
% 100.17/13.56 (((singletonsuniq) =>
% 100.17/13.56 (((setukpairinjL1) =>
% 100.17/13.56 (((kfstsingleton) =>
% 100.17/13.56 (((theprop) =>
% 100.17/13.56 (((kfstpairEq) =>
% 100.17/13.56 (((cartprodfstin) =>
% 100.17/13.56 (((setukpairinjL2) =>
% 100.17/13.56 (((setukpairinjL) =>
% 100.17/13.56 (((setukpairinjR11) =>
% 100.17/13.56 (((setukpairinjR12) =>
% 100.17/13.56 (((setukpairinjR1) =>
% 100.17/13.56 (((upairequniteq) =>
% 100.17/13.56 (((setukpairinjR2) =>
% 100.17/13.56 (((setukpairinjR) =>
% 100.17/13.56 (((ksndsingleton) =>
% 100.17/13.56 (((ksndpairEq) =>
% 100.17/13.56 (((kpairsurjEq) =>
% 100.17/13.56 (((cartprodsndin) =>
% 100.17/13.56 (((cartprodpairmemEL) =>
% 100.17/13.56 (((cartprodpairmemER) =>
% 100.17/13.56 (((cartprodmempaircEq) =>
% 100.17/13.56 (((cartprodfstpairEq) =>
% 100.17/13.56 (((cartprodsndpairEq) =>
% 100.17/13.56 (((cartprodpairsurjEq) =>
% 100.17/13.56 (((dpsetconstrI) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrSub) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrERa) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrEL1) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrEL2) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrER) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcImageSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (apProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (app) =>
% 100.17/13.56 ((
% 100.17/13.56 (infuncsetfunc) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcinfuncset) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall1) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ex1E2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp3) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcextLem) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp4) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq1) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq2) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2lamEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifp) =>
% 100.17/13.56 ((
% 100.17/13.56 (theeq) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrue) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueorfalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setminusT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setextT) =>
% 100.17/13.56 ((
% 100.17/13.56 (subsetTI) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTELcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTERcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT1) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT2) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT3) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub2) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTnotintersectT) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementImpComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementSubsetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementInPowersetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (contraSubsetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTcontraSubset) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTILcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTIRcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion2) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (intersectInPowersetIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpNotIn1) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpInComplement1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTE) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTEcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementUnionInPowersetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule0) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_5) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all2) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1SetBreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (choice2fnsingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all1) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compEex) =>
% 100.17/13.56 ((
% 100.17/13.56 (!!) @ (
% 100.17/13.56 (('#B') @ (
% 100.17/13.56 !!) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 !!))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#C') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1545])).
% 100.17/13.56 thf(zip_derived_cl1565, plain,
% 100.17/13.56 (~ (((singletonprop) =>
% 100.17/13.56 (((ex1E1) =>
% 100.17/13.56 (((ex1I) =>
% 100.17/13.56 (((ex1I2) =>
% 100.17/13.56 (((singletonsuniq) =>
% 100.17/13.56 (((setukpairinjL1) =>
% 100.17/13.56 (((kfstsingleton) =>
% 100.17/13.56 (((theprop) =>
% 100.17/13.56 (((kfstpairEq) =>
% 100.17/13.56 (((cartprodfstin) =>
% 100.17/13.56 (((setukpairinjL2) =>
% 100.17/13.56 (((setukpairinjL) =>
% 100.17/13.56 (((setukpairinjR11) =>
% 100.17/13.56 (((setukpairinjR12) =>
% 100.17/13.56 (((setukpairinjR1) =>
% 100.17/13.56 (((upairequniteq) =>
% 100.17/13.56 (((setukpairinjR2) =>
% 100.17/13.56 (((setukpairinjR) =>
% 100.17/13.56 (((ksndsingleton) =>
% 100.17/13.56 (((ksndpairEq) =>
% 100.17/13.56 (((kpairsurjEq) =>
% 100.17/13.56 (((cartprodsndin) =>
% 100.17/13.56 (((cartprodpairmemEL) =>
% 100.17/13.56 (((cartprodpairmemER) =>
% 100.17/13.56 (((cartprodmempaircEq) =>
% 100.17/13.56 (((cartprodfstpairEq) =>
% 100.17/13.56 (((cartprodsndpairEq) =>
% 100.17/13.56 (((cartprodpairsurjEq) =>
% 100.17/13.56 (((dpsetconstrI) =>
% 100.17/13.56 (((dpsetconstrSub) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrERa) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrEL1) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrEL2) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrER) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcImageSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (apProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (app) =>
% 100.17/13.56 ((
% 100.17/13.56 (infuncsetfunc) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcinfuncset) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall1) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ex1E2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp3) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcextLem) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp4) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq1) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq2) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2lamEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifp) =>
% 100.17/13.56 ((
% 100.17/13.56 (theeq) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrue) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueorfalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setminusT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setextT) =>
% 100.17/13.56 ((
% 100.17/13.56 (subsetTI) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTELcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTERcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT1) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT2) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT3) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub2) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTnotintersectT) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementImpComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementSubsetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementInPowersetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (contraSubsetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTcontraSubset) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTILcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTIRcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion2) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (intersectInPowersetIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpNotIn1) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpInComplement1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTE) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTEcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementUnionInPowersetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule0) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_5) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all2) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1SetBreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (choice2fnsingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all1) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compEex) =>
% 100.17/13.56 ((
% 100.17/13.56 (!!) @ (
% 100.17/13.56 (('#B') @ (
% 100.17/13.56 !!) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 !!))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#C') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1555])).
% 100.17/13.56 thf(zip_derived_cl1574, plain,
% 100.17/13.56 (~ (((ex1E1) =>
% 100.17/13.56 (((ex1I) =>
% 100.17/13.56 (((ex1I2) =>
% 100.17/13.56 (((singletonsuniq) =>
% 100.17/13.56 (((setukpairinjL1) =>
% 100.17/13.56 (((kfstsingleton) =>
% 100.17/13.56 (((theprop) =>
% 100.17/13.56 (((kfstpairEq) =>
% 100.17/13.56 (((cartprodfstin) =>
% 100.17/13.56 (((setukpairinjL2) =>
% 100.17/13.56 (((setukpairinjL) =>
% 100.17/13.56 (((setukpairinjR11) =>
% 100.17/13.56 (((setukpairinjR12) =>
% 100.17/13.56 (((setukpairinjR1) =>
% 100.17/13.56 (((upairequniteq) =>
% 100.17/13.56 (((setukpairinjR2) =>
% 100.17/13.56 (((setukpairinjR) =>
% 100.17/13.56 (((ksndsingleton) =>
% 100.17/13.56 (((ksndpairEq) =>
% 100.17/13.56 (((kpairsurjEq) =>
% 100.17/13.56 (((cartprodsndin) =>
% 100.17/13.56 (((cartprodpairmemEL) =>
% 100.17/13.56 (((cartprodpairmemER) =>
% 100.17/13.56 (((cartprodmempaircEq) =>
% 100.17/13.56 (((cartprodfstpairEq) =>
% 100.17/13.56 (((cartprodsndpairEq) =>
% 100.17/13.56 (((cartprodpairsurjEq) =>
% 100.17/13.56 (((dpsetconstrI) =>
% 100.17/13.56 (((dpsetconstrSub) =>
% 100.17/13.56 (((setOfPairsIsBReln) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrERa) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrEL1) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrEL2) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrER) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcImageSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (apProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (app) =>
% 100.17/13.56 ((
% 100.17/13.56 (infuncsetfunc) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcinfuncset) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall1) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ex1E2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp3) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcextLem) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp4) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq1) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq2) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2lamEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifp) =>
% 100.17/13.56 ((
% 100.17/13.56 (theeq) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrue) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueorfalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setminusT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setextT) =>
% 100.17/13.56 ((
% 100.17/13.56 (subsetTI) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTELcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTERcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT1) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT2) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT3) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub2) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTnotintersectT) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementImpComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementSubsetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementInPowersetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (contraSubsetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTcontraSubset) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTILcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTIRcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion2) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (intersectInPowersetIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpNotIn1) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpInComplement1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTE) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTEcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementUnionInPowersetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule0) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_5) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all2) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1SetBreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (choice2fnsingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all1) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compEex) =>
% 100.17/13.56 ((
% 100.17/13.56 (!!) @ (
% 100.17/13.56 (('#B') @ (
% 100.17/13.56 !!) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 !!))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#C') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1565])).
% 100.17/13.56 thf(zip_derived_cl1582, plain,
% 100.17/13.56 (~ (((ex1I) =>
% 100.17/13.56 (((ex1I2) =>
% 100.17/13.56 (((singletonsuniq) =>
% 100.17/13.56 (((setukpairinjL1) =>
% 100.17/13.56 (((kfstsingleton) =>
% 100.17/13.56 (((theprop) =>
% 100.17/13.56 (((kfstpairEq) =>
% 100.17/13.56 (((cartprodfstin) =>
% 100.17/13.56 (((setukpairinjL2) =>
% 100.17/13.56 (((setukpairinjL) =>
% 100.17/13.56 (((setukpairinjR11) =>
% 100.17/13.56 (((setukpairinjR12) =>
% 100.17/13.56 (((setukpairinjR1) =>
% 100.17/13.56 (((upairequniteq) =>
% 100.17/13.56 (((setukpairinjR2) =>
% 100.17/13.56 (((setukpairinjR) =>
% 100.17/13.56 (((ksndsingleton) =>
% 100.17/13.56 (((ksndpairEq) =>
% 100.17/13.56 (((kpairsurjEq) =>
% 100.17/13.56 (((cartprodsndin) =>
% 100.17/13.56 (((cartprodpairmemEL) =>
% 100.17/13.56 (((cartprodpairmemER) =>
% 100.17/13.56 (((cartprodmempaircEq) =>
% 100.17/13.56 (((cartprodfstpairEq) =>
% 100.17/13.56 (((cartprodsndpairEq) =>
% 100.17/13.56 (((cartprodpairsurjEq) =>
% 100.17/13.56 (((dpsetconstrI) =>
% 100.17/13.56 (((dpsetconstrSub) =>
% 100.17/13.56 (((setOfPairsIsBReln) =>
% 100.17/13.56 (((dpsetconstrERa) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrEL1) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrEL2) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrER) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcImageSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (apProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (app) =>
% 100.17/13.56 ((
% 100.17/13.56 (infuncsetfunc) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcinfuncset) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall1) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ex1E2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp3) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcextLem) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp4) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq1) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq2) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2lamEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifp) =>
% 100.17/13.56 ((
% 100.17/13.56 (theeq) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrue) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueorfalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setminusT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setextT) =>
% 100.17/13.56 ((
% 100.17/13.56 (subsetTI) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTELcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTERcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT1) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT2) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT3) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub2) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTnotintersectT) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementImpComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementSubsetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementInPowersetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (contraSubsetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTcontraSubset) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTILcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTIRcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion2) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (intersectInPowersetIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpNotIn1) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpInComplement1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTE) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTEcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementUnionInPowersetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule0) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_5) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all2) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1SetBreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (choice2fnsingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all1) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compEex) =>
% 100.17/13.56 ((
% 100.17/13.56 (!!) @ (
% 100.17/13.56 (('#B') @ (
% 100.17/13.56 !!) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 !!))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#C') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1574])).
% 100.17/13.56 thf(zip_derived_cl1591, plain,
% 100.17/13.56 (~ (((ex1I2) =>
% 100.17/13.56 (((singletonsuniq) =>
% 100.17/13.56 (((setukpairinjL1) =>
% 100.17/13.56 (((kfstsingleton) =>
% 100.17/13.56 (((theprop) =>
% 100.17/13.56 (((kfstpairEq) =>
% 100.17/13.56 (((cartprodfstin) =>
% 100.17/13.56 (((setukpairinjL2) =>
% 100.17/13.56 (((setukpairinjL) =>
% 100.17/13.56 (((setukpairinjR11) =>
% 100.17/13.56 (((setukpairinjR12) =>
% 100.17/13.56 (((setukpairinjR1) =>
% 100.17/13.56 (((upairequniteq) =>
% 100.17/13.56 (((setukpairinjR2) =>
% 100.17/13.56 (((setukpairinjR) =>
% 100.17/13.56 (((ksndsingleton) =>
% 100.17/13.56 (((ksndpairEq) =>
% 100.17/13.56 (((kpairsurjEq) =>
% 100.17/13.56 (((cartprodsndin) =>
% 100.17/13.56 (((cartprodpairmemEL) =>
% 100.17/13.56 (((cartprodpairmemER) =>
% 100.17/13.56 (((cartprodmempaircEq) =>
% 100.17/13.56 (((cartprodfstpairEq) =>
% 100.17/13.56 (((cartprodsndpairEq) =>
% 100.17/13.56 (((cartprodpairsurjEq) =>
% 100.17/13.56 (((dpsetconstrI) =>
% 100.17/13.56 (((dpsetconstrSub) =>
% 100.17/13.56 (((setOfPairsIsBReln) =>
% 100.17/13.56 (((dpsetconstrERa) =>
% 100.17/13.56 (((dpsetconstrEL1) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrEL2) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrER) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcImageSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (apProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (app) =>
% 100.17/13.56 ((
% 100.17/13.56 (infuncsetfunc) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcinfuncset) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall1) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ex1E2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp3) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcextLem) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp4) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq1) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq2) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2lamEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifp) =>
% 100.17/13.56 ((
% 100.17/13.56 (theeq) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrue) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueorfalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setminusT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setextT) =>
% 100.17/13.56 ((
% 100.17/13.56 (subsetTI) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTELcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTERcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT1) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT2) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT3) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub2) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTnotintersectT) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementImpComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementSubsetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementInPowersetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (contraSubsetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTcontraSubset) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTILcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTIRcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion2) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (intersectInPowersetIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpNotIn1) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpInComplement1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTE) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTEcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementUnionInPowersetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule0) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_5) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all2) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1SetBreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (choice2fnsingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all1) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compEex) =>
% 100.17/13.56 ((
% 100.17/13.56 (!!) @ (
% 100.17/13.56 (('#B') @ (
% 100.17/13.56 !!) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 !!))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#C') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1582])).
% 100.17/13.56 thf(zip_derived_cl1599, plain,
% 100.17/13.56 (~ (((singletonsuniq) =>
% 100.17/13.56 (((setukpairinjL1) =>
% 100.17/13.56 (((kfstsingleton) =>
% 100.17/13.56 (((theprop) =>
% 100.17/13.56 (((kfstpairEq) =>
% 100.17/13.56 (((cartprodfstin) =>
% 100.17/13.56 (((setukpairinjL2) =>
% 100.17/13.56 (((setukpairinjL) =>
% 100.17/13.56 (((setukpairinjR11) =>
% 100.17/13.56 (((setukpairinjR12) =>
% 100.17/13.56 (((setukpairinjR1) =>
% 100.17/13.56 (((upairequniteq) =>
% 100.17/13.56 (((setukpairinjR2) =>
% 100.17/13.56 (((setukpairinjR) =>
% 100.17/13.56 (((ksndsingleton) =>
% 100.17/13.56 (((ksndpairEq) =>
% 100.17/13.56 (((kpairsurjEq) =>
% 100.17/13.56 (((cartprodsndin) =>
% 100.17/13.56 (((cartprodpairmemEL) =>
% 100.17/13.56 (((cartprodpairmemER) =>
% 100.17/13.56 (((cartprodmempaircEq) =>
% 100.17/13.56 (((cartprodfstpairEq) =>
% 100.17/13.56 (((cartprodsndpairEq) =>
% 100.17/13.56 (((cartprodpairsurjEq) =>
% 100.17/13.56 (((dpsetconstrI) =>
% 100.17/13.56 (((dpsetconstrSub) =>
% 100.17/13.56 (((setOfPairsIsBReln) =>
% 100.17/13.56 (((dpsetconstrERa) =>
% 100.17/13.56 (((dpsetconstrEL1) =>
% 100.17/13.56 (((dpsetconstrEL2) =>
% 100.17/13.56 ((
% 100.17/13.56 (dpsetconstrER) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcImageSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (apProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (app) =>
% 100.17/13.56 ((
% 100.17/13.56 (infuncsetfunc) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcinfuncset) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall1) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ex1E2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp3) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcextLem) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp4) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq1) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq2) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2lamEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifp) =>
% 100.17/13.56 ((
% 100.17/13.56 (theeq) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrue) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueorfalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setminusT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setextT) =>
% 100.17/13.56 ((
% 100.17/13.56 (subsetTI) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTELcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTERcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT1) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT2) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT3) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub2) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTnotintersectT) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementImpComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementSubsetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementInPowersetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (contraSubsetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTcontraSubset) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTILcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTIRcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion2) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (intersectInPowersetIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpNotIn1) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpInComplement1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTE) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTEcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementUnionInPowersetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule0) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_5) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all2) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1SetBreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (choice2fnsingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all1) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compEex) =>
% 100.17/13.56 ((
% 100.17/13.56 (!!) @ (
% 100.17/13.56 (('#B') @ (
% 100.17/13.56 !!) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 !!))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#C') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1591])).
% 100.17/13.56 thf(zip_derived_cl1607, plain,
% 100.17/13.56 (~ (((setukpairinjL1) =>
% 100.17/13.56 (((kfstsingleton) =>
% 100.17/13.56 (((theprop) =>
% 100.17/13.56 (((kfstpairEq) =>
% 100.17/13.56 (((cartprodfstin) =>
% 100.17/13.56 (((setukpairinjL2) =>
% 100.17/13.56 (((setukpairinjL) =>
% 100.17/13.56 (((setukpairinjR11) =>
% 100.17/13.56 (((setukpairinjR12) =>
% 100.17/13.56 (((setukpairinjR1) =>
% 100.17/13.56 (((upairequniteq) =>
% 100.17/13.56 (((setukpairinjR2) =>
% 100.17/13.56 (((setukpairinjR) =>
% 100.17/13.56 (((ksndsingleton) =>
% 100.17/13.56 (((ksndpairEq) =>
% 100.17/13.56 (((kpairsurjEq) =>
% 100.17/13.56 (((cartprodsndin) =>
% 100.17/13.56 (((cartprodpairmemEL) =>
% 100.17/13.56 (((cartprodpairmemER) =>
% 100.17/13.56 (((cartprodmempaircEq) =>
% 100.17/13.56 (((cartprodfstpairEq) =>
% 100.17/13.56 (((cartprodsndpairEq) =>
% 100.17/13.56 (((cartprodpairsurjEq) =>
% 100.17/13.56 (((dpsetconstrI) =>
% 100.17/13.56 (((dpsetconstrSub) =>
% 100.17/13.56 (((setOfPairsIsBReln) =>
% 100.17/13.56 (((dpsetconstrERa) =>
% 100.17/13.56 (((dpsetconstrEL1) =>
% 100.17/13.56 (((dpsetconstrEL2) =>
% 100.17/13.56 (((dpsetconstrER) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcImageSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (apProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (app) =>
% 100.17/13.56 ((
% 100.17/13.56 (infuncsetfunc) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcinfuncset) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall1) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ex1E2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp3) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcextLem) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp4) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq1) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq2) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2lamEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifp) =>
% 100.17/13.56 ((
% 100.17/13.56 (theeq) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrue) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueorfalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setminusT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setextT) =>
% 100.17/13.56 ((
% 100.17/13.56 (subsetTI) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTELcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTERcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT1) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT2) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT3) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub2) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTnotintersectT) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementImpComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementSubsetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementInPowersetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (contraSubsetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTcontraSubset) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTILcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTIRcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion2) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (intersectInPowersetIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpNotIn1) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpInComplement1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTE) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTEcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementUnionInPowersetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule0) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_5) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all2) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1SetBreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (choice2fnsingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all1) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compEex) =>
% 100.17/13.56 ((
% 100.17/13.56 (!!) @ (
% 100.17/13.56 (('#B') @ (
% 100.17/13.56 !!) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 !!))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#C') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1599])).
% 100.17/13.56 thf(zip_derived_cl1615, plain,
% 100.17/13.56 (~ (((kfstsingleton) =>
% 100.17/13.56 (((theprop) =>
% 100.17/13.56 (((kfstpairEq) =>
% 100.17/13.56 (((cartprodfstin) =>
% 100.17/13.56 (((setukpairinjL2) =>
% 100.17/13.56 (((setukpairinjL) =>
% 100.17/13.56 (((setukpairinjR11) =>
% 100.17/13.56 (((setukpairinjR12) =>
% 100.17/13.56 (((setukpairinjR1) =>
% 100.17/13.56 (((upairequniteq) =>
% 100.17/13.56 (((setukpairinjR2) =>
% 100.17/13.56 (((setukpairinjR) =>
% 100.17/13.56 (((ksndsingleton) =>
% 100.17/13.56 (((ksndpairEq) =>
% 100.17/13.56 (((kpairsurjEq) =>
% 100.17/13.56 (((cartprodsndin) =>
% 100.17/13.56 (((cartprodpairmemEL) =>
% 100.17/13.56 (((cartprodpairmemER) =>
% 100.17/13.56 (((cartprodmempaircEq) =>
% 100.17/13.56 (((cartprodfstpairEq) =>
% 100.17/13.56 (((cartprodsndpairEq) =>
% 100.17/13.56 (((cartprodpairsurjEq) =>
% 100.17/13.56 (((dpsetconstrI) =>
% 100.17/13.56 (((dpsetconstrSub) =>
% 100.17/13.56 (((setOfPairsIsBReln) =>
% 100.17/13.56 (((dpsetconstrERa) =>
% 100.17/13.56 (((dpsetconstrEL1) =>
% 100.17/13.56 (((dpsetconstrEL2) =>
% 100.17/13.56 (((dpsetconstrER) =>
% 100.17/13.56 (((funcImageSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (apProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (app) =>
% 100.17/13.56 ((
% 100.17/13.56 (infuncsetfunc) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcinfuncset) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall1) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ex1E2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp3) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcextLem) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp4) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq1) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq2) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2lamEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifp) =>
% 100.17/13.56 ((
% 100.17/13.56 (theeq) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrue) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueorfalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setminusT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setextT) =>
% 100.17/13.56 ((
% 100.17/13.56 (subsetTI) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTELcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTERcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT1) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT2) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT3) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub2) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTnotintersectT) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementImpComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementSubsetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementInPowersetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (contraSubsetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTcontraSubset) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTILcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTIRcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion2) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (intersectInPowersetIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpNotIn1) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpInComplement1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTE) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTEcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementUnionInPowersetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule0) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_5) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all2) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1SetBreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (choice2fnsingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all1) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compEex) =>
% 100.17/13.56 ((
% 100.17/13.56 (!!) @ (
% 100.17/13.56 (('#B') @ (
% 100.17/13.56 !!) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 !!))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#C') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1607])).
% 100.17/13.56 thf(zip_derived_cl1625, plain,
% 100.17/13.56 (~ (((theprop) =>
% 100.17/13.56 (((kfstpairEq) =>
% 100.17/13.56 (((cartprodfstin) =>
% 100.17/13.56 (((setukpairinjL2) =>
% 100.17/13.56 (((setukpairinjL) =>
% 100.17/13.56 (((setukpairinjR11) =>
% 100.17/13.56 (((setukpairinjR12) =>
% 100.17/13.56 (((setukpairinjR1) =>
% 100.17/13.56 (((upairequniteq) =>
% 100.17/13.56 (((setukpairinjR2) =>
% 100.17/13.56 (((setukpairinjR) =>
% 100.17/13.56 (((ksndsingleton) =>
% 100.17/13.56 (((ksndpairEq) =>
% 100.17/13.56 (((kpairsurjEq) =>
% 100.17/13.56 (((cartprodsndin) =>
% 100.17/13.56 (((cartprodpairmemEL) =>
% 100.17/13.56 (((cartprodpairmemER) =>
% 100.17/13.56 (((cartprodmempaircEq) =>
% 100.17/13.56 (((cartprodfstpairEq) =>
% 100.17/13.56 (((cartprodsndpairEq) =>
% 100.17/13.56 (((cartprodpairsurjEq) =>
% 100.17/13.56 (((dpsetconstrI) =>
% 100.17/13.56 (((dpsetconstrSub) =>
% 100.17/13.56 (((setOfPairsIsBReln) =>
% 100.17/13.56 (((dpsetconstrERa) =>
% 100.17/13.56 (((dpsetconstrEL1) =>
% 100.17/13.56 (((dpsetconstrEL2) =>
% 100.17/13.56 (((dpsetconstrER) =>
% 100.17/13.56 (((funcImageSingleton) =>
% 100.17/13.56 (((apProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (app) =>
% 100.17/13.56 ((
% 100.17/13.56 (infuncsetfunc) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcinfuncset) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall1) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ex1E2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp3) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcextLem) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp4) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq1) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq2) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2lamEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifp) =>
% 100.17/13.56 ((
% 100.17/13.56 (theeq) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrue) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueorfalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setminusT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setextT) =>
% 100.17/13.56 ((
% 100.17/13.56 (subsetTI) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTELcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTERcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT1) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT2) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT3) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub2) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTnotintersectT) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementImpComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementSubsetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementInPowersetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (contraSubsetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTcontraSubset) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTILcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTIRcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion2) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (intersectInPowersetIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpNotIn1) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpInComplement1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTE) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTEcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementUnionInPowersetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule0) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_5) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all2) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1SetBreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (choice2fnsingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all1) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compEex) =>
% 100.17/13.56 ((
% 100.17/13.56 (!!) @ (
% 100.17/13.56 (('#B') @ (
% 100.17/13.56 !!) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 !!))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#C') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1615])).
% 100.17/13.56 thf(zip_derived_cl1637, plain,
% 100.17/13.56 (~ (((kfstpairEq) =>
% 100.17/13.56 (((cartprodfstin) =>
% 100.17/13.56 (((setukpairinjL2) =>
% 100.17/13.56 (((setukpairinjL) =>
% 100.17/13.56 (((setukpairinjR11) =>
% 100.17/13.56 (((setukpairinjR12) =>
% 100.17/13.56 (((setukpairinjR1) =>
% 100.17/13.56 (((upairequniteq) =>
% 100.17/13.56 (((setukpairinjR2) =>
% 100.17/13.56 (((setukpairinjR) =>
% 100.17/13.56 (((ksndsingleton) =>
% 100.17/13.56 (((ksndpairEq) =>
% 100.17/13.56 (((kpairsurjEq) =>
% 100.17/13.56 (((cartprodsndin) =>
% 100.17/13.56 (((cartprodpairmemEL) =>
% 100.17/13.56 (((cartprodpairmemER) =>
% 100.17/13.56 (((cartprodmempaircEq) =>
% 100.17/13.56 (((cartprodfstpairEq) =>
% 100.17/13.56 (((cartprodsndpairEq) =>
% 100.17/13.56 (((cartprodpairsurjEq) =>
% 100.17/13.56 (((dpsetconstrI) =>
% 100.17/13.56 (((dpsetconstrSub) =>
% 100.17/13.56 (((setOfPairsIsBReln) =>
% 100.17/13.56 (((dpsetconstrERa) =>
% 100.17/13.56 (((dpsetconstrEL1) =>
% 100.17/13.56 (((dpsetconstrEL2) =>
% 100.17/13.56 (((dpsetconstrER) =>
% 100.17/13.56 (((funcImageSingleton) =>
% 100.17/13.56 (((apProp) =>
% 100.17/13.56 (((app) =>
% 100.17/13.56 ((
% 100.17/13.56 (infuncsetfunc) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcinfuncset) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall1) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ex1E2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp3) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcextLem) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp4) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq1) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq2) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2lamEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifp) =>
% 100.17/13.56 ((
% 100.17/13.56 (theeq) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrue) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueorfalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setminusT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setextT) =>
% 100.17/13.56 ((
% 100.17/13.56 (subsetTI) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTELcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTERcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT1) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT2) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT3) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub2) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTnotintersectT) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementImpComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementSubsetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementInPowersetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (contraSubsetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTcontraSubset) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTILcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTIRcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion2) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (intersectInPowersetIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpNotIn1) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpInComplement1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTE) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTEcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementUnionInPowersetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule0) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_5) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all2) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1SetBreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (choice2fnsingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all1) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compEex) =>
% 100.17/13.56 ((
% 100.17/13.56 (!!) @ (
% 100.17/13.56 (('#B') @ (
% 100.17/13.56 !!) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 !!))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#C') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1625])).
% 100.17/13.56 thf(zip_derived_cl1649, plain,
% 100.17/13.56 (~ (((cartprodfstin) =>
% 100.17/13.56 (((setukpairinjL2) =>
% 100.17/13.56 (((setukpairinjL) =>
% 100.17/13.56 (((setukpairinjR11) =>
% 100.17/13.56 (((setukpairinjR12) =>
% 100.17/13.56 (((setukpairinjR1) =>
% 100.17/13.56 (((upairequniteq) =>
% 100.17/13.56 (((setukpairinjR2) =>
% 100.17/13.56 (((setukpairinjR) =>
% 100.17/13.56 (((ksndsingleton) =>
% 100.17/13.56 (((ksndpairEq) =>
% 100.17/13.56 (((kpairsurjEq) =>
% 100.17/13.56 (((cartprodsndin) =>
% 100.17/13.56 (((cartprodpairmemEL) =>
% 100.17/13.56 (((cartprodpairmemER) =>
% 100.17/13.56 (((cartprodmempaircEq) =>
% 100.17/13.56 (((cartprodfstpairEq) =>
% 100.17/13.56 (((cartprodsndpairEq) =>
% 100.17/13.56 (((cartprodpairsurjEq) =>
% 100.17/13.56 (((dpsetconstrI) =>
% 100.17/13.56 (((dpsetconstrSub) =>
% 100.17/13.56 (((setOfPairsIsBReln) =>
% 100.17/13.56 (((dpsetconstrERa) =>
% 100.17/13.56 (((dpsetconstrEL1) =>
% 100.17/13.56 (((dpsetconstrEL2) =>
% 100.17/13.56 (((dpsetconstrER) =>
% 100.17/13.56 (((funcImageSingleton) =>
% 100.17/13.56 (((apProp) =>
% 100.17/13.56 (((app) =>
% 100.17/13.56 (((infuncsetfunc) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcinfuncset) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall1) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ex1E2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp3) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcextLem) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp4) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq1) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq2) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2lamEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifp) =>
% 100.17/13.56 ((
% 100.17/13.56 (theeq) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrue) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueorfalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setminusT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setextT) =>
% 100.17/13.56 ((
% 100.17/13.56 (subsetTI) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTELcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTERcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT1) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT2) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT3) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub2) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTnotintersectT) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementImpComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementSubsetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementInPowersetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (contraSubsetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTcontraSubset) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTILcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTIRcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion2) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (intersectInPowersetIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpNotIn1) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpInComplement1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTE) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTEcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementUnionInPowersetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule0) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_5) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all2) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1SetBreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (choice2fnsingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all1) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compEex) =>
% 100.17/13.56 ((
% 100.17/13.56 (!!) @ (
% 100.17/13.56 (('#B') @ (
% 100.17/13.56 !!) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 !!))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#C') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1637])).
% 100.17/13.56 thf(zip_derived_cl1664, plain,
% 100.17/13.56 (~ (((setukpairinjL2) =>
% 100.17/13.56 (((setukpairinjL) =>
% 100.17/13.56 (((setukpairinjR11) =>
% 100.17/13.56 (((setukpairinjR12) =>
% 100.17/13.56 (((setukpairinjR1) =>
% 100.17/13.56 (((upairequniteq) =>
% 100.17/13.56 (((setukpairinjR2) =>
% 100.17/13.56 (((setukpairinjR) =>
% 100.17/13.56 (((ksndsingleton) =>
% 100.17/13.56 (((ksndpairEq) =>
% 100.17/13.56 (((kpairsurjEq) =>
% 100.17/13.56 (((cartprodsndin) =>
% 100.17/13.56 (((cartprodpairmemEL) =>
% 100.17/13.56 (((cartprodpairmemER) =>
% 100.17/13.56 (((cartprodmempaircEq) =>
% 100.17/13.56 (((cartprodfstpairEq) =>
% 100.17/13.56 (((cartprodsndpairEq) =>
% 100.17/13.56 (((cartprodpairsurjEq) =>
% 100.17/13.56 (((dpsetconstrI) =>
% 100.17/13.56 (((dpsetconstrSub) =>
% 100.17/13.56 (((setOfPairsIsBReln) =>
% 100.17/13.56 (((dpsetconstrERa) =>
% 100.17/13.56 (((dpsetconstrEL1) =>
% 100.17/13.56 (((dpsetconstrEL2) =>
% 100.17/13.56 (((dpsetconstrER) =>
% 100.17/13.56 (((funcImageSingleton) =>
% 100.17/13.56 (((apProp) =>
% 100.17/13.56 (((app) =>
% 100.17/13.56 (((infuncsetfunc) =>
% 100.17/13.56 (((ap2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcinfuncset) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall1) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ex1E2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp3) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcextLem) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp4) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq1) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq2) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2lamEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifp) =>
% 100.17/13.56 ((
% 100.17/13.56 (theeq) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrue) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueorfalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setminusT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setextT) =>
% 100.17/13.56 ((
% 100.17/13.56 (subsetTI) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTELcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTERcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT1) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT2) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT3) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub2) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTnotintersectT) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementImpComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementSubsetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementInPowersetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (contraSubsetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTcontraSubset) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTILcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTIRcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion2) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (intersectInPowersetIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpNotIn1) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpInComplement1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTE) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTEcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementUnionInPowersetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule0) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_5) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all2) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1SetBreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (choice2fnsingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all1) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compEex) =>
% 100.17/13.56 ((
% 100.17/13.56 (!!) @ (
% 100.17/13.56 (('#B') @ (
% 100.17/13.56 !!) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 !!))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#C') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1649])).
% 100.17/13.56 thf(zip_derived_cl1678, plain,
% 100.17/13.56 (~ (((setukpairinjL) =>
% 100.17/13.56 (((setukpairinjR11) =>
% 100.17/13.56 (((setukpairinjR12) =>
% 100.17/13.56 (((setukpairinjR1) =>
% 100.17/13.56 (((upairequniteq) =>
% 100.17/13.56 (((setukpairinjR2) =>
% 100.17/13.56 (((setukpairinjR) =>
% 100.17/13.56 (((ksndsingleton) =>
% 100.17/13.56 (((ksndpairEq) =>
% 100.17/13.56 (((kpairsurjEq) =>
% 100.17/13.56 (((cartprodsndin) =>
% 100.17/13.56 (((cartprodpairmemEL) =>
% 100.17/13.56 (((cartprodpairmemER) =>
% 100.17/13.56 (((cartprodmempaircEq) =>
% 100.17/13.56 (((cartprodfstpairEq) =>
% 100.17/13.56 (((cartprodsndpairEq) =>
% 100.17/13.56 (((cartprodpairsurjEq) =>
% 100.17/13.56 (((dpsetconstrI) =>
% 100.17/13.56 (((dpsetconstrSub) =>
% 100.17/13.56 (((setOfPairsIsBReln) =>
% 100.17/13.56 (((dpsetconstrERa) =>
% 100.17/13.56 (((dpsetconstrEL1) =>
% 100.17/13.56 (((dpsetconstrEL2) =>
% 100.17/13.56 (((dpsetconstrER) =>
% 100.17/13.56 (((funcImageSingleton) =>
% 100.17/13.56 (((apProp) =>
% 100.17/13.56 (((app) =>
% 100.17/13.56 (((infuncsetfunc) =>
% 100.17/13.56 (((ap2p) =>
% 100.17/13.56 (((funcinfuncset) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall1) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ex1E2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp3) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcextLem) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp4) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq1) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq2) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2lamEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifp) =>
% 100.17/13.56 ((
% 100.17/13.56 (theeq) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrue) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueorfalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setminusT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setextT) =>
% 100.17/13.56 ((
% 100.17/13.56 (subsetTI) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTELcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTERcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT1) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT2) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT3) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub2) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTnotintersectT) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementImpComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementSubsetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementInPowersetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (contraSubsetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTcontraSubset) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTILcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTIRcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion2) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (intersectInPowersetIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpNotIn1) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpInComplement1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTE) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTEcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementUnionInPowersetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule0) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_5) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all2) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1SetBreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (choice2fnsingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all1) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compEex) =>
% 100.17/13.56 ((
% 100.17/13.56 (!!) @ (
% 100.17/13.56 (('#B') @ (
% 100.17/13.56 !!) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 !!))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#C') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#B') @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1664])).
% 100.17/13.56 thf(zip_derived_cl1695, plain,
% 100.17/13.56 (~ (((setukpairinjR11) =>
% 100.17/13.56 (((setukpairinjR12) =>
% 100.17/13.56 (((setukpairinjR1) =>
% 100.17/13.56 (((upairequniteq) =>
% 100.17/13.56 (((setukpairinjR2) =>
% 100.17/13.56 (((setukpairinjR) =>
% 100.17/13.56 (((ksndsingleton) =>
% 100.17/13.56 (((ksndpairEq) =>
% 100.17/13.56 (((kpairsurjEq) =>
% 100.17/13.56 (((cartprodsndin) =>
% 100.17/13.56 (((cartprodpairmemEL) =>
% 100.17/13.56 (((cartprodpairmemER) =>
% 100.17/13.56 (((cartprodmempaircEq) =>
% 100.17/13.56 (((cartprodfstpairEq) =>
% 100.17/13.56 (((cartprodsndpairEq) =>
% 100.17/13.56 (((cartprodpairsurjEq) =>
% 100.17/13.56 (((dpsetconstrI) =>
% 100.17/13.56 (((dpsetconstrSub) =>
% 100.17/13.56 (((setOfPairsIsBReln) =>
% 100.17/13.56 (((dpsetconstrERa) =>
% 100.17/13.56 (((dpsetconstrEL1) =>
% 100.17/13.56 (((dpsetconstrEL2) =>
% 100.17/13.56 (((dpsetconstrER) =>
% 100.17/13.56 (((funcImageSingleton) =>
% 100.17/13.56 (((apProp) =>
% 100.17/13.56 (((app) =>
% 100.17/13.56 (((infuncsetfunc) =>
% 100.17/13.56 (((ap2p) =>
% 100.17/13.56 (((funcinfuncset) =>
% 100.17/13.56 (((lamProp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lamp) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2p) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall1) =>
% 100.17/13.56 ((
% 100.17/13.56 (brelnall2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ex1E2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp3) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcextLem) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcGraphProp4) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext) =>
% 100.17/13.56 ((
% 100.17/13.56 (funcext2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq1) =>
% 100.17/13.56 ((
% 100.17/13.56 (ap2apEq2) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta1) =>
% 100.17/13.56 ((
% 100.17/13.56 (lam2lamEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (beta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (eta2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalseProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp1) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueProp2) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifSingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (ifp) =>
% 100.17/13.56 ((
% 100.17/13.56 (theeq) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrue) =>
% 100.17/13.56 ((
% 100.17/13.56 (iffalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (iftrueorfalse) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setminusT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementT_lem) =>
% 100.17/13.56 ((
% 100.17/13.56 (setextT) =>
% 100.17/13.56 ((
% 100.17/13.56 (subsetTI) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (powersetTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTELcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binintersectTERcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT1) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT2) =>
% 100.17/13.56 ((
% 100.17/13.56 (contrasubsetT3) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementI1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementE1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub1) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementSub2) =>
% 100.17/13.56 ((
% 100.17/13.56 (doubleComplementEq) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTnotintersectT) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementImpComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementSubsetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementInPowersetComplementIntersect) =>
% 100.17/13.56 ((
% 100.17/13.56 (contraSubsetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementTcontraSubset) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTILcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTIRcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInUnion2) =>
% 100.17/13.56 ((
% 100.17/13.56 (inIntersectImpInIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (intersectInPowersetIntersectUnions) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpNotIn1) =>
% 100.17/13.56 ((
% 100.17/13.56 (inComplementUnionImpInComplement1) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTE) =>
% 100.17/13.56 ((
% 100.17/13.56 (binunionTEcontra) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a1) =>
% 100.17/13.56 ((
% 100.17/13.56 (complementUnionInPowersetComplement) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan1) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2a) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b2) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2b) =>
% 100.17/13.56 ((
% 100.17/13.56 (demorgan2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule0) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz13rule4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_1) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_2) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_3) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_4) =>
% 100.17/13.56 ((
% 100.17/13.56 (woz1_5) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all2) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1SetBreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (choice2fnsingleton) =>
% 100.17/13.56 ((
% 100.17/13.56 (setOfPairsIsBReln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1all1) =>
% 100.17/13.56 ((
% 100.17/13.56 (subbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (eqbreln1) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1invE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compprop) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compI) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compE) =>
% 100.17/13.56 ((
% 100.17/13.56 (breln1compEex) =>
% 100.17/13.56 ((
% 100.17/13.56 (!!) @ (
% 100.17/13.56 (('#B') @ (
% 100.17/13.56 !!) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 '#S') @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 =>))) @
% 100.17/13.56 breln1)))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 (
% 100.17/13.56 ('#B') @ (
% 100.17/13.56 !!))) @
% 100.17/13.56 (
% 100.17/13.56 (
% 100.17/13.56 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#C') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1678])).
% 100.17/13.57 thf(zip_derived_cl1711, plain,
% 100.17/13.57 (~ (((setukpairinjR12) =>
% 100.17/13.57 (((setukpairinjR1) =>
% 100.17/13.57 (((upairequniteq) =>
% 100.17/13.57 (((setukpairinjR2) =>
% 100.17/13.57 (((setukpairinjR) =>
% 100.17/13.57 (((ksndsingleton) =>
% 100.17/13.57 (((ksndpairEq) =>
% 100.17/13.57 (((kpairsurjEq) =>
% 100.17/13.57 (((cartprodsndin) =>
% 100.17/13.57 (((cartprodpairmemEL) =>
% 100.17/13.57 (((cartprodpairmemER) =>
% 100.17/13.57 (((cartprodmempaircEq) =>
% 100.17/13.57 (((cartprodfstpairEq) =>
% 100.17/13.57 (((cartprodsndpairEq) =>
% 100.17/13.57 (((cartprodpairsurjEq) =>
% 100.17/13.57 (((dpsetconstrI) =>
% 100.17/13.57 (((dpsetconstrSub) =>
% 100.17/13.57 (((setOfPairsIsBReln) =>
% 100.17/13.57 (((dpsetconstrERa) =>
% 100.17/13.57 (((dpsetconstrEL1) =>
% 100.17/13.57 (((dpsetconstrEL2) =>
% 100.17/13.57 (((dpsetconstrER) =>
% 100.17/13.57 (((funcImageSingleton) =>
% 100.17/13.57 (((apProp) =>
% 100.17/13.57 (((app) =>
% 100.17/13.57 (((infuncsetfunc) =>
% 100.17/13.57 (((ap2p) =>
% 100.17/13.57 (((funcinfuncset) =>
% 100.17/13.57 (((lamProp) =>
% 100.17/13.57 (((lamp) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2p) =>
% 100.17/13.57 ((
% 100.17/13.57 (brelnall1) =>
% 100.17/13.57 ((
% 100.17/13.57 (brelnall2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ex1E2) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp3) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcextLem) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp4) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq1) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq2) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2lamEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifSingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifp) =>
% 100.17/13.57 ((
% 100.17/13.57 (theeq) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrue) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueorfalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setminusT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setextT) =>
% 100.17/13.57 ((
% 100.17/13.57 (subsetTI) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTELcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTERcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT1) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT2) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT3) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub2) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTnotintersectT) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementImpComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementSubsetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementInPowersetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (contraSubsetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTcontraSubset) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTILcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTIRcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion2) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (intersectInPowersetIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpNotIn1) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpInComplement1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTE) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTEcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementUnionInPowersetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule0) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_5) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all2) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1SetBreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (choice2fnsingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (setOfPairsIsBReln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all1) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compEex) =>
% 100.17/13.57 ((
% 100.17/13.57 (!!) @ (
% 100.17/13.57 (('#B') @ (
% 100.17/13.57 !!) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 !!))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#C') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1695])).
% 100.17/13.57 thf(zip_derived_cl1725, plain,
% 100.17/13.57 (~ (((setukpairinjR1) =>
% 100.17/13.57 (((upairequniteq) =>
% 100.17/13.57 (((setukpairinjR2) =>
% 100.17/13.57 (((setukpairinjR) =>
% 100.17/13.57 (((ksndsingleton) =>
% 100.17/13.57 (((ksndpairEq) =>
% 100.17/13.57 (((kpairsurjEq) =>
% 100.17/13.57 (((cartprodsndin) =>
% 100.17/13.57 (((cartprodpairmemEL) =>
% 100.17/13.57 (((cartprodpairmemER) =>
% 100.17/13.57 (((cartprodmempaircEq) =>
% 100.17/13.57 (((cartprodfstpairEq) =>
% 100.17/13.57 (((cartprodsndpairEq) =>
% 100.17/13.57 (((cartprodpairsurjEq) =>
% 100.17/13.57 (((dpsetconstrI) =>
% 100.17/13.57 (((dpsetconstrSub) =>
% 100.17/13.57 (((setOfPairsIsBReln) =>
% 100.17/13.57 (((dpsetconstrERa) =>
% 100.17/13.57 (((dpsetconstrEL1) =>
% 100.17/13.57 (((dpsetconstrEL2) =>
% 100.17/13.57 (((dpsetconstrER) =>
% 100.17/13.57 (((funcImageSingleton) =>
% 100.17/13.57 (((apProp) =>
% 100.17/13.57 (((app) =>
% 100.17/13.57 (((infuncsetfunc) =>
% 100.17/13.57 (((ap2p) =>
% 100.17/13.57 (((funcinfuncset) =>
% 100.17/13.57 (((lamProp) =>
% 100.17/13.57 (((lamp) =>
% 100.17/13.57 (((lam2p) =>
% 100.17/13.57 ((
% 100.17/13.57 (brelnall1) =>
% 100.17/13.57 ((
% 100.17/13.57 (brelnall2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ex1E2) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp3) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcextLem) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp4) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq1) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq2) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2lamEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifSingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifp) =>
% 100.17/13.57 ((
% 100.17/13.57 (theeq) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrue) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueorfalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setminusT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setextT) =>
% 100.17/13.57 ((
% 100.17/13.57 (subsetTI) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTELcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTERcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT1) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT2) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT3) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub2) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTnotintersectT) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementImpComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementSubsetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementInPowersetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (contraSubsetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTcontraSubset) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTILcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTIRcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion2) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (intersectInPowersetIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpNotIn1) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpInComplement1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTE) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTEcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementUnionInPowersetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule0) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_5) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all2) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1SetBreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (choice2fnsingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (setOfPairsIsBReln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all1) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compEex) =>
% 100.17/13.57 ((
% 100.17/13.57 (!!) @ (
% 100.17/13.57 (('#B') @ (
% 100.17/13.57 !!) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 !!))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#C') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1711])).
% 100.17/13.57 thf(zip_derived_cl1738, plain,
% 100.17/13.57 (~ (((upairequniteq) =>
% 100.17/13.57 (((setukpairinjR2) =>
% 100.17/13.57 (((setukpairinjR) =>
% 100.17/13.57 (((ksndsingleton) =>
% 100.17/13.57 (((ksndpairEq) =>
% 100.17/13.57 (((kpairsurjEq) =>
% 100.17/13.57 (((cartprodsndin) =>
% 100.17/13.57 (((cartprodpairmemEL) =>
% 100.17/13.57 (((cartprodpairmemER) =>
% 100.17/13.57 (((cartprodmempaircEq) =>
% 100.17/13.57 (((cartprodfstpairEq) =>
% 100.17/13.57 (((cartprodsndpairEq) =>
% 100.17/13.57 (((cartprodpairsurjEq) =>
% 100.17/13.57 (((dpsetconstrI) =>
% 100.17/13.57 (((dpsetconstrSub) =>
% 100.17/13.57 (((setOfPairsIsBReln) =>
% 100.17/13.57 (((dpsetconstrERa) =>
% 100.17/13.57 (((dpsetconstrEL1) =>
% 100.17/13.57 (((dpsetconstrEL2) =>
% 100.17/13.57 (((dpsetconstrER) =>
% 100.17/13.57 (((funcImageSingleton) =>
% 100.17/13.57 (((apProp) =>
% 100.17/13.57 (((app) =>
% 100.17/13.57 (((infuncsetfunc) =>
% 100.17/13.57 (((ap2p) =>
% 100.17/13.57 (((funcinfuncset) =>
% 100.17/13.57 (((lamProp) =>
% 100.17/13.57 (((lamp) =>
% 100.17/13.57 (((lam2p) =>
% 100.17/13.57 (((brelnall1) =>
% 100.17/13.57 ((
% 100.17/13.57 (brelnall2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ex1E2) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp3) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcextLem) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp4) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq1) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq2) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2lamEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifSingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifp) =>
% 100.17/13.57 ((
% 100.17/13.57 (theeq) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrue) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueorfalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setminusT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setextT) =>
% 100.17/13.57 ((
% 100.17/13.57 (subsetTI) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTELcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTERcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT1) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT2) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT3) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub2) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTnotintersectT) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementImpComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementSubsetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementInPowersetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (contraSubsetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTcontraSubset) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTILcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTIRcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion2) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (intersectInPowersetIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpNotIn1) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpInComplement1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTE) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTEcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementUnionInPowersetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule0) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_5) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all2) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1SetBreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (choice2fnsingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (setOfPairsIsBReln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all1) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compEex) =>
% 100.17/13.57 ((
% 100.17/13.57 (!!) @ (
% 100.17/13.57 (('#B') @ (
% 100.17/13.57 !!) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 !!))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#C') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1725])).
% 100.17/13.57 thf(zip_derived_cl1749, plain,
% 100.17/13.57 (~ (((setukpairinjR2) =>
% 100.17/13.57 (((setukpairinjR) =>
% 100.17/13.57 (((ksndsingleton) =>
% 100.17/13.57 (((ksndpairEq) =>
% 100.17/13.57 (((kpairsurjEq) =>
% 100.17/13.57 (((cartprodsndin) =>
% 100.17/13.57 (((cartprodpairmemEL) =>
% 100.17/13.57 (((cartprodpairmemER) =>
% 100.17/13.57 (((cartprodmempaircEq) =>
% 100.17/13.57 (((cartprodfstpairEq) =>
% 100.17/13.57 (((cartprodsndpairEq) =>
% 100.17/13.57 (((cartprodpairsurjEq) =>
% 100.17/13.57 (((dpsetconstrI) =>
% 100.17/13.57 (((dpsetconstrSub) =>
% 100.17/13.57 (((setOfPairsIsBReln) =>
% 100.17/13.57 (((dpsetconstrERa) =>
% 100.17/13.57 (((dpsetconstrEL1) =>
% 100.17/13.57 (((dpsetconstrEL2) =>
% 100.17/13.57 (((dpsetconstrER) =>
% 100.17/13.57 (((funcImageSingleton) =>
% 100.17/13.57 (((apProp) =>
% 100.17/13.57 (((app) =>
% 100.17/13.57 (((infuncsetfunc) =>
% 100.17/13.57 (((ap2p) =>
% 100.17/13.57 (((funcinfuncset) =>
% 100.17/13.57 (((lamProp) =>
% 100.17/13.57 (((lamp) =>
% 100.17/13.57 (((lam2p) =>
% 100.17/13.57 (((brelnall1) =>
% 100.17/13.57 (((brelnall2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ex1E2) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp3) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcextLem) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp4) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq1) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq2) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2lamEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifSingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifp) =>
% 100.17/13.57 ((
% 100.17/13.57 (theeq) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrue) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueorfalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setminusT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setextT) =>
% 100.17/13.57 ((
% 100.17/13.57 (subsetTI) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTELcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTERcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT1) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT2) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT3) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub2) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTnotintersectT) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementImpComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementSubsetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementInPowersetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (contraSubsetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTcontraSubset) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTILcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTIRcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion2) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (intersectInPowersetIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpNotIn1) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpInComplement1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTE) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTEcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementUnionInPowersetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule0) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_5) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all2) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1SetBreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (choice2fnsingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (setOfPairsIsBReln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all1) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compEex) =>
% 100.17/13.57 ((
% 100.17/13.57 (!!) @ (
% 100.17/13.57 (('#B') @ (
% 100.17/13.57 !!) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 !!))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#C') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1738])).
% 100.17/13.57 thf(zip_derived_cl1760, plain,
% 100.17/13.57 (~ (((setukpairinjR) =>
% 100.17/13.57 (((ksndsingleton) =>
% 100.17/13.57 (((ksndpairEq) =>
% 100.17/13.57 (((kpairsurjEq) =>
% 100.17/13.57 (((cartprodsndin) =>
% 100.17/13.57 (((cartprodpairmemEL) =>
% 100.17/13.57 (((cartprodpairmemER) =>
% 100.17/13.57 (((cartprodmempaircEq) =>
% 100.17/13.57 (((cartprodfstpairEq) =>
% 100.17/13.57 (((cartprodsndpairEq) =>
% 100.17/13.57 (((cartprodpairsurjEq) =>
% 100.17/13.57 (((dpsetconstrI) =>
% 100.17/13.57 (((dpsetconstrSub) =>
% 100.17/13.57 (((setOfPairsIsBReln) =>
% 100.17/13.57 (((dpsetconstrERa) =>
% 100.17/13.57 (((dpsetconstrEL1) =>
% 100.17/13.57 (((dpsetconstrEL2) =>
% 100.17/13.57 (((dpsetconstrER) =>
% 100.17/13.57 (((funcImageSingleton) =>
% 100.17/13.57 (((apProp) =>
% 100.17/13.57 (((app) =>
% 100.17/13.57 (((infuncsetfunc) =>
% 100.17/13.57 (((ap2p) =>
% 100.17/13.57 (((funcinfuncset) =>
% 100.17/13.57 (((lamProp) =>
% 100.17/13.57 (((lamp) =>
% 100.17/13.57 (((lam2p) =>
% 100.17/13.57 (((brelnall1) =>
% 100.17/13.57 (((brelnall2) =>
% 100.17/13.57 (((ex1E2) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp3) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcextLem) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp4) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq1) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq2) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2lamEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifSingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifp) =>
% 100.17/13.57 ((
% 100.17/13.57 (theeq) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrue) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueorfalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setminusT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setextT) =>
% 100.17/13.57 ((
% 100.17/13.57 (subsetTI) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTELcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTERcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT1) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT2) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT3) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub2) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTnotintersectT) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementImpComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementSubsetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementInPowersetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (contraSubsetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTcontraSubset) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTILcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTIRcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion2) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (intersectInPowersetIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpNotIn1) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpInComplement1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTE) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTEcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementUnionInPowersetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule0) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_5) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all2) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1SetBreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (choice2fnsingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (setOfPairsIsBReln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all1) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compEex) =>
% 100.17/13.57 ((
% 100.17/13.57 (!!) @ (
% 100.17/13.57 (('#B') @ (
% 100.17/13.57 !!) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 !!))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#C') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1749])).
% 100.17/13.57 thf(zip_derived_cl1770, plain,
% 100.17/13.57 (~ (((ksndsingleton) =>
% 100.17/13.57 (((ksndpairEq) =>
% 100.17/13.57 (((kpairsurjEq) =>
% 100.17/13.57 (((cartprodsndin) =>
% 100.17/13.57 (((cartprodpairmemEL) =>
% 100.17/13.57 (((cartprodpairmemER) =>
% 100.17/13.57 (((cartprodmempaircEq) =>
% 100.17/13.57 (((cartprodfstpairEq) =>
% 100.17/13.57 (((cartprodsndpairEq) =>
% 100.17/13.57 (((cartprodpairsurjEq) =>
% 100.17/13.57 (((dpsetconstrI) =>
% 100.17/13.57 (((dpsetconstrSub) =>
% 100.17/13.57 (((setOfPairsIsBReln) =>
% 100.17/13.57 (((dpsetconstrERa) =>
% 100.17/13.57 (((dpsetconstrEL1) =>
% 100.17/13.57 (((dpsetconstrEL2) =>
% 100.17/13.57 (((dpsetconstrER) =>
% 100.17/13.57 (((funcImageSingleton) =>
% 100.17/13.57 (((apProp) =>
% 100.17/13.57 (((app) =>
% 100.17/13.57 (((infuncsetfunc) =>
% 100.17/13.57 (((ap2p) =>
% 100.17/13.57 (((funcinfuncset) =>
% 100.17/13.57 (((lamProp) =>
% 100.17/13.57 (((lamp) =>
% 100.17/13.57 (((lam2p) =>
% 100.17/13.57 (((brelnall1) =>
% 100.17/13.57 (((brelnall2) =>
% 100.17/13.57 (((ex1E2) =>
% 100.17/13.57 (((funcGraphProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp3) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcextLem) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp4) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq1) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq2) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2lamEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifSingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifp) =>
% 100.17/13.57 ((
% 100.17/13.57 (theeq) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrue) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueorfalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setminusT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setextT) =>
% 100.17/13.57 ((
% 100.17/13.57 (subsetTI) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTELcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTERcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT1) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT2) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT3) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub2) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTnotintersectT) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementImpComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementSubsetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementInPowersetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (contraSubsetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTcontraSubset) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTILcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTIRcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion2) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (intersectInPowersetIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpNotIn1) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpInComplement1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTE) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTEcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementUnionInPowersetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule0) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_5) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all2) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1SetBreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (choice2fnsingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (setOfPairsIsBReln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all1) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compEex) =>
% 100.17/13.57 ((
% 100.17/13.57 (!!) @ (
% 100.17/13.57 (('#B') @ (
% 100.17/13.57 !!) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 !!))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#C') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1760])).
% 100.17/13.57 thf(zip_derived_cl1779, plain,
% 100.17/13.57 (~ (((ksndpairEq) =>
% 100.17/13.57 (((kpairsurjEq) =>
% 100.17/13.57 (((cartprodsndin) =>
% 100.17/13.57 (((cartprodpairmemEL) =>
% 100.17/13.57 (((cartprodpairmemER) =>
% 100.17/13.57 (((cartprodmempaircEq) =>
% 100.17/13.57 (((cartprodfstpairEq) =>
% 100.17/13.57 (((cartprodsndpairEq) =>
% 100.17/13.57 (((cartprodpairsurjEq) =>
% 100.17/13.57 (((dpsetconstrI) =>
% 100.17/13.57 (((dpsetconstrSub) =>
% 100.17/13.57 (((setOfPairsIsBReln) =>
% 100.17/13.57 (((dpsetconstrERa) =>
% 100.17/13.57 (((dpsetconstrEL1) =>
% 100.17/13.57 (((dpsetconstrEL2) =>
% 100.17/13.57 (((dpsetconstrER) =>
% 100.17/13.57 (((funcImageSingleton) =>
% 100.17/13.57 (((apProp) =>
% 100.17/13.57 (((app) =>
% 100.17/13.57 (((infuncsetfunc) =>
% 100.17/13.57 (((ap2p) =>
% 100.17/13.57 (((funcinfuncset) =>
% 100.17/13.57 (((lamProp) =>
% 100.17/13.57 (((lamp) =>
% 100.17/13.57 (((lam2p) =>
% 100.17/13.57 (((brelnall1) =>
% 100.17/13.57 (((brelnall2) =>
% 100.17/13.57 (((ex1E2) =>
% 100.17/13.57 (((funcGraphProp1) =>
% 100.17/13.57 (((funcGraphProp3) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcextLem) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp4) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq1) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq2) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2lamEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifSingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifp) =>
% 100.17/13.57 ((
% 100.17/13.57 (theeq) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrue) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueorfalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setminusT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setextT) =>
% 100.17/13.57 ((
% 100.17/13.57 (subsetTI) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTELcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTERcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT1) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT2) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT3) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub2) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTnotintersectT) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementImpComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementSubsetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementInPowersetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (contraSubsetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTcontraSubset) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTILcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTIRcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion2) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (intersectInPowersetIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpNotIn1) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpInComplement1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTE) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTEcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementUnionInPowersetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule0) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_5) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all2) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1SetBreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (choice2fnsingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (setOfPairsIsBReln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all1) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compEex) =>
% 100.17/13.57 ((
% 100.17/13.57 (!!) @ (
% 100.17/13.57 (('#B') @ (
% 100.17/13.57 !!) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 !!))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#C') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1770])).
% 100.17/13.57 thf(zip_derived_cl1787, plain,
% 100.17/13.57 (~ (((kpairsurjEq) =>
% 100.17/13.57 (((cartprodsndin) =>
% 100.17/13.57 (((cartprodpairmemEL) =>
% 100.17/13.57 (((cartprodpairmemER) =>
% 100.17/13.57 (((cartprodmempaircEq) =>
% 100.17/13.57 (((cartprodfstpairEq) =>
% 100.17/13.57 (((cartprodsndpairEq) =>
% 100.17/13.57 (((cartprodpairsurjEq) =>
% 100.17/13.57 (((dpsetconstrI) =>
% 100.17/13.57 (((dpsetconstrSub) =>
% 100.17/13.57 (((setOfPairsIsBReln) =>
% 100.17/13.57 (((dpsetconstrERa) =>
% 100.17/13.57 (((dpsetconstrEL1) =>
% 100.17/13.57 (((dpsetconstrEL2) =>
% 100.17/13.57 (((dpsetconstrER) =>
% 100.17/13.57 (((funcImageSingleton) =>
% 100.17/13.57 (((apProp) =>
% 100.17/13.57 (((app) =>
% 100.17/13.57 (((infuncsetfunc) =>
% 100.17/13.57 (((ap2p) =>
% 100.17/13.57 (((funcinfuncset) =>
% 100.17/13.57 (((lamProp) =>
% 100.17/13.57 (((lamp) =>
% 100.17/13.57 (((lam2p) =>
% 100.17/13.57 (((brelnall1) =>
% 100.17/13.57 (((brelnall2) =>
% 100.17/13.57 (((ex1E2) =>
% 100.17/13.57 (((funcGraphProp1) =>
% 100.17/13.57 (((funcGraphProp3) =>
% 100.17/13.57 (((funcGraphProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcextLem) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp4) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq1) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq2) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2lamEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifSingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifp) =>
% 100.17/13.57 ((
% 100.17/13.57 (theeq) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrue) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueorfalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setminusT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setextT) =>
% 100.17/13.57 ((
% 100.17/13.57 (subsetTI) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTELcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTERcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT1) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT2) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT3) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub2) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTnotintersectT) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementImpComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementSubsetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementInPowersetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (contraSubsetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTcontraSubset) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTILcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTIRcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion2) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (intersectInPowersetIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpNotIn1) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpInComplement1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTE) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTEcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementUnionInPowersetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule0) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_5) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all2) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1SetBreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (choice2fnsingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (setOfPairsIsBReln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all1) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compEex) =>
% 100.17/13.57 ((
% 100.17/13.57 (!!) @ (
% 100.17/13.57 (('#B') @ (
% 100.17/13.57 !!) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 !!))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#C') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1779])).
% 100.17/13.57 thf(zip_derived_cl1796, plain,
% 100.17/13.57 (~ (((cartprodsndin) =>
% 100.17/13.57 (((cartprodpairmemEL) =>
% 100.17/13.57 (((cartprodpairmemER) =>
% 100.17/13.57 (((cartprodmempaircEq) =>
% 100.17/13.57 (((cartprodfstpairEq) =>
% 100.17/13.57 (((cartprodsndpairEq) =>
% 100.17/13.57 (((cartprodpairsurjEq) =>
% 100.17/13.57 (((dpsetconstrI) =>
% 100.17/13.57 (((dpsetconstrSub) =>
% 100.17/13.57 (((setOfPairsIsBReln) =>
% 100.17/13.57 (((dpsetconstrERa) =>
% 100.17/13.57 (((dpsetconstrEL1) =>
% 100.17/13.57 (((dpsetconstrEL2) =>
% 100.17/13.57 (((dpsetconstrER) =>
% 100.17/13.57 (((funcImageSingleton) =>
% 100.17/13.57 (((apProp) =>
% 100.17/13.57 (((app) =>
% 100.17/13.57 (((infuncsetfunc) =>
% 100.17/13.57 (((ap2p) =>
% 100.17/13.57 (((funcinfuncset) =>
% 100.17/13.57 (((lamProp) =>
% 100.17/13.57 (((lamp) =>
% 100.17/13.57 (((lam2p) =>
% 100.17/13.57 (((brelnall1) =>
% 100.17/13.57 (((brelnall2) =>
% 100.17/13.57 (((ex1E2) =>
% 100.17/13.57 (((funcGraphProp1) =>
% 100.17/13.57 (((funcGraphProp3) =>
% 100.17/13.57 (((funcGraphProp2) =>
% 100.17/13.57 (((funcextLem) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcGraphProp4) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq1) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq2) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2lamEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifSingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifp) =>
% 100.17/13.57 ((
% 100.17/13.57 (theeq) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrue) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueorfalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setminusT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setextT) =>
% 100.17/13.57 ((
% 100.17/13.57 (subsetTI) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTELcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTERcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT1) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT2) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT3) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub2) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTnotintersectT) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementImpComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementSubsetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementInPowersetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (contraSubsetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTcontraSubset) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTILcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTIRcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion2) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (intersectInPowersetIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpNotIn1) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpInComplement1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTE) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTEcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementUnionInPowersetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule0) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_5) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all2) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1SetBreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (choice2fnsingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (setOfPairsIsBReln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all1) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compEex) =>
% 100.17/13.57 ((
% 100.17/13.57 (!!) @ (
% 100.17/13.57 (('#B') @ (
% 100.17/13.57 !!) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 !!))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#C') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1787])).
% 100.17/13.57 thf(zip_derived_cl1807, plain,
% 100.17/13.57 (~ (((cartprodpairmemEL) =>
% 100.17/13.57 (((cartprodpairmemER) =>
% 100.17/13.57 (((cartprodmempaircEq) =>
% 100.17/13.57 (((cartprodfstpairEq) =>
% 100.17/13.57 (((cartprodsndpairEq) =>
% 100.17/13.57 (((cartprodpairsurjEq) =>
% 100.17/13.57 (((dpsetconstrI) =>
% 100.17/13.57 (((dpsetconstrSub) =>
% 100.17/13.57 (((setOfPairsIsBReln) =>
% 100.17/13.57 (((dpsetconstrERa) =>
% 100.17/13.57 (((dpsetconstrEL1) =>
% 100.17/13.57 (((dpsetconstrEL2) =>
% 100.17/13.57 (((dpsetconstrER) =>
% 100.17/13.57 (((funcImageSingleton) =>
% 100.17/13.57 (((apProp) =>
% 100.17/13.57 (((app) =>
% 100.17/13.57 (((infuncsetfunc) =>
% 100.17/13.57 (((ap2p) =>
% 100.17/13.57 (((funcinfuncset) =>
% 100.17/13.57 (((lamProp) =>
% 100.17/13.57 (((lamp) =>
% 100.17/13.57 (((lam2p) =>
% 100.17/13.57 (((brelnall1) =>
% 100.17/13.57 (((brelnall2) =>
% 100.17/13.57 (((ex1E2) =>
% 100.17/13.57 (((funcGraphProp1) =>
% 100.17/13.57 (((funcGraphProp3) =>
% 100.17/13.57 (((funcGraphProp2) =>
% 100.17/13.57 (((funcextLem) =>
% 100.17/13.57 (((funcGraphProp4) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq1) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq2) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2lamEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifSingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifp) =>
% 100.17/13.57 ((
% 100.17/13.57 (theeq) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrue) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueorfalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setminusT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setextT) =>
% 100.17/13.57 ((
% 100.17/13.57 (subsetTI) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTELcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTERcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT1) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT2) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT3) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub2) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTnotintersectT) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementImpComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementSubsetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementInPowersetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (contraSubsetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTcontraSubset) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTILcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTIRcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion2) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (intersectInPowersetIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpNotIn1) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpInComplement1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTE) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTEcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementUnionInPowersetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule0) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_5) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all2) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1SetBreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (choice2fnsingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (setOfPairsIsBReln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all1) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compEex) =>
% 100.17/13.57 ((
% 100.17/13.57 (!!) @ (
% 100.17/13.57 (('#B') @ (
% 100.17/13.57 !!) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 !!))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#C') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1796])).
% 100.17/13.57 thf(zip_derived_cl1816, plain,
% 100.17/13.57 (~ (((cartprodpairmemER) =>
% 100.17/13.57 (((cartprodmempaircEq) =>
% 100.17/13.57 (((cartprodfstpairEq) =>
% 100.17/13.57 (((cartprodsndpairEq) =>
% 100.17/13.57 (((cartprodpairsurjEq) =>
% 100.17/13.57 (((dpsetconstrI) =>
% 100.17/13.57 (((dpsetconstrSub) =>
% 100.17/13.57 (((setOfPairsIsBReln) =>
% 100.17/13.57 (((dpsetconstrERa) =>
% 100.17/13.57 (((dpsetconstrEL1) =>
% 100.17/13.57 (((dpsetconstrEL2) =>
% 100.17/13.57 (((dpsetconstrER) =>
% 100.17/13.57 (((funcImageSingleton) =>
% 100.17/13.57 (((apProp) =>
% 100.17/13.57 (((app) =>
% 100.17/13.57 (((infuncsetfunc) =>
% 100.17/13.57 (((ap2p) =>
% 100.17/13.57 (((funcinfuncset) =>
% 100.17/13.57 (((lamProp) =>
% 100.17/13.57 (((lamp) =>
% 100.17/13.57 (((lam2p) =>
% 100.17/13.57 (((brelnall1) =>
% 100.17/13.57 (((brelnall2) =>
% 100.17/13.57 (((ex1E2) =>
% 100.17/13.57 (((funcGraphProp1) =>
% 100.17/13.57 (((funcGraphProp3) =>
% 100.17/13.57 (((funcGraphProp2) =>
% 100.17/13.57 (((funcextLem) =>
% 100.17/13.57 (((funcGraphProp4) =>
% 100.17/13.57 (((subbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq1) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq2) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2lamEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifSingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifp) =>
% 100.17/13.57 ((
% 100.17/13.57 (theeq) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrue) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueorfalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setminusT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setextT) =>
% 100.17/13.57 ((
% 100.17/13.57 (subsetTI) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTELcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTERcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT1) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT2) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT3) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub2) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTnotintersectT) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementImpComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementSubsetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementInPowersetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (contraSubsetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTcontraSubset) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTILcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTIRcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion2) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (intersectInPowersetIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpNotIn1) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpInComplement1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTE) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTEcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementUnionInPowersetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule0) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_5) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all2) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1SetBreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (choice2fnsingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (setOfPairsIsBReln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all1) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compEex) =>
% 100.17/13.57 ((
% 100.17/13.57 (!!) @ (
% 100.17/13.57 (('#B') @ (
% 100.17/13.57 !!) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 !!))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#C') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1807])).
% 100.17/13.57 thf(zip_derived_cl1825, plain,
% 100.17/13.57 (~ (((cartprodmempaircEq) =>
% 100.17/13.57 (((cartprodfstpairEq) =>
% 100.17/13.57 (((cartprodsndpairEq) =>
% 100.17/13.57 (((cartprodpairsurjEq) =>
% 100.17/13.57 (((dpsetconstrI) =>
% 100.17/13.57 (((dpsetconstrSub) =>
% 100.17/13.57 (((setOfPairsIsBReln) =>
% 100.17/13.57 (((dpsetconstrERa) =>
% 100.17/13.57 (((dpsetconstrEL1) =>
% 100.17/13.57 (((dpsetconstrEL2) =>
% 100.17/13.57 (((dpsetconstrER) =>
% 100.17/13.57 (((funcImageSingleton) =>
% 100.17/13.57 (((apProp) =>
% 100.17/13.57 (((app) =>
% 100.17/13.57 (((infuncsetfunc) =>
% 100.17/13.57 (((ap2p) =>
% 100.17/13.57 (((funcinfuncset) =>
% 100.17/13.57 (((lamProp) =>
% 100.17/13.57 (((lamp) =>
% 100.17/13.57 (((lam2p) =>
% 100.17/13.57 (((brelnall1) =>
% 100.17/13.57 (((brelnall2) =>
% 100.17/13.57 (((ex1E2) =>
% 100.17/13.57 (((funcGraphProp1) =>
% 100.17/13.57 (((funcGraphProp3) =>
% 100.17/13.57 (((funcGraphProp2) =>
% 100.17/13.57 (((funcextLem) =>
% 100.17/13.57 (((funcGraphProp4) =>
% 100.17/13.57 (((subbreln) =>
% 100.17/13.57 (((eqbreln) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq1) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq2) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2lamEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifSingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifp) =>
% 100.17/13.57 ((
% 100.17/13.57 (theeq) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrue) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueorfalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setminusT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setextT) =>
% 100.17/13.57 ((
% 100.17/13.57 (subsetTI) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTELcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTERcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT1) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT2) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT3) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub2) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTnotintersectT) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementImpComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementSubsetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementInPowersetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (contraSubsetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTcontraSubset) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTILcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTIRcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion2) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (intersectInPowersetIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpNotIn1) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpInComplement1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTE) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTEcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementUnionInPowersetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule0) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_5) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all2) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1SetBreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (choice2fnsingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (setOfPairsIsBReln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all1) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compEex) =>
% 100.17/13.57 ((
% 100.17/13.57 (!!) @ (
% 100.17/13.57 (('#B') @ (
% 100.17/13.57 !!) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 !!))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#C') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1816])).
% 100.17/13.57 thf(zip_derived_cl1833, plain,
% 100.17/13.57 (~ (((cartprodfstpairEq) =>
% 100.17/13.57 (((cartprodsndpairEq) =>
% 100.17/13.57 (((cartprodpairsurjEq) =>
% 100.17/13.57 (((dpsetconstrI) =>
% 100.17/13.57 (((dpsetconstrSub) =>
% 100.17/13.57 (((setOfPairsIsBReln) =>
% 100.17/13.57 (((dpsetconstrERa) =>
% 100.17/13.57 (((dpsetconstrEL1) =>
% 100.17/13.57 (((dpsetconstrEL2) =>
% 100.17/13.57 (((dpsetconstrER) =>
% 100.17/13.57 (((funcImageSingleton) =>
% 100.17/13.57 (((apProp) =>
% 100.17/13.57 (((app) =>
% 100.17/13.57 (((infuncsetfunc) =>
% 100.17/13.57 (((ap2p) =>
% 100.17/13.57 (((funcinfuncset) =>
% 100.17/13.57 (((lamProp) =>
% 100.17/13.57 (((lamp) =>
% 100.17/13.57 (((lam2p) =>
% 100.17/13.57 (((brelnall1) =>
% 100.17/13.57 (((brelnall2) =>
% 100.17/13.57 (((ex1E2) =>
% 100.17/13.57 (((funcGraphProp1) =>
% 100.17/13.57 (((funcGraphProp3) =>
% 100.17/13.57 (((funcGraphProp2) =>
% 100.17/13.57 (((funcextLem) =>
% 100.17/13.57 (((funcGraphProp4) =>
% 100.17/13.57 (((subbreln) =>
% 100.17/13.57 (((eqbreln) =>
% 100.17/13.57 (((funcext) =>
% 100.17/13.57 ((
% 100.17/13.57 (funcext2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq1) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq2) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2lamEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifSingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifp) =>
% 100.17/13.57 ((
% 100.17/13.57 (theeq) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrue) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueorfalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setminusT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setextT) =>
% 100.17/13.57 ((
% 100.17/13.57 (subsetTI) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTELcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTERcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT1) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT2) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT3) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub2) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTnotintersectT) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementImpComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementSubsetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementInPowersetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (contraSubsetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTcontraSubset) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTILcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTIRcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion2) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (intersectInPowersetIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpNotIn1) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpInComplement1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTE) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTEcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementUnionInPowersetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule0) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_5) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all2) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1SetBreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (choice2fnsingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (setOfPairsIsBReln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all1) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compEex) =>
% 100.17/13.57 ((
% 100.17/13.57 (!!) @ (
% 100.17/13.57 (('#B') @ (
% 100.17/13.57 !!) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 !!))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#C') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1825])).
% 100.17/13.57 thf(zip_derived_cl1840, plain,
% 100.17/13.57 (~ (((cartprodsndpairEq) =>
% 100.17/13.57 (((cartprodpairsurjEq) =>
% 100.17/13.57 (((dpsetconstrI) =>
% 100.17/13.57 (((dpsetconstrSub) =>
% 100.17/13.57 (((setOfPairsIsBReln) =>
% 100.17/13.57 (((dpsetconstrERa) =>
% 100.17/13.57 (((dpsetconstrEL1) =>
% 100.17/13.57 (((dpsetconstrEL2) =>
% 100.17/13.57 (((dpsetconstrER) =>
% 100.17/13.57 (((funcImageSingleton) =>
% 100.17/13.57 (((apProp) =>
% 100.17/13.57 (((app) =>
% 100.17/13.57 (((infuncsetfunc) =>
% 100.17/13.57 (((ap2p) =>
% 100.17/13.57 (((funcinfuncset) =>
% 100.17/13.57 (((lamProp) =>
% 100.17/13.57 (((lamp) =>
% 100.17/13.57 (((lam2p) =>
% 100.17/13.57 (((brelnall1) =>
% 100.17/13.57 (((brelnall2) =>
% 100.17/13.57 (((ex1E2) =>
% 100.17/13.57 (((funcGraphProp1) =>
% 100.17/13.57 (((funcGraphProp3) =>
% 100.17/13.57 (((funcGraphProp2) =>
% 100.17/13.57 (((funcextLem) =>
% 100.17/13.57 (((funcGraphProp4) =>
% 100.17/13.57 (((subbreln) =>
% 100.17/13.57 (((eqbreln) =>
% 100.17/13.57 (((funcext) =>
% 100.17/13.57 (((funcext2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq1) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq2) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2lamEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifSingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifp) =>
% 100.17/13.57 ((
% 100.17/13.57 (theeq) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrue) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueorfalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setminusT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setextT) =>
% 100.17/13.57 ((
% 100.17/13.57 (subsetTI) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTELcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTERcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT1) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT2) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT3) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub2) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTnotintersectT) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementImpComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementSubsetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementInPowersetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (contraSubsetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTcontraSubset) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTILcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTIRcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion2) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (intersectInPowersetIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpNotIn1) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpInComplement1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTE) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTEcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementUnionInPowersetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule0) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_5) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all2) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1SetBreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (choice2fnsingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (setOfPairsIsBReln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all1) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compEex) =>
% 100.17/13.57 ((
% 100.17/13.57 (!!) @ (
% 100.17/13.57 (('#B') @ (
% 100.17/13.57 !!) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 !!))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#C') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1833])).
% 100.17/13.57 thf(zip_derived_cl1848, plain,
% 100.17/13.57 (~ (((cartprodpairsurjEq) =>
% 100.17/13.57 (((dpsetconstrI) =>
% 100.17/13.57 (((dpsetconstrSub) =>
% 100.17/13.57 (((setOfPairsIsBReln) =>
% 100.17/13.57 (((dpsetconstrERa) =>
% 100.17/13.57 (((dpsetconstrEL1) =>
% 100.17/13.57 (((dpsetconstrEL2) =>
% 100.17/13.57 (((dpsetconstrER) =>
% 100.17/13.57 (((funcImageSingleton) =>
% 100.17/13.57 (((apProp) =>
% 100.17/13.57 (((app) =>
% 100.17/13.57 (((infuncsetfunc) =>
% 100.17/13.57 (((ap2p) =>
% 100.17/13.57 (((funcinfuncset) =>
% 100.17/13.57 (((lamProp) =>
% 100.17/13.57 (((lamp) =>
% 100.17/13.57 (((lam2p) =>
% 100.17/13.57 (((brelnall1) =>
% 100.17/13.57 (((brelnall2) =>
% 100.17/13.57 (((ex1E2) =>
% 100.17/13.57 (((funcGraphProp1) =>
% 100.17/13.57 (((funcGraphProp3) =>
% 100.17/13.57 (((funcGraphProp2) =>
% 100.17/13.57 (((funcextLem) =>
% 100.17/13.57 (((funcGraphProp4) =>
% 100.17/13.57 (((subbreln) =>
% 100.17/13.57 (((eqbreln) =>
% 100.17/13.57 (((funcext) =>
% 100.17/13.57 (((funcext2) =>
% 100.17/13.57 (((ap2apEq1) =>
% 100.17/13.57 ((
% 100.17/13.57 (ap2apEq2) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2lamEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifSingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifp) =>
% 100.17/13.57 ((
% 100.17/13.57 (theeq) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrue) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueorfalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setminusT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setextT) =>
% 100.17/13.57 ((
% 100.17/13.57 (subsetTI) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTELcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTERcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT1) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT2) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT3) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub2) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTnotintersectT) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementImpComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementSubsetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementInPowersetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (contraSubsetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTcontraSubset) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTILcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTIRcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion2) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (intersectInPowersetIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpNotIn1) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpInComplement1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTE) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTEcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementUnionInPowersetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule0) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_5) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all2) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1SetBreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (choice2fnsingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (setOfPairsIsBReln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all1) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compEex) =>
% 100.17/13.57 ((
% 100.17/13.57 (!!) @ (
% 100.17/13.57 (('#B') @ (
% 100.17/13.57 !!) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 !!))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#C') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1840])).
% 100.17/13.57 thf(zip_derived_cl1856, plain,
% 100.17/13.57 (~ (((dpsetconstrI) =>
% 100.17/13.57 (((dpsetconstrSub) =>
% 100.17/13.57 (((setOfPairsIsBReln) =>
% 100.17/13.57 (((dpsetconstrERa) =>
% 100.17/13.57 (((dpsetconstrEL1) =>
% 100.17/13.57 (((dpsetconstrEL2) =>
% 100.17/13.57 (((dpsetconstrER) =>
% 100.17/13.57 (((funcImageSingleton) =>
% 100.17/13.57 (((apProp) =>
% 100.17/13.57 (((app) =>
% 100.17/13.57 (((infuncsetfunc) =>
% 100.17/13.57 (((ap2p) =>
% 100.17/13.57 (((funcinfuncset) =>
% 100.17/13.57 (((lamProp) =>
% 100.17/13.57 (((lamp) =>
% 100.17/13.57 (((lam2p) =>
% 100.17/13.57 (((brelnall1) =>
% 100.17/13.57 (((brelnall2) =>
% 100.17/13.57 (((ex1E2) =>
% 100.17/13.57 (((funcGraphProp1) =>
% 100.17/13.57 (((funcGraphProp3) =>
% 100.17/13.57 (((funcGraphProp2) =>
% 100.17/13.57 (((funcextLem) =>
% 100.17/13.57 (((funcGraphProp4) =>
% 100.17/13.57 (((subbreln) =>
% 100.17/13.57 (((eqbreln) =>
% 100.17/13.57 (((funcext) =>
% 100.17/13.57 (((funcext2) =>
% 100.17/13.57 (((ap2apEq1) =>
% 100.17/13.57 (((ap2apEq2) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2lamEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (beta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalseProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp1) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueProp2) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifSingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (ifp) =>
% 100.17/13.57 ((
% 100.17/13.57 (theeq) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrue) =>
% 100.17/13.57 ((
% 100.17/13.57 (iffalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (iftrueorfalse) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setminusT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementT_lem) =>
% 100.17/13.57 ((
% 100.17/13.57 (setextT) =>
% 100.17/13.57 ((
% 100.17/13.57 (subsetTI) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (powersetTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTELcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binintersectTERcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT1) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT2) =>
% 100.17/13.57 ((
% 100.17/13.57 (contrasubsetT3) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementI1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementE1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub1) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementSub2) =>
% 100.17/13.57 ((
% 100.17/13.57 (doubleComplementEq) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTnotintersectT) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementImpComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementSubsetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementInPowersetComplementIntersect) =>
% 100.17/13.57 ((
% 100.17/13.57 (contraSubsetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementTcontraSubset) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTILcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTIRcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInUnion2) =>
% 100.17/13.57 ((
% 100.17/13.57 (inIntersectImpInIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (intersectInPowersetIntersectUnions) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpNotIn1) =>
% 100.17/13.57 ((
% 100.17/13.57 (inComplementUnionImpInComplement1) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTE) =>
% 100.17/13.57 ((
% 100.17/13.57 (binunionTEcontra) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a1) =>
% 100.17/13.57 ((
% 100.17/13.57 (complementUnionInPowersetComplement) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan1) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2a) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b2) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2b) =>
% 100.17/13.57 ((
% 100.17/13.57 (demorgan2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule0) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz13rule4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_1) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_2) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_3) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_4) =>
% 100.17/13.57 ((
% 100.17/13.57 (woz1_5) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all2) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1SetBreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (choice2fnsingleton) =>
% 100.17/13.57 ((
% 100.17/13.57 (setOfPairsIsBReln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1all1) =>
% 100.17/13.57 ((
% 100.17/13.57 (subbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eqbreln1) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1invE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compprop) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compI) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compE) =>
% 100.17/13.57 ((
% 100.17/13.57 (breln1compEex) =>
% 100.17/13.57 ((
% 100.17/13.57 (!!) @ (
% 100.17/13.57 (('#B') @ (
% 100.17/13.57 !!) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 !!))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#S') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#S') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 =>))) @
% 100.17/13.57 breln1)))))) @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#C') @ (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 (
% 100.17/13.57 (
% 100.17/13.57 ('#B') @ (
% 100.17/13.57 '#B') @
% 100.17/13.57 breln1)))) @
% 100.17/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.17/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1848])).
% 100.17/13.57 thf(zip_derived_cl1865, plain,
% 100.17/13.57 (~ (((dpsetconstrSub) =>
% 100.17/13.57 (((setOfPairsIsBReln) =>
% 100.17/13.57 (((dpsetconstrERa) =>
% 100.17/13.57 (((dpsetconstrEL1) =>
% 100.17/13.57 (((dpsetconstrEL2) =>
% 100.17/13.57 (((dpsetconstrER) =>
% 100.17/13.57 (((funcImageSingleton) =>
% 100.17/13.57 (((apProp) =>
% 100.17/13.57 (((app) =>
% 100.17/13.57 (((infuncsetfunc) =>
% 100.17/13.57 (((ap2p) =>
% 100.17/13.57 (((funcinfuncset) =>
% 100.17/13.57 (((lamProp) =>
% 100.17/13.57 (((lamp) =>
% 100.17/13.57 (((lam2p) =>
% 100.17/13.57 (((brelnall1) =>
% 100.17/13.57 (((brelnall2) =>
% 100.17/13.57 (((ex1E2) =>
% 100.17/13.57 (((funcGraphProp1) =>
% 100.17/13.57 (((funcGraphProp3) =>
% 100.17/13.57 (((funcGraphProp2) =>
% 100.17/13.57 (((funcextLem) =>
% 100.17/13.57 (((funcGraphProp4) =>
% 100.17/13.57 (((subbreln) =>
% 100.17/13.57 (((eqbreln) =>
% 100.17/13.57 (((funcext) =>
% 100.17/13.57 (((funcext2) =>
% 100.17/13.57 (((ap2apEq1) =>
% 100.17/13.57 (((ap2apEq2) =>
% 100.17/13.57 (((beta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (eta1) =>
% 100.17/13.57 ((
% 100.17/13.57 (lam2lamEq) =>
% 100.31/13.57 ((
% 100.31/13.57 (beta2) =>
% 100.31/13.57 ((
% 100.31/13.57 (eta2) =>
% 100.31/13.57 ((
% 100.31/13.57 (iffalseProp1) =>
% 100.31/13.57 ((
% 100.31/13.57 (iffalseProp2) =>
% 100.31/13.57 ((
% 100.31/13.57 (iftrueProp1) =>
% 100.31/13.57 ((
% 100.31/13.57 (iftrueProp2) =>
% 100.31/13.57 ((
% 100.31/13.57 (ifSingleton) =>
% 100.31/13.57 ((
% 100.31/13.57 (ifp) =>
% 100.31/13.57 ((
% 100.31/13.57 (theeq) =>
% 100.31/13.57 ((
% 100.31/13.57 (iftrue) =>
% 100.31/13.57 ((
% 100.31/13.57 (iffalse) =>
% 100.31/13.57 ((
% 100.31/13.57 (iftrueorfalse) =>
% 100.31/13.57 ((
% 100.31/13.57 (binintersectT_lem) =>
% 100.31/13.57 ((
% 100.31/13.57 (binunionT_lem) =>
% 100.31/13.57 ((
% 100.31/13.57 (powersetT_lem) =>
% 100.31/13.57 ((
% 100.31/13.57 (setminusT_lem) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementT_lem) =>
% 100.31/13.57 ((
% 100.31/13.57 (setextT) =>
% 100.31/13.57 ((
% 100.31/13.57 (subsetTI) =>
% 100.31/13.57 ((
% 100.31/13.57 (powersetTI1) =>
% 100.31/13.57 ((
% 100.31/13.57 (powersetTE1) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementTI1) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementTE1) =>
% 100.31/13.57 ((
% 100.31/13.57 (binintersectTELcontra) =>
% 100.31/13.57 ((
% 100.31/13.57 (binintersectTERcontra) =>
% 100.31/13.57 ((
% 100.31/13.57 (contrasubsetT) =>
% 100.31/13.57 ((
% 100.31/13.57 (contrasubsetT1) =>
% 100.31/13.57 ((
% 100.31/13.57 (contrasubsetT2) =>
% 100.31/13.57 ((
% 100.31/13.57 (contrasubsetT3) =>
% 100.31/13.57 ((
% 100.31/13.57 (doubleComplementI1) =>
% 100.31/13.57 ((
% 100.31/13.57 (doubleComplementE1) =>
% 100.31/13.57 ((
% 100.31/13.57 (doubleComplementSub1) =>
% 100.31/13.57 ((
% 100.31/13.57 (doubleComplementSub2) =>
% 100.31/13.57 ((
% 100.31/13.57 (doubleComplementEq) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementTnotintersectT) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementImpComplementIntersect) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementSubsetComplementIntersect) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementInPowersetComplementIntersect) =>
% 100.31/13.57 ((
% 100.31/13.57 (contraSubsetComplement) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementTcontraSubset) =>
% 100.31/13.57 ((
% 100.31/13.57 (binunionTILcontra) =>
% 100.31/13.57 ((
% 100.31/13.57 (binunionTIRcontra) =>
% 100.31/13.57 ((
% 100.31/13.57 (inIntersectImpInUnion) =>
% 100.31/13.57 ((
% 100.31/13.57 (inIntersectImpInUnion2) =>
% 100.31/13.57 ((
% 100.31/13.57 (inIntersectImpInIntersectUnions) =>
% 100.31/13.57 ((
% 100.31/13.57 (intersectInPowersetIntersectUnions) =>
% 100.31/13.57 ((
% 100.31/13.57 (inComplementUnionImpNotIn1) =>
% 100.31/13.57 ((
% 100.31/13.57 (inComplementUnionImpInComplement1) =>
% 100.31/13.57 ((
% 100.31/13.57 (binunionTE) =>
% 100.31/13.57 ((
% 100.31/13.57 (binunionTEcontra) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2a1) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementUnionInPowersetComplement) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2a2) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan1a) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan1b) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan1) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2a) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2b2) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2b) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz13rule0) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz13rule1) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz13rule2) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz13rule3) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz13rule4) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz1_1) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz1_2) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz1_3) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz1_4) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz1_5) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1all2) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1SetBreln1) =>
% 100.31/13.57 ((
% 100.31/13.57 (choice2fnsingleton) =>
% 100.31/13.57 ((
% 100.31/13.57 (setOfPairsIsBReln1) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1all1) =>
% 100.31/13.57 ((
% 100.31/13.57 (subbreln1) =>
% 100.31/13.57 ((
% 100.31/13.57 (eqbreln1) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1invprop) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1invI) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1invE) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1compprop) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1compI) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1compE) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1compEex) =>
% 100.31/13.57 ((
% 100.31/13.57 (!!) @ (
% 100.31/13.57 (('#B') @ (
% 100.31/13.57 !!) @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#S') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 '#S') @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 =>))) @
% 100.31/13.57 breln1)))) @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 !!))) @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#S') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 '#B') @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 '#S') @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 =>))) @
% 100.31/13.57 breln1)))))) @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#C') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 '#B') @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 '#B') @
% 100.31/13.57 breln1)))) @
% 100.31/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1856])).
% 100.31/13.57 thf(zip_derived_cl1874, plain,
% 100.31/13.57 (~ (((setOfPairsIsBReln) =>
% 100.31/13.57 (((dpsetconstrERa) =>
% 100.31/13.57 (((dpsetconstrEL1) =>
% 100.31/13.57 (((dpsetconstrEL2) =>
% 100.31/13.57 (((dpsetconstrER) =>
% 100.31/13.57 (((funcImageSingleton) =>
% 100.31/13.57 (((apProp) =>
% 100.31/13.57 (((app) =>
% 100.31/13.57 (((infuncsetfunc) =>
% 100.31/13.57 (((ap2p) =>
% 100.31/13.57 (((funcinfuncset) =>
% 100.31/13.57 (((lamProp) =>
% 100.31/13.57 (((lamp) =>
% 100.31/13.57 (((lam2p) =>
% 100.31/13.57 (((brelnall1) =>
% 100.31/13.57 (((brelnall2) =>
% 100.31/13.57 (((ex1E2) =>
% 100.31/13.57 (((funcGraphProp1) =>
% 100.31/13.57 (((funcGraphProp3) =>
% 100.31/13.57 (((funcGraphProp2) =>
% 100.31/13.57 (((funcextLem) =>
% 100.31/13.57 (((funcGraphProp4) =>
% 100.31/13.57 (((subbreln) =>
% 100.31/13.57 (((eqbreln) =>
% 100.31/13.57 (((funcext) =>
% 100.31/13.57 (((funcext2) =>
% 100.31/13.57 (((ap2apEq1) =>
% 100.31/13.57 (((ap2apEq2) =>
% 100.31/13.57 (((beta1) =>
% 100.31/13.57 (((eta1) =>
% 100.31/13.57 ((
% 100.31/13.57 (lam2lamEq) =>
% 100.31/13.57 ((
% 100.31/13.57 (beta2) =>
% 100.31/13.57 ((
% 100.31/13.57 (eta2) =>
% 100.31/13.57 ((
% 100.31/13.57 (iffalseProp1) =>
% 100.31/13.57 ((
% 100.31/13.57 (iffalseProp2) =>
% 100.31/13.57 ((
% 100.31/13.57 (iftrueProp1) =>
% 100.31/13.57 ((
% 100.31/13.57 (iftrueProp2) =>
% 100.31/13.57 ((
% 100.31/13.57 (ifSingleton) =>
% 100.31/13.57 ((
% 100.31/13.57 (ifp) =>
% 100.31/13.57 ((
% 100.31/13.57 (theeq) =>
% 100.31/13.57 ((
% 100.31/13.57 (iftrue) =>
% 100.31/13.57 ((
% 100.31/13.57 (iffalse) =>
% 100.31/13.57 ((
% 100.31/13.57 (iftrueorfalse) =>
% 100.31/13.57 ((
% 100.31/13.57 (binintersectT_lem) =>
% 100.31/13.57 ((
% 100.31/13.57 (binunionT_lem) =>
% 100.31/13.57 ((
% 100.31/13.57 (powersetT_lem) =>
% 100.31/13.57 ((
% 100.31/13.57 (setminusT_lem) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementT_lem) =>
% 100.31/13.57 ((
% 100.31/13.57 (setextT) =>
% 100.31/13.57 ((
% 100.31/13.57 (subsetTI) =>
% 100.31/13.57 ((
% 100.31/13.57 (powersetTI1) =>
% 100.31/13.57 ((
% 100.31/13.57 (powersetTE1) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementTI1) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementTE1) =>
% 100.31/13.57 ((
% 100.31/13.57 (binintersectTELcontra) =>
% 100.31/13.57 ((
% 100.31/13.57 (binintersectTERcontra) =>
% 100.31/13.57 ((
% 100.31/13.57 (contrasubsetT) =>
% 100.31/13.57 ((
% 100.31/13.57 (contrasubsetT1) =>
% 100.31/13.57 ((
% 100.31/13.57 (contrasubsetT2) =>
% 100.31/13.57 ((
% 100.31/13.57 (contrasubsetT3) =>
% 100.31/13.57 ((
% 100.31/13.57 (doubleComplementI1) =>
% 100.31/13.57 ((
% 100.31/13.57 (doubleComplementE1) =>
% 100.31/13.57 ((
% 100.31/13.57 (doubleComplementSub1) =>
% 100.31/13.57 ((
% 100.31/13.57 (doubleComplementSub2) =>
% 100.31/13.57 ((
% 100.31/13.57 (doubleComplementEq) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementTnotintersectT) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementImpComplementIntersect) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementSubsetComplementIntersect) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementInPowersetComplementIntersect) =>
% 100.31/13.57 ((
% 100.31/13.57 (contraSubsetComplement) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementTcontraSubset) =>
% 100.31/13.57 ((
% 100.31/13.57 (binunionTILcontra) =>
% 100.31/13.57 ((
% 100.31/13.57 (binunionTIRcontra) =>
% 100.31/13.57 ((
% 100.31/13.57 (inIntersectImpInUnion) =>
% 100.31/13.57 ((
% 100.31/13.57 (inIntersectImpInUnion2) =>
% 100.31/13.57 ((
% 100.31/13.57 (inIntersectImpInIntersectUnions) =>
% 100.31/13.57 ((
% 100.31/13.57 (intersectInPowersetIntersectUnions) =>
% 100.31/13.57 ((
% 100.31/13.57 (inComplementUnionImpNotIn1) =>
% 100.31/13.57 ((
% 100.31/13.57 (inComplementUnionImpInComplement1) =>
% 100.31/13.57 ((
% 100.31/13.57 (binunionTE) =>
% 100.31/13.57 ((
% 100.31/13.57 (binunionTEcontra) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2a1) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementUnionInPowersetComplement) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2a2) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan1a) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan1b) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan1) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2a) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2b2) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2b) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz13rule0) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz13rule1) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz13rule2) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz13rule3) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz13rule4) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz1_1) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz1_2) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz1_3) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz1_4) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz1_5) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1all2) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1SetBreln1) =>
% 100.31/13.57 ((
% 100.31/13.57 (choice2fnsingleton) =>
% 100.31/13.57 ((
% 100.31/13.57 (setOfPairsIsBReln1) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1all1) =>
% 100.31/13.57 ((
% 100.31/13.57 (subbreln1) =>
% 100.31/13.57 ((
% 100.31/13.57 (eqbreln1) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1invprop) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1invI) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1invE) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1compprop) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1compI) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1compE) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1compEex) =>
% 100.31/13.57 ((
% 100.31/13.57 (!!) @ (
% 100.31/13.57 (('#B') @ (
% 100.31/13.57 !!) @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#S') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 '#S') @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 =>))) @
% 100.31/13.57 breln1)))) @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 !!))) @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#S') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 '#B') @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 '#S') @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 =>))) @
% 100.31/13.57 breln1)))))) @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#C') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 '#B') @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 '#B') @
% 100.31/13.57 breln1)))) @
% 100.31/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1865])).
% 100.31/13.57 thf(zip_derived_cl1883, plain,
% 100.31/13.57 (~ (((dpsetconstrERa) =>
% 100.31/13.57 (((dpsetconstrEL1) =>
% 100.31/13.57 (((dpsetconstrEL2) =>
% 100.31/13.57 (((dpsetconstrER) =>
% 100.31/13.57 (((funcImageSingleton) =>
% 100.31/13.57 (((apProp) =>
% 100.31/13.57 (((app) =>
% 100.31/13.57 (((infuncsetfunc) =>
% 100.31/13.57 (((ap2p) =>
% 100.31/13.57 (((funcinfuncset) =>
% 100.31/13.57 (((lamProp) =>
% 100.31/13.57 (((lamp) =>
% 100.31/13.57 (((lam2p) =>
% 100.31/13.57 (((brelnall1) =>
% 100.31/13.57 (((brelnall2) =>
% 100.31/13.57 (((ex1E2) =>
% 100.31/13.57 (((funcGraphProp1) =>
% 100.31/13.57 (((funcGraphProp3) =>
% 100.31/13.57 (((funcGraphProp2) =>
% 100.31/13.57 (((funcextLem) =>
% 100.31/13.57 (((funcGraphProp4) =>
% 100.31/13.57 (((subbreln) =>
% 100.31/13.57 (((eqbreln) =>
% 100.31/13.57 (((funcext) =>
% 100.31/13.57 (((funcext2) =>
% 100.31/13.57 (((ap2apEq1) =>
% 100.31/13.57 (((ap2apEq2) =>
% 100.31/13.57 (((beta1) =>
% 100.31/13.57 (((eta1) =>
% 100.31/13.57 (((lam2lamEq) =>
% 100.31/13.57 ((
% 100.31/13.57 (beta2) =>
% 100.31/13.57 ((
% 100.31/13.57 (eta2) =>
% 100.31/13.57 ((
% 100.31/13.57 (iffalseProp1) =>
% 100.31/13.57 ((
% 100.31/13.57 (iffalseProp2) =>
% 100.31/13.57 ((
% 100.31/13.57 (iftrueProp1) =>
% 100.31/13.57 ((
% 100.31/13.57 (iftrueProp2) =>
% 100.31/13.57 ((
% 100.31/13.57 (ifSingleton) =>
% 100.31/13.57 ((
% 100.31/13.57 (ifp) =>
% 100.31/13.57 ((
% 100.31/13.57 (theeq) =>
% 100.31/13.57 ((
% 100.31/13.57 (iftrue) =>
% 100.31/13.57 ((
% 100.31/13.57 (iffalse) =>
% 100.31/13.57 ((
% 100.31/13.57 (iftrueorfalse) =>
% 100.31/13.57 ((
% 100.31/13.57 (binintersectT_lem) =>
% 100.31/13.57 ((
% 100.31/13.57 (binunionT_lem) =>
% 100.31/13.57 ((
% 100.31/13.57 (powersetT_lem) =>
% 100.31/13.57 ((
% 100.31/13.57 (setminusT_lem) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementT_lem) =>
% 100.31/13.57 ((
% 100.31/13.57 (setextT) =>
% 100.31/13.57 ((
% 100.31/13.57 (subsetTI) =>
% 100.31/13.57 ((
% 100.31/13.57 (powersetTI1) =>
% 100.31/13.57 ((
% 100.31/13.57 (powersetTE1) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementTI1) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementTE1) =>
% 100.31/13.57 ((
% 100.31/13.57 (binintersectTELcontra) =>
% 100.31/13.57 ((
% 100.31/13.57 (binintersectTERcontra) =>
% 100.31/13.57 ((
% 100.31/13.57 (contrasubsetT) =>
% 100.31/13.57 ((
% 100.31/13.57 (contrasubsetT1) =>
% 100.31/13.57 ((
% 100.31/13.57 (contrasubsetT2) =>
% 100.31/13.57 ((
% 100.31/13.57 (contrasubsetT3) =>
% 100.31/13.57 ((
% 100.31/13.57 (doubleComplementI1) =>
% 100.31/13.57 ((
% 100.31/13.57 (doubleComplementE1) =>
% 100.31/13.57 ((
% 100.31/13.57 (doubleComplementSub1) =>
% 100.31/13.57 ((
% 100.31/13.57 (doubleComplementSub2) =>
% 100.31/13.57 ((
% 100.31/13.57 (doubleComplementEq) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementTnotintersectT) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementImpComplementIntersect) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementSubsetComplementIntersect) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementInPowersetComplementIntersect) =>
% 100.31/13.57 ((
% 100.31/13.57 (contraSubsetComplement) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementTcontraSubset) =>
% 100.31/13.57 ((
% 100.31/13.57 (binunionTILcontra) =>
% 100.31/13.57 ((
% 100.31/13.57 (binunionTIRcontra) =>
% 100.31/13.57 ((
% 100.31/13.57 (inIntersectImpInUnion) =>
% 100.31/13.57 ((
% 100.31/13.57 (inIntersectImpInUnion2) =>
% 100.31/13.57 ((
% 100.31/13.57 (inIntersectImpInIntersectUnions) =>
% 100.31/13.57 ((
% 100.31/13.57 (intersectInPowersetIntersectUnions) =>
% 100.31/13.57 ((
% 100.31/13.57 (inComplementUnionImpNotIn1) =>
% 100.31/13.57 ((
% 100.31/13.57 (inComplementUnionImpInComplement1) =>
% 100.31/13.57 ((
% 100.31/13.57 (binunionTE) =>
% 100.31/13.57 ((
% 100.31/13.57 (binunionTEcontra) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2a1) =>
% 100.31/13.57 ((
% 100.31/13.57 (complementUnionInPowersetComplement) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2a2) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan1a) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan1b) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan1) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2a) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2b2) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2b) =>
% 100.31/13.57 ((
% 100.31/13.57 (demorgan2) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz13rule0) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz13rule1) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz13rule2) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz13rule3) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz13rule4) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz1_1) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz1_2) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz1_3) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz1_4) =>
% 100.31/13.57 ((
% 100.31/13.57 (woz1_5) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1all2) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1SetBreln1) =>
% 100.31/13.57 ((
% 100.31/13.57 (choice2fnsingleton) =>
% 100.31/13.57 ((
% 100.31/13.57 (setOfPairsIsBReln1) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1all1) =>
% 100.31/13.57 ((
% 100.31/13.57 (subbreln1) =>
% 100.31/13.57 ((
% 100.31/13.57 (eqbreln1) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1invprop) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1invI) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1invE) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1compprop) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1compI) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1compE) =>
% 100.31/13.57 ((
% 100.31/13.57 (breln1compEex) =>
% 100.31/13.57 ((
% 100.31/13.57 (!!) @ (
% 100.31/13.57 (('#B') @ (
% 100.31/13.57 !!) @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#S') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 '#S') @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 =>))) @
% 100.31/13.57 breln1)))) @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 !!))) @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#S') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 '#B') @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 '#S') @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 =>))) @
% 100.31/13.57 breln1)))))) @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#C') @ (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 '#B') @
% 100.31/13.57 (
% 100.31/13.57 (
% 100.31/13.57 ('#B') @ (
% 100.31/13.57 '#B') @
% 100.31/13.57 breln1)))) @
% 100.31/13.57 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1874])).
% 100.31/13.57 thf(zip_derived_cl1893, plain,
% 100.31/13.57 (~ (((dpsetconstrEL1) =>
% 100.31/13.57 (((dpsetconstrEL2) =>
% 100.31/13.57 (((dpsetconstrER) =>
% 100.31/13.57 (((funcImageSingleton) =>
% 100.31/13.57 (((apProp) =>
% 100.31/13.57 (((app) =>
% 100.31/13.57 (((infuncsetfunc) =>
% 100.31/13.57 (((ap2p) =>
% 100.31/13.57 (((funcinfuncset) =>
% 100.31/13.57 (((lamProp) =>
% 100.31/13.57 (((lamp) =>
% 100.31/13.57 (((lam2p) =>
% 100.31/13.57 (((brelnall1) =>
% 100.31/13.57 (((brelnall2) =>
% 100.31/13.57 (((ex1E2) =>
% 100.31/13.58 (((funcGraphProp1) =>
% 100.31/13.58 (((funcGraphProp3) =>
% 100.31/13.58 (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 ((
% 100.31/13.58 (eta2) =>
% 100.31/13.58 ((
% 100.31/13.58 (iffalseProp1) =>
% 100.31/13.58 ((
% 100.31/13.58 (iffalseProp2) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueProp1) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueProp2) =>
% 100.31/13.58 ((
% 100.31/13.58 (ifSingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (ifp) =>
% 100.31/13.58 ((
% 100.31/13.58 (theeq) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrue) =>
% 100.31/13.58 ((
% 100.31/13.58 (iffalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueorfalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setminusT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1883])).
% 100.31/13.58 thf(zip_derived_cl1903, plain,
% 100.31/13.58 (~ (((dpsetconstrEL2) =>
% 100.31/13.58 (((dpsetconstrER) =>
% 100.31/13.58 (((funcImageSingleton) =>
% 100.31/13.58 (((apProp) =>
% 100.31/13.58 (((app) =>
% 100.31/13.58 (((infuncsetfunc) =>
% 100.31/13.58 (((ap2p) =>
% 100.31/13.58 (((funcinfuncset) =>
% 100.31/13.58 (((lamProp) =>
% 100.31/13.58 (((lamp) =>
% 100.31/13.58 (((lam2p) =>
% 100.31/13.58 (((brelnall1) =>
% 100.31/13.58 (((brelnall2) =>
% 100.31/13.58 (((ex1E2) =>
% 100.31/13.58 (((funcGraphProp1) =>
% 100.31/13.58 (((funcGraphProp3) =>
% 100.31/13.58 (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 ((
% 100.31/13.58 (iffalseProp1) =>
% 100.31/13.58 ((
% 100.31/13.58 (iffalseProp2) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueProp1) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueProp2) =>
% 100.31/13.58 ((
% 100.31/13.58 (ifSingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (ifp) =>
% 100.31/13.58 ((
% 100.31/13.58 (theeq) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrue) =>
% 100.31/13.58 ((
% 100.31/13.58 (iffalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueorfalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setminusT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1893])).
% 100.31/13.58 thf(zip_derived_cl1914, plain,
% 100.31/13.58 (~ (((dpsetconstrER) =>
% 100.31/13.58 (((funcImageSingleton) =>
% 100.31/13.58 (((apProp) =>
% 100.31/13.58 (((app) =>
% 100.31/13.58 (((infuncsetfunc) =>
% 100.31/13.58 (((ap2p) =>
% 100.31/13.58 (((funcinfuncset) =>
% 100.31/13.58 (((lamProp) =>
% 100.31/13.58 (((lamp) =>
% 100.31/13.58 (((lam2p) =>
% 100.31/13.58 (((brelnall1) =>
% 100.31/13.58 (((brelnall2) =>
% 100.31/13.58 (((ex1E2) =>
% 100.31/13.58 (((funcGraphProp1) =>
% 100.31/13.58 (((funcGraphProp3) =>
% 100.31/13.58 (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 ((
% 100.31/13.58 (iffalseProp2) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueProp1) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueProp2) =>
% 100.31/13.58 ((
% 100.31/13.58 (ifSingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (ifp) =>
% 100.31/13.58 ((
% 100.31/13.58 (theeq) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrue) =>
% 100.31/13.58 ((
% 100.31/13.58 (iffalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueorfalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setminusT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1903])).
% 100.31/13.58 thf(zip_derived_cl1923, plain,
% 100.31/13.58 (~ (((funcImageSingleton) =>
% 100.31/13.58 (((apProp) =>
% 100.31/13.58 (((app) =>
% 100.31/13.58 (((infuncsetfunc) =>
% 100.31/13.58 (((ap2p) =>
% 100.31/13.58 (((funcinfuncset) =>
% 100.31/13.58 (((lamProp) =>
% 100.31/13.58 (((lamp) =>
% 100.31/13.58 (((lam2p) =>
% 100.31/13.58 (((brelnall1) =>
% 100.31/13.58 (((brelnall2) =>
% 100.31/13.58 (((ex1E2) =>
% 100.31/13.58 (((funcGraphProp1) =>
% 100.31/13.58 (((funcGraphProp3) =>
% 100.31/13.58 (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueProp1) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueProp2) =>
% 100.31/13.58 ((
% 100.31/13.58 (ifSingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (ifp) =>
% 100.31/13.58 ((
% 100.31/13.58 (theeq) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrue) =>
% 100.31/13.58 ((
% 100.31/13.58 (iffalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueorfalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setminusT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1914])).
% 100.31/13.58 thf(zip_derived_cl1932, plain,
% 100.31/13.58 (~ (((apProp) =>
% 100.31/13.58 (((app) =>
% 100.31/13.58 (((infuncsetfunc) =>
% 100.31/13.58 (((ap2p) =>
% 100.31/13.58 (((funcinfuncset) =>
% 100.31/13.58 (((lamProp) =>
% 100.31/13.58 (((lamp) =>
% 100.31/13.58 (((lam2p) =>
% 100.31/13.58 (((brelnall1) =>
% 100.31/13.58 (((brelnall2) =>
% 100.31/13.58 (((ex1E2) =>
% 100.31/13.58 (((funcGraphProp1) =>
% 100.31/13.58 (((funcGraphProp3) =>
% 100.31/13.58 (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueProp2) =>
% 100.31/13.58 ((
% 100.31/13.58 (ifSingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (ifp) =>
% 100.31/13.58 ((
% 100.31/13.58 (theeq) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrue) =>
% 100.31/13.58 ((
% 100.31/13.58 (iffalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueorfalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setminusT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1923])).
% 100.31/13.58 thf(zip_derived_cl1941, plain,
% 100.31/13.58 (~ (((app) =>
% 100.31/13.58 (((infuncsetfunc) =>
% 100.31/13.58 (((ap2p) =>
% 100.31/13.58 (((funcinfuncset) =>
% 100.31/13.58 (((lamProp) =>
% 100.31/13.58 (((lamp) =>
% 100.31/13.58 (((lam2p) =>
% 100.31/13.58 (((brelnall1) =>
% 100.31/13.58 (((brelnall2) =>
% 100.31/13.58 (((ex1E2) =>
% 100.31/13.58 (((funcGraphProp1) =>
% 100.31/13.58 (((funcGraphProp3) =>
% 100.31/13.58 (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 ((
% 100.31/13.58 (ifSingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (ifp) =>
% 100.31/13.58 ((
% 100.31/13.58 (theeq) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrue) =>
% 100.31/13.58 ((
% 100.31/13.58 (iffalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueorfalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setminusT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1932])).
% 100.31/13.58 thf(zip_derived_cl1951, plain,
% 100.31/13.58 (~ (((infuncsetfunc) =>
% 100.31/13.58 (((ap2p) =>
% 100.31/13.58 (((funcinfuncset) =>
% 100.31/13.58 (((lamProp) =>
% 100.31/13.58 (((lamp) =>
% 100.31/13.58 (((lam2p) =>
% 100.31/13.58 (((brelnall1) =>
% 100.31/13.58 (((brelnall2) =>
% 100.31/13.58 (((ex1E2) =>
% 100.31/13.58 (((funcGraphProp1) =>
% 100.31/13.58 (((funcGraphProp3) =>
% 100.31/13.58 (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 (((ifSingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (ifp) =>
% 100.31/13.58 ((
% 100.31/13.58 (theeq) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrue) =>
% 100.31/13.58 ((
% 100.31/13.58 (iffalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueorfalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setminusT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1941])).
% 100.31/13.58 thf(zip_derived_cl1961, plain,
% 100.31/13.58 (~ (((ap2p) =>
% 100.31/13.58 (((funcinfuncset) =>
% 100.31/13.58 (((lamProp) =>
% 100.31/13.58 (((lamp) =>
% 100.31/13.58 (((lam2p) =>
% 100.31/13.58 (((brelnall1) =>
% 100.31/13.58 (((brelnall2) =>
% 100.31/13.58 (((ex1E2) =>
% 100.31/13.58 (((funcGraphProp1) =>
% 100.31/13.58 (((funcGraphProp3) =>
% 100.31/13.58 (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 (((ifSingleton) =>
% 100.31/13.58 (((ifp) =>
% 100.31/13.58 ((
% 100.31/13.58 (theeq) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrue) =>
% 100.31/13.58 ((
% 100.31/13.58 (iffalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueorfalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setminusT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1951])).
% 100.31/13.58 thf(zip_derived_cl1972, plain,
% 100.31/13.58 (~ (((funcinfuncset) =>
% 100.31/13.58 (((lamProp) =>
% 100.31/13.58 (((lamp) =>
% 100.31/13.58 (((lam2p) =>
% 100.31/13.58 (((brelnall1) =>
% 100.31/13.58 (((brelnall2) =>
% 100.31/13.58 (((ex1E2) =>
% 100.31/13.58 (((funcGraphProp1) =>
% 100.31/13.58 (((funcGraphProp3) =>
% 100.31/13.58 (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 (((ifSingleton) =>
% 100.31/13.58 (((ifp) =>
% 100.31/13.58 (((theeq) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrue) =>
% 100.31/13.58 ((
% 100.31/13.58 (iffalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueorfalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setminusT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1961])).
% 100.31/13.58 thf(zip_derived_cl1983, plain,
% 100.31/13.58 (~ (((lamProp) =>
% 100.31/13.58 (((lamp) =>
% 100.31/13.58 (((lam2p) =>
% 100.31/13.58 (((brelnall1) =>
% 100.31/13.58 (((brelnall2) =>
% 100.31/13.58 (((ex1E2) =>
% 100.31/13.58 (((funcGraphProp1) =>
% 100.31/13.58 (((funcGraphProp3) =>
% 100.31/13.58 (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 (((ifSingleton) =>
% 100.31/13.58 (((ifp) =>
% 100.31/13.58 (((theeq) =>
% 100.31/13.58 (((iftrue) =>
% 100.31/13.58 ((
% 100.31/13.58 (iffalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueorfalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setminusT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1972])).
% 100.31/13.58 thf(zip_derived_cl1993, plain,
% 100.31/13.58 (~ (((lamp) =>
% 100.31/13.58 (((lam2p) =>
% 100.31/13.58 (((brelnall1) =>
% 100.31/13.58 (((brelnall2) =>
% 100.31/13.58 (((ex1E2) =>
% 100.31/13.58 (((funcGraphProp1) =>
% 100.31/13.58 (((funcGraphProp3) =>
% 100.31/13.58 (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 (((ifSingleton) =>
% 100.31/13.58 (((ifp) =>
% 100.31/13.58 (((theeq) =>
% 100.31/13.58 (((iftrue) =>
% 100.31/13.58 (((iffalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (iftrueorfalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setminusT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1983])).
% 100.31/13.58 thf(zip_derived_cl2003, plain,
% 100.31/13.58 (~ (((lam2p) =>
% 100.31/13.58 (((brelnall1) =>
% 100.31/13.58 (((brelnall2) =>
% 100.31/13.58 (((ex1E2) =>
% 100.31/13.58 (((funcGraphProp1) =>
% 100.31/13.58 (((funcGraphProp3) =>
% 100.31/13.58 (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 (((ifSingleton) =>
% 100.31/13.58 (((ifp) =>
% 100.31/13.58 (((theeq) =>
% 100.31/13.58 (((iftrue) =>
% 100.31/13.58 (((iffalse) =>
% 100.31/13.58 (((iftrueorfalse) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setminusT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1993])).
% 100.31/13.58 thf(zip_derived_cl2013, plain,
% 100.31/13.58 (~ (((brelnall1) =>
% 100.31/13.58 (((brelnall2) =>
% 100.31/13.58 (((ex1E2) =>
% 100.31/13.58 (((funcGraphProp1) =>
% 100.31/13.58 (((funcGraphProp3) =>
% 100.31/13.58 (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 (((ifSingleton) =>
% 100.31/13.58 (((ifp) =>
% 100.31/13.58 (((theeq) =>
% 100.31/13.58 (((iftrue) =>
% 100.31/13.58 (((iffalse) =>
% 100.31/13.58 (((iftrueorfalse) =>
% 100.31/13.58 (((binintersectT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setminusT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2003])).
% 100.31/13.58 thf(zip_derived_cl2022, plain,
% 100.31/13.58 (~ (((brelnall2) =>
% 100.31/13.58 (((ex1E2) =>
% 100.31/13.58 (((funcGraphProp1) =>
% 100.31/13.58 (((funcGraphProp3) =>
% 100.31/13.58 (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 (((ifSingleton) =>
% 100.31/13.58 (((ifp) =>
% 100.31/13.58 (((theeq) =>
% 100.31/13.58 (((iftrue) =>
% 100.31/13.58 (((iffalse) =>
% 100.31/13.58 (((iftrueorfalse) =>
% 100.31/13.58 (((binintersectT_lem) =>
% 100.31/13.58 (((binunionT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setminusT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2013])).
% 100.31/13.58 thf(zip_derived_cl2031, plain,
% 100.31/13.58 (~ (((ex1E2) =>
% 100.31/13.58 (((funcGraphProp1) =>
% 100.31/13.58 (((funcGraphProp3) =>
% 100.31/13.58 (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 (((ifSingleton) =>
% 100.31/13.58 (((ifp) =>
% 100.31/13.58 (((theeq) =>
% 100.31/13.58 (((iftrue) =>
% 100.31/13.58 (((iffalse) =>
% 100.31/13.58 (((iftrueorfalse) =>
% 100.31/13.58 (((binintersectT_lem) =>
% 100.31/13.58 (((binunionT_lem) =>
% 100.31/13.58 (((powersetT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setminusT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2022])).
% 100.31/13.58 thf(zip_derived_cl2040, plain,
% 100.31/13.58 (~ (((funcGraphProp1) =>
% 100.31/13.58 (((funcGraphProp3) =>
% 100.31/13.58 (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 (((ifSingleton) =>
% 100.31/13.58 (((ifp) =>
% 100.31/13.58 (((theeq) =>
% 100.31/13.58 (((iftrue) =>
% 100.31/13.58 (((iffalse) =>
% 100.31/13.58 (((iftrueorfalse) =>
% 100.31/13.58 (((binintersectT_lem) =>
% 100.31/13.58 (((binunionT_lem) =>
% 100.31/13.58 (((powersetT_lem) =>
% 100.31/13.58 (((setminusT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2031])).
% 100.31/13.58 thf(zip_derived_cl2049, plain,
% 100.31/13.58 (~ (((funcGraphProp3) =>
% 100.31/13.58 (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 (((ifSingleton) =>
% 100.31/13.58 (((ifp) =>
% 100.31/13.58 (((theeq) =>
% 100.31/13.58 (((iftrue) =>
% 100.31/13.58 (((iffalse) =>
% 100.31/13.58 (((iftrueorfalse) =>
% 100.31/13.58 (((binintersectT_lem) =>
% 100.31/13.58 (((binunionT_lem) =>
% 100.31/13.58 (((powersetT_lem) =>
% 100.31/13.58 (((setminusT_lem) =>
% 100.31/13.58 (((complementT_lem) =>
% 100.31/13.58 ((
% 100.31/13.58 (setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2040])).
% 100.31/13.58 thf(zip_derived_cl2060, plain,
% 100.31/13.58 (~ (((funcGraphProp2) =>
% 100.31/13.58 (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 (((ifSingleton) =>
% 100.31/13.58 (((ifp) =>
% 100.31/13.58 (((theeq) =>
% 100.31/13.58 (((iftrue) =>
% 100.31/13.58 (((iffalse) =>
% 100.31/13.58 (((iftrueorfalse) =>
% 100.31/13.58 (((binintersectT_lem) =>
% 100.31/13.58 (((binunionT_lem) =>
% 100.31/13.58 (((powersetT_lem) =>
% 100.31/13.58 (((setminusT_lem) =>
% 100.31/13.58 (((complementT_lem) =>
% 100.31/13.58 (((setextT) =>
% 100.31/13.58 ((
% 100.31/13.58 (subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2049])).
% 100.31/13.58 thf(zip_derived_cl2072, plain,
% 100.31/13.58 (~ (((funcextLem) =>
% 100.31/13.58 (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 (((ifSingleton) =>
% 100.31/13.58 (((ifp) =>
% 100.31/13.58 (((theeq) =>
% 100.31/13.58 (((iftrue) =>
% 100.31/13.58 (((iffalse) =>
% 100.31/13.58 (((iftrueorfalse) =>
% 100.31/13.58 (((binintersectT_lem) =>
% 100.31/13.58 (((binunionT_lem) =>
% 100.31/13.58 (((powersetT_lem) =>
% 100.31/13.58 (((setminusT_lem) =>
% 100.31/13.58 (((complementT_lem) =>
% 100.31/13.58 (((setextT) =>
% 100.31/13.58 (((subsetTI) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2060])).
% 100.31/13.58 thf(zip_derived_cl2084, plain,
% 100.31/13.58 (~ (((funcGraphProp4) =>
% 100.31/13.58 (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 (((ifSingleton) =>
% 100.31/13.58 (((ifp) =>
% 100.31/13.58 (((theeq) =>
% 100.31/13.58 (((iftrue) =>
% 100.31/13.58 (((iffalse) =>
% 100.31/13.58 (((iftrueorfalse) =>
% 100.31/13.58 (((binintersectT_lem) =>
% 100.31/13.58 (((binunionT_lem) =>
% 100.31/13.58 (((powersetT_lem) =>
% 100.31/13.58 (((setminusT_lem) =>
% 100.31/13.58 (((complementT_lem) =>
% 100.31/13.58 (((setextT) =>
% 100.31/13.58 (((subsetTI) =>
% 100.31/13.58 (((powersetTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2072])).
% 100.31/13.58 thf(zip_derived_cl2094, plain,
% 100.31/13.58 (~ (((subbreln) =>
% 100.31/13.58 (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 (((ifSingleton) =>
% 100.31/13.58 (((ifp) =>
% 100.31/13.58 (((theeq) =>
% 100.31/13.58 (((iftrue) =>
% 100.31/13.58 (((iffalse) =>
% 100.31/13.58 (((iftrueorfalse) =>
% 100.31/13.58 (((binintersectT_lem) =>
% 100.31/13.58 (((binunionT_lem) =>
% 100.31/13.58 (((powersetT_lem) =>
% 100.31/13.58 (((setminusT_lem) =>
% 100.31/13.58 (((complementT_lem) =>
% 100.31/13.58 (((setextT) =>
% 100.31/13.58 (((subsetTI) =>
% 100.31/13.58 (((powersetTI1) =>
% 100.31/13.58 (((powersetTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2084])).
% 100.31/13.58 thf(zip_derived_cl2105, plain,
% 100.31/13.58 (~ (((eqbreln) =>
% 100.31/13.58 (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 (((ifSingleton) =>
% 100.31/13.58 (((ifp) =>
% 100.31/13.58 (((theeq) =>
% 100.31/13.58 (((iftrue) =>
% 100.31/13.58 (((iffalse) =>
% 100.31/13.58 (((iftrueorfalse) =>
% 100.31/13.58 (((binintersectT_lem) =>
% 100.31/13.58 (((binunionT_lem) =>
% 100.31/13.58 (((powersetT_lem) =>
% 100.31/13.58 (((setminusT_lem) =>
% 100.31/13.58 (((complementT_lem) =>
% 100.31/13.58 (((setextT) =>
% 100.31/13.58 (((subsetTI) =>
% 100.31/13.58 (((powersetTI1) =>
% 100.31/13.58 (((powersetTE1) =>
% 100.31/13.58 (((complementTI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#C') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2094])).
% 100.31/13.58 thf(zip_derived_cl2118, plain,
% 100.31/13.58 (~ (((funcext) =>
% 100.31/13.58 (((funcext2) =>
% 100.31/13.58 (((ap2apEq1) =>
% 100.31/13.58 (((ap2apEq2) =>
% 100.31/13.58 (((beta1) =>
% 100.31/13.58 (((eta1) =>
% 100.31/13.58 (((lam2lamEq) =>
% 100.31/13.58 (((beta2) =>
% 100.31/13.58 (((eta2) =>
% 100.31/13.58 (((iffalseProp1) =>
% 100.31/13.58 (((iffalseProp2) =>
% 100.31/13.58 (((iftrueProp1) =>
% 100.31/13.58 (((iftrueProp2) =>
% 100.31/13.58 (((ifSingleton) =>
% 100.31/13.58 (((ifp) =>
% 100.31/13.58 (((theeq) =>
% 100.31/13.58 (((iftrue) =>
% 100.31/13.58 (((iffalse) =>
% 100.31/13.58 (((iftrueorfalse) =>
% 100.31/13.58 (((binintersectT_lem) =>
% 100.31/13.58 (((binunionT_lem) =>
% 100.31/13.58 (((powersetT_lem) =>
% 100.31/13.58 (((setminusT_lem) =>
% 100.31/13.58 (((complementT_lem) =>
% 100.31/13.58 (((setextT) =>
% 100.31/13.58 (((subsetTI) =>
% 100.31/13.58 (((powersetTI1) =>
% 100.31/13.58 (((powersetTE1) =>
% 100.31/13.58 (((complementTI1) =>
% 100.31/13.58 (((complementTE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTELcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binintersectTERcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT1) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT2) =>
% 100.31/13.58 ((
% 100.31/13.58 (contrasubsetT3) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementI1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementE1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub1) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementSub2) =>
% 100.31/13.58 ((
% 100.31/13.58 (doubleComplementEq) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTnotintersectT) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementImpComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementSubsetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementInPowersetComplementIntersect) =>
% 100.31/13.58 ((
% 100.31/13.58 (contraSubsetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementTcontraSubset) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTILcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTIRcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInUnion2) =>
% 100.31/13.58 ((
% 100.31/13.58 (inIntersectImpInIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (intersectInPowersetIntersectUnions) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpNotIn1) =>
% 100.31/13.58 ((
% 100.31/13.58 (inComplementUnionImpInComplement1) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTE) =>
% 100.31/13.58 ((
% 100.31/13.58 (binunionTEcontra) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a1) =>
% 100.31/13.58 ((
% 100.31/13.58 (complementUnionInPowersetComplement) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan1) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2a) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b2) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2b) =>
% 100.31/13.58 ((
% 100.31/13.58 (demorgan2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule0) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz13rule4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_1) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_2) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_3) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_4) =>
% 100.31/13.58 ((
% 100.31/13.58 (woz1_5) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all2) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1SetBreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (choice2fnsingleton) =>
% 100.31/13.58 ((
% 100.31/13.58 (setOfPairsIsBReln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1all1) =>
% 100.31/13.58 ((
% 100.31/13.58 (subbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (eqbreln1) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1invE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compprop) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compI) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compE) =>
% 100.31/13.58 ((
% 100.31/13.58 (breln1compEex) =>
% 100.31/13.58 ((
% 100.31/13.58 (!!) @ (
% 100.31/13.58 (('#B') @ (
% 100.31/13.58 !!) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 =>))) @
% 100.31/13.58 breln1)))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 !!))) @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#S') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#B') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 '#S') @
% 100.31/13.58 (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.58 (
% 100.31/13.58 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2105])).
% 100.31/13.59 thf(zip_derived_cl2133, plain,
% 100.31/13.59 (~ (((funcext2) =>
% 100.31/13.59 (((ap2apEq1) =>
% 100.31/13.59 (((ap2apEq2) =>
% 100.31/13.59 (((beta1) =>
% 100.31/13.59 (((eta1) =>
% 100.31/13.59 (((lam2lamEq) =>
% 100.31/13.59 (((beta2) =>
% 100.31/13.59 (((eta2) =>
% 100.31/13.59 (((iffalseProp1) =>
% 100.31/13.59 (((iffalseProp2) =>
% 100.31/13.59 (((iftrueProp1) =>
% 100.31/13.59 (((iftrueProp2) =>
% 100.31/13.59 (((ifSingleton) =>
% 100.31/13.59 (((ifp) =>
% 100.31/13.59 (((theeq) =>
% 100.31/13.59 (((iftrue) =>
% 100.31/13.59 (((iffalse) =>
% 100.31/13.59 (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binintersectTERcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (contrasubsetT) =>
% 100.31/13.59 ((
% 100.31/13.59 (contrasubsetT1) =>
% 100.31/13.59 ((
% 100.31/13.59 (contrasubsetT2) =>
% 100.31/13.59 ((
% 100.31/13.59 (contrasubsetT3) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementI1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementE1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementSub1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementSub2) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementEq) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTnotintersectT) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementImpComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementSubsetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementInPowersetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (contraSubsetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTcontraSubset) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2118])).
% 100.31/13.59 thf(zip_derived_cl2149, plain,
% 100.31/13.59 (~ (((ap2apEq1) =>
% 100.31/13.59 (((ap2apEq2) =>
% 100.31/13.59 (((beta1) =>
% 100.31/13.59 (((eta1) =>
% 100.31/13.59 (((lam2lamEq) =>
% 100.31/13.59 (((beta2) =>
% 100.31/13.59 (((eta2) =>
% 100.31/13.59 (((iffalseProp1) =>
% 100.31/13.59 (((iffalseProp2) =>
% 100.31/13.59 (((iftrueProp1) =>
% 100.31/13.59 (((iftrueProp2) =>
% 100.31/13.59 (((ifSingleton) =>
% 100.31/13.59 (((ifp) =>
% 100.31/13.59 (((theeq) =>
% 100.31/13.59 (((iftrue) =>
% 100.31/13.59 (((iffalse) =>
% 100.31/13.59 (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (contrasubsetT) =>
% 100.31/13.59 ((
% 100.31/13.59 (contrasubsetT1) =>
% 100.31/13.59 ((
% 100.31/13.59 (contrasubsetT2) =>
% 100.31/13.59 ((
% 100.31/13.59 (contrasubsetT3) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementI1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementE1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementSub1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementSub2) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementEq) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTnotintersectT) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementImpComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementSubsetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementInPowersetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (contraSubsetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTcontraSubset) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2133])).
% 100.31/13.59 thf(zip_derived_cl2166, plain,
% 100.31/13.59 (~ (((ap2apEq2) =>
% 100.31/13.59 (((beta1) =>
% 100.31/13.59 (((eta1) =>
% 100.31/13.59 (((lam2lamEq) =>
% 100.31/13.59 (((beta2) =>
% 100.31/13.59 (((eta2) =>
% 100.31/13.59 (((iffalseProp1) =>
% 100.31/13.59 (((iffalseProp2) =>
% 100.31/13.59 (((iftrueProp1) =>
% 100.31/13.59 (((iftrueProp2) =>
% 100.31/13.59 (((ifSingleton) =>
% 100.31/13.59 (((ifp) =>
% 100.31/13.59 (((theeq) =>
% 100.31/13.59 (((iftrue) =>
% 100.31/13.59 (((iffalse) =>
% 100.31/13.59 (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 ((
% 100.31/13.59 (contrasubsetT1) =>
% 100.31/13.59 ((
% 100.31/13.59 (contrasubsetT2) =>
% 100.31/13.59 ((
% 100.31/13.59 (contrasubsetT3) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementI1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementE1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementSub1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementSub2) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementEq) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTnotintersectT) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementImpComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementSubsetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementInPowersetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (contraSubsetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTcontraSubset) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2149])).
% 100.31/13.59 thf(zip_derived_cl2185, plain,
% 100.31/13.59 (~ (((beta1) =>
% 100.31/13.59 (((eta1) =>
% 100.31/13.59 (((lam2lamEq) =>
% 100.31/13.59 (((beta2) =>
% 100.31/13.59 (((eta2) =>
% 100.31/13.59 (((iffalseProp1) =>
% 100.31/13.59 (((iffalseProp2) =>
% 100.31/13.59 (((iftrueProp1) =>
% 100.31/13.59 (((iftrueProp2) =>
% 100.31/13.59 (((ifSingleton) =>
% 100.31/13.59 (((ifp) =>
% 100.31/13.59 (((theeq) =>
% 100.31/13.59 (((iftrue) =>
% 100.31/13.59 (((iffalse) =>
% 100.31/13.59 (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 ((
% 100.31/13.59 (contrasubsetT2) =>
% 100.31/13.59 ((
% 100.31/13.59 (contrasubsetT3) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementI1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementE1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementSub1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementSub2) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementEq) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTnotintersectT) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementImpComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementSubsetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementInPowersetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (contraSubsetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTcontraSubset) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2166])).
% 100.31/13.59 thf(zip_derived_cl2203, plain,
% 100.31/13.59 (~ (((eta1) =>
% 100.31/13.59 (((lam2lamEq) =>
% 100.31/13.59 (((beta2) =>
% 100.31/13.59 (((eta2) =>
% 100.31/13.59 (((iffalseProp1) =>
% 100.31/13.59 (((iffalseProp2) =>
% 100.31/13.59 (((iftrueProp1) =>
% 100.31/13.59 (((iftrueProp2) =>
% 100.31/13.59 (((ifSingleton) =>
% 100.31/13.59 (((ifp) =>
% 100.31/13.59 (((theeq) =>
% 100.31/13.59 (((iftrue) =>
% 100.31/13.59 (((iffalse) =>
% 100.31/13.59 (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 ((
% 100.31/13.59 (contrasubsetT3) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementI1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementE1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementSub1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementSub2) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementEq) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTnotintersectT) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementImpComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementSubsetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementInPowersetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (contraSubsetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTcontraSubset) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2185])).
% 100.31/13.59 thf(zip_derived_cl2219, plain,
% 100.31/13.59 (~ (((lam2lamEq) =>
% 100.31/13.59 (((beta2) =>
% 100.31/13.59 (((eta2) =>
% 100.31/13.59 (((iffalseProp1) =>
% 100.31/13.59 (((iffalseProp2) =>
% 100.31/13.59 (((iftrueProp1) =>
% 100.31/13.59 (((iftrueProp2) =>
% 100.31/13.59 (((ifSingleton) =>
% 100.31/13.59 (((ifp) =>
% 100.31/13.59 (((theeq) =>
% 100.31/13.59 (((iftrue) =>
% 100.31/13.59 (((iffalse) =>
% 100.31/13.59 (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementI1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementE1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementSub1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementSub2) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementEq) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTnotintersectT) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementImpComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementSubsetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementInPowersetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (contraSubsetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTcontraSubset) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2203])).
% 100.31/13.59 thf(zip_derived_cl2235, plain,
% 100.31/13.59 (~ (((beta2) =>
% 100.31/13.59 (((eta2) =>
% 100.31/13.59 (((iffalseProp1) =>
% 100.31/13.59 (((iffalseProp2) =>
% 100.31/13.59 (((iftrueProp1) =>
% 100.31/13.59 (((iftrueProp2) =>
% 100.31/13.59 (((ifSingleton) =>
% 100.31/13.59 (((ifp) =>
% 100.31/13.59 (((theeq) =>
% 100.31/13.59 (((iftrue) =>
% 100.31/13.59 (((iffalse) =>
% 100.31/13.59 (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementE1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementSub1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementSub2) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementEq) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTnotintersectT) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementImpComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementSubsetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementInPowersetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (contraSubsetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTcontraSubset) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2219])).
% 100.31/13.59 thf(zip_derived_cl2251, plain,
% 100.31/13.59 (~ (((eta2) =>
% 100.31/13.59 (((iffalseProp1) =>
% 100.31/13.59 (((iffalseProp2) =>
% 100.31/13.59 (((iftrueProp1) =>
% 100.31/13.59 (((iftrueProp2) =>
% 100.31/13.59 (((ifSingleton) =>
% 100.31/13.59 (((ifp) =>
% 100.31/13.59 (((theeq) =>
% 100.31/13.59 (((iftrue) =>
% 100.31/13.59 (((iffalse) =>
% 100.31/13.59 (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementSub1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementSub2) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementEq) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTnotintersectT) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementImpComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementSubsetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementInPowersetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (contraSubsetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTcontraSubset) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2235])).
% 100.31/13.59 thf(zip_derived_cl2268, plain,
% 100.31/13.59 (~ (((iffalseProp1) =>
% 100.31/13.59 (((iffalseProp2) =>
% 100.31/13.59 (((iftrueProp1) =>
% 100.31/13.59 (((iftrueProp2) =>
% 100.31/13.59 (((ifSingleton) =>
% 100.31/13.59 (((ifp) =>
% 100.31/13.59 (((theeq) =>
% 100.31/13.59 (((iftrue) =>
% 100.31/13.59 (((iffalse) =>
% 100.31/13.59 (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementSub2) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementEq) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTnotintersectT) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementImpComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementSubsetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementInPowersetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (contraSubsetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTcontraSubset) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2251])).
% 100.31/13.59 thf(zip_derived_cl2286, plain,
% 100.31/13.59 (~ (((iffalseProp2) =>
% 100.31/13.59 (((iftrueProp1) =>
% 100.31/13.59 (((iftrueProp2) =>
% 100.31/13.59 (((ifSingleton) =>
% 100.31/13.59 (((ifp) =>
% 100.31/13.59 (((theeq) =>
% 100.31/13.59 (((iftrue) =>
% 100.31/13.59 (((iffalse) =>
% 100.31/13.59 (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 ((
% 100.31/13.59 (doubleComplementEq) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTnotintersectT) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementImpComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementSubsetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementInPowersetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (contraSubsetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTcontraSubset) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2268])).
% 100.31/13.59 thf(zip_derived_cl2306, plain,
% 100.31/13.59 (~ (((iftrueProp1) =>
% 100.31/13.59 (((iftrueProp2) =>
% 100.31/13.59 (((ifSingleton) =>
% 100.31/13.59 (((ifp) =>
% 100.31/13.59 (((theeq) =>
% 100.31/13.59 (((iftrue) =>
% 100.31/13.59 (((iffalse) =>
% 100.31/13.59 (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTnotintersectT) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementImpComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementSubsetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementInPowersetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (contraSubsetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTcontraSubset) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2286])).
% 100.31/13.59 thf(zip_derived_cl2328, plain,
% 100.31/13.59 (~ (((iftrueProp2) =>
% 100.31/13.59 (((ifSingleton) =>
% 100.31/13.59 (((ifp) =>
% 100.31/13.59 (((theeq) =>
% 100.31/13.59 (((iftrue) =>
% 100.31/13.59 (((iffalse) =>
% 100.31/13.59 (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementImpComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementSubsetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementInPowersetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (contraSubsetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTcontraSubset) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2306])).
% 100.31/13.59 thf(zip_derived_cl2344, plain,
% 100.31/13.59 (~ (((ifSingleton) =>
% 100.31/13.59 (((ifp) =>
% 100.31/13.59 (((theeq) =>
% 100.31/13.59 (((iftrue) =>
% 100.31/13.59 (((iffalse) =>
% 100.31/13.59 (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementSubsetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementInPowersetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (contraSubsetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTcontraSubset) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2328])).
% 100.31/13.59 thf(zip_derived_cl2360, plain,
% 100.31/13.59 (~ (((ifp) =>
% 100.31/13.59 (((theeq) =>
% 100.31/13.59 (((iftrue) =>
% 100.31/13.59 (((iffalse) =>
% 100.31/13.59 (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 (((complementSubsetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementInPowersetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (contraSubsetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTcontraSubset) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2344])).
% 100.31/13.59 thf(zip_derived_cl2381, plain,
% 100.31/13.59 (~ (((theeq) =>
% 100.31/13.59 (((iftrue) =>
% 100.31/13.59 (((iffalse) =>
% 100.31/13.59 (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 (((complementSubsetComplementIntersect) =>
% 100.31/13.59 (((complementInPowersetComplementIntersect) =>
% 100.31/13.59 ((
% 100.31/13.59 (contraSubsetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTcontraSubset) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2360])).
% 100.31/13.59 thf(zip_derived_cl2399, plain,
% 100.31/13.59 (~ (((iftrue) =>
% 100.31/13.59 (((iffalse) =>
% 100.31/13.59 (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 (((complementSubsetComplementIntersect) =>
% 100.31/13.59 (((complementInPowersetComplementIntersect) =>
% 100.31/13.59 (((contraSubsetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementTcontraSubset) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2381])).
% 100.31/13.59 thf(zip_derived_cl2415, plain,
% 100.31/13.59 (~ (((iffalse) =>
% 100.31/13.59 (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 (((complementSubsetComplementIntersect) =>
% 100.31/13.59 (((complementInPowersetComplementIntersect) =>
% 100.31/13.59 (((contraSubsetComplement) =>
% 100.31/13.59 (((complementTcontraSubset) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2399])).
% 100.31/13.59 thf(zip_derived_cl2434, plain,
% 100.31/13.59 (~ (((iftrueorfalse) =>
% 100.31/13.59 (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 (((complementSubsetComplementIntersect) =>
% 100.31/13.59 (((complementInPowersetComplementIntersect) =>
% 100.31/13.59 (((contraSubsetComplement) =>
% 100.31/13.59 (((complementTcontraSubset) =>
% 100.31/13.59 (((binunionTILcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2415])).
% 100.31/13.59 thf(zip_derived_cl2449, plain,
% 100.31/13.59 (~ (((binintersectT_lem) =>
% 100.31/13.59 (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 (((complementSubsetComplementIntersect) =>
% 100.31/13.59 (((complementInPowersetComplementIntersect) =>
% 100.31/13.59 (((contraSubsetComplement) =>
% 100.31/13.59 (((complementTcontraSubset) =>
% 100.31/13.59 (((binunionTILcontra) =>
% 100.31/13.59 (((binunionTIRcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2434])).
% 100.31/13.59 thf(zip_derived_cl2461, plain,
% 100.31/13.59 (~ (((binunionT_lem) =>
% 100.31/13.59 (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 (((complementSubsetComplementIntersect) =>
% 100.31/13.59 (((complementInPowersetComplementIntersect) =>
% 100.31/13.59 (((contraSubsetComplement) =>
% 100.31/13.59 (((complementTcontraSubset) =>
% 100.31/13.59 (((binunionTILcontra) =>
% 100.31/13.59 (((binunionTIRcontra) =>
% 100.31/13.59 (((inIntersectImpInUnion) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2449])).
% 100.31/13.59 thf(zip_derived_cl2472, plain,
% 100.31/13.59 (~ (((powersetT_lem) =>
% 100.31/13.59 (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 (((complementSubsetComplementIntersect) =>
% 100.31/13.59 (((complementInPowersetComplementIntersect) =>
% 100.31/13.59 (((contraSubsetComplement) =>
% 100.31/13.59 (((complementTcontraSubset) =>
% 100.31/13.59 (((binunionTILcontra) =>
% 100.31/13.59 (((binunionTIRcontra) =>
% 100.31/13.59 (((inIntersectImpInUnion) =>
% 100.31/13.59 (((inIntersectImpInUnion2) =>
% 100.31/13.59 ((
% 100.31/13.59 (inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2461])).
% 100.31/13.59 thf(zip_derived_cl2483, plain,
% 100.31/13.59 (~ (((setminusT_lem) =>
% 100.31/13.59 (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 (((complementSubsetComplementIntersect) =>
% 100.31/13.59 (((complementInPowersetComplementIntersect) =>
% 100.31/13.59 (((contraSubsetComplement) =>
% 100.31/13.59 (((complementTcontraSubset) =>
% 100.31/13.59 (((binunionTILcontra) =>
% 100.31/13.59 (((binunionTIRcontra) =>
% 100.31/13.59 (((inIntersectImpInUnion) =>
% 100.31/13.59 (((inIntersectImpInUnion2) =>
% 100.31/13.59 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2472])).
% 100.31/13.59 thf(zip_derived_cl2492, plain,
% 100.31/13.59 (~ (((complementT_lem) =>
% 100.31/13.59 (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 (((complementSubsetComplementIntersect) =>
% 100.31/13.59 (((complementInPowersetComplementIntersect) =>
% 100.31/13.59 (((contraSubsetComplement) =>
% 100.31/13.59 (((complementTcontraSubset) =>
% 100.31/13.59 (((binunionTILcontra) =>
% 100.31/13.59 (((binunionTIRcontra) =>
% 100.31/13.59 (((inIntersectImpInUnion) =>
% 100.31/13.59 (((inIntersectImpInUnion2) =>
% 100.31/13.59 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.59 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2483])).
% 100.31/13.59 thf(zip_derived_cl2502, plain,
% 100.31/13.59 (~ (((setextT) =>
% 100.31/13.59 (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 (((complementSubsetComplementIntersect) =>
% 100.31/13.59 (((complementInPowersetComplementIntersect) =>
% 100.31/13.59 (((contraSubsetComplement) =>
% 100.31/13.59 (((complementTcontraSubset) =>
% 100.31/13.59 (((binunionTILcontra) =>
% 100.31/13.59 (((binunionTIRcontra) =>
% 100.31/13.59 (((inIntersectImpInUnion) =>
% 100.31/13.59 (((inIntersectImpInUnion2) =>
% 100.31/13.59 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.59 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.59 (((inComplementUnionImpNotIn1) =>
% 100.31/13.59 ((
% 100.31/13.59 (inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2492])).
% 100.31/13.59 thf(zip_derived_cl2513, plain,
% 100.31/13.59 (~ (((subsetTI) =>
% 100.31/13.59 (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 (((complementSubsetComplementIntersect) =>
% 100.31/13.59 (((complementInPowersetComplementIntersect) =>
% 100.31/13.59 (((contraSubsetComplement) =>
% 100.31/13.59 (((complementTcontraSubset) =>
% 100.31/13.59 (((binunionTILcontra) =>
% 100.31/13.59 (((binunionTIRcontra) =>
% 100.31/13.59 (((inIntersectImpInUnion) =>
% 100.31/13.59 (((inIntersectImpInUnion2) =>
% 100.31/13.59 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.59 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.59 (((inComplementUnionImpNotIn1) =>
% 100.31/13.59 (((inComplementUnionImpInComplement1) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2502])).
% 100.31/13.59 thf(zip_derived_cl2525, plain,
% 100.31/13.59 (~ (((powersetTI1) =>
% 100.31/13.59 (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 (((complementSubsetComplementIntersect) =>
% 100.31/13.59 (((complementInPowersetComplementIntersect) =>
% 100.31/13.59 (((contraSubsetComplement) =>
% 100.31/13.59 (((complementTcontraSubset) =>
% 100.31/13.59 (((binunionTILcontra) =>
% 100.31/13.59 (((binunionTIRcontra) =>
% 100.31/13.59 (((inIntersectImpInUnion) =>
% 100.31/13.59 (((inIntersectImpInUnion2) =>
% 100.31/13.59 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.59 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.59 (((inComplementUnionImpNotIn1) =>
% 100.31/13.59 (((inComplementUnionImpInComplement1) =>
% 100.31/13.59 (((binunionTE) =>
% 100.31/13.59 ((
% 100.31/13.59 (binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2513])).
% 100.31/13.59 thf(zip_derived_cl2534, plain,
% 100.31/13.59 (~ (((powersetTE1) =>
% 100.31/13.59 (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 (((complementSubsetComplementIntersect) =>
% 100.31/13.59 (((complementInPowersetComplementIntersect) =>
% 100.31/13.59 (((contraSubsetComplement) =>
% 100.31/13.59 (((complementTcontraSubset) =>
% 100.31/13.59 (((binunionTILcontra) =>
% 100.31/13.59 (((binunionTIRcontra) =>
% 100.31/13.59 (((inIntersectImpInUnion) =>
% 100.31/13.59 (((inIntersectImpInUnion2) =>
% 100.31/13.59 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.59 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.59 (((inComplementUnionImpNotIn1) =>
% 100.31/13.59 (((inComplementUnionImpInComplement1) =>
% 100.31/13.59 (((binunionTE) =>
% 100.31/13.59 (((binunionTEcontra) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2525])).
% 100.31/13.59 thf(zip_derived_cl2542, plain,
% 100.31/13.59 (~ (((complementTI1) =>
% 100.31/13.59 (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 (((complementSubsetComplementIntersect) =>
% 100.31/13.59 (((complementInPowersetComplementIntersect) =>
% 100.31/13.59 (((contraSubsetComplement) =>
% 100.31/13.59 (((complementTcontraSubset) =>
% 100.31/13.59 (((binunionTILcontra) =>
% 100.31/13.59 (((binunionTIRcontra) =>
% 100.31/13.59 (((inIntersectImpInUnion) =>
% 100.31/13.59 (((inIntersectImpInUnion2) =>
% 100.31/13.59 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.59 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.59 (((inComplementUnionImpNotIn1) =>
% 100.31/13.59 (((inComplementUnionImpInComplement1) =>
% 100.31/13.59 (((binunionTE) =>
% 100.31/13.59 (((binunionTEcontra) =>
% 100.31/13.59 (((demorgan2a1) =>
% 100.31/13.59 ((
% 100.31/13.59 (complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2534])).
% 100.31/13.59 thf(zip_derived_cl2550, plain,
% 100.31/13.59 (~ (((complementTE1) =>
% 100.31/13.59 (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 (((complementSubsetComplementIntersect) =>
% 100.31/13.59 (((complementInPowersetComplementIntersect) =>
% 100.31/13.59 (((contraSubsetComplement) =>
% 100.31/13.59 (((complementTcontraSubset) =>
% 100.31/13.59 (((binunionTILcontra) =>
% 100.31/13.59 (((binunionTIRcontra) =>
% 100.31/13.59 (((inIntersectImpInUnion) =>
% 100.31/13.59 (((inIntersectImpInUnion2) =>
% 100.31/13.59 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.59 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.59 (((inComplementUnionImpNotIn1) =>
% 100.31/13.59 (((inComplementUnionImpInComplement1) =>
% 100.31/13.59 (((binunionTE) =>
% 100.31/13.59 (((binunionTEcontra) =>
% 100.31/13.59 (((demorgan2a1) =>
% 100.31/13.59 (((complementUnionInPowersetComplement) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#C') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2542])).
% 100.31/13.59 thf(zip_derived_cl2558, plain,
% 100.31/13.59 (~ (((binintersectTELcontra) =>
% 100.31/13.59 (((binintersectTERcontra) =>
% 100.31/13.59 (((contrasubsetT) =>
% 100.31/13.59 (((contrasubsetT1) =>
% 100.31/13.59 (((contrasubsetT2) =>
% 100.31/13.59 (((contrasubsetT3) =>
% 100.31/13.59 (((doubleComplementI1) =>
% 100.31/13.59 (((doubleComplementE1) =>
% 100.31/13.59 (((doubleComplementSub1) =>
% 100.31/13.59 (((doubleComplementSub2) =>
% 100.31/13.59 (((doubleComplementEq) =>
% 100.31/13.59 (((complementTnotintersectT) =>
% 100.31/13.59 (((complementImpComplementIntersect) =>
% 100.31/13.59 (((complementSubsetComplementIntersect) =>
% 100.31/13.59 (((complementInPowersetComplementIntersect) =>
% 100.31/13.59 (((contraSubsetComplement) =>
% 100.31/13.59 (((complementTcontraSubset) =>
% 100.31/13.59 (((binunionTILcontra) =>
% 100.31/13.59 (((binunionTIRcontra) =>
% 100.31/13.59 (((inIntersectImpInUnion) =>
% 100.31/13.59 (((inIntersectImpInUnion2) =>
% 100.31/13.59 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.59 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.59 (((inComplementUnionImpNotIn1) =>
% 100.31/13.59 (((inComplementUnionImpInComplement1) =>
% 100.31/13.59 (((binunionTE) =>
% 100.31/13.59 (((binunionTEcontra) =>
% 100.31/13.59 (((demorgan2a1) =>
% 100.31/13.59 (((complementUnionInPowersetComplement) =>
% 100.31/13.59 (((demorgan2a2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan1) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2a) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b2) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2b) =>
% 100.31/13.59 ((
% 100.31/13.59 (demorgan2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule0) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz13rule4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_1) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_2) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_3) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_4) =>
% 100.31/13.59 ((
% 100.31/13.59 (woz1_5) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all2) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1SetBreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (choice2fnsingleton) =>
% 100.31/13.59 ((
% 100.31/13.59 (setOfPairsIsBReln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1all1) =>
% 100.31/13.59 ((
% 100.31/13.59 (subbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (eqbreln1) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1invE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compprop) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compI) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compE) =>
% 100.31/13.59 ((
% 100.31/13.59 (breln1compEex) =>
% 100.31/13.59 ((
% 100.31/13.59 (!!) @ (
% 100.31/13.59 (('#B') @ (
% 100.31/13.59 !!) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.59 breln1)))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 !!))) @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#S') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#B') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 '#S') @
% 100.31/13.59 (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 (
% 100.31/13.59 ('#B') @ (
% 100.31/13.59 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2550])).
% 100.31/13.60 thf(zip_derived_cl2567, plain,
% 100.31/13.60 (~ (((binintersectTERcontra) =>
% 100.31/13.60 (((contrasubsetT) =>
% 100.31/13.60 (((contrasubsetT1) =>
% 100.31/13.60 (((contrasubsetT2) =>
% 100.31/13.60 (((contrasubsetT3) =>
% 100.31/13.60 (((doubleComplementI1) =>
% 100.31/13.60 (((doubleComplementE1) =>
% 100.31/13.60 (((doubleComplementSub1) =>
% 100.31/13.60 (((doubleComplementSub2) =>
% 100.31/13.60 (((doubleComplementEq) =>
% 100.31/13.60 (((complementTnotintersectT) =>
% 100.31/13.60 (((complementImpComplementIntersect) =>
% 100.31/13.60 (((complementSubsetComplementIntersect) =>
% 100.31/13.60 (((complementInPowersetComplementIntersect) =>
% 100.31/13.60 (((contraSubsetComplement) =>
% 100.31/13.60 (((complementTcontraSubset) =>
% 100.31/13.60 (((binunionTILcontra) =>
% 100.31/13.60 (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan1b) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan1) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2a) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2b2) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2b) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule0) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_5) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2558])).
% 100.31/13.60 thf(zip_derived_cl2577, plain,
% 100.31/13.60 (~ (((contrasubsetT) =>
% 100.31/13.60 (((contrasubsetT1) =>
% 100.31/13.60 (((contrasubsetT2) =>
% 100.31/13.60 (((contrasubsetT3) =>
% 100.31/13.60 (((doubleComplementI1) =>
% 100.31/13.60 (((doubleComplementE1) =>
% 100.31/13.60 (((doubleComplementSub1) =>
% 100.31/13.60 (((doubleComplementSub2) =>
% 100.31/13.60 (((doubleComplementEq) =>
% 100.31/13.60 (((complementTnotintersectT) =>
% 100.31/13.60 (((complementImpComplementIntersect) =>
% 100.31/13.60 (((complementSubsetComplementIntersect) =>
% 100.31/13.60 (((complementInPowersetComplementIntersect) =>
% 100.31/13.60 (((contraSubsetComplement) =>
% 100.31/13.60 (((complementTcontraSubset) =>
% 100.31/13.60 (((binunionTILcontra) =>
% 100.31/13.60 (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan1) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2a) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2b2) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2b) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule0) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_5) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2567])).
% 100.31/13.60 thf(zip_derived_cl2588, plain,
% 100.31/13.60 (~ (((contrasubsetT1) =>
% 100.31/13.60 (((contrasubsetT2) =>
% 100.31/13.60 (((contrasubsetT3) =>
% 100.31/13.60 (((doubleComplementI1) =>
% 100.31/13.60 (((doubleComplementE1) =>
% 100.31/13.60 (((doubleComplementSub1) =>
% 100.31/13.60 (((doubleComplementSub2) =>
% 100.31/13.60 (((doubleComplementEq) =>
% 100.31/13.60 (((complementTnotintersectT) =>
% 100.31/13.60 (((complementImpComplementIntersect) =>
% 100.31/13.60 (((complementSubsetComplementIntersect) =>
% 100.31/13.60 (((complementInPowersetComplementIntersect) =>
% 100.31/13.60 (((contraSubsetComplement) =>
% 100.31/13.60 (((complementTcontraSubset) =>
% 100.31/13.60 (((binunionTILcontra) =>
% 100.31/13.60 (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2a) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2b2) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2b) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule0) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_5) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2577])).
% 100.31/13.60 thf(zip_derived_cl2601, plain,
% 100.31/13.60 (~ (((contrasubsetT2) =>
% 100.31/13.60 (((contrasubsetT3) =>
% 100.31/13.60 (((doubleComplementI1) =>
% 100.31/13.60 (((doubleComplementE1) =>
% 100.31/13.60 (((doubleComplementSub1) =>
% 100.31/13.60 (((doubleComplementSub2) =>
% 100.31/13.60 (((doubleComplementEq) =>
% 100.31/13.60 (((complementTnotintersectT) =>
% 100.31/13.60 (((complementImpComplementIntersect) =>
% 100.31/13.60 (((complementSubsetComplementIntersect) =>
% 100.31/13.60 (((complementInPowersetComplementIntersect) =>
% 100.31/13.60 (((contraSubsetComplement) =>
% 100.31/13.60 (((complementTcontraSubset) =>
% 100.31/13.60 (((binunionTILcontra) =>
% 100.31/13.60 (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2b2) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2b) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule0) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_5) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2588])).
% 100.31/13.60 thf(zip_derived_cl2617, plain,
% 100.31/13.60 (~ (((contrasubsetT3) =>
% 100.31/13.60 (((doubleComplementI1) =>
% 100.31/13.60 (((doubleComplementE1) =>
% 100.31/13.60 (((doubleComplementSub1) =>
% 100.31/13.60 (((doubleComplementSub2) =>
% 100.31/13.60 (((doubleComplementEq) =>
% 100.31/13.60 (((complementTnotintersectT) =>
% 100.31/13.60 (((complementImpComplementIntersect) =>
% 100.31/13.60 (((complementSubsetComplementIntersect) =>
% 100.31/13.60 (((complementInPowersetComplementIntersect) =>
% 100.31/13.60 (((contraSubsetComplement) =>
% 100.31/13.60 (((complementTcontraSubset) =>
% 100.31/13.60 (((binunionTILcontra) =>
% 100.31/13.60 (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2b) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule0) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_5) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2601])).
% 100.31/13.60 thf(zip_derived_cl2636, plain,
% 100.31/13.60 (~ (((doubleComplementI1) =>
% 100.31/13.60 (((doubleComplementE1) =>
% 100.31/13.60 (((doubleComplementSub1) =>
% 100.31/13.60 (((doubleComplementSub2) =>
% 100.31/13.60 (((doubleComplementEq) =>
% 100.31/13.60 (((complementTnotintersectT) =>
% 100.31/13.60 (((complementImpComplementIntersect) =>
% 100.31/13.60 (((complementSubsetComplementIntersect) =>
% 100.31/13.60 (((complementInPowersetComplementIntersect) =>
% 100.31/13.60 (((contraSubsetComplement) =>
% 100.31/13.60 (((complementTcontraSubset) =>
% 100.31/13.60 (((binunionTILcontra) =>
% 100.31/13.60 (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 ((
% 100.31/13.60 (demorgan2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule0) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_5) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2617])).
% 100.31/13.60 thf(zip_derived_cl2655, plain,
% 100.31/13.60 (~ (((doubleComplementE1) =>
% 100.31/13.60 (((doubleComplementSub1) =>
% 100.31/13.60 (((doubleComplementSub2) =>
% 100.31/13.60 (((doubleComplementEq) =>
% 100.31/13.60 (((complementTnotintersectT) =>
% 100.31/13.60 (((complementImpComplementIntersect) =>
% 100.31/13.60 (((complementSubsetComplementIntersect) =>
% 100.31/13.60 (((complementInPowersetComplementIntersect) =>
% 100.31/13.60 (((contraSubsetComplement) =>
% 100.31/13.60 (((complementTcontraSubset) =>
% 100.31/13.60 (((binunionTILcontra) =>
% 100.31/13.60 (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule0) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_5) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2636])).
% 100.31/13.60 thf(zip_derived_cl2672, plain,
% 100.31/13.60 (~ (((doubleComplementSub1) =>
% 100.31/13.60 (((doubleComplementSub2) =>
% 100.31/13.60 (((doubleComplementEq) =>
% 100.31/13.60 (((complementTnotintersectT) =>
% 100.31/13.60 (((complementImpComplementIntersect) =>
% 100.31/13.60 (((complementSubsetComplementIntersect) =>
% 100.31/13.60 (((complementInPowersetComplementIntersect) =>
% 100.31/13.60 (((contraSubsetComplement) =>
% 100.31/13.60 (((complementTcontraSubset) =>
% 100.31/13.60 (((binunionTILcontra) =>
% 100.31/13.60 (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_5) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2655])).
% 100.31/13.60 thf(zip_derived_cl2687, plain,
% 100.31/13.60 (~ (((doubleComplementSub2) =>
% 100.31/13.60 (((doubleComplementEq) =>
% 100.31/13.60 (((complementTnotintersectT) =>
% 100.31/13.60 (((complementImpComplementIntersect) =>
% 100.31/13.60 (((complementSubsetComplementIntersect) =>
% 100.31/13.60 (((complementInPowersetComplementIntersect) =>
% 100.31/13.60 (((contraSubsetComplement) =>
% 100.31/13.60 (((complementTcontraSubset) =>
% 100.31/13.60 (((binunionTILcontra) =>
% 100.31/13.60 (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_5) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2672])).
% 100.31/13.60 thf(zip_derived_cl2699, plain,
% 100.31/13.60 (~ (((doubleComplementEq) =>
% 100.31/13.60 (((complementTnotintersectT) =>
% 100.31/13.60 (((complementImpComplementIntersect) =>
% 100.31/13.60 (((complementSubsetComplementIntersect) =>
% 100.31/13.60 (((complementInPowersetComplementIntersect) =>
% 100.31/13.60 (((contraSubsetComplement) =>
% 100.31/13.60 (((complementTcontraSubset) =>
% 100.31/13.60 (((binunionTILcontra) =>
% 100.31/13.60 (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_5) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2687])).
% 100.31/13.60 thf(zip_derived_cl2711, plain,
% 100.31/13.60 (~ (((complementTnotintersectT) =>
% 100.31/13.60 (((complementImpComplementIntersect) =>
% 100.31/13.60 (((complementSubsetComplementIntersect) =>
% 100.31/13.60 (((complementInPowersetComplementIntersect) =>
% 100.31/13.60 (((contraSubsetComplement) =>
% 100.31/13.60 (((complementTcontraSubset) =>
% 100.31/13.60 (((binunionTILcontra) =>
% 100.31/13.60 (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz13rule4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_5) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2699])).
% 100.31/13.60 thf(zip_derived_cl2723, plain,
% 100.31/13.60 (~ (((complementImpComplementIntersect) =>
% 100.31/13.60 (((complementSubsetComplementIntersect) =>
% 100.31/13.60 (((complementInPowersetComplementIntersect) =>
% 100.31/13.60 (((contraSubsetComplement) =>
% 100.31/13.60 (((complementTcontraSubset) =>
% 100.31/13.60 (((binunionTILcontra) =>
% 100.31/13.60 (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_5) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2711])).
% 100.31/13.60 thf(zip_derived_cl2735, plain,
% 100.31/13.60 (~ (((complementSubsetComplementIntersect) =>
% 100.31/13.60 (((complementInPowersetComplementIntersect) =>
% 100.31/13.60 (((contraSubsetComplement) =>
% 100.31/13.60 (((complementTcontraSubset) =>
% 100.31/13.60 (((binunionTILcontra) =>
% 100.31/13.60 (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_5) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2723])).
% 100.31/13.60 thf(zip_derived_cl2745, plain,
% 100.31/13.60 (~ (((complementInPowersetComplementIntersect) =>
% 100.31/13.60 (((contraSubsetComplement) =>
% 100.31/13.60 (((complementTcontraSubset) =>
% 100.31/13.60 (((binunionTILcontra) =>
% 100.31/13.60 (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_5) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2735])).
% 100.31/13.60 thf(zip_derived_cl2753, plain,
% 100.31/13.60 (~ (((contraSubsetComplement) =>
% 100.31/13.60 (((complementTcontraSubset) =>
% 100.31/13.60 (((binunionTILcontra) =>
% 100.31/13.60 (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_5) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2745])).
% 100.31/13.60 thf(zip_derived_cl2761, plain,
% 100.31/13.60 (~ (((complementTcontraSubset) =>
% 100.31/13.60 (((binunionTILcontra) =>
% 100.31/13.60 (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 ((
% 100.31/13.60 (woz1_5) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2753])).
% 100.31/13.60 thf(zip_derived_cl2769, plain,
% 100.31/13.60 (~ (((binunionTILcontra) =>
% 100.31/13.60 (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2761])).
% 100.31/13.60 thf(zip_derived_cl2778, plain,
% 100.31/13.60 (~ (((binunionTIRcontra) =>
% 100.31/13.60 (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2769])).
% 100.31/13.60 thf(zip_derived_cl2788, plain,
% 100.31/13.60 (~ (((inIntersectImpInUnion) =>
% 100.31/13.60 (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2778])).
% 100.31/13.60 thf(zip_derived_cl2799, plain,
% 100.31/13.60 (~ (((inIntersectImpInUnion2) =>
% 100.31/13.60 (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 ((
% 100.31/13.60 (setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2788])).
% 100.31/13.60 thf(zip_derived_cl2810, plain,
% 100.31/13.60 (~ (((inIntersectImpInIntersectUnions) =>
% 100.31/13.60 (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2799])).
% 100.31/13.60 thf(zip_derived_cl2820, plain,
% 100.31/13.60 (~ (((intersectInPowersetIntersectUnions) =>
% 100.31/13.60 (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 ((
% 100.31/13.60 (subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2810])).
% 100.31/13.60 thf(zip_derived_cl2830, plain,
% 100.31/13.60 (~ (((inComplementUnionImpNotIn1) =>
% 100.31/13.60 (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2820])).
% 100.31/13.60 thf(zip_derived_cl2841, plain,
% 100.31/13.60 (~ (((inComplementUnionImpInComplement1) =>
% 100.31/13.60 (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2830])).
% 100.31/13.60 thf(zip_derived_cl2852, plain,
% 100.31/13.60 (~ (((binunionTE) =>
% 100.31/13.60 (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2841])).
% 100.31/13.60 thf(zip_derived_cl2864, plain,
% 100.31/13.60 (~ (((binunionTEcontra) =>
% 100.31/13.60 (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2852])).
% 100.31/13.60 thf(zip_derived_cl2876, plain,
% 100.31/13.60 (~ (((demorgan2a1) =>
% 100.31/13.60 (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2864])).
% 100.31/13.60 thf(zip_derived_cl2888, plain,
% 100.31/13.60 (~ (((complementUnionInPowersetComplement) =>
% 100.31/13.60 (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2876])).
% 100.31/13.60 thf(zip_derived_cl2900, plain,
% 100.31/13.60 (~ (((demorgan2a2) =>
% 100.31/13.60 (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2888])).
% 100.31/13.60 thf(zip_derived_cl2913, plain,
% 100.31/13.60 (~ (((demorgan1a) =>
% 100.31/13.60 (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 ((
% 100.31/13.60 (breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2900])).
% 100.31/13.60 thf(zip_derived_cl2927, plain,
% 100.31/13.60 (~ (((demorgan1b) =>
% 100.31/13.60 (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 ((
% 100.31/13.60 (!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2913])).
% 100.31/13.60 thf(zip_derived_cl2940, plain,
% 100.31/13.60 (~ (((demorgan1) =>
% 100.31/13.60 (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2927])).
% 100.31/13.60 thf(zip_derived_cl2953, plain,
% 100.31/13.60 (~ (((demorgan2a) =>
% 100.31/13.60 (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 ((('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2940])).
% 100.31/13.60 thf(zip_derived_cl2965, plain,
% 100.31/13.60 (~ (((demorgan2b2) =>
% 100.31/13.60 (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 ((('#S') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2953])).
% 100.31/13.60 thf(zip_derived_cl2977, plain,
% 100.31/13.60 (~ (((demorgan2b) =>
% 100.31/13.60 (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 ((('#S') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 ((('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2965])).
% 100.31/13.60 thf(zip_derived_cl2989, plain,
% 100.31/13.60 (~ (((demorgan2) =>
% 100.31/13.60 (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2977])).
% 100.31/13.60 thf(zip_derived_cl3002, plain,
% 100.31/13.60 (~ (((woz13rule0) =>
% 100.31/13.60 (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 ((('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2989])).
% 100.31/13.60 thf(zip_derived_cl3015, plain,
% 100.31/13.60 (~ (((woz13rule1) =>
% 100.31/13.60 (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 ((('#S') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3002])).
% 100.31/13.60 thf(zip_derived_cl3029, plain,
% 100.31/13.60 (~ (((woz13rule2) =>
% 100.31/13.60 (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 ((('#S') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 ((('#S') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3015])).
% 100.31/13.60 thf(zip_derived_cl3045, plain,
% 100.31/13.60 (~ (((woz13rule3) =>
% 100.31/13.60 (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (
% 100.31/13.60 !!) @
% 100.31/13.60 ((('#S') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 ((('#S') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3029])).
% 100.31/13.60 thf(zip_derived_cl3058, plain,
% 100.31/13.60 (~ (((woz13rule4) =>
% 100.31/13.60 (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (=>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3045])).
% 100.31/13.60 thf(zip_derived_cl3069, plain,
% 100.31/13.60 (~ (((woz1_1) =>
% 100.31/13.60 (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3058])).
% 100.31/13.60 thf(zip_derived_cl3081, plain,
% 100.31/13.60 (~ (((woz1_2) =>
% 100.31/13.60 (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ ((
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 ((('#S') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3069])).
% 100.31/13.60 thf(zip_derived_cl3093, plain,
% 100.31/13.60 (~ (((woz1_3) =>
% 100.31/13.60 (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 ((('#S') @ ((
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 '#B') @ breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3081])).
% 100.31/13.60 thf(zip_derived_cl3105, plain,
% 100.31/13.60 (~ (((woz1_4) =>
% 100.31/13.60 (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (
% 100.31/13.60 !!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ ((
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3093])).
% 100.31/13.60 thf(zip_derived_cl3116, plain,
% 100.31/13.60 (~ (((woz1_5) =>
% 100.31/13.60 (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (=>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 (
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((
% 100.31/13.60 ('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3105])).
% 100.31/13.60 thf(zip_derived_cl3127, plain,
% 100.31/13.60 (~ (((breln1all2) =>
% 100.31/13.60 (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (=>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3116])).
% 100.31/13.60 thf(zip_derived_cl3139, plain,
% 100.31/13.60 (~ (((breln1SetBreln1) =>
% 100.31/13.60 (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (=>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3127])).
% 100.31/13.60 thf(zip_derived_cl3151, plain,
% 100.31/13.60 (~ (((choice2fnsingleton) =>
% 100.31/13.60 (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (=>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 '#B') @ breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3139])).
% 100.31/13.60 thf(zip_derived_cl3162, plain,
% 100.31/13.60 (~ (((setOfPairsIsBReln1) =>
% 100.31/13.60 (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 '#S') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (=>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ (
% 100.31/13.60 '#B') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 '#B') @ breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3151])).
% 100.31/13.60 thf(zip_derived_cl3174, plain,
% 100.31/13.60 (~ (((breln1all1) =>
% 100.31/13.60 (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 (('#B') @ (=>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ (
% 100.31/13.60 '#B') @ breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3162])).
% 100.31/13.60 thf(zip_derived_cl3187, plain,
% 100.31/13.60 (~ (((subbreln1) =>
% 100.31/13.60 (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3174])).
% 100.31/13.60 thf(zip_derived_cl3201, plain,
% 100.31/13.60 (~ (((eqbreln1) =>
% 100.31/13.60 (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (
% 100.31/13.60 =>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#B') @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3187])).
% 100.31/13.60 thf(zip_derived_cl3211, plain,
% 100.31/13.60 (~ (((breln1invprop) =>
% 100.31/13.60 (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#B') @ breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3201])).
% 100.31/13.60 thf(zip_derived_cl3221, plain,
% 100.31/13.60 (~ (((breln1invI) =>
% 100.31/13.60 (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#B') @ breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3211])).
% 100.31/13.60 thf(zip_derived_cl3232, plain,
% 100.31/13.60 (~ (((breln1invE) =>
% 100.31/13.60 (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @
% 100.31/13.60 breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#B') @ breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3221])).
% 100.31/13.60 thf(zip_derived_cl3245, plain,
% 100.31/13.60 (~ (((breln1compprop) =>
% 100.31/13.60 (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @ breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#B') @ breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3232])).
% 100.31/13.60 thf(zip_derived_cl3260, plain,
% 100.31/13.60 (~ (((breln1compI) =>
% 100.31/13.60 (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @ breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#B') @ breln1)))) @
% 100.31/13.60 binunion))))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3245])).
% 100.31/13.60 thf(zip_derived_cl3277, plain,
% 100.31/13.60 (~ (((breln1compE) =>
% 100.31/13.60 (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @ breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @
% 100.31/13.60 breln1)))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#B') @ breln1)))) @
% 100.31/13.60 binunion))))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3260])).
% 100.31/13.60 thf(zip_derived_cl3295, plain,
% 100.31/13.60 (~ (((breln1compEex) =>
% 100.31/13.60 (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @ breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @ breln1)))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#B') @ breln1)))) @
% 100.31/13.60 binunion))))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3277])).
% 100.31/13.60 thf(zip_derived_cl3312, plain,
% 100.31/13.60 (~ (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @ breln1)))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @ breln1)))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#B') @ breln1)))) @
% 100.31/13.60 binunion))))))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3295])).
% 100.31/13.60 thf(zip_derived_cl3329, plain,
% 100.31/13.60 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (breln1 @ '#sk43'))) @
% 100.31/13.60 ((('#B') @ (!!) @
% 100.31/13.60 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 100.31/13.60 (breln1 @ '#sk43'))))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (breln1 @ '#sk43'))) @ binunion))))))))))),
% 100.31/13.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3312])).
% 100.31/13.60 thf(zip_derived_cl3345, plain,
% 100.31/13.60 (~ (((breln1 @ '#sk43' @ '#sk44') =>
% 100.31/13.60 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (breln1 @ '#sk43'))) @
% 100.31/13.60 ((('#B') @ (breln1 @ '#sk43') @ (binunion @ '#sk44')))))))))),
% 100.31/13.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3329])).
% 100.31/13.60 thf(breln, axiom,(( breln @ (X1)@ (X2)@ (X0)) =
% 100.31/13.60 ((subset @ X0 @ (cartprod @ X1 @ X2))))).
% 100.31/13.60 thf('4', plain,
% 100.31/13.60 (![X2:$i,X1:$i,X0:$i]:
% 100.31/13.60 ( ( breln @ X1 @ X2 @ X0 ) = ( subset @ X0 @ ( cartprod @ X1 @ X2 ) ) )),
% 100.31/13.60 define([status(thm)])).
% 100.31/13.60 thf(breln1, axiom,(( breln1 @ (X0)@ (X1)) = ((breln @ X0 @ X0 @ X1)))).
% 100.31/13.60 thf('5', plain,
% 100.31/13.60 (![X1:$i,X0:$i]: ( ( breln1 @ X0 @ X1 ) = ( breln @ X0 @ X0 @ X1 ) )),
% 100.31/13.60 define([status(thm)])).
% 100.31/13.60 thf(zip_derived_cl3362, plain,
% 100.31/13.60 (~ (((subset @ '#sk44' @ (cartprod @ '#sk43' @ '#sk43')) =>
% 100.31/13.60 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (breln1 @ '#sk43'))) @
% 100.31/13.60 ((('#B') @ (breln1 @ '#sk43') @ (binunion @ '#sk44')))))))))),
% 100.31/13.60 inference('rw', [status(thm)], [zip_derived_cl3345, '4', '5'])).
% 100.31/13.60 thf(zip_derived_cl3364, plain,
% 100.31/13.60 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (breln1 @ '#sk43'))) @
% 100.31/13.60 ((('#B') @ (breln1 @ '#sk43') @ (binunion @ '#sk44')))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3362])).
% 100.31/13.60 thf(zip_derived_cl3380, plain,
% 100.31/13.60 (~ (((breln1 @ '#sk43' @ '#sk45') => (breln1 @ '#sk43' @
% 100.31/13.60 (binunion @ '#sk44' @ '#sk45'))))),
% 100.31/13.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3364])).
% 100.31/13.60 thf(zip_derived_cl3391, plain,
% 100.31/13.60 (~ (((subset @ '#sk45' @ (cartprod @ '#sk43' @ '#sk43')) => (subset @
% 100.31/13.60 (binunion @ '#sk44' @ '#sk45') @ (cartprod @ '#sk43' @ '#sk43'))))),
% 100.31/13.60 inference('rw', [status(thm)], [zip_derived_cl3380, '4', '4', '5', '5'])).
% 100.31/13.60 thf(zip_derived_cl3392, plain,
% 100.31/13.60 ( (subset @ '#sk45' @ (cartprod @ '#sk43' @ '#sk43'))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3391])).
% 100.31/13.60 thf(zip_derived_cl3363, plain,
% 100.31/13.60 ( (subset @ '#sk44' @ (cartprod @ '#sk43' @ '#sk43'))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3362])).
% 100.31/13.60 thf(zip_derived_cl2471, plain, ( (binunionT_lem)),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2461])).
% 100.31/13.60 thf(binunionT_lem, axiom, (binunionT_lem) =>
% 100.31/13.60 ((((!!) @ (^[Y0 : $i]:
% 100.31/13.60 (((!!) @ (^[Y1 : $i]:
% 100.31/13.60 (((in @ Y1 @ (powerset @ Y0)) =>
% 100.31/13.60 (((!!) @ (^[Y2 : $i]:
% 100.31/13.60 (((in @ Y2 @ (powerset @ Y0)) =>
% 100.31/13.60 (in @ (binunion @ Y1 @ Y2) @
% 100.31/13.60 (powerset @ Y0)))))))))))))))
% 100.31/13.60 = ($true))).
% 100.31/13.60 thf('6', plain,
% 100.31/13.60 (( binunionT_lem ) <=>
% 100.31/13.60 ( ![X5:$i,X7:$i]:
% 100.31/13.60 ( ( in @ X7 @ ( powerset @ X5 ) ) =>
% 100.31/13.60 ( ![X9:$i]:
% 100.31/13.60 ( ( in @ X9 @ ( powerset @ X5 ) ) =>
% 100.31/13.60 ( in @ ( binunion @ X7 @ X9 ) @ ( powerset @ X5 ) ) ) ) ) )),
% 100.31/13.60 inference('rw.lit', [status(esa)], [binunionT_lem])).
% 100.31/13.60 thf(zip_derived_cl2481, plain,
% 100.31/13.60 ( (((!!) @ (^[Y0 : $i]:
% 100.31/13.60 (((!!) @ (^[Y1 : $i]:
% 100.31/13.60 (((in @ Y1 @ (powerset @ Y0)) =>
% 100.31/13.60 (((!!) @ (^[Y2 : $i]:
% 100.31/13.60 (((in @ Y2 @ (powerset @ Y0)) =>
% 100.31/13.60 (in @ (binunion @ Y1 @ Y2) @
% 100.31/13.60 (powerset @ Y0)))))))))))))))),
% 100.31/13.60 inference('rw_clause', [status(thm)], [zip_derived_cl2471, '6'])).
% 100.31/13.60 thf(zip_derived_cl2488, plain,
% 100.31/13.60 ( (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @
% 100.31/13.60 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @
% 100.31/13.60 ((('#B') @ ((('#B') @ (!!))) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#B') @
% 100.31/13.60 ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @
% 100.31/13.60 ((('#B') @ ((('#C') @ in)) @ powerset)))))))) @
% 100.31/13.60 ((('#B') @ ((('#C') @ ((('#B') @ ('#C') @
% 100.31/13.60 ((('#B') @ ((('#B') @ in)) @
% 100.31/13.60 binunion)))))) @
% 100.31/13.60 powerset))))))))))))),
% 100.31/13.60 inference('comb-normalize', [status(thm)], [zip_derived_cl2481])).
% 100.31/13.60 thf(zip_derived_cl2489, plain,
% 100.31/13.60 (![X2 : $i]:
% 100.31/13.60 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 100.31/13.60 ((('#C') @ in @ (powerset @ X2))))) @
% 100.31/13.60 ((('#B') @ (!!) @
% 100.31/13.60 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 100.31/13.60 ((('#C') @ in @ (powerset @ X2))))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ ('#C') @
% 100.31/13.60 ((('#B') @ ((('#B') @ in)) @ binunion)))) @
% 100.31/13.60 (powerset @ X2)))))))))))),
% 100.31/13.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2488])).
% 100.31/13.60 thf(zip_derived_cl2497, plain,
% 100.31/13.60 (![X2 : $i, X4 : $i]:
% 100.31/13.60 (((in @ X4 @ (powerset @ X2)) =>
% 100.31/13.60 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 100.31/13.60 ((('#C') @ in @ (powerset @ X2))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ in @ (binunion @ X4))) @
% 100.31/13.60 (powerset @ X2)))))))))),
% 100.31/13.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2489])).
% 100.31/13.60 thf(zip_derived_cl2507, plain,
% 100.31/13.60 (![X2 : $i, X4 : $i]:
% 100.31/13.60 (~ (in @ X4 @ (powerset @ X2))
% 100.31/13.60 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 100.31/13.60 ((('#C') @ in @ (powerset @ X2))))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ in @ (binunion @ X4))) @
% 100.31/13.60 (powerset @ X2))))))))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2497])).
% 100.31/13.60 thf(zip_derived_cl2518, plain,
% 100.31/13.60 (![X2 : $i, X4 : $i, X6 : $i]:
% 100.31/13.60 ( (((in @ X6 @ (powerset @ X2)) => (in @ (binunion @ X4 @ X6) @
% 100.31/13.60 (powerset @ X2))))
% 100.31/13.60 | ~ (in @ X4 @ (powerset @ X2)))),
% 100.31/13.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2507])).
% 100.31/13.60 thf(zip_derived_cl2527, plain,
% 100.31/13.60 (![X2 : $i, X4 : $i, X6 : $i]:
% 100.31/13.60 (~ (in @ X6 @ (powerset @ X2))
% 100.31/13.60 | (in @ (binunion @ X4 @ X6) @ (powerset @ X2))
% 100.31/13.60 | ~ (in @ X4 @ (powerset @ X2)))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2518])).
% 100.31/13.60 thf(zip_derived_cl3393, plain,
% 100.31/13.60 (~ (subset @ (binunion @ '#sk44' @ '#sk45') @
% 100.31/13.60 (cartprod @ '#sk43' @ '#sk43'))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3391])).
% 100.31/13.60 thf(zip_derived_cl1014, plain, ( (subset2powerset)),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1000])).
% 100.31/13.60 thf(subset2powerset, axiom, (subset2powerset) =>
% 100.31/13.60 ((((!!) @ (^[Y0 : $i]:
% 100.31/13.60 (((!!) @ (^[Y1 : $i]:
% 100.31/13.60 (((subset @ Y0 @ Y1) => (in @ Y0 @
% 100.31/13.60 (powerset @ Y1))))))))))
% 100.31/13.60 = ($true))).
% 100.31/13.60 thf('7', plain,
% 100.31/13.60 (( subset2powerset ) <=>
% 100.31/13.60 ( ![X5:$i,X7:$i]:
% 100.31/13.60 ( ( subset @ X5 @ X7 ) => ( in @ X5 @ ( powerset @ X7 ) ) ) )),
% 100.31/13.60 inference('rw.lit', [status(esa)], [subset2powerset])).
% 100.31/13.60 thf(zip_derived_cl1025, plain,
% 100.31/13.60 ( (((!!) @ (^[Y0 : $i]:
% 100.31/13.60 (((!!) @ (^[Y1 : $i]:
% 100.31/13.60 (((subset @ Y0 @ Y1) => (in @ Y0 @
% 100.31/13.60 (powerset @ Y1))))))))))),
% 100.31/13.60 inference('rw_clause', [status(thm)], [zip_derived_cl1014, '7'])).
% 100.31/13.60 thf(zip_derived_cl1035, plain,
% 100.31/13.60 ( (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @ subset)))) @
% 100.31/13.60 ((('#C') @ ((('#B') @ ('#B') @ in)) @ powerset))))))))),
% 100.31/13.60 inference('comb-normalize', [status(thm)], [zip_derived_cl1025])).
% 100.31/13.60 thf(zip_derived_cl1036, plain,
% 100.31/13.60 (![X2 : $i]:
% 100.31/13.60 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (subset @ X2))) @
% 100.31/13.60 ((('#B') @ (in @ X2) @ powerset))))))),
% 100.31/13.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1035])).
% 100.31/13.60 thf(zip_derived_cl1050, plain,
% 100.31/13.60 (![X2 : $i, X4 : $i]:
% 100.31/13.60 (((subset @ X2 @ X4) => (in @ X2 @ (powerset @ X4))))),
% 100.31/13.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1036])).
% 100.31/13.60 thf(zip_derived_cl1061, plain,
% 100.31/13.60 (![X2 : $i, X4 : $i]:
% 100.31/13.60 (~ (subset @ X2 @ X4) | (in @ X2 @ (powerset @ X4)))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1050])).
% 100.31/13.60 thf(zip_derived_cl1066, plain, ( (powersetE1)),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1055])).
% 100.31/13.60 thf(powersetE1, axiom, (powersetE1) =>
% 100.31/13.60 ((((!!) @ (^[Y0 : $i]:
% 100.31/13.60 (((!!) @ (^[Y1 : $i]:
% 100.31/13.60 (((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @
% 100.31/13.60 Y0)))))))))
% 100.31/13.60 = ($true))).
% 100.31/13.60 thf('8', plain,
% 100.31/13.60 (( powersetE1 ) <=>
% 100.31/13.60 ( ![X5:$i,X7:$i]:
% 100.31/13.60 ( ( in @ X7 @ ( powerset @ X5 ) ) => ( subset @ X7 @ X5 ) ) )),
% 100.31/13.60 inference('rw.lit', [status(esa)], [powersetE1])).
% 100.31/13.60 thf(zip_derived_cl1072, plain,
% 100.31/13.60 ( (((!!) @ (^[Y0 : $i]:
% 100.31/13.60 (((!!) @ (^[Y1 : $i]:
% 100.31/13.60 (((in @ Y1 @ (powerset @ Y0)) => (subset @
% 100.31/13.60 Y1 @ Y0)))))))))),
% 100.31/13.60 inference('rw_clause', [status(thm)], [zip_derived_cl1066, '8'])).
% 100.31/13.60 thf(zip_derived_cl1078, plain,
% 100.31/13.60 ( (((!!) @ ((('#B') @ (!!) @
% 100.31/13.60 ((('#S') @ ((('#B') @ ('#S') @
% 100.31/13.60 ((('#B') @ ((('#B') @ (=>))) @
% 100.31/13.60 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @
% 100.31/13.60 ((('#C') @ subset))))))))),
% 100.31/13.60 inference('comb-normalize', [status(thm)], [zip_derived_cl1072])).
% 100.31/13.60 thf(zip_derived_cl1079, plain,
% 100.31/13.60 (![X2 : $i]:
% 100.31/13.60 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 100.31/13.60 ((('#C') @ in @ (powerset @ X2))))) @
% 100.31/13.60 ((('#C') @ subset @ X2))))))),
% 100.31/13.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1078])).
% 100.31/13.60 thf(zip_derived_cl1085, plain,
% 100.31/13.60 (![X2 : $i, X4 : $i]:
% 100.31/13.60 (((in @ X4 @ (powerset @ X2)) => (subset @ X4 @ X2)))),
% 100.31/13.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1079])).
% 100.31/13.60 thf(zip_derived_cl1091, plain,
% 100.31/13.60 (![X2 : $i, X4 : $i]:
% 100.31/13.60 (~ (in @ X4 @ (powerset @ X2)) | (subset @ X4 @ X2))),
% 100.31/13.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1085])).
% 100.31/13.60 thf(zip_derived_cl8322, plain, ($false),
% 100.31/13.60 inference('eprover', [status(thm)],
% 100.31/13.60 [zip_derived_cl3392, zip_derived_cl3363, zip_derived_cl2527,
% 100.31/13.60 zip_derived_cl3393, zip_derived_cl1061, zip_derived_cl1091])).
% 100.31/13.60
% 100.31/13.60 % SZS output end Refutation
% 100.31/13.60
% 100.31/13.60
% 100.31/13.61 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 100.31/13.61 % Terminating...
% 100.79/13.73 % Runner terminated.
% 100.79/13.75 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------