%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU799^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Uu4grHim7T true
% Computer : n032.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 19:17:48 EDT 2023
% Result : Theorem 98.41s 13.24s
% Output : Refutation 99.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU799^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Uu4grHim7T true
% 0.12/0.31 % Computer : n032.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Wed Aug 23 17:34:26 EDT 2023
% 0.12/0.31 % CPUTime :
% 0.12/0.31 % Running portfolio for 300 s
% 0.12/0.31 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.31 % Number of cores: 8
% 0.12/0.31 % Python version: Python 3.6.8
% 0.12/0.32 % Running in HO mode
% 0.16/0.56 % Total configuration time : 828
% 0.16/0.56 % Estimated wc time : 1656
% 0.16/0.56 % Estimated cpu time (8 cpus) : 207.0
% 0.16/0.60 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.16/0.61 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.16/0.61 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.16/0.62 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.16/0.62 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.16/0.62 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.16/0.64 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.16/0.65 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 98.41/13.24 % Solved by lams/40_b.comb.sh.
% 98.41/13.24 % done 362 iterations in 12.170s
% 98.41/13.24 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 98.41/13.24 % SZS output start Refutation
% 98.41/13.24 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 98.41/13.24 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 98.41/13.24 thf('#sk48_type', type, '#sk48': $i).
% 98.41/13.24 thf(notdexE_type, type, notdexE: $o).
% 98.41/13.24 thf(setunionAx_type, type, setunionAx: $o).
% 98.41/13.24 thf(setminusELneg_type, type, setminusELneg: $o).
% 98.41/13.24 thf(breln1unionEcases_type, type, breln1unionEcases: $o).
% 98.41/13.24 thf(powersetE_type, type, powersetE: $o).
% 98.41/13.24 thf(woz1_1_type, type, woz1_1: $o).
% 98.41/13.24 thf(omegaSAx_type, type, omegaSAx: $o).
% 98.41/13.24 thf(breln1unionI_type, type, breln1unionI: $o).
% 98.41/13.24 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 98.41/13.24 $o).
% 98.41/13.24 thf('#sk12_type', type, '#sk12': $i > $i > $i).
% 98.41/13.24 thf(exuI1_type, type, exuI1: $o).
% 98.41/13.24 thf(exuI2_type, type, exuI2: $o).
% 98.41/13.24 thf(notequalI2_type, type, notequalI2: $o).
% 98.41/13.24 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 98.41/13.24 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 98.41/13.24 thf(upairsubunion_type, type, upairsubunion: $o).
% 98.41/13.24 thf(binunionTE_type, type, binunionTE: $o).
% 98.41/13.24 thf(binunionTEcontra_type, type, binunionTEcontra: $o).
% 98.41/13.24 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 98.41/13.24 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 98.41/13.24 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 98.41/13.24 thf(setminusILneg_type, type, setminusILneg: $o).
% 98.41/13.24 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 98.41/13.24 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 98.41/13.24 thf(funcextLem_type, type, funcextLem: $o).
% 98.41/13.24 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 98.41/13.24 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 98.41/13.24 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 98.41/13.24 thf(eta1_type, type, eta1: $o).
% 98.41/13.24 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 98.41/13.24 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 98.41/13.24 thf(apProp_type, type, apProp: $o).
% 98.41/13.24 thf(setextT_type, type, setextT: $o).
% 98.41/13.24 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions:
% 98.41/13.24 $o).
% 98.41/13.24 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 98.41/13.24 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 98.41/13.24 thf(breln1invprop_type, type, breln1invprop: $o).
% 98.41/13.24 thf(lamProp_type, type, lamProp: $o).
% 98.41/13.24 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 98.41/13.24 thf(ex1E1_type, type, ex1E1: $o).
% 98.41/13.24 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 98.41/13.24 thf(setukpairIR_type, type, setukpairIR: $o).
% 98.41/13.24 thf(brelnall1_type, type, brelnall1: $o).
% 98.41/13.24 thf(binunionE_type, type, binunionE: $o).
% 98.41/13.24 thf(setext_type, type, setext: $o).
% 98.41/13.24 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 98.41/13.24 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 98.41/13.24 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 98.41/13.24 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 98.41/13.24 thf(iftrue_type, type, iftrue: $o).
% 98.41/13.24 thf(woz13rule4_type, type, woz13rule4: $o).
% 98.41/13.24 thf(descr__Cong_type, type, descr__Cong: $o).
% 98.41/13.24 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 98.41/13.24 thf(theprop_type, type, theprop: $o).
% 98.41/13.24 thf(image1I_type, type, image1I: $o).
% 98.41/13.24 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 98.41/13.24 thf(in_type, type, in: $i > $i > $o).
% 98.41/13.24 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 98.41/13.24 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 98.41/13.24 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 98.41/13.24 thf(demorgan1_type, type, demorgan1: $o).
% 98.41/13.24 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 98.41/13.24 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 98.41/13.24 $o).
% 98.41/13.24 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 98.41/13.24 thf(breln1SetBreln1_type, type, breln1SetBreln1: $o).
% 98.41/13.24 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 98.41/13.24 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 98.41/13.24 thf(ex1I2_type, type, ex1I2: $o).
% 98.41/13.24 thf(symdiffI2_type, type, symdiffI2: $o).
% 98.41/13.24 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 98.41/13.24 thf(ifSingleton_type, type, ifSingleton: $o).
% 98.41/13.24 thf(upairset2IR_type, type, upairset2IR: $o).
% 98.41/13.24 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 98.41/13.24 thf(complementTI1_type, type, complementTI1: $o).
% 98.41/13.24 thf(subsetE_type, type, subsetE: $o).
% 98.41/13.24 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 98.41/13.24 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 98.41/13.24 thf(complementUnionInPowersetComplement_type, type, complementUnionInPowersetComplement:
% 98.41/13.24 $o).
% 98.41/13.24 thf(iffalse_type, type, iffalse: $o).
% 98.41/13.24 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 98.41/13.24 thf(setbeta_type, type, setbeta: $o).
% 98.41/13.24 thf(eqinunit_type, type, eqinunit: $o).
% 98.41/13.24 thf(upairsetIL_type, type, upairsetIL: $o).
% 98.41/13.24 thf(powersetI1_type, type, powersetI1: $o).
% 98.41/13.24 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 98.41/13.24 thf(lamp_type, type, lamp: $o).
% 98.41/13.24 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 98.41/13.24 thf(breln1invI_type, type, breln1invI: $o).
% 98.41/13.24 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 98.41/13.24 thf(breln1unionE_type, type, breln1unionE: $o).
% 98.41/13.24 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 98.41/13.24 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 98.41/13.24 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 98.41/13.24 thf(powersetAx_type, type, powersetAx: $o).
% 98.41/13.24 thf(woz2Ex_type, type, woz2Ex: $o).
% 98.41/13.24 thf(eta2_type, type, eta2: $o).
% 98.41/13.24 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 98.41/13.24 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 98.41/13.24 thf(image1Ex_type, type, image1Ex: $o).
% 98.41/13.24 thf(powersetI_type, type, powersetI: $o).
% 98.41/13.24 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 98.41/13.24 thf(powersetTE1_type, type, powersetTE1: $o).
% 98.41/13.24 thf(upairsetIR_type, type, upairsetIR: $o).
% 98.41/13.24 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 98.41/13.24 thf(lam2p_type, type, lam2p: $o).
% 98.41/13.24 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 98.41/13.24 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 98.41/13.24 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 98.41/13.24 thf(setOfPairsIsBReln1_type, type, setOfPairsIsBReln1: $o).
% 98.41/13.24 thf(inCongP_type, type, inCongP: $o).
% 98.41/13.24 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 98.41/13.24 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 98.41/13.24 thf(exuE3e_type, type, exuE3e: $o).
% 98.41/13.24 thf(emptysetE_type, type, emptysetE: $o).
% 98.41/13.24 thf(woz13rule2_type, type, woz13rule2: $o).
% 98.41/13.24 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 98.41/13.24 thf(image1E_type, type, image1E: $o).
% 98.41/13.24 thf(setunionI_type, type, setunionI: $o).
% 98.41/13.24 thf(breln1unionIR_type, type, breln1unionIR: $o).
% 98.41/13.24 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 98.41/13.24 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 98.41/13.24 thf(prop2setI_type, type, prop2setI: $o).
% 98.41/13.24 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 98.41/13.24 thf(setminusER_type, type, setminusER: $o).
% 98.41/13.24 thf(exuE2_type, type, exuE2: $o).
% 98.41/13.24 thf(woz1_2_type, type, woz1_2: $o).
% 98.41/13.24 thf(emptyset_type, type, emptyset: $i).
% 98.41/13.24 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 98.41/13.24 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 98.41/13.24 thf(powersetsubset_type, type, powersetsubset: $o).
% 98.41/13.24 thf(upairequniteq_type, type, upairequniteq: $o).
% 98.41/13.24 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 98.41/13.24 thf(subPowSU_type, type, subPowSU: $o).
% 98.41/13.24 thf(breln1compprop_type, type, breln1compprop: $o).
% 98.41/13.24 thf(woz2B_type, type, woz2B: $o).
% 98.41/13.24 thf(notequalI1_type, type, notequalI1: $o).
% 98.41/13.24 thf(demorgan2b_type, type, demorgan2b: $o).
% 98.41/13.24 thf(notinemptyset_type, type, notinemptyset: $o).
% 98.41/13.24 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 98.41/13.24 thf(breln1unionIL_type, type, breln1unionIL: $o).
% 98.41/13.24 thf(subsetTrans_type, type, subsetTrans: $o).
% 98.41/13.24 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 98.41/13.24 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 98.41/13.24 thf(kpairp_type, type, kpairp: $o).
% 98.41/13.24 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 98.41/13.24 thf(setminusI_type, type, setminusI: $o).
% 98.41/13.24 thf(binunionIL_type, type, binunionIL: $o).
% 98.41/13.24 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 98.41/13.24 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 98.41/13.24 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 98.41/13.24 thf(powersetTI1_type, type, powersetTI1: $o).
% 98.41/13.24 thf(subsetE2_type, type, subsetE2: $o).
% 98.41/13.24 thf(image1Ex1_type, type, image1Ex1: $o).
% 98.41/13.24 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 98.41/13.24 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 98.41/13.24 thf(setextsub_type, type, setextsub: $o).
% 98.41/13.24 thf(binunionLsub_type, type, binunionLsub: $o).
% 98.41/13.24 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 98.41/13.24 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 98.41/13.24 thf(breln1compE_type, type, breln1compE: $o).
% 98.41/13.24 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 98.41/13.24 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 98.41/13.24 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 98.41/13.24 thf(setunionE_type, type, setunionE: $o).
% 98.41/13.24 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 98.41/13.24 thf(complementT_lem_type, type, complementT_lem: $o).
% 98.41/13.24 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 98.41/13.24 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 98.41/13.24 thf(binunionIR_type, type, binunionIR: $o).
% 98.41/13.24 thf(setadjoinE_type, type, setadjoinE: $o).
% 98.41/13.24 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 98.41/13.24 thf(eqbreln1_type, type, eqbreln1: $o).
% 98.41/13.24 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 98.41/13.24 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 98.41/13.24 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 98.41/13.24 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 98.41/13.24 thf(exuE1_type, type, exuE1: $o).
% 98.41/13.24 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 98.41/13.24 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 98.41/13.24 thf(setminusLsub_type, type, setminusLsub: $o).
% 98.41/13.24 thf(notinsingleton_type, type, notinsingleton: $o).
% 98.41/13.24 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions:
% 98.41/13.24 $o).
% 98.41/13.24 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 98.41/13.24 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 98.41/13.24 thf(exuEu_type, type, exuEu: $o).
% 98.41/13.24 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 98.41/13.24 thf(upairsetE_type, type, upairsetE: $o).
% 98.41/13.24 thf(omega0Ax_type, type, omega0Ax: $o).
% 98.41/13.24 thf(breln1invE_type, type, breln1invE: $o).
% 98.41/13.24 thf(breln1unionCommutes_type, type, breln1unionCommutes: $o).
% 98.41/13.24 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 98.41/13.24 thf(app_type, type, app: $o).
% 98.41/13.24 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 98.41/13.24 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 98.41/13.24 thf(notsubsetI_type, type, notsubsetI: $o).
% 98.41/13.24 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 98.41/13.24 thf(woz2W_type, type, woz2W: $o).
% 98.41/13.24 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 98.41/13.24 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 98.41/13.24 thf(setextAx_type, type, setextAx: $o).
% 98.41/13.24 thf(breln1all1_type, type, breln1all1: $o).
% 98.41/13.24 thf(choice2fnsingleton_type, type, choice2fnsingleton: $o).
% 98.41/13.24 thf(breln1compI_type, type, breln1compI: $o).
% 98.41/13.24 thf(demorgan2a1_type, type, demorgan2a1: $o).
% 98.41/13.24 thf(powersetE1_type, type, powersetE1: $o).
% 98.41/13.24 thf(bs114d_type, type, bs114d: $o).
% 98.41/13.24 thf(complementTE1_type, type, complementTE1: $o).
% 98.41/13.24 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 98.41/13.24 thf(breln1all2_type, type, breln1all2: $o).
% 98.41/13.24 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 98.41/13.24 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 98.41/13.24 thf(demorgan2b2_type, type, demorgan2b2: $o).
% 98.41/13.24 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 98.41/13.24 thf(subsetI1_type, type, subsetI1: $o).
% 98.41/13.24 thf(symdiffE_type, type, symdiffE: $o).
% 98.41/13.24 thf(woz13rule1_type, type, woz13rule1: $o).
% 98.41/13.24 thf(breln1unionprop_type, type, breln1unionprop: $o).
% 98.41/13.24 thf(descrp_type, type, descrp: $o).
% 98.41/13.24 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 98.41/13.24 thf(foundationAx_type, type, foundationAx: $o).
% 98.41/13.24 thf(brelnall2_type, type, brelnall2: $o).
% 98.41/13.24 thf(emptysetAx_type, type, emptysetAx: $o).
% 98.41/13.24 thf(emptyI_type, type, emptyI: $o).
% 98.41/13.24 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 98.41/13.24 thf(binintersectEL_type, type, binintersectEL: $o).
% 98.41/13.24 thf(emptyE1_type, type, emptyE1: $o).
% 98.41/13.24 thf(demorgan2a_type, type, demorgan2a: $o).
% 98.41/13.24 thf(woz1_3_type, type, woz1_3: $o).
% 98.41/13.24 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 98.41/13.24 thf(vacuousDall_type, type, vacuousDall: $o).
% 98.41/13.24 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 98.41/13.24 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 98.41/13.24 thf(demorgan1a_type, type, demorgan1a: $o).
% 98.41/13.24 thf(ifp_type, type, ifp: $o).
% 98.41/13.24 thf(funcSet_type, type, funcSet: $i > $i > $i).
% 98.41/13.24 thf(binintersectI_type, type, binintersectI: $o).
% 98.41/13.24 thf(beta1_type, type, beta1: $o).
% 98.41/13.24 thf(funcext2_type, type, funcext2: $o).
% 98.41/13.24 thf(subbreln_type, type, subbreln: $o).
% 98.41/13.24 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 98.41/13.24 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 98.41/13.24 thf(subbreln1_type, type, subbreln1: $o).
% 98.41/13.24 thf(demorgan2a2_type, type, demorgan2a2: $o).
% 98.41/13.24 thf(image1Equiv_type, type, image1Equiv: $o).
% 98.41/13.24 thf(subsetTI_type, type, subsetTI: $o).
% 98.41/13.24 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 98.41/13.24 thf(ap2p_type, type, ap2p: $o).
% 98.41/13.24 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 98.41/13.24 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 98.41/13.24 thf(symdiffI1_type, type, symdiffI1: $o).
% 98.41/13.24 thf(woz1_4_type, type, woz1_4: $o).
% 98.41/13.24 thf('#sk47_type', type, '#sk47': $i).
% 98.41/13.24 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 98.41/13.24 thf(subsetI2_type, type, subsetI2: $o).
% 98.41/13.24 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 98.41/13.24 thf(theeq_type, type, theeq: $o).
% 98.41/13.24 thf(setminusERneg_type, type, setminusERneg: $o).
% 98.41/13.24 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 98.41/13.24 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 98.41/13.24 thf(omega__Cong_type, type, omega__Cong: $o).
% 98.41/13.24 thf(demorgan1b_type, type, demorgan1b: $o).
% 98.41/13.24 thf(subsetRefl_type, type, subsetRefl: $o).
% 98.41/13.24 thf(uniqinunit_type, type, uniqinunit: $o).
% 98.41/13.24 thf(eqbreln_type, type, eqbreln: $o).
% 98.41/13.24 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o).
% 98.41/13.24 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 98.41/13.24 thf(breln1compEex_type, type, breln1compEex: $o).
% 98.41/13.24 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 98.41/13.24 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 98.41/13.25 thf(prop2setE_type, type, prop2setE: $o).
% 98.41/13.25 thf(binunionEcases_type, type, binunionEcases: $o).
% 98.41/13.25 thf(omega_type, type, omega: $i).
% 98.41/13.25 thf(nonemptyI_type, type, nonemptyI: $o).
% 98.41/13.25 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 98.41/13.25 thf(woz2A_type, type, woz2A: $o).
% 98.41/13.25 thf(injective_type, type, injective: $i > $i > $i > $o).
% 98.41/13.25 thf(exuE3u_type, type, exuE3u: $o).
% 98.41/13.25 thf(setminusEL_type, type, setminusEL: $o).
% 98.41/13.25 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 98.41/13.25 thf(woz1_5_type, type, woz1_5: $o).
% 98.41/13.25 thf(demorgan2_type, type, demorgan2: $o).
% 98.41/13.25 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 98.41/13.25 thf(sepSubset_type, type, sepSubset: $o).
% 98.41/13.25 thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1:
% 98.41/13.25 $o).
% 98.41/13.25 thf(funcext_type, type, funcext: $o).
% 98.41/13.25 thf(upairset2E_type, type, upairset2E: $o).
% 98.41/13.25 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 98.41/13.25 thf(exuI3_type, type, exuI3: $o).
% 98.41/13.25 thf(notdallE_type, type, notdallE: $o).
% 98.41/13.25 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 98.41/13.25 thf(binintersectER_type, type, binintersectER: $o).
% 98.41/13.25 thf(woz13rule0_type, type, woz13rule0: $o).
% 98.41/13.25 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 98.41/13.25 thf(beta2_type, type, beta2: $o).
% 98.41/13.25 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 98.41/13.25 thf(exu__Cong_type, type, exu__Cong: $o).
% 98.41/13.25 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 98.41/13.25 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 98.41/13.25 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 98.41/13.25 thf(ex1I_type, type, ex1I: $o).
% 98.41/13.25 thf(secondinupair_type, type, secondinupair: $o).
% 98.41/13.25 thf(singletonprop_type, type, singletonprop: $o).
% 98.41/13.25 thf(singletonsubset_type, type, singletonsubset: $o).
% 98.41/13.25 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 98.41/13.25 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 98.41/13.25 thf(injFuncInInjFuncSet_type, type, injFuncInInjFuncSet: $o).
% 98.41/13.25 thf(ex1E2_type, type, ex1E2: $o).
% 98.41/13.25 thf(replAx_type, type, replAx: $o).
% 98.41/13.25 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 98.41/13.25 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 98.41/13.25 thf(setukpairIL_type, type, setukpairIL: $o).
% 98.41/13.25 thf(setunionE2_type, type, setunionE2: $o).
% 98.41/13.25 thf(inPowerset_type, type, inPowerset: $o).
% 98.41/13.25 thf(injFuncSet_type, type, injFuncSet: $i > $i > $i).
% 98.41/13.25 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 98.41/13.25 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 98.41/13.25 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 98.41/13.25 thf(woz13rule3_type, type, woz13rule3: $o).
% 98.41/13.25 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 98.41/13.25 $o).
% 98.41/13.25 thf(in__Cong_type, type, in__Cong: $o).
% 98.41/13.25 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 98.41/13.25 thf(binunionRsub_type, type, binunionRsub: $o).
% 98.41/13.25 thf(subset2powerset_type, type, subset2powerset: $o).
% 98.41/13.25 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 98.41/13.25 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 98.41/13.25 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 98.41/13.25 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 98.41/13.25 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 98.41/13.25 thf(injFuncSetFuncIn, conjecture,
% 98.41/13.25 (( setextAx ) =>
% 98.41/13.25 ( ( emptysetAx ) =>
% 98.41/13.25 ( ( setadjoinAx ) =>
% 98.41/13.25 ( ( powersetAx ) =>
% 98.41/13.25 ( ( setunionAx ) =>
% 98.41/13.25 ( ( omega0Ax ) =>
% 98.41/13.25 ( ( omegaSAx ) =>
% 98.41/13.25 ( ( omegaIndAx ) =>
% 98.41/13.25 ( ( replAx ) =>
% 98.41/13.25 ( ( foundationAx ) =>
% 98.41/13.25 ( ( wellorderingAx ) =>
% 98.41/13.25 ( ( descrp ) =>
% 98.41/13.25 ( ( dsetconstrI ) =>
% 98.41/13.25 ( ( dsetconstrEL ) =>
% 98.41/13.25 ( ( dsetconstrER ) =>
% 98.41/13.25 ( ( exuE1 ) =>
% 98.41/13.25 ( ( prop2setE ) =>
% 98.41/13.25 ( ( emptysetE ) =>
% 98.41/13.25 ( ( emptysetimpfalse ) =>
% 98.41/13.25 ( ( notinemptyset ) =>
% 98.41/13.25 ( ( exuE3e ) =>
% 98.41/13.25 ( ( setext ) =>
% 98.41/13.25 ( ( emptyI ) =>
% 98.41/13.25 ( ( noeltsimpempty ) =>
% 98.41/13.25 ( ( setbeta ) =>
% 98.41/13.25 ( ( nonemptyE1 ) =>
% 98.41/13.25 ( ( nonemptyI ) =>
% 98.41/13.25 ( ( nonemptyI1 ) =>
% 98.41/13.25 ( ( setadjoinIL ) =>
% 98.41/13.25 ( ( emptyinunitempty ) =>
% 98.41/13.25 ( ( setadjoinIR ) =>
% 98.41/13.25 ( ( setadjoinE ) =>
% 98.41/13.25 ( (
% 98.41/13.25 setadjoinOr ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setoftrueEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powersetI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 emptyinPowerset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 emptyInPowerset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powersetE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setunionI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setunionE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subPowSU ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 exuE2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 nonemptyImpWitness ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 uniqinunit ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 notinsingleton ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 eqinunit ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 singletonsswitch ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 upairsetE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 upairsetIL ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 upairsetIR ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 emptyE1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 vacuousDall ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 quantDeMorgan1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 quantDeMorgan2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 quantDeMorgan3 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 quantDeMorgan4 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 prop2setI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 prop2set2propI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 notdexE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 notdallE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 exuI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 exuI3 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 exuI2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 inCongP ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 in__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 exuE3u ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 exu__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 emptyset__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setadjoin__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powerset__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setunion__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 omega__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 exuEu ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 descr__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 dsetconstr__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subsetI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 eqimpsubset2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 eqimpsubset1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subsetI2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 emptysetsubset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subsetE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subsetE2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 notsubsetI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 notequalI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 notequalI2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subsetRefl ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subsetTrans ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setadjoinSub ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setadjoinSub2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subset2powerset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setextsub ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subsetemptysetimpeq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powersetI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powersetE1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 inPowerset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powersetsubset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 sepInPowerset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 sepSubset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionIL ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 upairset2IR ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionIR ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionEcases ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionLsub ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionRsub ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectSubset5 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectEL ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectLsub ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectSubset2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectSubset3 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectER ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 disjointsetsI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectRsub ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectSubset4 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectSubset1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 bs114d ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusEL ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusER ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusSubset2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusERneg ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusELneg ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusILneg ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusIRneg ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusLsub ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusSubset1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 symdiffE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 symdiffI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 symdiffI2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 symdiffIneg1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 symdiffIneg2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 secondinupair ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairIL ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairIR ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 kpairiskpair ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 kpairp ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 singletonsubset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 singletoninpowerset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 singletoninpowunion ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 upairset2E ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 upairsubunion ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 upairinpowunion ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ubforcartprodlem1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ubforcartprodlem2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ubforcartprodlem3 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodpairin ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodmempair1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodmempair ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setunionE2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setunionsingleton1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setunionsingleton2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setunionsingleton ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 singletonprop ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ex1E1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ex1I ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ex1I2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 singletonsuniq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairinjL1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 kfstsingleton ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 theprop ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 kfstpairEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodfstin ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairinjL2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairinjL ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairinjR11 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairinjR12 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairinjR1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 upairequniteq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairinjR2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairinjR ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ksndsingleton ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ksndpairEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 kpairsurjEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodsndin ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodpairmemEL ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodpairmemER ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodmempaircEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodfstpairEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodsndpairEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodpairsurjEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 dpsetconstrI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 dpsetconstrSub ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setOfPairsIsBReln ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 dpsetconstrERa ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 dpsetconstrEL1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 dpsetconstrEL2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 dpsetconstrER ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcImageSingleton ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 apProp ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 app ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 infuncsetfunc ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ap2p ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcinfuncset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 lamProp ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 lamp ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 lam2p ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 brelnall1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 brelnall2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ex1E2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcGraphProp1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcGraphProp3 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcGraphProp2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcextLem ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcGraphProp4 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subbreln ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 eqbreln ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcext ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcext2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ap2apEq1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ap2apEq2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 beta1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 eta1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 lam2lamEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 beta2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 eta2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 iffalseProp1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 iffalseProp2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 iftrueProp1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 iftrueProp2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ifSingleton ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ifp ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 theeq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 iftrue ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 iffalse ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 iftrueorfalse ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectT_lem ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionT_lem ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powersetT_lem ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusT_lem ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementT_lem ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setextT ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subsetTI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powersetTI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powersetTE1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementTI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementTE1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectTELcontra ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectTERcontra ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 contrasubsetT ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 contrasubsetT1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 contrasubsetT2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 contrasubsetT3 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 doubleComplementI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 doubleComplementE1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 doubleComplementSub1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 doubleComplementSub2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 doubleComplementEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementTnotintersectT ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementImpComplementIntersect ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementSubsetComplementIntersect ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementInPowersetComplementIntersect ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 contraSubsetComplement ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementTcontraSubset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionTILcontra ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionTIRcontra ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 inIntersectImpInUnion ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 inIntersectImpInUnion2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 inIntersectImpInIntersectUnions ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 intersectInPowersetIntersectUnions ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 inComplementUnionImpNotIn1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 inComplementUnionImpInComplement1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionTE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionTEcontra ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan2a1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementUnionInPowersetComplement ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan2a2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan1a ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan1b ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan2a ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan2b2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan2b ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz13rule0 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz13rule1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz13rule2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz13rule3 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz13rule4 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz1_1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz1_2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz1_3 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz1_4 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz1_5 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1all2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1SetBreln1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 choice2fnsingleton ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setOfPairsIsBReln1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1all1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subbreln1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 eqbreln1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1invprop ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1invI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1invE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1compprop ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1compI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1compE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1compEex ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1unionprop ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1unionIL ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1unionIR ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1unionI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1unionE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1unionEcases ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1unionCommutes ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz2Ex ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz2W ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz2A ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz2B ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 image1Ex ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 image1Ex1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 image1Equiv ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 image1E ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 image1I ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 injFuncInInjFuncSet ) =>
% 98.41/13.25 (
% 98.41/13.25 ![
% 98.41/13.25 A:$i,B:$i,
% 98.41/13.25 Xf:$i]:
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 in @
% 98.41/13.25 Xf @
% 98.41/13.25 (
% 98.41/13.25 injFuncSet
% 98.41/13.25 @
% 98.41/13.25 A @ B ) ) =>
% 98.41/13.25 (
% 98.41/13.25 in @
% 98.41/13.25 Xf @
% 98.41/13.25 (
% 98.41/13.25 funcSet @
% 98.41/13.25 A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 98.41/13.25 thf(zf_stmt_0, negated_conjecture,
% 98.41/13.25 (~( ( setextAx ) =>
% 98.41/13.25 ( ( emptysetAx ) =>
% 98.41/13.25 ( ( setadjoinAx ) =>
% 98.41/13.25 ( ( powersetAx ) =>
% 98.41/13.25 ( ( setunionAx ) =>
% 98.41/13.25 ( ( omega0Ax ) =>
% 98.41/13.25 ( ( omegaSAx ) =>
% 98.41/13.25 ( ( omegaIndAx ) =>
% 98.41/13.25 ( ( replAx ) =>
% 98.41/13.25 ( ( foundationAx ) =>
% 98.41/13.25 ( ( wellorderingAx ) =>
% 98.41/13.25 ( ( descrp ) =>
% 98.41/13.25 ( ( dsetconstrI ) =>
% 98.41/13.25 ( ( dsetconstrEL ) =>
% 98.41/13.25 ( ( dsetconstrER ) =>
% 98.41/13.25 ( ( exuE1 ) =>
% 98.41/13.25 ( ( prop2setE ) =>
% 98.41/13.25 ( ( emptysetE ) =>
% 98.41/13.25 ( ( emptysetimpfalse ) =>
% 98.41/13.25 ( ( notinemptyset ) =>
% 98.41/13.25 ( ( exuE3e ) =>
% 98.41/13.25 ( ( setext ) =>
% 98.41/13.25 ( ( emptyI ) =>
% 98.41/13.25 ( ( noeltsimpempty ) =>
% 98.41/13.25 ( ( setbeta ) =>
% 98.41/13.25 ( ( nonemptyE1 ) =>
% 98.41/13.25 ( ( nonemptyI ) =>
% 98.41/13.25 ( ( nonemptyI1 ) =>
% 98.41/13.25 ( ( setadjoinIL ) =>
% 98.41/13.25 ( ( emptyinunitempty ) =>
% 98.41/13.25 ( ( setadjoinIR ) =>
% 98.41/13.25 ( (
% 98.41/13.25 setadjoinE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setadjoinOr ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setoftrueEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powersetI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 emptyinPowerset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 emptyInPowerset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powersetE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setunionI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setunionE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subPowSU ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 exuE2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 nonemptyImpWitness ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 uniqinunit ) =>
% 98.41/13.25 (
% 98.41/13.25 (
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% 98.41/13.25 (
% 98.41/13.25 singletonsswitch ) =>
% 98.41/13.25 (
% 98.41/13.25 (
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% 98.41/13.25 (
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% 98.41/13.25 (
% 98.41/13.25 (
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% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 emptyE1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 vacuousDall ) =>
% 98.41/13.25 (
% 98.41/13.25 (
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% 98.41/13.25 (
% 98.41/13.25 (
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% 98.41/13.25 (
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% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 quantDeMorgan4 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
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% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 prop2set2propI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 notdexE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 notdallE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 exuI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 exuI3 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 exuI2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 inCongP ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 in__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 exuE3u ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 exu__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 emptyset__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setadjoin__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powerset__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setunion__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 omega__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 exuEu ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 descr__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 dsetconstr__Cong ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subsetI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 eqimpsubset2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
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% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subsetI2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
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% 98.41/13.25 (
% 98.41/13.25 subsetE ) =>
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% 98.41/13.25 (
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% 98.41/13.25 (
% 98.41/13.25 notsubsetI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 notequalI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 notequalI2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subsetRefl ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subsetTrans ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setadjoinSub ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setadjoinSub2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subset2powerset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
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% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subsetemptysetimpeq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powersetI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powersetE1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 inPowerset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powersetsubset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 sepInPowerset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 sepSubset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionIL ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 upairset2IR ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionIR ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionEcases ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionLsub ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionRsub ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectSubset5 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectEL ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectLsub ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectSubset2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectSubset3 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectER ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 disjointsetsI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectRsub ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectSubset4 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectSubset1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 bs114d ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusEL ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusER ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusSubset2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusERneg ) =>
% 98.41/13.25 (
% 98.41/13.25 (
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% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusILneg ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusIRneg ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusLsub ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusSubset1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 symdiffE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 symdiffI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 symdiffI2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 symdiffIneg1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 symdiffIneg2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 secondinupair ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairIL ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairIR ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 kpairiskpair ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 kpairp ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 singletonsubset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 singletoninpowerset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 singletoninpowunion ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 upairset2E ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 upairsubunion ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 upairinpowunion ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ubforcartprodlem1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ubforcartprodlem2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ubforcartprodlem3 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodpairin ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodmempair1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodmempair ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setunionE2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setunionsingleton1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setunionsingleton2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setunionsingleton ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 singletonprop ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ex1E1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ex1I ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ex1I2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 singletonsuniq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairinjL1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 kfstsingleton ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 theprop ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 kfstpairEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodfstin ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairinjL2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairinjL ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairinjR11 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairinjR12 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairinjR1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 upairequniteq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairinjR2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setukpairinjR ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ksndsingleton ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ksndpairEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 kpairsurjEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodsndin ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodpairmemEL ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodpairmemER ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodmempaircEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodfstpairEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodsndpairEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 cartprodpairsurjEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 dpsetconstrI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 dpsetconstrSub ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setOfPairsIsBReln ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 dpsetconstrERa ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 dpsetconstrEL1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 dpsetconstrEL2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 dpsetconstrER ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcImageSingleton ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 apProp ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 app ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 infuncsetfunc ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ap2p ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcinfuncset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 lamProp ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 lamp ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 lam2p ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 brelnall1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 brelnall2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ex1E2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcGraphProp1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcGraphProp3 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcGraphProp2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcextLem ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcGraphProp4 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subbreln ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 eqbreln ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcext ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 funcext2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ap2apEq1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ap2apEq2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 beta1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 eta1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 lam2lamEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 beta2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 eta2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 iffalseProp1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 iffalseProp2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 iftrueProp1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 iftrueProp2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ifSingleton ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ifp ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 theeq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 iftrue ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 iffalse ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 iftrueorfalse ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectT_lem ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionT_lem ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powersetT_lem ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setminusT_lem ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementT_lem ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setextT ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subsetTI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powersetTI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 powersetTE1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementTI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementTE1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectTELcontra ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binintersectTERcontra ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 contrasubsetT ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 contrasubsetT1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 contrasubsetT2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 contrasubsetT3 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 doubleComplementI1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 doubleComplementE1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 doubleComplementSub1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 doubleComplementSub2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 doubleComplementEq ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementTnotintersectT ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementImpComplementIntersect ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementSubsetComplementIntersect ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementInPowersetComplementIntersect ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 contraSubsetComplement ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementTcontraSubset ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionTILcontra ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionTIRcontra ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 inIntersectImpInUnion ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 inIntersectImpInUnion2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 inIntersectImpInIntersectUnions ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 intersectInPowersetIntersectUnions ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 inComplementUnionImpNotIn1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 inComplementUnionImpInComplement1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionTE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 binunionTEcontra ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan2a1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 complementUnionInPowersetComplement ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan2a2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan1a ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan1b ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan2a ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan2b2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan2b ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 demorgan2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz13rule0 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz13rule1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz13rule2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz13rule3 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz13rule4 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz1_1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz1_2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz1_3 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz1_4 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz1_5 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1all2 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1SetBreln1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 choice2fnsingleton ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 setOfPairsIsBReln1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1all1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 subbreln1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 eqbreln1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1invprop ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1invI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1invE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1compprop ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1compI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1compE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1compEex ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1unionprop ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1unionIL ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1unionIR ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1unionI ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1unionE ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1unionEcases ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 breln1unionCommutes ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz2Ex ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz2W ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz2A ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 woz2B ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 image1Ex ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 image1Ex1 ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 image1Equiv ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 image1E ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 image1I ) =>
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 injFuncInInjFuncSet ) =>
% 98.41/13.25 (
% 98.41/13.25 ![
% 98.41/13.25 A:$i,
% 98.41/13.25 B:$i,
% 98.41/13.25 Xf:$i]:
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 in @
% 98.41/13.25 Xf @
% 98.41/13.25 (
% 98.41/13.25 injFuncSet
% 98.41/13.25 @
% 98.41/13.25 A @ B ) ) =>
% 98.41/13.25 (
% 98.41/13.25 in @
% 98.41/13.25 Xf @
% 98.41/13.25 (
% 98.41/13.25 funcSet @
% 98.41/13.25 A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 98.41/13.25 inference('cnf.neg', [status(esa)], [injFuncSetFuncIn])).
% 98.41/13.25 thf(zip_derived_cl0, plain,
% 98.41/13.25 (~ (((setextAx) =>
% 98.41/13.25 (((emptysetAx) =>
% 98.41/13.25 (((setadjoinAx) =>
% 98.41/13.25 (((powersetAx) =>
% 98.41/13.25 (((setunionAx) =>
% 98.41/13.25 (((omega0Ax) =>
% 98.41/13.25 (((omegaSAx) =>
% 98.41/13.25 (((omegaIndAx) =>
% 98.41/13.25 (((replAx) =>
% 98.41/13.25 (((foundationAx) =>
% 98.41/13.25 (((wellorderingAx) =>
% 98.41/13.25 (((descrp) =>
% 98.41/13.25 (((dsetconstrI) =>
% 98.41/13.25 (((dsetconstrEL) =>
% 98.41/13.25 (((dsetconstrER) =>
% 98.41/13.25 (((exuE1) =>
% 98.41/13.25 (((prop2setE) =>
% 98.41/13.25 (((emptysetE) =>
% 98.41/13.25 (((emptysetimpfalse) =>
% 98.41/13.25 (((notinemptyset) =>
% 98.41/13.25 (((exuE3e) =>
% 98.41/13.25 (((setext) =>
% 98.41/13.25 (((emptyI) =>
% 98.41/13.25 (((noeltsimpempty) =>
% 98.41/13.25 (((setbeta) =>
% 98.41/13.25 (((nonemptyE1) =>
% 98.41/13.25 (((nonemptyI) =>
% 98.41/13.25 (((nonemptyI1) =>
% 98.41/13.25 (((setadjoinIL) =>
% 98.41/13.25 (((emptyinunitempty) =>
% 98.41/13.25 ((
% 98.41/13.25 (setadjoinIR) =>
% 98.41/13.25 ((
% 98.41/13.25 (setadjoinE) =>
% 98.41/13.25 ((
% 98.41/13.25 (setadjoinOr) =>
% 98.41/13.25 ((
% 98.41/13.25 (setoftrueEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (powersetI) =>
% 98.41/13.25 ((
% 98.41/13.25 (emptyinPowerset) =>
% 98.41/13.25 ((
% 98.41/13.25 (emptyInPowerset) =>
% 98.41/13.25 ((
% 98.41/13.25 (powersetE) =>
% 98.41/13.25 ((
% 98.41/13.25 (setunionI) =>
% 98.41/13.25 ((
% 98.41/13.25 (setunionE) =>
% 98.41/13.25 ((
% 98.41/13.25 (subPowSU) =>
% 98.41/13.25 ((
% 98.41/13.25 (exuE2) =>
% 98.41/13.25 ((
% 98.41/13.25 (nonemptyImpWitness) =>
% 98.41/13.25 ((
% 98.41/13.25 (uniqinunit) =>
% 98.41/13.25 ((
% 98.41/13.25 (notinsingleton) =>
% 98.41/13.25 ((
% 98.41/13.25 (eqinunit) =>
% 98.41/13.25 ((
% 98.41/13.25 (singletonsswitch) =>
% 98.41/13.25 ((
% 98.41/13.25 (upairsetE) =>
% 98.41/13.25 ((
% 98.41/13.25 (upairsetIL) =>
% 98.41/13.25 ((
% 98.41/13.25 (upairsetIR) =>
% 98.41/13.25 ((
% 98.41/13.25 (emptyE1) =>
% 98.41/13.25 ((
% 98.41/13.25 (vacuousDall) =>
% 98.41/13.25 ((
% 98.41/13.25 (quantDeMorgan1) =>
% 98.41/13.25 ((
% 98.41/13.25 (quantDeMorgan2) =>
% 98.41/13.25 ((
% 98.41/13.25 (quantDeMorgan3) =>
% 98.41/13.25 ((
% 98.41/13.25 (quantDeMorgan4) =>
% 98.41/13.25 ((
% 98.41/13.25 (prop2setI) =>
% 98.41/13.25 ((
% 98.41/13.25 (prop2set2propI) =>
% 98.41/13.25 ((
% 98.41/13.25 (notdexE) =>
% 98.41/13.25 ((
% 98.41/13.25 (notdallE) =>
% 98.41/13.25 ((
% 98.41/13.25 (exuI1) =>
% 98.41/13.25 ((
% 98.41/13.25 (exuI3) =>
% 98.41/13.25 ((
% 98.41/13.25 (exuI2) =>
% 98.41/13.25 ((
% 98.41/13.25 (inCongP) =>
% 98.41/13.25 ((
% 98.41/13.25 (in__Cong) =>
% 98.41/13.25 ((
% 98.41/13.25 (exuE3u) =>
% 98.41/13.25 ((
% 98.41/13.25 (exu__Cong) =>
% 98.41/13.25 ((
% 98.41/13.25 (emptyset__Cong) =>
% 98.41/13.25 ((
% 98.41/13.25 (setadjoin__Cong) =>
% 98.41/13.25 ((
% 98.41/13.25 (powerset__Cong) =>
% 98.41/13.25 ((
% 98.41/13.25 (setunion__Cong) =>
% 98.41/13.25 ((
% 98.41/13.25 (omega__Cong) =>
% 98.41/13.25 ((
% 98.41/13.25 (exuEu) =>
% 98.41/13.25 ((
% 98.41/13.25 (descr__Cong) =>
% 98.41/13.25 ((
% 98.41/13.25 (dsetconstr__Cong) =>
% 98.41/13.25 ((
% 98.41/13.25 (subsetI1) =>
% 98.41/13.25 ((
% 98.41/13.25 (eqimpsubset2) =>
% 98.41/13.25 ((
% 98.41/13.25 (eqimpsubset1) =>
% 98.41/13.25 ((
% 98.41/13.25 (subsetI2) =>
% 98.41/13.25 ((
% 98.41/13.25 (emptysetsubset) =>
% 98.41/13.25 ((
% 98.41/13.25 (subsetE) =>
% 98.41/13.25 ((
% 98.41/13.25 (subsetE2) =>
% 98.41/13.25 ((
% 98.41/13.25 (notsubsetI) =>
% 98.41/13.25 ((
% 98.41/13.25 (notequalI1) =>
% 98.41/13.25 ((
% 98.41/13.25 (notequalI2) =>
% 98.41/13.25 ((
% 98.41/13.25 (subsetRefl) =>
% 98.41/13.25 ((
% 98.41/13.25 (subsetTrans) =>
% 98.41/13.25 ((
% 98.41/13.25 (setadjoinSub) =>
% 98.41/13.25 ((
% 98.41/13.25 (setadjoinSub2) =>
% 98.41/13.25 ((
% 98.41/13.25 (subset2powerset) =>
% 98.41/13.25 ((
% 98.41/13.25 (setextsub) =>
% 98.41/13.25 ((
% 98.41/13.25 (subsetemptysetimpeq) =>
% 98.41/13.25 ((
% 98.41/13.25 (powersetI1) =>
% 98.41/13.25 ((
% 98.41/13.25 (powersetE1) =>
% 98.41/13.25 ((
% 98.41/13.25 (inPowerset) =>
% 98.41/13.25 ((
% 98.41/13.25 (powersetsubset) =>
% 98.41/13.25 ((
% 98.41/13.25 (sepInPowerset) =>
% 98.41/13.25 ((
% 98.41/13.25 (sepSubset) =>
% 98.41/13.25 ((
% 98.41/13.25 (binunionIL) =>
% 98.41/13.25 ((
% 98.41/13.25 (upairset2IR) =>
% 98.41/13.25 ((
% 98.41/13.25 (binunionIR) =>
% 98.41/13.25 ((
% 98.41/13.25 (binunionEcases) =>
% 98.41/13.25 ((
% 98.41/13.25 (binunionE) =>
% 98.41/13.25 ((
% 98.41/13.25 (binunionLsub) =>
% 98.41/13.25 ((
% 98.41/13.25 (binunionRsub) =>
% 98.41/13.25 ((
% 98.41/13.25 (binintersectI) =>
% 98.41/13.25 ((
% 98.41/13.25 (binintersectSubset5) =>
% 98.41/13.25 ((
% 98.41/13.25 (binintersectEL) =>
% 98.41/13.25 ((
% 98.41/13.25 (binintersectLsub) =>
% 98.41/13.25 ((
% 98.41/13.25 (binintersectSubset2) =>
% 98.41/13.25 ((
% 98.41/13.25 (binintersectSubset3) =>
% 98.41/13.25 ((
% 98.41/13.25 (binintersectER) =>
% 98.41/13.25 ((
% 98.41/13.25 (disjointsetsI1) =>
% 98.41/13.25 ((
% 98.41/13.25 (binintersectRsub) =>
% 98.41/13.25 ((
% 98.41/13.25 (binintersectSubset4) =>
% 98.41/13.25 ((
% 98.41/13.25 (binintersectSubset1) =>
% 98.41/13.25 ((
% 98.41/13.25 (bs114d) =>
% 98.41/13.25 ((
% 98.41/13.25 (setminusI) =>
% 98.41/13.25 ((
% 98.41/13.25 (setminusEL) =>
% 98.41/13.25 ((
% 98.41/13.25 (setminusER) =>
% 98.41/13.25 ((
% 98.41/13.25 (setminusSubset2) =>
% 98.41/13.25 ((
% 98.41/13.25 (setminusERneg) =>
% 98.41/13.25 ((
% 98.41/13.25 (setminusELneg) =>
% 98.41/13.25 ((
% 98.41/13.25 (setminusILneg) =>
% 98.41/13.25 ((
% 98.41/13.25 (setminusIRneg) =>
% 98.41/13.25 ((
% 98.41/13.25 (setminusLsub) =>
% 98.41/13.25 ((
% 98.41/13.25 (setminusSubset1) =>
% 98.41/13.25 ((
% 98.41/13.25 (symdiffE) =>
% 98.41/13.25 ((
% 98.41/13.25 (symdiffI1) =>
% 98.41/13.25 ((
% 98.41/13.25 (symdiffI2) =>
% 98.41/13.25 ((
% 98.41/13.25 (symdiffIneg1) =>
% 98.41/13.25 ((
% 98.41/13.25 (symdiffIneg2) =>
% 98.41/13.25 ((
% 98.41/13.25 (secondinupair) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairIL) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairIR) =>
% 98.41/13.25 ((
% 98.41/13.25 (kpairiskpair) =>
% 98.41/13.25 ((
% 98.41/13.25 (kpairp) =>
% 98.41/13.25 ((
% 98.41/13.25 (singletonsubset) =>
% 98.41/13.25 ((
% 98.41/13.25 (singletoninpowerset) =>
% 98.41/13.25 ((
% 98.41/13.25 (singletoninpowunion) =>
% 98.41/13.25 ((
% 98.41/13.25 (upairset2E) =>
% 98.41/13.25 ((
% 98.41/13.25 (upairsubunion) =>
% 98.41/13.25 ((
% 98.41/13.25 (upairinpowunion) =>
% 98.41/13.25 ((
% 98.41/13.25 (ubforcartprodlem1) =>
% 98.41/13.25 ((
% 98.41/13.25 (ubforcartprodlem2) =>
% 98.41/13.25 ((
% 98.41/13.25 (ubforcartprodlem3) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodpairin) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodmempair1) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodmempair) =>
% 98.41/13.25 ((
% 98.41/13.25 (setunionE2) =>
% 98.41/13.25 ((
% 98.41/13.25 (setunionsingleton1) =>
% 98.41/13.25 ((
% 98.41/13.25 (setunionsingleton2) =>
% 98.41/13.25 ((
% 98.41/13.25 (setunionsingleton) =>
% 98.41/13.25 ((
% 98.41/13.25 (singletonprop) =>
% 98.41/13.25 ((
% 98.41/13.25 (ex1E1) =>
% 98.41/13.25 ((
% 98.41/13.25 (ex1I) =>
% 98.41/13.25 ((
% 98.41/13.25 (ex1I2) =>
% 98.41/13.25 ((
% 98.41/13.25 (singletonsuniq) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairinjL1) =>
% 98.41/13.25 ((
% 98.41/13.25 (kfstsingleton) =>
% 98.41/13.25 ((
% 98.41/13.25 (theprop) =>
% 98.41/13.25 ((
% 98.41/13.25 (kfstpairEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodfstin) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairinjL2) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairinjL) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairinjR11) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairinjR12) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairinjR1) =>
% 98.41/13.25 ((
% 98.41/13.25 (upairequniteq) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairinjR2) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairinjR) =>
% 98.41/13.25 ((
% 98.41/13.25 (ksndsingleton) =>
% 98.41/13.25 ((
% 98.41/13.25 (ksndpairEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (kpairsurjEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodsndin) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodpairmemEL) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodpairmemER) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodmempaircEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodfstpairEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodsndpairEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodpairsurjEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (dpsetconstrI) =>
% 98.41/13.25 ((
% 98.41/13.25 (dpsetconstrSub) =>
% 98.41/13.25 ((
% 98.41/13.25 (setOfPairsIsBReln) =>
% 98.41/13.25 ((
% 98.41/13.25 (dpsetconstrERa) =>
% 98.41/13.25 ((
% 98.41/13.25 (dpsetconstrEL1) =>
% 98.41/13.25 ((
% 98.41/13.25 (dpsetconstrEL2) =>
% 98.41/13.25 ((
% 98.41/13.25 (dpsetconstrER) =>
% 98.41/13.25 ((
% 98.41/13.25 (funcImageSingleton) =>
% 98.41/13.25 ((
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% 98.41/13.25 (singletonsuniq) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairinjL1) =>
% 98.41/13.25 ((
% 98.41/13.25 (kfstsingleton) =>
% 98.41/13.25 ((
% 98.41/13.25 (theprop) =>
% 98.41/13.25 ((
% 98.41/13.25 (kfstpairEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodfstin) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairinjL2) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairinjL) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairinjR11) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairinjR12) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairinjR1) =>
% 98.41/13.25 ((
% 98.41/13.25 (upairequniteq) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairinjR2) =>
% 98.41/13.25 ((
% 98.41/13.25 (setukpairinjR) =>
% 98.41/13.25 ((
% 98.41/13.25 (ksndsingleton) =>
% 98.41/13.25 ((
% 98.41/13.25 (ksndpairEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (kpairsurjEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodsndin) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodpairmemEL) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodpairmemER) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodmempaircEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodfstpairEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodsndpairEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (cartprodpairsurjEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (dpsetconstrI) =>
% 98.41/13.25 ((
% 98.41/13.25 (dpsetconstrSub) =>
% 98.41/13.25 ((
% 98.41/13.25 (setOfPairsIsBReln) =>
% 98.41/13.25 ((
% 98.41/13.25 (dpsetconstrERa) =>
% 98.41/13.25 ((
% 98.41/13.25 (dpsetconstrEL1) =>
% 98.41/13.25 ((
% 98.41/13.25 (dpsetconstrEL2) =>
% 98.41/13.25 ((
% 98.41/13.25 (dpsetconstrER) =>
% 98.41/13.25 ((
% 98.41/13.25 (funcImageSingleton) =>
% 98.41/13.25 ((
% 98.41/13.25 (apProp) =>
% 98.41/13.25 ((
% 98.41/13.25 (app) =>
% 98.41/13.25 ((
% 98.41/13.25 (infuncsetfunc) =>
% 98.41/13.25 ((
% 98.41/13.25 (ap2p) =>
% 98.41/13.25 ((
% 98.41/13.25 (funcinfuncset) =>
% 98.41/13.25 ((
% 98.41/13.25 (lamProp) =>
% 98.41/13.25 ((
% 98.41/13.25 (lamp) =>
% 98.41/13.25 ((
% 98.41/13.25 (lam2p) =>
% 98.41/13.25 ((
% 98.41/13.25 (brelnall1) =>
% 98.41/13.25 ((
% 98.41/13.25 (brelnall2) =>
% 98.41/13.25 ((
% 98.41/13.25 (ex1E2) =>
% 98.41/13.25 ((
% 98.41/13.25 (funcGraphProp1) =>
% 98.41/13.25 ((
% 98.41/13.25 (funcGraphProp3) =>
% 98.41/13.25 ((
% 98.41/13.25 (funcGraphProp2) =>
% 98.41/13.25 ((
% 98.41/13.25 (funcextLem) =>
% 98.41/13.25 ((
% 98.41/13.25 (funcGraphProp4) =>
% 98.41/13.25 ((
% 98.41/13.25 (subbreln) =>
% 98.41/13.25 ((
% 98.41/13.25 (eqbreln) =>
% 98.41/13.25 ((
% 98.41/13.25 (funcext) =>
% 98.41/13.25 ((
% 98.41/13.25 (funcext2) =>
% 98.41/13.25 ((
% 98.41/13.25 (ap2apEq1) =>
% 98.41/13.25 ((
% 98.41/13.25 (ap2apEq2) =>
% 98.41/13.25 ((
% 98.41/13.25 (beta1) =>
% 98.41/13.25 ((
% 98.41/13.25 (eta1) =>
% 98.41/13.25 ((
% 98.41/13.25 (lam2lamEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (beta2) =>
% 98.41/13.25 ((
% 98.41/13.25 (eta2) =>
% 98.41/13.25 ((
% 98.41/13.25 (iffalseProp1) =>
% 98.41/13.25 ((
% 98.41/13.25 (iffalseProp2) =>
% 98.41/13.25 ((
% 98.41/13.25 (iftrueProp1) =>
% 98.41/13.25 ((
% 98.41/13.25 (iftrueProp2) =>
% 98.41/13.25 ((
% 98.41/13.25 (ifSingleton) =>
% 98.41/13.25 ((
% 98.41/13.25 (ifp) =>
% 98.41/13.25 ((
% 98.41/13.25 (theeq) =>
% 98.41/13.25 ((
% 98.41/13.25 (iftrue) =>
% 98.41/13.25 ((
% 98.41/13.25 (iffalse) =>
% 98.41/13.25 ((
% 98.41/13.25 (iftrueorfalse) =>
% 98.41/13.25 ((
% 98.41/13.25 (binintersectT_lem) =>
% 98.41/13.25 ((
% 98.41/13.25 (binunionT_lem) =>
% 98.41/13.25 ((
% 98.41/13.25 (powersetT_lem) =>
% 98.41/13.25 ((
% 98.41/13.25 (setminusT_lem) =>
% 98.41/13.25 ((
% 98.41/13.25 (complementT_lem) =>
% 98.41/13.25 ((
% 98.41/13.25 (setextT) =>
% 98.41/13.25 ((
% 98.41/13.25 (subsetTI) =>
% 98.41/13.25 ((
% 98.41/13.25 (powersetTI1) =>
% 98.41/13.25 ((
% 98.41/13.25 (powersetTE1) =>
% 98.41/13.25 ((
% 98.41/13.25 (complementTI1) =>
% 98.41/13.25 ((
% 98.41/13.25 (complementTE1) =>
% 98.41/13.25 ((
% 98.41/13.25 (binintersectTELcontra) =>
% 98.41/13.25 ((
% 98.41/13.25 (binintersectTERcontra) =>
% 98.41/13.25 ((
% 98.41/13.25 (contrasubsetT) =>
% 98.41/13.25 ((
% 98.41/13.25 (contrasubsetT1) =>
% 98.41/13.25 ((
% 98.41/13.25 (contrasubsetT2) =>
% 98.41/13.25 ((
% 98.41/13.25 (contrasubsetT3) =>
% 98.41/13.25 ((
% 98.41/13.25 (doubleComplementI1) =>
% 98.41/13.25 ((
% 98.41/13.25 (doubleComplementE1) =>
% 98.41/13.25 ((
% 98.41/13.25 (doubleComplementSub1) =>
% 98.41/13.25 ((
% 98.41/13.25 (doubleComplementSub2) =>
% 98.41/13.25 ((
% 98.41/13.25 (doubleComplementEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (complementTnotintersectT) =>
% 98.41/13.25 ((
% 98.41/13.25 (complementImpComplementIntersect) =>
% 98.41/13.25 ((
% 98.41/13.25 (complementSubsetComplementIntersect) =>
% 98.41/13.25 ((
% 98.41/13.25 (complementInPowersetComplementIntersect) =>
% 98.41/13.25 ((
% 98.41/13.25 (contraSubsetComplement) =>
% 98.41/13.25 ((
% 98.41/13.25 (complementTcontraSubset) =>
% 98.41/13.25 ((
% 98.41/13.25 (binunionTILcontra) =>
% 98.41/13.25 ((
% 98.41/13.25 (binunionTIRcontra) =>
% 98.41/13.25 ((
% 98.41/13.25 (inIntersectImpInUnion) =>
% 98.41/13.25 ((
% 98.41/13.25 (inIntersectImpInUnion2) =>
% 98.41/13.25 ((
% 98.41/13.25 (inIntersectImpInIntersectUnions) =>
% 98.41/13.25 ((
% 98.41/13.25 (intersectInPowersetIntersectUnions) =>
% 98.41/13.25 ((
% 98.41/13.25 (inComplementUnionImpNotIn1) =>
% 98.41/13.25 ((
% 98.41/13.25 (inComplementUnionImpInComplement1) =>
% 98.41/13.25 ((
% 98.41/13.25 (binunionTE) =>
% 98.41/13.25 ((
% 98.41/13.25 (binunionTEcontra) =>
% 98.41/13.25 ((
% 98.41/13.25 (demorgan2a1) =>
% 98.41/13.25 ((
% 98.41/13.25 (complementUnionInPowersetComplement) =>
% 98.41/13.25 ((
% 98.41/13.25 (demorgan2a2) =>
% 98.41/13.25 ((
% 98.41/13.25 (demorgan1a) =>
% 98.41/13.25 ((
% 98.41/13.25 (demorgan1b) =>
% 98.41/13.25 ((
% 98.41/13.25 (demorgan1) =>
% 98.41/13.25 ((
% 98.41/13.25 (demorgan2a) =>
% 98.41/13.25 ((
% 98.41/13.25 (demorgan2b2) =>
% 98.41/13.25 ((
% 98.41/13.25 (demorgan2b) =>
% 98.41/13.25 ((
% 98.41/13.25 (demorgan2) =>
% 98.41/13.25 ((
% 98.41/13.25 (woz13rule0) =>
% 98.41/13.25 ((
% 98.41/13.25 (woz13rule1) =>
% 98.41/13.25 ((
% 98.41/13.25 (woz13rule2) =>
% 98.41/13.25 ((
% 98.41/13.25 (woz13rule3) =>
% 98.41/13.25 ((
% 98.41/13.25 (woz13rule4) =>
% 98.41/13.25 ((
% 98.41/13.25 (woz1_1) =>
% 98.41/13.25 ((
% 98.41/13.25 (woz1_2) =>
% 98.41/13.25 ((
% 98.41/13.25 (woz1_3) =>
% 98.41/13.25 ((
% 98.41/13.25 (woz1_4) =>
% 98.41/13.25 ((
% 98.41/13.25 (woz1_5) =>
% 98.41/13.25 ((
% 98.41/13.25 (breln1all2) =>
% 98.41/13.25 ((
% 98.41/13.25 (breln1SetBreln1) =>
% 98.41/13.25 ((
% 98.41/13.25 (choice2fnsingleton) =>
% 98.41/13.25 ((
% 98.41/13.25 (setOfPairsIsBReln1) =>
% 98.41/13.25 ((
% 98.41/13.25 (breln1all1) =>
% 98.41/13.25 ((
% 98.41/13.25 (subbreln1) =>
% 98.41/13.25 ((
% 98.41/13.25 (eqbreln1) =>
% 98.41/13.25 ((
% 98.41/13.25 (breln1invprop) =>
% 98.41/13.25 ((
% 98.41/13.25 (breln1invI) =>
% 98.41/13.25 ((
% 98.41/13.25 (breln1invE) =>
% 98.41/13.25 ((
% 98.41/13.25 (breln1compprop) =>
% 98.41/13.25 ((
% 98.41/13.25 (breln1compI) =>
% 98.41/13.25 ((
% 98.41/13.25 (breln1compE) =>
% 98.41/13.25 ((
% 98.41/13.25 (breln1compEex) =>
% 98.41/13.25 ((
% 98.41/13.25 (breln1unionprop) =>
% 98.41/13.25 ((
% 98.41/13.25 (breln1unionIL) =>
% 98.41/13.25 ((
% 98.41/13.25 (breln1unionIR) =>
% 98.41/13.25 ((
% 98.41/13.25 (breln1unionI) =>
% 98.41/13.25 ((
% 98.41/13.25 (breln1unionE) =>
% 98.41/13.25 ((
% 98.41/13.25 (breln1unionEcases) =>
% 98.41/13.25 ((
% 98.41/13.25 (breln1unionCommutes) =>
% 98.41/13.25 ((
% 98.41/13.25 (woz2Ex) =>
% 98.41/13.25 ((
% 98.41/13.25 (woz2W) =>
% 98.41/13.25 ((
% 98.41/13.25 (woz2A) =>
% 98.41/13.25 ((
% 98.41/13.25 (woz2B) =>
% 98.41/13.25 ((
% 98.41/13.25 (image1Ex) =>
% 98.41/13.25 ((
% 98.41/13.25 (image1Ex1) =>
% 98.41/13.25 ((
% 98.41/13.25 (image1Equiv) =>
% 98.41/13.25 ((
% 98.41/13.25 (image1E) =>
% 98.41/13.25 ((
% 98.41/13.25 (image1I) =>
% 98.41/13.25 ((
% 98.41/13.25 (injFuncInInjFuncSet) =>
% 98.41/13.25 ((
% 98.41/13.25 (!!) @ (
% 98.41/13.25 (('#B') @ (
% 98.41/13.25 !!) @
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ('#B') @ (
% 98.41/13.25 (
% 98.41/13.25 ('#B') @ (
% 98.41/13.25 !!))) @
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ('#S') @ (
% 98.41/13.25 (
% 98.41/13.25 ('#B') @ (
% 98.41/13.25 '#S') @
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ('#B') @ (
% 98.41/13.25 (
% 98.41/13.25 ('#B') @ (
% 98.41/13.25 '#S'))) @
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ('#B') @ (
% 98.41/13.25 (
% 98.41/13.25 ('#B') @ (
% 98.41/13.25 (
% 98.41/13.25 ('#B') @ (
% 98.41/13.25 =>))))) @
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ('#B') @ (
% 98.41/13.25 (
% 98.41/13.25 ('#B') @ (
% 98.41/13.25 (
% 98.41/13.25 ('#C') @ in)))) @
% 98.41/13.25 injFuncSet)))))))) @
% 98.41/13.25 (
% 98.41/13.25 (
% 98.41/13.25 ('#B') @ (
% 98.41/13.25 (
% 98.41/13.25 ('#B') @ (
% 98.41/13.25 (
% 98.41/13.25 ('#C') @ in)))) @
% 98.41/13.25 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.25 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 98.41/13.25 thf(omega0Ax, axiom,(( omega0Ax ) = ((in @ emptyset @ omega)))).
% 98.41/13.25 thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 98.41/13.25 define([status(thm)])).
% 98.41/13.25 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 98.41/13.25 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))).
% 98.41/13.25 thf('1', plain,
% 98.41/13.25 (( emptyinunitempty ) =
% 98.41/13.25 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 98.41/13.25 define([status(thm)])).
% 98.41/13.25 thf(emptyset__Cong, axiom,(( emptyset__Cong ) =
% 98.41/13.25 ((((emptyset) = (emptyset)))))).
% 98.41/13.25 thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 98.41/13.25 define([status(thm)])).
% 98.41/13.25 thf(omega__Cong, axiom,(( omega__Cong ) = ((((omega) = (omega)))))).
% 98.41/13.25 thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 98.41/13.25 define([status(thm)])).
% 98.41/13.25 thf(zip_derived_cl2, plain,
% 98.41/13.25 (~ (((setextAx) =>
% 98.41/13.25 (((emptysetAx) =>
% 98.41/13.25 (((setadjoinAx) =>
% 98.41/13.25 (((powersetAx) =>
% 98.41/13.25 (((setunionAx) =>
% 98.41/13.25 (((in @ emptyset @ omega) =>
% 98.41/13.25 (((omegaSAx) =>
% 98.41/13.25 (((omegaIndAx) =>
% 98.41/13.25 (((replAx) =>
% 98.41/13.25 (((foundationAx) =>
% 98.41/13.25 (((wellorderingAx) =>
% 98.41/13.25 (((descrp) =>
% 98.41/13.25 (((dsetconstrI) =>
% 98.41/13.25 (((dsetconstrEL) =>
% 98.41/13.25 (((dsetconstrER) =>
% 98.41/13.25 (((exuE1) =>
% 98.41/13.25 (((prop2setE) =>
% 98.41/13.25 (((emptysetE) =>
% 98.41/13.25 (((emptysetimpfalse) =>
% 98.41/13.25 (((notinemptyset) =>
% 98.41/13.25 (((exuE3e) =>
% 98.41/13.25 (((setext) =>
% 98.41/13.25 (((emptyI) =>
% 98.41/13.25 (((noeltsimpempty) =>
% 98.41/13.25 (((setbeta) =>
% 98.41/13.25 (((nonemptyE1) =>
% 98.41/13.25 (((nonemptyI) =>
% 98.41/13.25 (((nonemptyI1) =>
% 98.41/13.25 (((setadjoinIL) =>
% 98.41/13.25 (((in @
% 98.41/13.25 emptyset @
% 98.41/13.25 (setadjoin @
% 98.41/13.25 emptyset @
% 98.41/13.25 emptyset)) =>
% 98.41/13.25 ((
% 98.41/13.25 (setadjoinIR) =>
% 98.41/13.25 ((
% 98.41/13.25 (setadjoinE) =>
% 98.41/13.25 ((
% 98.41/13.25 (setadjoinOr) =>
% 98.41/13.25 ((
% 98.41/13.25 (setoftrueEq) =>
% 98.41/13.25 ((
% 98.41/13.25 (powersetI) =>
% 98.41/13.25 ((
% 98.41/13.25 (emptyinPowerset) =>
% 98.41/13.25 ((
% 98.41/13.25 (emptyInPowerset) =>
% 98.41/13.25 ((
% 98.41/13.25 (powersetE) =>
% 98.41/13.25 ((
% 98.41/13.25 (setunionI) =>
% 98.41/13.25 ((
% 98.41/13.25 (setunionE) =>
% 98.41/13.25 ((
% 98.41/13.25 (subPowSU) =>
% 98.41/13.25 ((
% 98.41/13.25 (exuE2) =>
% 98.41/13.25 ((
% 98.41/13.25 (nonemptyImpWitness) =>
% 98.41/13.25 ((
% 98.41/13.25 (uniqinunit) =>
% 98.41/13.25 ((
% 98.41/13.25 (notinsingleton) =>
% 98.41/13.25 ((
% 98.41/13.25 (eqinunit) =>
% 98.41/13.25 ((
% 98.41/13.25 (singletonsswitch) =>
% 98.41/13.25 ((
% 98.41/13.25 (upairsetE) =>
% 98.41/13.25 ((
% 98.41/13.25 (upairsetIL) =>
% 98.41/13.25 ((
% 98.41/13.25 (upairsetIR) =>
% 98.41/13.25 ((
% 98.41/13.25 (emptyE1) =>
% 98.41/13.25 ((
% 98.41/13.25 (vacuousDall) =>
% 98.41/13.25 ((
% 98.41/13.25 (quantDeMorgan1) =>
% 98.41/13.25 ((
% 98.41/13.25 (quantDeMorgan2) =>
% 98.41/13.25 ((
% 98.41/13.25 (quantDeMorgan3) =>
% 98.41/13.25 ((
% 98.41/13.25 (quantDeMorgan4) =>
% 98.41/13.25 ((
% 98.41/13.25 (prop2setI) =>
% 98.41/13.25 ((
% 98.41/13.25 (prop2set2propI) =>
% 98.41/13.25 ((
% 98.41/13.25 (notdexE) =>
% 98.41/13.25 ((
% 98.41/13.25 (notdallE) =>
% 98.41/13.25 ((
% 98.41/13.25 (exuI1) =>
% 98.41/13.25 ((
% 98.41/13.25 (exuI3) =>
% 98.41/13.25 ((
% 98.41/13.25 (exuI2) =>
% 98.41/13.25 ((
% 98.41/13.25 (inCongP) =>
% 98.41/13.25 ((
% 98.41/13.25 (in__Cong) =>
% 98.41/13.25 ((
% 98.41/13.25 (exuE3u) =>
% 98.41/13.25 ((
% 98.41/13.25 (exu__Cong) =>
% 98.41/13.25 ((
% 98.41/13.25 ((
% 98.41/13.25 (emptyset) =
% 98.41/13.25 (emptyset))) =>
% 98.41/13.25 ((
% 98.41/13.25 (setadjoin__Cong) =>
% 98.41/13.25 ((
% 98.41/13.25 (powerset__Cong) =>
% 98.41/13.25 ((
% 98.41/13.25 (setunion__Cong) =>
% 98.41/13.25 ((
% 98.41/13.25 ((
% 98.41/13.25 (omega) =
% 98.41/13.25 (omega))) =>
% 98.41/13.25 ((
% 98.41/13.25 (exuEu) =>
% 98.41/13.25 ((
% 98.41/13.25 (descr__Cong) =>
% 98.41/13.25 ((
% 98.41/13.25 (dsetconstr__Cong) =>
% 98.41/13.25 ((
% 98.41/13.25 (subsetI1) =>
% 98.41/13.25 ((
% 98.41/13.25 (eqimpsubset2) =>
% 98.41/13.25 ((
% 98.41/13.25 (eqimpsubset1) =>
% 98.41/13.25 ((
% 98.41/13.25 (subsetI2) =>
% 98.41/13.25 ((
% 98.41/13.25 (emptysetsubset) =>
% 98.41/13.25 ((
% 98.41/13.25 (subsetE) =>
% 98.41/13.25 ((
% 98.41/13.25 (subsetE2) =>
% 98.41/13.25 ((
% 98.41/13.25 (notsubsetI) =>
% 98.41/13.25 ((
% 98.41/13.25 (notequalI1) =>
% 98.41/13.25 ((
% 98.41/13.25 (notequalI2) =>
% 98.41/13.25 ((
% 98.41/13.25 (subsetRefl) =>
% 98.41/13.25 ((
% 98.41/13.25 (subsetTrans) =>
% 98.41/13.25 ((
% 98.41/13.25 (setadjoinSub) =>
% 98.41/13.25 ((
% 98.41/13.25 (setadjoinSub2) =>
% 98.41/13.25 ((
% 98.41/13.25 (subset2powerset) =>
% 98.41/13.25 ((
% 98.41/13.25 (setextsub) =>
% 98.41/13.25 ((
% 98.41/13.25 (subsetemptysetimpeq) =>
% 98.41/13.25 ((
% 98.41/13.25 (powersetI1) =>
% 98.41/13.25 ((
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% 98.41/13.25 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.25 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl2])).
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (kpairsurjEq) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodsndin) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodpairmemEL) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodpairmemER) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodmempaircEq) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodfstpairEq) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodsndpairEq) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodpairsurjEq) =>
% 98.41/13.26 ((
% 98.41/13.26 (dpsetconstrI) =>
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% 98.41/13.26 (dpsetconstrSub) =>
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% 98.41/13.26 (dpsetconstrEL2) =>
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% 98.41/13.26 (dpsetconstrER) =>
% 98.41/13.26 ((
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% 98.41/13.26 (app) =>
% 98.41/13.26 ((
% 98.41/13.26 (infuncsetfunc) =>
% 98.41/13.26 ((
% 98.41/13.26 (ap2p) =>
% 98.41/13.26 ((
% 98.41/13.26 (funcinfuncset) =>
% 98.41/13.26 ((
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% 98.41/13.26 (lamp) =>
% 98.41/13.26 ((
% 98.41/13.26 (lam2p) =>
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% 98.41/13.26 (brelnall2) =>
% 98.41/13.26 ((
% 98.41/13.26 (ex1E2) =>
% 98.41/13.26 ((
% 98.41/13.26 (funcGraphProp1) =>
% 98.41/13.26 ((
% 98.41/13.26 (funcGraphProp3) =>
% 98.41/13.26 ((
% 98.41/13.26 (funcGraphProp2) =>
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% 98.41/13.26 (complementSubsetComplementIntersect) =>
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% 98.41/13.26 (complementInPowersetComplementIntersect) =>
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% 98.41/13.26 (contraSubsetComplement) =>
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% 98.41/13.26 ((
% 98.41/13.26 (binunionTIRcontra) =>
% 98.41/13.26 ((
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% 98.41/13.26 (inIntersectImpInUnion2) =>
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% 98.41/13.26 (demorgan2b) =>
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% 98.41/13.26 ((
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% 98.41/13.26 (woz13rule4) =>
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% 98.41/13.26 (woz1_4) =>
% 98.41/13.26 ((
% 98.41/13.26 (woz1_5) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1all2) =>
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% 98.41/13.26 (breln1SetBreln1) =>
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% 98.41/13.26 ((
% 98.41/13.26 (eqbreln1) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1invprop) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1invI) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1invE) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1compprop) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1compI) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1compE) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1compEex) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1unionprop) =>
% 98.41/13.26 ((
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% 98.41/13.26 (breln1unionIR) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1unionI) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1unionE) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1unionEcases) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1unionCommutes) =>
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (woz2B) =>
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% 98.41/13.26 ((
% 98.41/13.26 (image1Ex1) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (image1E) =>
% 98.41/13.26 ((
% 98.41/13.26 (image1I) =>
% 98.41/13.26 ((
% 98.41/13.26 (injFuncInInjFuncSet) =>
% 98.41/13.26 ((
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% 98.41/13.26 (
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% 98.41/13.26 ((
% 98.41/13.26 (setminusEL) =>
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% 98.41/13.26 (kpairp) =>
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% 98.41/13.26 ((
% 98.41/13.26 (ubforcartprodlem2) =>
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% 98.41/13.26 (ubforcartprodlem3) =>
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% 98.41/13.26 ((
% 98.41/13.26 (cartprodmempair) =>
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% 98.41/13.26 ((
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% 98.41/13.26 (setukpairinjR1) =>
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% 98.41/13.26 ((
% 98.41/13.26 (kpairsurjEq) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodsndin) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodpairmemEL) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodpairmemER) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodmempaircEq) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodfstpairEq) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodsndpairEq) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodpairsurjEq) =>
% 98.41/13.26 ((
% 98.41/13.26 (dpsetconstrI) =>
% 98.41/13.26 ((
% 98.41/13.26 (dpsetconstrSub) =>
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% 98.41/13.26 (dpsetconstrERa) =>
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% 98.41/13.26 (dpsetconstrEL1) =>
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% 98.41/13.26 (dpsetconstrEL2) =>
% 98.41/13.26 ((
% 98.41/13.26 (dpsetconstrER) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (app) =>
% 98.41/13.26 ((
% 98.41/13.26 (infuncsetfunc) =>
% 98.41/13.26 ((
% 98.41/13.26 (ap2p) =>
% 98.41/13.26 ((
% 98.41/13.26 (funcinfuncset) =>
% 98.41/13.26 ((
% 98.41/13.26 (lamProp) =>
% 98.41/13.26 ((
% 98.41/13.26 (lamp) =>
% 98.41/13.26 ((
% 98.41/13.26 (lam2p) =>
% 98.41/13.26 ((
% 98.41/13.26 (brelnall1) =>
% 98.41/13.26 ((
% 98.41/13.26 (brelnall2) =>
% 98.41/13.26 ((
% 98.41/13.26 (ex1E2) =>
% 98.41/13.26 ((
% 98.41/13.26 (funcGraphProp1) =>
% 98.41/13.26 ((
% 98.41/13.26 (funcGraphProp3) =>
% 98.41/13.26 ((
% 98.41/13.26 (funcGraphProp2) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (funcGraphProp4) =>
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (ap2apEq2) =>
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% 98.41/13.26 (beta1) =>
% 98.41/13.26 ((
% 98.41/13.26 (eta1) =>
% 98.41/13.26 ((
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% 98.41/13.26 (beta2) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (binintersectTERcontra) =>
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% 98.41/13.26 (contrasubsetT) =>
% 98.41/13.26 ((
% 98.41/13.26 (contrasubsetT1) =>
% 98.41/13.26 ((
% 98.41/13.26 (contrasubsetT2) =>
% 98.41/13.26 ((
% 98.41/13.26 (contrasubsetT3) =>
% 98.41/13.26 ((
% 98.41/13.26 (doubleComplementI1) =>
% 98.41/13.26 ((
% 98.41/13.26 (doubleComplementE1) =>
% 98.41/13.26 ((
% 98.41/13.26 (doubleComplementSub1) =>
% 98.41/13.26 ((
% 98.41/13.26 (doubleComplementSub2) =>
% 98.41/13.26 ((
% 98.41/13.26 (doubleComplementEq) =>
% 98.41/13.26 ((
% 98.41/13.26 (complementTnotintersectT) =>
% 98.41/13.26 ((
% 98.41/13.26 (complementImpComplementIntersect) =>
% 98.41/13.26 ((
% 98.41/13.26 (complementSubsetComplementIntersect) =>
% 98.41/13.26 ((
% 98.41/13.26 (complementInPowersetComplementIntersect) =>
% 98.41/13.26 ((
% 98.41/13.26 (contraSubsetComplement) =>
% 98.41/13.26 ((
% 98.41/13.26 (complementTcontraSubset) =>
% 98.41/13.26 ((
% 98.41/13.26 (binunionTILcontra) =>
% 98.41/13.26 ((
% 98.41/13.26 (binunionTIRcontra) =>
% 98.41/13.26 ((
% 98.41/13.26 (inIntersectImpInUnion) =>
% 98.41/13.26 ((
% 98.41/13.26 (inIntersectImpInUnion2) =>
% 98.41/13.26 ((
% 98.41/13.26 (inIntersectImpInIntersectUnions) =>
% 98.41/13.26 ((
% 98.41/13.26 (intersectInPowersetIntersectUnions) =>
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% 98.41/13.26 (inComplementUnionImpNotIn1) =>
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% 98.41/13.26 (inComplementUnionImpInComplement1) =>
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (complementUnionInPowersetComplement) =>
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (demorgan1) =>
% 98.41/13.26 ((
% 98.41/13.26 (demorgan2a) =>
% 98.41/13.26 ((
% 98.41/13.26 (demorgan2b2) =>
% 98.41/13.26 ((
% 98.41/13.26 (demorgan2b) =>
% 98.41/13.26 ((
% 98.41/13.26 (demorgan2) =>
% 98.41/13.26 ((
% 98.41/13.26 (woz13rule0) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (woz13rule2) =>
% 98.41/13.26 ((
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% 98.41/13.26 (woz13rule4) =>
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% 98.41/13.26 (woz1_4) =>
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% 98.41/13.26 (woz1_5) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1all2) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (breln1invI) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1invE) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1compprop) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1compI) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1compE) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1compEex) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1unionprop) =>
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% 98.41/13.26 ((
% 98.41/13.26 (breln1unionIR) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1unionI) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1unionE) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1unionEcases) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1unionCommutes) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (image1Ex1) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (image1E) =>
% 98.41/13.26 ((
% 98.41/13.26 (image1I) =>
% 98.41/13.26 ((
% 98.41/13.26 (injFuncInInjFuncSet) =>
% 98.41/13.26 ((
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% 98.41/13.26 (
% 98.41/13.26 (
% 98.41/13.26 ('#B') @ (
% 98.41/13.26 (
% 98.41/13.26 ('#B') @ (
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% 98.41/13.26 (
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% 98.41/13.26 (
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% 98.41/13.26 (
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% 98.41/13.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])).
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% 98.41/13.26 ((
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% 98.41/13.26 (exuE3u) =>
% 98.41/13.26 ((
% 98.41/13.26 (exu__Cong) =>
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% 98.41/13.26 (setadjoin__Cong) =>
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% 98.41/13.26 (powerset__Cong) =>
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% 98.41/13.26 (setunion__Cong) =>
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% 98.41/13.26 (descr__Cong) =>
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% 98.41/13.26 '#S'))) @
% 98.41/13.26 (
% 98.41/13.26 (
% 98.41/13.26 ('#B') @ (
% 98.41/13.26 (
% 98.41/13.26 ('#B') @ (
% 98.41/13.26 (
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% 98.41/13.26 =>))))) @
% 98.41/13.26 (
% 98.41/13.26 (
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% 98.41/13.26 ('#B') @ (
% 98.41/13.26 (
% 98.41/13.26 ('#C') @ in)))) @
% 98.41/13.26 injFuncSet)))))))) @
% 98.41/13.26 (
% 98.41/13.26 (
% 98.41/13.26 ('#B') @ (
% 98.41/13.26 (
% 98.41/13.26 ('#B') @ (
% 98.41/13.26 (
% 98.41/13.26 ('#C') @ in)))) @
% 98.41/13.26 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
% 98.41/13.26 thf(zip_derived_cl46, plain,
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% 98.41/13.26 (setunionE) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (exuE3u) =>
% 98.41/13.26 ((
% 98.41/13.26 (exu__Cong) =>
% 98.41/13.26 ((
% 98.41/13.26 (setadjoin__Cong) =>
% 98.41/13.26 ((
% 98.41/13.26 (powerset__Cong) =>
% 98.41/13.26 ((
% 98.41/13.26 (setunion__Cong) =>
% 98.41/13.26 ((
% 98.41/13.26 (exuEu) =>
% 98.41/13.26 ((
% 98.41/13.26 (descr__Cong) =>
% 98.41/13.26 ((
% 98.41/13.26 (dsetconstr__Cong) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (subsetE2) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (notequalI2) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (binintersectSubset5) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (binintersectLsub) =>
% 98.41/13.26 ((
% 98.41/13.26 (binintersectSubset2) =>
% 98.41/13.26 ((
% 98.41/13.26 (binintersectSubset3) =>
% 98.41/13.26 ((
% 98.41/13.26 (binintersectER) =>
% 98.41/13.26 ((
% 98.41/13.26 (disjointsetsI1) =>
% 98.41/13.26 ((
% 98.41/13.26 (binintersectRsub) =>
% 98.41/13.26 ((
% 98.41/13.26 (binintersectSubset4) =>
% 98.41/13.26 ((
% 98.41/13.26 (binintersectSubset1) =>
% 98.41/13.26 ((
% 98.41/13.26 (bs114d) =>
% 98.41/13.26 ((
% 98.41/13.26 (setminusI) =>
% 98.41/13.26 ((
% 98.41/13.26 (setminusEL) =>
% 98.41/13.26 ((
% 98.41/13.26 (setminusER) =>
% 98.41/13.26 ((
% 98.41/13.26 (setminusSubset2) =>
% 98.41/13.26 ((
% 98.41/13.26 (setminusERneg) =>
% 98.41/13.26 ((
% 98.41/13.26 (setminusELneg) =>
% 98.41/13.26 ((
% 98.41/13.26 (setminusILneg) =>
% 98.41/13.26 ((
% 98.41/13.26 (setminusIRneg) =>
% 98.41/13.26 ((
% 98.41/13.26 (setminusLsub) =>
% 98.41/13.26 ((
% 98.41/13.26 (setminusSubset1) =>
% 98.41/13.26 ((
% 98.41/13.26 (symdiffE) =>
% 98.41/13.26 ((
% 98.41/13.26 (symdiffI1) =>
% 98.41/13.26 ((
% 98.41/13.26 (symdiffI2) =>
% 98.41/13.26 ((
% 98.41/13.26 (symdiffIneg1) =>
% 98.41/13.26 ((
% 98.41/13.26 (symdiffIneg2) =>
% 98.41/13.26 ((
% 98.41/13.26 (secondinupair) =>
% 98.41/13.26 ((
% 98.41/13.26 (setukpairIL) =>
% 98.41/13.26 ((
% 98.41/13.26 (setukpairIR) =>
% 98.41/13.26 ((
% 98.41/13.26 (kpairiskpair) =>
% 98.41/13.26 ((
% 98.41/13.26 (kpairp) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (singletoninpowerset) =>
% 98.41/13.26 ((
% 98.41/13.26 (singletoninpowunion) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (ubforcartprodlem3) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodpairin) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodmempair1) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodmempair) =>
% 98.41/13.26 ((
% 98.41/13.26 (setunionE2) =>
% 98.41/13.26 ((
% 98.41/13.26 (setunionsingleton1) =>
% 98.41/13.26 ((
% 98.41/13.26 (setunionsingleton2) =>
% 98.41/13.26 ((
% 98.41/13.26 (setunionsingleton) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 (kfstpairEq) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (setukpairinjL) =>
% 98.41/13.26 ((
% 98.41/13.26 (setukpairinjR11) =>
% 98.41/13.26 ((
% 98.41/13.26 (setukpairinjR12) =>
% 98.41/13.26 ((
% 98.41/13.26 (setukpairinjR1) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (setukpairinjR) =>
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (kpairsurjEq) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (cartprodpairmemER) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodmempaircEq) =>
% 98.41/13.26 ((
% 98.41/13.26 (cartprodfstpairEq) =>
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% 98.41/13.26 (cartprodsndpairEq) =>
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% 98.41/13.26 ((
% 98.41/13.26 (dpsetconstrEL2) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (app) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (breln1invI) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1invE) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1compprop) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1compI) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1compE) =>
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% 98.41/13.26 (breln1compEex) =>
% 98.41/13.26 ((
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% 98.41/13.26 (breln1unionIR) =>
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% 98.41/13.26 (breln1unionI) =>
% 98.41/13.26 ((
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% 98.41/13.26 (breln1unionEcases) =>
% 98.41/13.26 ((
% 98.41/13.26 (breln1unionCommutes) =>
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% 98.41/13.26 ((
% 98.41/13.26 (woz2W) =>
% 98.41/13.26 ((
% 98.41/13.26 (woz2A) =>
% 98.41/13.26 ((
% 98.41/13.26 (woz2B) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (image1Ex1) =>
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% 98.41/13.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])).
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% 98.41/13.26 (powerset__Cong) =>
% 98.41/13.26 ((
% 98.41/13.26 (setunion__Cong) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (binintersectSubset3) =>
% 98.41/13.26 ((
% 98.41/13.26 (binintersectER) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (binintersectRsub) =>
% 98.41/13.26 ((
% 98.41/13.26 (binintersectSubset4) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (setminusSubset2) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (setminusILneg) =>
% 98.41/13.26 ((
% 98.41/13.26 (setminusIRneg) =>
% 98.41/13.26 ((
% 98.41/13.26 (setminusLsub) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
% 98.41/13.26 (symdiffI1) =>
% 98.41/13.26 ((
% 98.41/13.26 (symdiffI2) =>
% 98.41/13.26 ((
% 98.41/13.26 (symdiffIneg1) =>
% 98.41/13.26 ((
% 98.41/13.26 (symdiffIneg2) =>
% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 ((
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% 98.41/13.26 (cartprodmempair) =>
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% 98.41/13.26 ((
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% 98.41/13.27 ((
% 98.41/13.27 (complementTcontraSubset) =>
% 98.41/13.27 ((
% 98.41/13.27 (binunionTILcontra) =>
% 98.41/13.27 ((
% 98.41/13.27 (binunionTIRcontra) =>
% 98.41/13.27 ((
% 98.41/13.27 (inIntersectImpInUnion) =>
% 98.41/13.27 ((
% 98.41/13.27 (inIntersectImpInUnion2) =>
% 98.41/13.27 ((
% 98.41/13.27 (inIntersectImpInIntersectUnions) =>
% 98.41/13.27 ((
% 98.41/13.27 (intersectInPowersetIntersectUnions) =>
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% 98.41/13.27 (inComplementUnionImpNotIn1) =>
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% 98.41/13.27 (inComplementUnionImpInComplement1) =>
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% 98.41/13.27 ((
% 98.41/13.27 (binunionTEcontra) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2a1) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementUnionInPowersetComplement) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2a2) =>
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% 98.41/13.27 (demorgan1a) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan1b) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan1) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2a) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2b2) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2b) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule0) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule1) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule2) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule3) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule4) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_1) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_2) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_3) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_4) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_5) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1all2) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1SetBreln1) =>
% 98.41/13.27 ((
% 98.41/13.27 (choice2fnsingleton) =>
% 98.41/13.27 ((
% 98.41/13.27 (setOfPairsIsBReln1) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1all1) =>
% 98.41/13.27 ((
% 98.41/13.27 (subbreln1) =>
% 98.41/13.27 ((
% 98.41/13.27 (eqbreln1) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1invprop) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1invI) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1invE) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compprop) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compI) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compE) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compEex) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionprop) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionIL) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionIR) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionI) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionE) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionEcases) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionCommutes) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz2Ex) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz2W) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz2A) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz2B) =>
% 98.41/13.27 ((
% 98.41/13.27 (image1Ex) =>
% 98.41/13.27 ((
% 98.41/13.27 (image1Ex1) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (image1E) =>
% 98.41/13.27 ((
% 98.41/13.27 (image1I) =>
% 98.41/13.27 ((
% 98.41/13.27 (injFuncInInjFuncSet) =>
% 98.41/13.27 ((
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% 98.41/13.27 (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
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% 98.41/13.27 (
% 98.41/13.27 (
% 98.41/13.27 ('#S') @ (
% 98.41/13.27 (
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% 98.41/13.27 (
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% 98.41/13.27 (
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% 98.41/13.27 (
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% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
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% 98.41/13.27 injFuncSet)))))))) @
% 98.41/13.27 (
% 98.41/13.27 (
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% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#C') @ in)))) @
% 98.41/13.27 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])).
% 98.41/13.27 thf(zip_derived_cl58, plain,
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (quantDeMorgan1) =>
% 98.41/13.27 ((
% 98.41/13.27 (quantDeMorgan2) =>
% 98.41/13.27 ((
% 98.41/13.27 (quantDeMorgan3) =>
% 98.41/13.27 ((
% 98.41/13.27 (quantDeMorgan4) =>
% 98.41/13.27 ((
% 98.41/13.27 (prop2setI) =>
% 98.41/13.27 ((
% 98.41/13.27 (prop2set2propI) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (inCongP) =>
% 98.41/13.27 ((
% 98.41/13.27 (in__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (exuE3u) =>
% 98.41/13.27 ((
% 98.41/13.27 (exu__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (setadjoin__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (powerset__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (setunion__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (exuEu) =>
% 98.41/13.27 ((
% 98.41/13.27 (descr__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (dsetconstr__Cong) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (subsetTrans) =>
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (binintersectSubset2) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectSubset3) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectER) =>
% 98.41/13.27 ((
% 98.41/13.27 (disjointsetsI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectRsub) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectSubset4) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectSubset1) =>
% 98.41/13.27 ((
% 98.41/13.27 (bs114d) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusI) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusEL) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusER) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusSubset2) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusERneg) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusELneg) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusILneg) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusIRneg) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusLsub) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusSubset1) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffE) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffI2) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffIneg1) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffIneg2) =>
% 98.41/13.27 ((
% 98.41/13.27 (secondinupair) =>
% 98.41/13.27 ((
% 98.41/13.27 (setukpairIL) =>
% 98.41/13.27 ((
% 98.41/13.27 (setukpairIR) =>
% 98.41/13.27 ((
% 98.41/13.27 (kpairiskpair) =>
% 98.41/13.27 ((
% 98.41/13.27 (kpairp) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (singletoninpowerset) =>
% 98.41/13.27 ((
% 98.41/13.27 (singletoninpowunion) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairset2E) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairsubunion) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairinpowunion) =>
% 98.41/13.27 ((
% 98.41/13.27 (ubforcartprodlem1) =>
% 98.41/13.27 ((
% 98.41/13.27 (ubforcartprodlem2) =>
% 98.41/13.27 ((
% 98.41/13.27 (ubforcartprodlem3) =>
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (cartprodmempair) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (setunionsingleton1) =>
% 98.41/13.27 ((
% 98.41/13.27 (setunionsingleton2) =>
% 98.41/13.27 ((
% 98.41/13.27 (setunionsingleton) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (setukpairinjR12) =>
% 98.41/13.27 ((
% 98.41/13.27 (setukpairinjR1) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (setukpairinjR) =>
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 (iffalseProp2) =>
% 98.41/13.27 ((
% 98.41/13.27 (iftrueProp1) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (binintersectTERcontra) =>
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% 98.41/13.27 (contrasubsetT) =>
% 98.41/13.27 ((
% 98.41/13.27 (contrasubsetT1) =>
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% 98.41/13.27 (contrasubsetT2) =>
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% 98.41/13.27 (contrasubsetT3) =>
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% 98.41/13.27 (doubleComplementE1) =>
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% 98.41/13.27 (doubleComplementSub2) =>
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% 98.41/13.27 (inIntersectImpInUnion2) =>
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% 98.41/13.27 (demorgan2b2) =>
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% 98.41/13.27 (demorgan2b) =>
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% 98.41/13.27 (demorgan2) =>
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (woz13rule2) =>
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% 98.41/13.27 (woz13rule3) =>
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% 98.41/13.27 (woz13rule4) =>
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% 98.41/13.27 (woz1_4) =>
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% 98.41/13.27 (woz1_5) =>
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% 98.41/13.27 (breln1all2) =>
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% 98.41/13.27 (subbreln1) =>
% 98.41/13.27 ((
% 98.41/13.27 (eqbreln1) =>
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% 98.41/13.27 ((
% 98.41/13.27 (breln1invI) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1invE) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compprop) =>
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% 98.41/13.27 (breln1compI) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compE) =>
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% 98.41/13.27 (breln1compEex) =>
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% 98.41/13.27 ((
% 98.41/13.27 (breln1unionI) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionE) =>
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% 98.41/13.27 (breln1unionEcases) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionCommutes) =>
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% 98.41/13.27 (woz2W) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (image1E) =>
% 98.41/13.27 ((
% 98.41/13.27 (image1I) =>
% 98.41/13.27 ((
% 98.41/13.27 (injFuncInInjFuncSet) =>
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% 98.41/13.27 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])).
% 98.41/13.27 thf(zip_derived_cl64, plain,
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% 98.41/13.27 ((
% 98.41/13.27 (descr__Cong) =>
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 (dpsetconstrSub) =>
% 98.41/13.27 ((
% 98.41/13.27 (setOfPairsIsBReln) =>
% 98.41/13.27 ((
% 98.41/13.27 (dpsetconstrERa) =>
% 98.41/13.27 ((
% 98.41/13.27 (dpsetconstrEL1) =>
% 98.41/13.27 ((
% 98.41/13.27 (dpsetconstrEL2) =>
% 98.41/13.27 ((
% 98.41/13.27 (dpsetconstrER) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcImageSingleton) =>
% 98.41/13.27 ((
% 98.41/13.27 (apProp) =>
% 98.41/13.27 ((
% 98.41/13.27 (app) =>
% 98.41/13.27 ((
% 98.41/13.27 (infuncsetfunc) =>
% 98.41/13.27 ((
% 98.41/13.27 (ap2p) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcinfuncset) =>
% 98.41/13.27 ((
% 98.41/13.27 (lamProp) =>
% 98.41/13.27 ((
% 98.41/13.27 (lamp) =>
% 98.41/13.27 ((
% 98.41/13.27 (lam2p) =>
% 98.41/13.27 ((
% 98.41/13.27 (brelnall1) =>
% 98.41/13.27 ((
% 98.41/13.27 (brelnall2) =>
% 98.41/13.27 ((
% 98.41/13.27 (ex1E2) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcGraphProp1) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcGraphProp3) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcGraphProp2) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcextLem) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcGraphProp4) =>
% 98.41/13.27 ((
% 98.41/13.27 (subbreln) =>
% 98.41/13.27 ((
% 98.41/13.27 (eqbreln) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcext) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcext2) =>
% 98.41/13.27 ((
% 98.41/13.27 (ap2apEq1) =>
% 98.41/13.27 ((
% 98.41/13.27 (ap2apEq2) =>
% 98.41/13.27 ((
% 98.41/13.27 (beta1) =>
% 98.41/13.27 ((
% 98.41/13.27 (eta1) =>
% 98.41/13.27 ((
% 98.41/13.27 (lam2lamEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (beta2) =>
% 98.41/13.27 ((
% 98.41/13.27 (eta2) =>
% 98.41/13.27 ((
% 98.41/13.27 (iffalseProp1) =>
% 98.41/13.27 ((
% 98.41/13.27 (iffalseProp2) =>
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% 98.41/13.27 (iftrueProp1) =>
% 98.41/13.27 ((
% 98.41/13.27 (iftrueProp2) =>
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% 98.41/13.27 (ifp) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (powersetT_lem) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (complementT_lem) =>
% 98.41/13.27 ((
% 98.41/13.27 (setextT) =>
% 98.41/13.27 ((
% 98.41/13.27 (subsetTI) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (powersetTE1) =>
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% 98.41/13.27 (complementTI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementTE1) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectTELcontra) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectTERcontra) =>
% 98.41/13.27 ((
% 98.41/13.27 (contrasubsetT) =>
% 98.41/13.27 ((
% 98.41/13.27 (contrasubsetT1) =>
% 98.41/13.27 ((
% 98.41/13.27 (contrasubsetT2) =>
% 98.41/13.27 ((
% 98.41/13.27 (contrasubsetT3) =>
% 98.41/13.27 ((
% 98.41/13.27 (doubleComplementI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (doubleComplementE1) =>
% 98.41/13.27 ((
% 98.41/13.27 (doubleComplementSub1) =>
% 98.41/13.27 ((
% 98.41/13.27 (doubleComplementSub2) =>
% 98.41/13.27 ((
% 98.41/13.27 (doubleComplementEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementTnotintersectT) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementImpComplementIntersect) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementSubsetComplementIntersect) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementInPowersetComplementIntersect) =>
% 98.41/13.27 ((
% 98.41/13.27 (contraSubsetComplement) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementTcontraSubset) =>
% 98.41/13.27 ((
% 98.41/13.27 (binunionTILcontra) =>
% 98.41/13.27 ((
% 98.41/13.27 (binunionTIRcontra) =>
% 98.41/13.27 ((
% 98.41/13.27 (inIntersectImpInUnion) =>
% 98.41/13.27 ((
% 98.41/13.27 (inIntersectImpInUnion2) =>
% 98.41/13.27 ((
% 98.41/13.27 (inIntersectImpInIntersectUnions) =>
% 98.41/13.27 ((
% 98.41/13.27 (intersectInPowersetIntersectUnions) =>
% 98.41/13.27 ((
% 98.41/13.27 (inComplementUnionImpNotIn1) =>
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% 98.41/13.27 (inComplementUnionImpInComplement1) =>
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% 98.41/13.27 ((
% 98.41/13.27 (binunionTEcontra) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2a1) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementUnionInPowersetComplement) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2a2) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan1a) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan1b) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan1) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2a) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2b2) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2b) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule0) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule1) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule2) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule3) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule4) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_1) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_2) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_3) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_4) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_5) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1all2) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1SetBreln1) =>
% 98.41/13.27 ((
% 98.41/13.27 (choice2fnsingleton) =>
% 98.41/13.27 ((
% 98.41/13.27 (setOfPairsIsBReln1) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1all1) =>
% 98.41/13.27 ((
% 98.41/13.27 (subbreln1) =>
% 98.41/13.27 ((
% 98.41/13.27 (eqbreln1) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1invprop) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1invI) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1invE) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compprop) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compI) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compE) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compEex) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionprop) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionIL) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionIR) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionI) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionE) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionEcases) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionCommutes) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz2Ex) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz2W) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz2A) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz2B) =>
% 98.41/13.27 ((
% 98.41/13.27 (image1Ex) =>
% 98.41/13.27 ((
% 98.41/13.27 (image1Ex1) =>
% 98.41/13.27 ((
% 98.41/13.27 (image1Equiv) =>
% 98.41/13.27 ((
% 98.41/13.27 (image1E) =>
% 98.41/13.27 ((
% 98.41/13.27 (image1I) =>
% 98.41/13.27 ((
% 98.41/13.27 (injFuncInInjFuncSet) =>
% 98.41/13.27 ((
% 98.41/13.27 (!!) @ (
% 98.41/13.27 (('#B') @ (
% 98.41/13.27 !!) @
% 98.41/13.27 (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 !!))) @
% 98.41/13.27 (
% 98.41/13.27 (
% 98.41/13.27 ('#S') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 '#S') @
% 98.41/13.27 (
% 98.41/13.27 (
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% 98.41/13.27 (
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% 98.41/13.27 (
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% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 =>))))) @
% 98.41/13.27 (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#C') @ in)))) @
% 98.41/13.27 injFuncSet)))))))) @
% 98.41/13.27 (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#C') @ in)))) @
% 98.41/13.27 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])).
% 98.41/13.27 thf(zip_derived_cl71, plain,
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (quantDeMorgan2) =>
% 98.41/13.27 ((
% 98.41/13.27 (quantDeMorgan3) =>
% 98.41/13.27 ((
% 98.41/13.27 (quantDeMorgan4) =>
% 98.41/13.27 ((
% 98.41/13.27 (prop2setI) =>
% 98.41/13.27 ((
% 98.41/13.27 (prop2set2propI) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 (in__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (exuE3u) =>
% 98.41/13.27 ((
% 98.41/13.27 (exu__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (setadjoin__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (powerset__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (setunion__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (exuEu) =>
% 98.41/13.27 ((
% 98.41/13.27 (descr__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (dsetconstr__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (subsetI1) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (binintersectER) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (binintersectRsub) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectSubset4) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectSubset1) =>
% 98.41/13.27 ((
% 98.41/13.27 (bs114d) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusI) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusEL) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusER) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusSubset2) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusERneg) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusELneg) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusILneg) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusIRneg) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusLsub) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusSubset1) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffE) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffI2) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffIneg1) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffIneg2) =>
% 98.41/13.27 ((
% 98.41/13.27 (secondinupair) =>
% 98.41/13.27 ((
% 98.41/13.27 (setukpairIL) =>
% 98.41/13.27 ((
% 98.41/13.27 (setukpairIR) =>
% 98.41/13.27 ((
% 98.41/13.27 (kpairiskpair) =>
% 98.41/13.27 ((
% 98.41/13.27 (kpairp) =>
% 98.41/13.27 ((
% 98.41/13.27 (singletonsubset) =>
% 98.41/13.27 ((
% 98.41/13.27 (singletoninpowerset) =>
% 98.41/13.27 ((
% 98.41/13.27 (singletoninpowunion) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairset2E) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairsubunion) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairinpowunion) =>
% 98.41/13.27 ((
% 98.41/13.27 (ubforcartprodlem1) =>
% 98.41/13.27 ((
% 98.41/13.27 (ubforcartprodlem2) =>
% 98.41/13.27 ((
% 98.41/13.27 (ubforcartprodlem3) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodpairin) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (cartprodmempair) =>
% 98.41/13.27 ((
% 98.41/13.27 (setunionE2) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (kfstpairEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodfstin) =>
% 98.41/13.27 ((
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% 98.41/13.27 (setukpairinjR1) =>
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% 98.41/13.27 (setukpairinjR) =>
% 98.41/13.27 ((
% 98.41/13.27 (ksndsingleton) =>
% 98.41/13.27 ((
% 98.41/13.27 (ksndpairEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (kpairsurjEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodsndin) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodpairmemEL) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodpairmemER) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodmempaircEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodfstpairEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodsndpairEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodpairsurjEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (dpsetconstrI) =>
% 98.41/13.27 ((
% 98.41/13.27 (dpsetconstrSub) =>
% 98.41/13.27 ((
% 98.41/13.27 (setOfPairsIsBReln) =>
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% 98.41/13.27 (dpsetconstrERa) =>
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% 98.41/13.27 ((
% 98.41/13.27 (dpsetconstrEL2) =>
% 98.41/13.27 ((
% 98.41/13.27 (dpsetconstrER) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcImageSingleton) =>
% 98.41/13.27 ((
% 98.41/13.27 (apProp) =>
% 98.41/13.27 ((
% 98.41/13.27 (app) =>
% 98.41/13.27 ((
% 98.41/13.27 (infuncsetfunc) =>
% 98.41/13.27 ((
% 98.41/13.27 (ap2p) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcinfuncset) =>
% 98.41/13.27 ((
% 98.41/13.27 (lamProp) =>
% 98.41/13.27 ((
% 98.41/13.27 (lamp) =>
% 98.41/13.27 ((
% 98.41/13.27 (lam2p) =>
% 98.41/13.27 ((
% 98.41/13.27 (brelnall1) =>
% 98.41/13.27 ((
% 98.41/13.27 (brelnall2) =>
% 98.41/13.27 ((
% 98.41/13.27 (ex1E2) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcGraphProp1) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcGraphProp3) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcGraphProp2) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (funcGraphProp4) =>
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% 98.41/13.27 (eqbreln) =>
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% 98.41/13.27 (funcext2) =>
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% 98.41/13.27 ((
% 98.41/13.27 (ap2apEq2) =>
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% 98.41/13.27 (beta1) =>
% 98.41/13.27 ((
% 98.41/13.27 (eta1) =>
% 98.41/13.27 ((
% 98.41/13.27 (lam2lamEq) =>
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% 98.41/13.27 (beta2) =>
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (binintersectTERcontra) =>
% 98.41/13.27 ((
% 98.41/13.27 (contrasubsetT) =>
% 98.41/13.27 ((
% 98.41/13.27 (contrasubsetT1) =>
% 98.41/13.27 ((
% 98.41/13.27 (contrasubsetT2) =>
% 98.41/13.27 ((
% 98.41/13.27 (contrasubsetT3) =>
% 98.41/13.27 ((
% 98.41/13.27 (doubleComplementI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (doubleComplementE1) =>
% 98.41/13.27 ((
% 98.41/13.27 (doubleComplementSub1) =>
% 98.41/13.27 ((
% 98.41/13.27 (doubleComplementSub2) =>
% 98.41/13.27 ((
% 98.41/13.27 (doubleComplementEq) =>
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% 98.41/13.27 (complementTnotintersectT) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementImpComplementIntersect) =>
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% 98.41/13.27 (complementSubsetComplementIntersect) =>
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% 98.41/13.27 (complementInPowersetComplementIntersect) =>
% 98.41/13.27 ((
% 98.41/13.27 (contraSubsetComplement) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementTcontraSubset) =>
% 98.41/13.27 ((
% 98.41/13.27 (binunionTILcontra) =>
% 98.41/13.27 ((
% 98.41/13.27 (binunionTIRcontra) =>
% 98.41/13.27 ((
% 98.41/13.27 (inIntersectImpInUnion) =>
% 98.41/13.27 ((
% 98.41/13.27 (inIntersectImpInUnion2) =>
% 98.41/13.27 ((
% 98.41/13.27 (inIntersectImpInIntersectUnions) =>
% 98.41/13.27 ((
% 98.41/13.27 (intersectInPowersetIntersectUnions) =>
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% 98.41/13.27 ((
% 98.41/13.27 (binunionTEcontra) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (complementUnionInPowersetComplement) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2a2) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan1a) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan1b) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan1) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2a) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2b2) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2b) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule0) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule1) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule2) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule3) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule4) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_1) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_2) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_3) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_4) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_5) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1all2) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1SetBreln1) =>
% 98.41/13.27 ((
% 98.41/13.27 (choice2fnsingleton) =>
% 98.41/13.27 ((
% 98.41/13.27 (setOfPairsIsBReln1) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1all1) =>
% 98.41/13.27 ((
% 98.41/13.27 (subbreln1) =>
% 98.41/13.27 ((
% 98.41/13.27 (eqbreln1) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1invprop) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1invI) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1invE) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compprop) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compI) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compE) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compEex) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionprop) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionIL) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionIR) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionI) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionE) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionEcases) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionCommutes) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (woz2A) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz2B) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (image1Ex1) =>
% 98.41/13.27 ((
% 98.41/13.27 (image1Equiv) =>
% 98.41/13.27 ((
% 98.41/13.27 (image1E) =>
% 98.41/13.27 ((
% 98.41/13.27 (image1I) =>
% 98.41/13.27 ((
% 98.41/13.27 (injFuncInInjFuncSet) =>
% 98.41/13.27 ((
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% 98.41/13.27 (('#B') @ (
% 98.41/13.27 !!) @
% 98.41/13.27 (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 !!))) @
% 98.41/13.27 (
% 98.41/13.27 (
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% 98.41/13.27 (
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% 98.41/13.27 (
% 98.41/13.27 (
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% 98.41/13.27 (
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% 98.41/13.27 (
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% 98.41/13.27 =>))))) @
% 98.41/13.27 (
% 98.41/13.27 (
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% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
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% 98.41/13.27 injFuncSet)))))))) @
% 98.41/13.27 (
% 98.41/13.27 (
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% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#C') @ in)))) @
% 98.41/13.27 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])).
% 98.41/13.27 thf(zip_derived_cl79, plain,
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (quantDeMorgan4) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (prop2set2propI) =>
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (exu__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (setadjoin__Cong) =>
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% 98.41/13.27 (powerset__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (setunion__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (exuEu) =>
% 98.41/13.27 ((
% 98.41/13.27 (descr__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (dsetconstr__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (subsetI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (eqimpsubset2) =>
% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (binintersectSubset5) =>
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% 98.41/13.27 ((
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% 98.41/13.27 ((
% 98.41/13.27 (binintersectSubset4) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectSubset1) =>
% 98.41/13.27 ((
% 98.41/13.27 (bs114d) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusI) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusEL) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusER) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusSubset2) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusERneg) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusELneg) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusILneg) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusIRneg) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusLsub) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusSubset1) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffE) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffI2) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffIneg1) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffIneg2) =>
% 98.41/13.27 ((
% 98.41/13.27 (secondinupair) =>
% 98.41/13.27 ((
% 98.41/13.27 (setukpairIL) =>
% 98.41/13.27 ((
% 98.41/13.27 (setukpairIR) =>
% 98.41/13.27 ((
% 98.41/13.27 (kpairiskpair) =>
% 98.41/13.27 ((
% 98.41/13.27 (kpairp) =>
% 98.41/13.27 ((
% 98.41/13.27 (singletonsubset) =>
% 98.41/13.27 ((
% 98.41/13.27 (singletoninpowerset) =>
% 98.41/13.27 ((
% 98.41/13.27 (singletoninpowunion) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairset2E) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairsubunion) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairinpowunion) =>
% 98.41/13.27 ((
% 98.41/13.27 (ubforcartprodlem1) =>
% 98.41/13.27 ((
% 98.41/13.27 (ubforcartprodlem2) =>
% 98.41/13.27 ((
% 98.41/13.27 (ubforcartprodlem3) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodpairin) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodmempair1) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodmempair) =>
% 98.41/13.27 ((
% 98.41/13.27 (setunionE2) =>
% 98.41/13.27 ((
% 98.41/13.27 (setunionsingleton1) =>
% 98.41/13.27 ((
% 98.41/13.27 (setunionsingleton2) =>
% 98.41/13.27 ((
% 98.41/13.27 (setunionsingleton) =>
% 98.41/13.27 ((
% 98.41/13.27 (singletonprop) =>
% 98.41/13.27 ((
% 98.41/13.27 (ex1E1) =>
% 98.41/13.27 ((
% 98.41/13.27 (ex1I) =>
% 98.41/13.27 ((
% 98.41/13.27 (ex1I2) =>
% 98.41/13.27 ((
% 98.41/13.27 (singletonsuniq) =>
% 98.41/13.27 ((
% 98.41/13.27 (setukpairinjL1) =>
% 98.41/13.27 ((
% 98.41/13.27 (kfstsingleton) =>
% 98.41/13.27 ((
% 98.41/13.27 (theprop) =>
% 98.41/13.27 ((
% 98.41/13.27 (kfstpairEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodfstin) =>
% 98.41/13.27 ((
% 98.41/13.27 (setukpairinjL2) =>
% 98.41/13.27 ((
% 98.41/13.27 (setukpairinjL) =>
% 98.41/13.27 ((
% 98.41/13.27 (setukpairinjR11) =>
% 98.41/13.27 ((
% 98.41/13.27 (setukpairinjR12) =>
% 98.41/13.27 ((
% 98.41/13.27 (setukpairinjR1) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairequniteq) =>
% 98.41/13.27 ((
% 98.41/13.27 (setukpairinjR2) =>
% 98.41/13.27 ((
% 98.41/13.27 (setukpairinjR) =>
% 98.41/13.27 ((
% 98.41/13.27 (ksndsingleton) =>
% 98.41/13.27 ((
% 98.41/13.27 (ksndpairEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (kpairsurjEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodsndin) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodpairmemEL) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodpairmemER) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodmempaircEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodfstpairEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodsndpairEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodpairsurjEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (dpsetconstrI) =>
% 98.41/13.27 ((
% 98.41/13.27 (dpsetconstrSub) =>
% 98.41/13.27 ((
% 98.41/13.27 (setOfPairsIsBReln) =>
% 98.41/13.27 ((
% 98.41/13.27 (dpsetconstrERa) =>
% 98.41/13.27 ((
% 98.41/13.27 (dpsetconstrEL1) =>
% 98.41/13.27 ((
% 98.41/13.27 (dpsetconstrEL2) =>
% 98.41/13.27 ((
% 98.41/13.27 (dpsetconstrER) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcImageSingleton) =>
% 98.41/13.27 ((
% 98.41/13.27 (apProp) =>
% 98.41/13.27 ((
% 98.41/13.27 (app) =>
% 98.41/13.27 ((
% 98.41/13.27 (infuncsetfunc) =>
% 98.41/13.27 ((
% 98.41/13.27 (ap2p) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcinfuncset) =>
% 98.41/13.27 ((
% 98.41/13.27 (lamProp) =>
% 98.41/13.27 ((
% 98.41/13.27 (lamp) =>
% 98.41/13.27 ((
% 98.41/13.27 (lam2p) =>
% 98.41/13.27 ((
% 98.41/13.27 (brelnall1) =>
% 98.41/13.27 ((
% 98.41/13.27 (brelnall2) =>
% 98.41/13.27 ((
% 98.41/13.27 (ex1E2) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcGraphProp1) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcGraphProp3) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcGraphProp2) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcextLem) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcGraphProp4) =>
% 98.41/13.27 ((
% 98.41/13.27 (subbreln) =>
% 98.41/13.27 ((
% 98.41/13.27 (eqbreln) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcext) =>
% 98.41/13.27 ((
% 98.41/13.27 (funcext2) =>
% 98.41/13.27 ((
% 98.41/13.27 (ap2apEq1) =>
% 98.41/13.27 ((
% 98.41/13.27 (ap2apEq2) =>
% 98.41/13.27 ((
% 98.41/13.27 (beta1) =>
% 98.41/13.27 ((
% 98.41/13.27 (eta1) =>
% 98.41/13.27 ((
% 98.41/13.27 (lam2lamEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (beta2) =>
% 98.41/13.27 ((
% 98.41/13.27 (eta2) =>
% 98.41/13.27 ((
% 98.41/13.27 (iffalseProp1) =>
% 98.41/13.27 ((
% 98.41/13.27 (iffalseProp2) =>
% 98.41/13.27 ((
% 98.41/13.27 (iftrueProp1) =>
% 98.41/13.27 ((
% 98.41/13.27 (iftrueProp2) =>
% 98.41/13.27 ((
% 98.41/13.27 (ifSingleton) =>
% 98.41/13.27 ((
% 98.41/13.27 (ifp) =>
% 98.41/13.27 ((
% 98.41/13.27 (theeq) =>
% 98.41/13.27 ((
% 98.41/13.27 (iftrue) =>
% 98.41/13.27 ((
% 98.41/13.27 (iffalse) =>
% 98.41/13.27 ((
% 98.41/13.27 (iftrueorfalse) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectT_lem) =>
% 98.41/13.27 ((
% 98.41/13.27 (binunionT_lem) =>
% 98.41/13.27 ((
% 98.41/13.27 (powersetT_lem) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusT_lem) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementT_lem) =>
% 98.41/13.27 ((
% 98.41/13.27 (setextT) =>
% 98.41/13.27 ((
% 98.41/13.27 (subsetTI) =>
% 98.41/13.27 ((
% 98.41/13.27 (powersetTI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (powersetTE1) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementTI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementTE1) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectTELcontra) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectTERcontra) =>
% 98.41/13.27 ((
% 98.41/13.27 (contrasubsetT) =>
% 98.41/13.27 ((
% 98.41/13.27 (contrasubsetT1) =>
% 98.41/13.27 ((
% 98.41/13.27 (contrasubsetT2) =>
% 98.41/13.27 ((
% 98.41/13.27 (contrasubsetT3) =>
% 98.41/13.27 ((
% 98.41/13.27 (doubleComplementI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (doubleComplementE1) =>
% 98.41/13.27 ((
% 98.41/13.27 (doubleComplementSub1) =>
% 98.41/13.27 ((
% 98.41/13.27 (doubleComplementSub2) =>
% 98.41/13.27 ((
% 98.41/13.27 (doubleComplementEq) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementTnotintersectT) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementImpComplementIntersect) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementSubsetComplementIntersect) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementInPowersetComplementIntersect) =>
% 98.41/13.27 ((
% 98.41/13.27 (contraSubsetComplement) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementTcontraSubset) =>
% 98.41/13.27 ((
% 98.41/13.27 (binunionTILcontra) =>
% 98.41/13.27 ((
% 98.41/13.27 (binunionTIRcontra) =>
% 98.41/13.27 ((
% 98.41/13.27 (inIntersectImpInUnion) =>
% 98.41/13.27 ((
% 98.41/13.27 (inIntersectImpInUnion2) =>
% 98.41/13.27 ((
% 98.41/13.27 (inIntersectImpInIntersectUnions) =>
% 98.41/13.27 ((
% 98.41/13.27 (intersectInPowersetIntersectUnions) =>
% 98.41/13.27 ((
% 98.41/13.27 (inComplementUnionImpNotIn1) =>
% 98.41/13.27 ((
% 98.41/13.27 (inComplementUnionImpInComplement1) =>
% 98.41/13.27 ((
% 98.41/13.27 (binunionTE) =>
% 98.41/13.27 ((
% 98.41/13.27 (binunionTEcontra) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2a1) =>
% 98.41/13.27 ((
% 98.41/13.27 (complementUnionInPowersetComplement) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2a2) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan1a) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan1b) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan1) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2a) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2b2) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2b) =>
% 98.41/13.27 ((
% 98.41/13.27 (demorgan2) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule0) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule1) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule2) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule3) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz13rule4) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_1) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_2) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_3) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_4) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz1_5) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1all2) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1SetBreln1) =>
% 98.41/13.27 ((
% 98.41/13.27 (choice2fnsingleton) =>
% 98.41/13.27 ((
% 98.41/13.27 (setOfPairsIsBReln1) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1all1) =>
% 98.41/13.27 ((
% 98.41/13.27 (subbreln1) =>
% 98.41/13.27 ((
% 98.41/13.27 (eqbreln1) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1invprop) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1invI) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1invE) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compprop) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compI) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compE) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1compEex) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionprop) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionIL) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionIR) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionI) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionE) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionEcases) =>
% 98.41/13.27 ((
% 98.41/13.27 (breln1unionCommutes) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz2Ex) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz2W) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz2A) =>
% 98.41/13.27 ((
% 98.41/13.27 (woz2B) =>
% 98.41/13.27 ((
% 98.41/13.27 (image1Ex) =>
% 98.41/13.27 ((
% 98.41/13.27 (image1Ex1) =>
% 98.41/13.27 ((
% 98.41/13.27 (image1Equiv) =>
% 98.41/13.27 ((
% 98.41/13.27 (image1E) =>
% 98.41/13.27 ((
% 98.41/13.27 (image1I) =>
% 98.41/13.27 ((
% 98.41/13.27 (injFuncInInjFuncSet) =>
% 98.41/13.27 ((
% 98.41/13.27 (!!) @ (
% 98.41/13.27 (('#B') @ (
% 98.41/13.27 !!) @
% 98.41/13.27 (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 !!))) @
% 98.41/13.27 (
% 98.41/13.27 (
% 98.41/13.27 ('#S') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 '#S') @
% 98.41/13.27 (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 '#S'))) @
% 98.41/13.27 (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 =>))))) @
% 98.41/13.27 (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#C') @ in)))) @
% 98.41/13.27 injFuncSet)))))))) @
% 98.41/13.27 (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#B') @ (
% 98.41/13.27 (
% 98.41/13.27 ('#C') @ in)))) @
% 98.41/13.27 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])).
% 98.41/13.27 thf(zip_derived_cl89, plain,
% 98.41/13.27 (~ (((dsetconstrER) =>
% 98.41/13.27 (((exuE1) =>
% 98.41/13.27 (((prop2setE) =>
% 98.41/13.27 (((emptysetE) =>
% 98.41/13.27 (((emptysetimpfalse) =>
% 98.41/13.27 (((notinemptyset) =>
% 98.41/13.27 (((exuE3e) =>
% 98.41/13.27 (((setext) =>
% 98.41/13.27 (((emptyI) =>
% 98.41/13.27 (((noeltsimpempty) =>
% 98.41/13.27 (((setbeta) =>
% 98.41/13.27 (((nonemptyE1) =>
% 98.41/13.27 (((nonemptyI) =>
% 98.41/13.27 (((nonemptyI1) =>
% 98.41/13.27 (((setadjoinIL) =>
% 98.41/13.27 (((in @ emptyset @
% 98.41/13.27 (setadjoin @ emptyset @ emptyset)) =>
% 98.41/13.27 (((setadjoinIR) =>
% 98.41/13.27 (((setadjoinE) =>
% 98.41/13.27 (((setadjoinOr) =>
% 98.41/13.27 (((setoftrueEq) =>
% 98.41/13.27 (((powersetI) =>
% 98.41/13.27 (((emptyinPowerset) =>
% 98.41/13.27 (((emptyInPowerset) =>
% 98.41/13.27 (((powersetE) =>
% 98.41/13.27 (((setunionI) =>
% 98.41/13.27 (((setunionE) =>
% 98.41/13.27 (((subPowSU) =>
% 98.41/13.27 (((exuE2) =>
% 98.41/13.27 (((nonemptyImpWitness) =>
% 98.41/13.27 (((uniqinunit) =>
% 98.41/13.27 ((
% 98.41/13.27 (notinsingleton) =>
% 98.41/13.27 ((
% 98.41/13.27 (eqinunit) =>
% 98.41/13.27 ((
% 98.41/13.27 (singletonsswitch) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairsetE) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairsetIL) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairsetIR) =>
% 98.41/13.27 ((
% 98.41/13.27 (emptyE1) =>
% 98.41/13.27 ((
% 98.41/13.27 (vacuousDall) =>
% 98.41/13.27 ((
% 98.41/13.27 (quantDeMorgan1) =>
% 98.41/13.27 ((
% 98.41/13.27 (quantDeMorgan2) =>
% 98.41/13.27 ((
% 98.41/13.27 (quantDeMorgan3) =>
% 98.41/13.27 ((
% 98.41/13.27 (quantDeMorgan4) =>
% 98.41/13.27 ((
% 98.41/13.27 (prop2setI) =>
% 98.41/13.27 ((
% 98.41/13.27 (prop2set2propI) =>
% 98.41/13.27 ((
% 98.41/13.27 (notdexE) =>
% 98.41/13.27 ((
% 98.41/13.27 (notdallE) =>
% 98.41/13.27 ((
% 98.41/13.27 (exuI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (exuI3) =>
% 98.41/13.27 ((
% 98.41/13.27 (exuI2) =>
% 98.41/13.27 ((
% 98.41/13.27 (inCongP) =>
% 98.41/13.27 ((
% 98.41/13.27 (in__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (exuE3u) =>
% 98.41/13.27 ((
% 98.41/13.27 (exu__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (setadjoin__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (powerset__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (setunion__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (exuEu) =>
% 98.41/13.27 ((
% 98.41/13.27 (descr__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (dsetconstr__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (subsetI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (eqimpsubset2) =>
% 98.41/13.27 ((
% 98.41/13.27 (eqimpsubset1) =>
% 98.41/13.27 ((
% 98.41/13.27 (subsetI2) =>
% 98.41/13.27 ((
% 98.41/13.27 (emptysetsubset) =>
% 98.41/13.27 ((
% 98.41/13.27 (subsetE) =>
% 98.41/13.27 ((
% 98.41/13.27 (subsetE2) =>
% 98.41/13.27 ((
% 98.41/13.27 (notsubsetI) =>
% 98.41/13.27 ((
% 98.41/13.27 (notequalI1) =>
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% 98.41/13.27 (
% 98.41/13.27 ('#C') @ in)))) @
% 98.41/13.27 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl89])).
% 98.41/13.27 thf(zip_derived_cl123, plain,
% 98.41/13.27 (~ (((prop2setE) =>
% 98.41/13.27 (((emptysetE) =>
% 98.41/13.27 (((emptysetimpfalse) =>
% 98.41/13.27 (((notinemptyset) =>
% 98.41/13.27 (((exuE3e) =>
% 98.41/13.27 (((setext) =>
% 98.41/13.27 (((emptyI) =>
% 98.41/13.27 (((noeltsimpempty) =>
% 98.41/13.27 (((setbeta) =>
% 98.41/13.27 (((nonemptyE1) =>
% 98.41/13.27 (((nonemptyI) =>
% 98.41/13.27 (((nonemptyI1) =>
% 98.41/13.27 (((setadjoinIL) =>
% 98.41/13.27 (((in @ emptyset @
% 98.41/13.27 (setadjoin @ emptyset @ emptyset)) =>
% 98.41/13.27 (((setadjoinIR) =>
% 98.41/13.27 (((setadjoinE) =>
% 98.41/13.27 (((setadjoinOr) =>
% 98.41/13.27 (((setoftrueEq) =>
% 98.41/13.27 (((powersetI) =>
% 98.41/13.27 (((emptyinPowerset) =>
% 98.41/13.27 (((emptyInPowerset) =>
% 98.41/13.27 (((powersetE) =>
% 98.41/13.27 (((setunionI) =>
% 98.41/13.27 (((setunionE) =>
% 98.41/13.27 (((subPowSU) =>
% 98.41/13.27 (((exuE2) =>
% 98.41/13.27 (((nonemptyImpWitness) =>
% 98.41/13.27 (((uniqinunit) =>
% 98.41/13.27 (((notinsingleton) =>
% 98.41/13.27 (((eqinunit) =>
% 98.41/13.27 ((
% 98.41/13.27 (singletonsswitch) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairsetE) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairsetIL) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairsetIR) =>
% 98.41/13.27 ((
% 98.41/13.27 (emptyE1) =>
% 98.41/13.27 ((
% 98.41/13.27 (vacuousDall) =>
% 98.41/13.27 ((
% 98.41/13.27 (quantDeMorgan1) =>
% 98.41/13.27 ((
% 98.41/13.27 (quantDeMorgan2) =>
% 98.41/13.27 ((
% 98.41/13.27 (quantDeMorgan3) =>
% 98.41/13.27 ((
% 98.41/13.27 (quantDeMorgan4) =>
% 98.41/13.27 ((
% 98.41/13.27 (prop2setI) =>
% 98.41/13.27 ((
% 98.41/13.27 (prop2set2propI) =>
% 98.41/13.27 ((
% 98.41/13.27 (notdexE) =>
% 98.41/13.27 ((
% 98.41/13.27 (notdallE) =>
% 98.41/13.27 ((
% 98.41/13.27 (exuI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (exuI3) =>
% 98.41/13.27 ((
% 98.41/13.27 (exuI2) =>
% 98.41/13.27 ((
% 98.41/13.27 (inCongP) =>
% 98.41/13.27 ((
% 98.41/13.27 (in__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (exuE3u) =>
% 98.41/13.27 ((
% 98.41/13.27 (exu__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (setadjoin__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (powerset__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (setunion__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (exuEu) =>
% 98.41/13.27 ((
% 98.41/13.27 (descr__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (dsetconstr__Cong) =>
% 98.41/13.27 ((
% 98.41/13.27 (subsetI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (eqimpsubset2) =>
% 98.41/13.27 ((
% 98.41/13.27 (eqimpsubset1) =>
% 98.41/13.27 ((
% 98.41/13.27 (subsetI2) =>
% 98.41/13.27 ((
% 98.41/13.27 (emptysetsubset) =>
% 98.41/13.27 ((
% 98.41/13.27 (subsetE) =>
% 98.41/13.27 ((
% 98.41/13.27 (subsetE2) =>
% 98.41/13.27 ((
% 98.41/13.27 (notsubsetI) =>
% 98.41/13.27 ((
% 98.41/13.27 (notequalI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (notequalI2) =>
% 98.41/13.27 ((
% 98.41/13.27 (subsetRefl) =>
% 98.41/13.27 ((
% 98.41/13.27 (subsetTrans) =>
% 98.41/13.27 ((
% 98.41/13.27 (setadjoinSub) =>
% 98.41/13.27 ((
% 98.41/13.27 (setadjoinSub2) =>
% 98.41/13.27 ((
% 98.41/13.27 (subset2powerset) =>
% 98.41/13.27 ((
% 98.41/13.27 (setextsub) =>
% 98.41/13.27 ((
% 98.41/13.27 (subsetemptysetimpeq) =>
% 98.41/13.27 ((
% 98.41/13.27 (powersetI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (powersetE1) =>
% 98.41/13.27 ((
% 98.41/13.27 (inPowerset) =>
% 98.41/13.27 ((
% 98.41/13.27 (powersetsubset) =>
% 98.41/13.27 ((
% 98.41/13.27 (sepInPowerset) =>
% 98.41/13.27 ((
% 98.41/13.27 (sepSubset) =>
% 98.41/13.27 ((
% 98.41/13.27 (binunionIL) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairset2IR) =>
% 98.41/13.27 ((
% 98.41/13.27 (binunionIR) =>
% 98.41/13.27 ((
% 98.41/13.27 (binunionEcases) =>
% 98.41/13.27 ((
% 98.41/13.27 (binunionE) =>
% 98.41/13.27 ((
% 98.41/13.27 (binunionLsub) =>
% 98.41/13.27 ((
% 98.41/13.27 (binunionRsub) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectI) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectSubset5) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectEL) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectLsub) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectSubset2) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectSubset3) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectER) =>
% 98.41/13.27 ((
% 98.41/13.27 (disjointsetsI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectRsub) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectSubset4) =>
% 98.41/13.27 ((
% 98.41/13.27 (binintersectSubset1) =>
% 98.41/13.27 ((
% 98.41/13.27 (bs114d) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusI) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusEL) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusER) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusSubset2) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusERneg) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusELneg) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusILneg) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusIRneg) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusLsub) =>
% 98.41/13.27 ((
% 98.41/13.27 (setminusSubset1) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffE) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffI1) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffI2) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffIneg1) =>
% 98.41/13.27 ((
% 98.41/13.27 (symdiffIneg2) =>
% 98.41/13.27 ((
% 98.41/13.27 (secondinupair) =>
% 98.41/13.27 ((
% 98.41/13.27 (setukpairIL) =>
% 98.41/13.27 ((
% 98.41/13.27 (setukpairIR) =>
% 98.41/13.27 ((
% 98.41/13.27 (kpairiskpair) =>
% 98.41/13.27 ((
% 98.41/13.27 (kpairp) =>
% 98.41/13.27 ((
% 98.41/13.27 (singletonsubset) =>
% 98.41/13.27 ((
% 98.41/13.27 (singletoninpowerset) =>
% 98.41/13.27 ((
% 98.41/13.27 (singletoninpowunion) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairset2E) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairsubunion) =>
% 98.41/13.27 ((
% 98.41/13.27 (upairinpowunion) =>
% 98.41/13.27 ((
% 98.41/13.27 (ubforcartprodlem1) =>
% 98.41/13.27 ((
% 98.41/13.27 (ubforcartprodlem2) =>
% 98.41/13.27 ((
% 98.41/13.27 (ubforcartprodlem3) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodpairin) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodmempair1) =>
% 98.41/13.27 ((
% 98.41/13.27 (cartprodmempair) =>
% 98.41/13.27 ((
% 98.41/13.27 (setunionE2) =>
% 98.41/13.27 ((
% 98.41/13.27 (setunionsingleton1) =>
% 98.41/13.27 ((
% 98.41/13.27 (setunionsingleton2) =>
% 98.41/13.27 ((
% 98.41/13.27 (setunionsingleton) =>
% 98.41/13.27 ((
% 98.41/13.28 (singletonprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I2) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonsuniq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (theprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstin) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR11) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR12) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR1) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairequniteq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndin) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemER) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempaircEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrI) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrSub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setOfPairsIsBReln) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrERa) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrER) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcImageSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (apProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (app) =>
% 98.41/13.28 ((
% 98.41/13.28 (infuncsetfunc) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcinfuncset) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall1) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp3) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcextLem) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp4) =>
% 98.41/13.28 ((
% 98.41/13.28 (subbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq2) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2lamEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifp) =>
% 98.41/13.28 ((
% 98.41/13.28 (theeq) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrue) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueorfalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (setextT) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetTI) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetTI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetTE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectTELcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectTERcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT1) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT2) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT3) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementSub1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementSub2) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTnotintersectT) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementImpComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementSubsetComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementInPowersetComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (contraSubsetComplement) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTcontraSubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTILcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTIRcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInUnion) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInUnion2) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInIntersectUnions) =>
% 98.41/13.28 ((
% 98.41/13.28 (intersectInPowersetIntersectUnions) =>
% 98.41/13.28 ((
% 98.41/13.28 (inComplementUnionImpNotIn1) =>
% 98.41/13.28 ((
% 98.41/13.28 (inComplementUnionImpInComplement1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTE) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTEcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementUnionInPowersetComplement) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a2) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1a) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1b) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2b2) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2b) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule0) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule1) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule3) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule4) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_1) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_3) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_4) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_5) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1all2) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1SetBreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (choice2fnsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (setOfPairsIsBReln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1all1) =>
% 98.41/13.28 ((
% 98.41/13.28 (subbreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqbreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compEex) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionprop) =>
% 98.41/13.28 ((
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% 98.41/13.28 ((
% 98.41/13.28 (breln1unionIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionEcases) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionCommutes) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2Ex) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2W) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2A) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2B) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Ex) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Ex1) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Equiv) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1E) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1I) =>
% 98.41/13.28 ((
% 98.41/13.28 (injFuncInInjFuncSet) =>
% 98.41/13.28 ((
% 98.41/13.28 (!!) @ (
% 98.41/13.28 (('#B') @ (
% 98.41/13.28 !!) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 !!))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#S') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 '#S') @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 '#S'))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 =>))))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#C') @ in)))) @
% 98.41/13.28 injFuncSet)))))))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#C') @ in)))) @
% 98.41/13.28 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])).
% 98.41/13.28 thf(zip_derived_cl142, plain,
% 98.41/13.28 (~ (((emptysetE) =>
% 98.41/13.28 (((emptysetimpfalse) =>
% 98.41/13.28 (((notinemptyset) =>
% 98.41/13.28 (((exuE3e) =>
% 98.41/13.28 (((setext) =>
% 98.41/13.28 (((emptyI) =>
% 98.41/13.28 (((noeltsimpempty) =>
% 98.41/13.28 (((setbeta) =>
% 98.41/13.28 (((nonemptyE1) =>
% 98.41/13.28 (((nonemptyI) =>
% 98.41/13.28 (((nonemptyI1) =>
% 98.41/13.28 (((setadjoinIL) =>
% 98.41/13.28 (((in @ emptyset @
% 98.41/13.28 (setadjoin @ emptyset @ emptyset)) =>
% 98.41/13.28 (((setadjoinIR) =>
% 98.41/13.28 (((setadjoinE) =>
% 98.41/13.28 (((setadjoinOr) =>
% 98.41/13.28 (((setoftrueEq) =>
% 98.41/13.28 (((powersetI) =>
% 98.41/13.28 (((emptyinPowerset) =>
% 98.41/13.28 (((emptyInPowerset) =>
% 98.41/13.28 (((powersetE) =>
% 98.41/13.28 (((setunionI) =>
% 98.41/13.28 (((setunionE) =>
% 98.41/13.28 (((subPowSU) =>
% 98.41/13.28 (((exuE2) =>
% 98.41/13.28 (((nonemptyImpWitness) =>
% 98.41/13.28 (((uniqinunit) =>
% 98.41/13.28 (((notinsingleton) =>
% 98.41/13.28 (((eqinunit) =>
% 98.41/13.28 (((singletonsswitch) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairsetE) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairsetIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairsetIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (emptyE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (vacuousDall) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan1) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan2) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan3) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan4) =>
% 98.41/13.28 ((
% 98.41/13.28 (prop2setI) =>
% 98.41/13.28 ((
% 98.41/13.28 (prop2set2propI) =>
% 98.41/13.28 ((
% 98.41/13.28 (notdexE) =>
% 98.41/13.28 ((
% 98.41/13.28 (notdallE) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI3) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (inCongP) =>
% 98.41/13.28 ((
% 98.41/13.28 (in__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuE3u) =>
% 98.41/13.28 ((
% 98.41/13.28 (exu__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoin__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (powerset__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunion__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuEu) =>
% 98.41/13.28 ((
% 98.41/13.28 (descr__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (dsetconstr__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqimpsubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqimpsubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (emptysetsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetE) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetE2) =>
% 98.41/13.28 ((
% 98.41/13.28 (notsubsetI) =>
% 98.41/13.28 ((
% 98.41/13.28 (notequalI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (notequalI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetRefl) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetTrans) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoinSub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoinSub2) =>
% 98.41/13.28 ((
% 98.41/13.28 (subset2powerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (setextsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetemptysetimpeq) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (inPowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (sepInPowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (sepSubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairset2IR) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionEcases) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionE) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionRsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectI) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset5) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset3) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectER) =>
% 98.41/13.28 ((
% 98.41/13.28 (disjointsetsI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectRsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset4) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (bs114d) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusI) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusER) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusSubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusERneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusELneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusILneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusIRneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusSubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffE) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffIneg1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffIneg2) =>
% 98.41/13.28 ((
% 98.41/13.28 (secondinupair) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairiskpair) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairp) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletoninpowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletoninpowunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairset2E) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairsubunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairinpowunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem3) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairin) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempair1) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempair) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionE2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton1) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I2) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonsuniq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (theprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstin) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR11) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR12) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR1) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairequniteq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndin) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemER) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempaircEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrI) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrSub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setOfPairsIsBReln) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrERa) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrER) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcImageSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (apProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (app) =>
% 98.41/13.28 ((
% 98.41/13.28 (infuncsetfunc) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcinfuncset) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall1) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp3) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcextLem) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp4) =>
% 98.41/13.28 ((
% 98.41/13.28 (subbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq2) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2lamEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifp) =>
% 98.41/13.28 ((
% 98.41/13.28 (theeq) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrue) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueorfalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (setextT) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetTI) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetTI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetTE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectTELcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectTERcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT1) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT2) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT3) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementSub1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementSub2) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTnotintersectT) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementImpComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementSubsetComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementInPowersetComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (contraSubsetComplement) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTcontraSubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTILcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTIRcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInUnion) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInUnion2) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInIntersectUnions) =>
% 98.41/13.28 ((
% 98.41/13.28 (intersectInPowersetIntersectUnions) =>
% 98.41/13.28 ((
% 98.41/13.28 (inComplementUnionImpNotIn1) =>
% 98.41/13.28 ((
% 98.41/13.28 (inComplementUnionImpInComplement1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTE) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTEcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementUnionInPowersetComplement) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a2) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1a) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1b) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2b2) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2b) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule0) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule1) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule3) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule4) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_1) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_3) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_4) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_5) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1all2) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1SetBreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (choice2fnsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (setOfPairsIsBReln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1all1) =>
% 98.41/13.28 ((
% 98.41/13.28 (subbreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqbreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compEex) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionEcases) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionCommutes) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2Ex) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2W) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2A) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2B) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Ex) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Ex1) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Equiv) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1E) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1I) =>
% 98.41/13.28 ((
% 98.41/13.28 (injFuncInInjFuncSet) =>
% 98.41/13.28 ((
% 98.41/13.28 (!!) @ (
% 98.41/13.28 (('#B') @ (
% 98.41/13.28 !!) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 !!))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#S') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 '#S') @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 '#S'))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 =>))))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#C') @ in)))) @
% 98.41/13.28 injFuncSet)))))))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#C') @ in)))) @
% 98.41/13.28 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])).
% 98.41/13.28 thf(zip_derived_cl158, plain,
% 98.41/13.28 (~ (((emptysetimpfalse) =>
% 98.41/13.28 (((notinemptyset) =>
% 98.41/13.28 (((exuE3e) =>
% 98.41/13.28 (((setext) =>
% 98.41/13.28 (((emptyI) =>
% 98.41/13.28 (((noeltsimpempty) =>
% 98.41/13.28 (((setbeta) =>
% 98.41/13.28 (((nonemptyE1) =>
% 98.41/13.28 (((nonemptyI) =>
% 98.41/13.28 (((nonemptyI1) =>
% 98.41/13.28 (((setadjoinIL) =>
% 98.41/13.28 (((in @ emptyset @
% 98.41/13.28 (setadjoin @ emptyset @ emptyset)) =>
% 98.41/13.28 (((setadjoinIR) =>
% 98.41/13.28 (((setadjoinE) =>
% 98.41/13.28 (((setadjoinOr) =>
% 98.41/13.28 (((setoftrueEq) =>
% 98.41/13.28 (((powersetI) =>
% 98.41/13.28 (((emptyinPowerset) =>
% 98.41/13.28 (((emptyInPowerset) =>
% 98.41/13.28 (((powersetE) =>
% 98.41/13.28 (((setunionI) =>
% 98.41/13.28 (((setunionE) =>
% 98.41/13.28 (((subPowSU) =>
% 98.41/13.28 (((exuE2) =>
% 98.41/13.28 (((nonemptyImpWitness) =>
% 98.41/13.28 (((uniqinunit) =>
% 98.41/13.28 (((notinsingleton) =>
% 98.41/13.28 (((eqinunit) =>
% 98.41/13.28 (((singletonsswitch) =>
% 98.41/13.28 (((upairsetE) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairsetIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairsetIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (emptyE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (vacuousDall) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan1) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan2) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan3) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan4) =>
% 98.41/13.28 ((
% 98.41/13.28 (prop2setI) =>
% 98.41/13.28 ((
% 98.41/13.28 (prop2set2propI) =>
% 98.41/13.28 ((
% 98.41/13.28 (notdexE) =>
% 98.41/13.28 ((
% 98.41/13.28 (notdallE) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI3) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (inCongP) =>
% 98.41/13.28 ((
% 98.41/13.28 (in__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuE3u) =>
% 98.41/13.28 ((
% 98.41/13.28 (exu__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoin__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (powerset__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunion__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuEu) =>
% 98.41/13.28 ((
% 98.41/13.28 (descr__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (dsetconstr__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqimpsubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqimpsubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (emptysetsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetE) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetE2) =>
% 98.41/13.28 ((
% 98.41/13.28 (notsubsetI) =>
% 98.41/13.28 ((
% 98.41/13.28 (notequalI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (notequalI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetRefl) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetTrans) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoinSub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoinSub2) =>
% 98.41/13.28 ((
% 98.41/13.28 (subset2powerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (setextsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetemptysetimpeq) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (inPowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (sepInPowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (sepSubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairset2IR) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionEcases) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionE) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionRsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectI) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset5) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset3) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectER) =>
% 98.41/13.28 ((
% 98.41/13.28 (disjointsetsI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectRsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset4) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (bs114d) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusI) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusER) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusSubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusERneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusELneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusILneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusIRneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusSubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffE) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffIneg1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffIneg2) =>
% 98.41/13.28 ((
% 98.41/13.28 (secondinupair) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairiskpair) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairp) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletoninpowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletoninpowunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairset2E) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairsubunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairinpowunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem3) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairin) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempair1) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempair) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionE2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton1) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I2) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonsuniq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (theprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstin) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR11) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR12) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR1) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairequniteq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndin) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemER) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempaircEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrI) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrSub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setOfPairsIsBReln) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrERa) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrER) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcImageSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (apProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (app) =>
% 98.41/13.28 ((
% 98.41/13.28 (infuncsetfunc) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcinfuncset) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall1) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp3) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcextLem) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp4) =>
% 98.41/13.28 ((
% 98.41/13.28 (subbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq2) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2lamEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifp) =>
% 98.41/13.28 ((
% 98.41/13.28 (theeq) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrue) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueorfalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (setextT) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetTI) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetTI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetTE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectTELcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectTERcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT1) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT2) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT3) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementSub1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementSub2) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTnotintersectT) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementImpComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementSubsetComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementInPowersetComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (contraSubsetComplement) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTcontraSubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTILcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTIRcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInUnion) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInUnion2) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInIntersectUnions) =>
% 98.41/13.28 ((
% 98.41/13.28 (intersectInPowersetIntersectUnions) =>
% 98.41/13.28 ((
% 98.41/13.28 (inComplementUnionImpNotIn1) =>
% 98.41/13.28 ((
% 98.41/13.28 (inComplementUnionImpInComplement1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTE) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTEcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementUnionInPowersetComplement) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a2) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1a) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1b) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2b2) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2b) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule0) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule1) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule3) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule4) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_1) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_3) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_4) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_5) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1all2) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1SetBreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (choice2fnsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (setOfPairsIsBReln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1all1) =>
% 98.41/13.28 ((
% 98.41/13.28 (subbreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqbreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compEex) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionEcases) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionCommutes) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2Ex) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2W) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2A) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2B) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Ex) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Ex1) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Equiv) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1E) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1I) =>
% 98.41/13.28 ((
% 98.41/13.28 (injFuncInInjFuncSet) =>
% 98.41/13.28 ((
% 98.41/13.28 (!!) @ (
% 98.41/13.28 (('#B') @ (
% 98.41/13.28 !!) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 !!))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#S') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 '#S') @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 '#S'))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 =>))))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#C') @ in)))) @
% 98.41/13.28 injFuncSet)))))))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#C') @ in)))) @
% 98.41/13.28 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])).
% 98.41/13.28 thf(zip_derived_cl174, plain,
% 98.41/13.28 (~ (((notinemptyset) =>
% 98.41/13.28 (((exuE3e) =>
% 98.41/13.28 (((setext) =>
% 98.41/13.28 (((emptyI) =>
% 98.41/13.28 (((noeltsimpempty) =>
% 98.41/13.28 (((setbeta) =>
% 98.41/13.28 (((nonemptyE1) =>
% 98.41/13.28 (((nonemptyI) =>
% 98.41/13.28 (((nonemptyI1) =>
% 98.41/13.28 (((setadjoinIL) =>
% 98.41/13.28 (((in @ emptyset @
% 98.41/13.28 (setadjoin @ emptyset @ emptyset)) =>
% 98.41/13.28 (((setadjoinIR) =>
% 98.41/13.28 (((setadjoinE) =>
% 98.41/13.28 (((setadjoinOr) =>
% 98.41/13.28 (((setoftrueEq) =>
% 98.41/13.28 (((powersetI) =>
% 98.41/13.28 (((emptyinPowerset) =>
% 98.41/13.28 (((emptyInPowerset) =>
% 98.41/13.28 (((powersetE) =>
% 98.41/13.28 (((setunionI) =>
% 98.41/13.28 (((setunionE) =>
% 98.41/13.28 (((subPowSU) =>
% 98.41/13.28 (((exuE2) =>
% 98.41/13.28 (((nonemptyImpWitness) =>
% 98.41/13.28 (((uniqinunit) =>
% 98.41/13.28 (((notinsingleton) =>
% 98.41/13.28 (((eqinunit) =>
% 98.41/13.28 (((singletonsswitch) =>
% 98.41/13.28 (((upairsetE) =>
% 98.41/13.28 (((upairsetIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairsetIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (emptyE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (vacuousDall) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan1) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan2) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan3) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan4) =>
% 98.41/13.28 ((
% 98.41/13.28 (prop2setI) =>
% 98.41/13.28 ((
% 98.41/13.28 (prop2set2propI) =>
% 98.41/13.28 ((
% 98.41/13.28 (notdexE) =>
% 98.41/13.28 ((
% 98.41/13.28 (notdallE) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI3) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (inCongP) =>
% 98.41/13.28 ((
% 98.41/13.28 (in__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuE3u) =>
% 98.41/13.28 ((
% 98.41/13.28 (exu__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoin__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (powerset__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunion__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuEu) =>
% 98.41/13.28 ((
% 98.41/13.28 (descr__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (dsetconstr__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqimpsubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqimpsubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (emptysetsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetE) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetE2) =>
% 98.41/13.28 ((
% 98.41/13.28 (notsubsetI) =>
% 98.41/13.28 ((
% 98.41/13.28 (notequalI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (notequalI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetRefl) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetTrans) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoinSub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoinSub2) =>
% 98.41/13.28 ((
% 98.41/13.28 (subset2powerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (setextsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetemptysetimpeq) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (inPowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (sepInPowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (sepSubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairset2IR) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionEcases) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionE) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionRsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectI) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset5) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset3) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectER) =>
% 98.41/13.28 ((
% 98.41/13.28 (disjointsetsI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectRsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset4) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (bs114d) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusI) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusER) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusSubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusERneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusELneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusILneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusIRneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusSubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffE) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffIneg1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffIneg2) =>
% 98.41/13.28 ((
% 98.41/13.28 (secondinupair) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairiskpair) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairp) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletoninpowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletoninpowunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairset2E) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairsubunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairinpowunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem3) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairin) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempair1) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempair) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionE2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton1) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I2) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonsuniq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (theprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstin) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR11) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR12) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR1) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairequniteq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndin) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemER) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempaircEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrI) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrSub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setOfPairsIsBReln) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrERa) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrER) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcImageSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (apProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (app) =>
% 98.41/13.28 ((
% 98.41/13.28 (infuncsetfunc) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcinfuncset) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall1) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp3) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcextLem) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp4) =>
% 98.41/13.28 ((
% 98.41/13.28 (subbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq2) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2lamEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifp) =>
% 98.41/13.28 ((
% 98.41/13.28 (theeq) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrue) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueorfalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (setextT) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetTI) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetTI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetTE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectTELcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectTERcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT1) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT2) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT3) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementSub1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementSub2) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTnotintersectT) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementImpComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementSubsetComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementInPowersetComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (contraSubsetComplement) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTcontraSubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTILcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTIRcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInUnion) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInUnion2) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInIntersectUnions) =>
% 98.41/13.28 ((
% 98.41/13.28 (intersectInPowersetIntersectUnions) =>
% 98.41/13.28 ((
% 98.41/13.28 (inComplementUnionImpNotIn1) =>
% 98.41/13.28 ((
% 98.41/13.28 (inComplementUnionImpInComplement1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTE) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTEcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementUnionInPowersetComplement) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a2) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1a) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1b) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2b2) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2b) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule0) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule1) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule3) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule4) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_1) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_3) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_4) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_5) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1all2) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1SetBreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (choice2fnsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (setOfPairsIsBReln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1all1) =>
% 98.41/13.28 ((
% 98.41/13.28 (subbreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqbreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compEex) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionEcases) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionCommutes) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2Ex) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2W) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2A) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2B) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Ex) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Ex1) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Equiv) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1E) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1I) =>
% 98.41/13.28 ((
% 98.41/13.28 (injFuncInInjFuncSet) =>
% 98.41/13.28 ((
% 98.41/13.28 (!!) @ (
% 98.41/13.28 (('#B') @ (
% 98.41/13.28 !!) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 !!))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#S') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 '#S') @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 '#S'))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 =>))))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#C') @ in)))) @
% 98.41/13.28 injFuncSet)))))))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#C') @ in)))) @
% 98.41/13.28 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])).
% 98.41/13.28 thf(zip_derived_cl189, plain,
% 98.41/13.28 (~ (((exuE3e) =>
% 98.41/13.28 (((setext) =>
% 98.41/13.28 (((emptyI) =>
% 98.41/13.28 (((noeltsimpempty) =>
% 98.41/13.28 (((setbeta) =>
% 98.41/13.28 (((nonemptyE1) =>
% 98.41/13.28 (((nonemptyI) =>
% 98.41/13.28 (((nonemptyI1) =>
% 98.41/13.28 (((setadjoinIL) =>
% 98.41/13.28 (((in @ emptyset @
% 98.41/13.28 (setadjoin @ emptyset @ emptyset)) =>
% 98.41/13.28 (((setadjoinIR) =>
% 98.41/13.28 (((setadjoinE) =>
% 98.41/13.28 (((setadjoinOr) =>
% 98.41/13.28 (((setoftrueEq) =>
% 98.41/13.28 (((powersetI) =>
% 98.41/13.28 (((emptyinPowerset) =>
% 98.41/13.28 (((emptyInPowerset) =>
% 98.41/13.28 (((powersetE) =>
% 98.41/13.28 (((setunionI) =>
% 98.41/13.28 (((setunionE) =>
% 98.41/13.28 (((subPowSU) =>
% 98.41/13.28 (((exuE2) =>
% 98.41/13.28 (((nonemptyImpWitness) =>
% 98.41/13.28 (((uniqinunit) =>
% 98.41/13.28 (((notinsingleton) =>
% 98.41/13.28 (((eqinunit) =>
% 98.41/13.28 (((singletonsswitch) =>
% 98.41/13.28 (((upairsetE) =>
% 98.41/13.28 (((upairsetIL) =>
% 98.41/13.28 (((upairsetIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (emptyE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (vacuousDall) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan1) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan2) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan3) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan4) =>
% 98.41/13.28 ((
% 98.41/13.28 (prop2setI) =>
% 98.41/13.28 ((
% 98.41/13.28 (prop2set2propI) =>
% 98.41/13.28 ((
% 98.41/13.28 (notdexE) =>
% 98.41/13.28 ((
% 98.41/13.28 (notdallE) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI3) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (inCongP) =>
% 98.41/13.28 ((
% 98.41/13.28 (in__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuE3u) =>
% 98.41/13.28 ((
% 98.41/13.28 (exu__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoin__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (powerset__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunion__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuEu) =>
% 98.41/13.28 ((
% 98.41/13.28 (descr__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (dsetconstr__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqimpsubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqimpsubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (emptysetsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetE) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetE2) =>
% 98.41/13.28 ((
% 98.41/13.28 (notsubsetI) =>
% 98.41/13.28 ((
% 98.41/13.28 (notequalI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (notequalI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetRefl) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetTrans) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoinSub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoinSub2) =>
% 98.41/13.28 ((
% 98.41/13.28 (subset2powerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (setextsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetemptysetimpeq) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (inPowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (sepInPowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (sepSubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairset2IR) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionEcases) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionE) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionRsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectI) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset5) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset3) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectER) =>
% 98.41/13.28 ((
% 98.41/13.28 (disjointsetsI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectRsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset4) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (bs114d) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusI) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusER) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusSubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusERneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusELneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusILneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusIRneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusSubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffE) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffIneg1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffIneg2) =>
% 98.41/13.28 ((
% 98.41/13.28 (secondinupair) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairiskpair) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairp) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletoninpowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletoninpowunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairset2E) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairsubunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairinpowunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem3) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairin) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempair1) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempair) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionE2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton1) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I2) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonsuniq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (theprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstin) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR11) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR12) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR1) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairequniteq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndin) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemER) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempaircEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrI) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrSub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setOfPairsIsBReln) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrERa) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrER) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcImageSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (apProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (app) =>
% 98.41/13.28 ((
% 98.41/13.28 (infuncsetfunc) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcinfuncset) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall1) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp3) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcextLem) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp4) =>
% 98.41/13.28 ((
% 98.41/13.28 (subbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq2) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2lamEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifp) =>
% 98.41/13.28 ((
% 98.41/13.28 (theeq) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrue) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueorfalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (setextT) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetTI) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetTI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetTE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectTELcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectTERcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT1) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT2) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT3) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementSub1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementSub2) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTnotintersectT) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementImpComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementSubsetComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementInPowersetComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (contraSubsetComplement) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTcontraSubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTILcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTIRcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInUnion) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInUnion2) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInIntersectUnions) =>
% 98.41/13.28 ((
% 98.41/13.28 (intersectInPowersetIntersectUnions) =>
% 98.41/13.28 ((
% 98.41/13.28 (inComplementUnionImpNotIn1) =>
% 98.41/13.28 ((
% 98.41/13.28 (inComplementUnionImpInComplement1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTE) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTEcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementUnionInPowersetComplement) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a2) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1a) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1b) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2b2) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2b) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule0) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule1) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule3) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule4) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_1) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_3) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_4) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_5) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1all2) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1SetBreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (choice2fnsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (setOfPairsIsBReln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1all1) =>
% 98.41/13.28 ((
% 98.41/13.28 (subbreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqbreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compEex) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionEcases) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionCommutes) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2Ex) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2W) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2A) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2B) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Ex) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Ex1) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Equiv) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1E) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1I) =>
% 98.41/13.28 ((
% 98.41/13.28 (injFuncInInjFuncSet) =>
% 98.41/13.28 ((
% 98.41/13.28 (!!) @ (
% 98.41/13.28 (('#B') @ (
% 98.41/13.28 !!) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 !!))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#S') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 '#S') @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 '#S'))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 =>))))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#C') @ in)))) @
% 98.41/13.28 injFuncSet)))))))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#C') @ in)))) @
% 98.41/13.28 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl174])).
% 98.41/13.28 thf(zip_derived_cl206, plain,
% 98.41/13.28 (~ (((setext) =>
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% 98.41/13.28 (((noeltsimpempty) =>
% 98.41/13.28 (((setbeta) =>
% 98.41/13.28 (((nonemptyE1) =>
% 98.41/13.28 (((nonemptyI) =>
% 98.41/13.28 (((nonemptyI1) =>
% 98.41/13.28 (((setadjoinIL) =>
% 98.41/13.28 (((in @ emptyset @
% 98.41/13.28 (setadjoin @ emptyset @ emptyset)) =>
% 98.41/13.28 (((setadjoinIR) =>
% 98.41/13.28 (((setadjoinE) =>
% 98.41/13.28 (((setadjoinOr) =>
% 98.41/13.28 (((setoftrueEq) =>
% 98.41/13.28 (((powersetI) =>
% 98.41/13.28 (((emptyinPowerset) =>
% 98.41/13.28 (((emptyInPowerset) =>
% 98.41/13.28 (((powersetE) =>
% 98.41/13.28 (((setunionI) =>
% 98.41/13.28 (((setunionE) =>
% 98.41/13.28 (((subPowSU) =>
% 98.41/13.28 (((exuE2) =>
% 98.41/13.28 (((nonemptyImpWitness) =>
% 98.41/13.28 (((uniqinunit) =>
% 98.41/13.28 (((notinsingleton) =>
% 98.41/13.28 (((eqinunit) =>
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% 98.41/13.28 (((upairsetIR) =>
% 98.41/13.28 (((emptyE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (vacuousDall) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan1) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan2) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan3) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan4) =>
% 98.41/13.28 ((
% 98.41/13.28 (prop2setI) =>
% 98.41/13.28 ((
% 98.41/13.28 (prop2set2propI) =>
% 98.41/13.28 ((
% 98.41/13.28 (notdexE) =>
% 98.41/13.28 ((
% 98.41/13.28 (notdallE) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI3) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (inCongP) =>
% 98.41/13.28 ((
% 98.41/13.28 (in__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuE3u) =>
% 98.41/13.28 ((
% 98.41/13.28 (exu__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoin__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (powerset__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunion__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuEu) =>
% 98.41/13.28 ((
% 98.41/13.28 (descr__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (dsetconstr__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqimpsubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqimpsubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (emptysetsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetE) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetE2) =>
% 98.41/13.28 ((
% 98.41/13.28 (notsubsetI) =>
% 98.41/13.28 ((
% 98.41/13.28 (notequalI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (notequalI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetRefl) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetTrans) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoinSub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoinSub2) =>
% 98.41/13.28 ((
% 98.41/13.28 (subset2powerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (setextsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetemptysetimpeq) =>
% 98.41/13.28 ((
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% 98.41/13.28 ((
% 98.41/13.28 (powersetE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (inPowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (sepInPowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (sepSubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairset2IR) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionEcases) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionE) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionRsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectI) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset5) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset3) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectER) =>
% 98.41/13.28 ((
% 98.41/13.28 (disjointsetsI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectRsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset4) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (bs114d) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusI) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusER) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusSubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusERneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusELneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusILneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusIRneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusSubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffE) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffIneg1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffIneg2) =>
% 98.41/13.28 ((
% 98.41/13.28 (secondinupair) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairiskpair) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairp) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletoninpowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletoninpowunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairset2E) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairsubunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairinpowunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem3) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairin) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempair1) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempair) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionE2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton1) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I2) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonsuniq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (theprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstin) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR11) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR12) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR1) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairequniteq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndin) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemER) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempaircEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrI) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrSub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setOfPairsIsBReln) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrERa) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrER) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcImageSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (apProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (app) =>
% 98.41/13.28 ((
% 98.41/13.28 (infuncsetfunc) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcinfuncset) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall1) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp3) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcextLem) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp4) =>
% 98.41/13.28 ((
% 98.41/13.28 (subbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq2) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2lamEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifp) =>
% 98.41/13.28 ((
% 98.41/13.28 (theeq) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrue) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueorfalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (setextT) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetTI) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetTI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetTE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectTELcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectTERcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT1) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT2) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT3) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementSub1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementSub2) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTnotintersectT) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementImpComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementSubsetComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementInPowersetComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (contraSubsetComplement) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTcontraSubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTILcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTIRcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInUnion) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInUnion2) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInIntersectUnions) =>
% 98.41/13.28 ((
% 98.41/13.28 (intersectInPowersetIntersectUnions) =>
% 98.41/13.28 ((
% 98.41/13.28 (inComplementUnionImpNotIn1) =>
% 98.41/13.28 ((
% 98.41/13.28 (inComplementUnionImpInComplement1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTE) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTEcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementUnionInPowersetComplement) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a2) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1a) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1b) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2b2) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2b) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule0) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule1) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule3) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule4) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_1) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_3) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_4) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_5) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1all2) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1SetBreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (choice2fnsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (setOfPairsIsBReln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1all1) =>
% 98.41/13.28 ((
% 98.41/13.28 (subbreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqbreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compEex) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionEcases) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionCommutes) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2Ex) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2W) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2A) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2B) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Ex) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Ex1) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Equiv) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1E) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1I) =>
% 98.41/13.28 ((
% 98.41/13.28 (injFuncInInjFuncSet) =>
% 98.41/13.28 ((
% 98.41/13.28 (!!) @ (
% 98.41/13.28 (('#B') @ (
% 98.41/13.28 !!) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 !!))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#S') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 '#S') @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 '#S'))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 =>))))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#C') @ in)))) @
% 98.41/13.28 injFuncSet)))))))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#C') @ in)))) @
% 98.41/13.28 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl189])).
% 98.41/13.28 thf(zip_derived_cl222, plain,
% 98.41/13.28 (~ (((emptyI) =>
% 98.41/13.28 (((noeltsimpempty) =>
% 98.41/13.28 (((setbeta) =>
% 98.41/13.28 (((nonemptyE1) =>
% 98.41/13.28 (((nonemptyI) =>
% 98.41/13.28 (((nonemptyI1) =>
% 98.41/13.28 (((setadjoinIL) =>
% 98.41/13.28 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 98.41/13.28 (((setadjoinIR) =>
% 98.41/13.28 (((setadjoinE) =>
% 98.41/13.28 (((setadjoinOr) =>
% 98.41/13.28 (((setoftrueEq) =>
% 98.41/13.28 (((powersetI) =>
% 98.41/13.28 (((emptyinPowerset) =>
% 98.41/13.28 (((emptyInPowerset) =>
% 98.41/13.28 (((powersetE) =>
% 98.41/13.28 (((setunionI) =>
% 98.41/13.28 (((setunionE) =>
% 98.41/13.28 (((subPowSU) =>
% 98.41/13.28 (((exuE2) =>
% 98.41/13.28 (((nonemptyImpWitness) =>
% 98.41/13.28 (((uniqinunit) =>
% 98.41/13.28 (((notinsingleton) =>
% 98.41/13.28 (((eqinunit) =>
% 98.41/13.28 (((singletonsswitch) =>
% 98.41/13.28 (((upairsetE) =>
% 98.41/13.28 (((upairsetIL) =>
% 98.41/13.28 (((upairsetIR) =>
% 98.41/13.28 (((emptyE1) =>
% 98.41/13.28 (((vacuousDall) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan1) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan2) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan3) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan4) =>
% 98.41/13.28 ((
% 98.41/13.28 (prop2setI) =>
% 98.41/13.28 ((
% 98.41/13.28 (prop2set2propI) =>
% 98.41/13.28 ((
% 98.41/13.28 (notdexE) =>
% 98.41/13.28 ((
% 98.41/13.28 (notdallE) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI3) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (inCongP) =>
% 98.41/13.28 ((
% 98.41/13.28 (in__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuE3u) =>
% 98.41/13.28 ((
% 98.41/13.28 (exu__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoin__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (powerset__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunion__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuEu) =>
% 98.41/13.28 ((
% 98.41/13.28 (descr__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (dsetconstr__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqimpsubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqimpsubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (emptysetsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetE) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetE2) =>
% 98.41/13.28 ((
% 98.41/13.28 (notsubsetI) =>
% 98.41/13.28 ((
% 98.41/13.28 (notequalI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (notequalI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetRefl) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetTrans) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoinSub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoinSub2) =>
% 98.41/13.28 ((
% 98.41/13.28 (subset2powerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (setextsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetemptysetimpeq) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (inPowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (sepInPowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (sepSubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairset2IR) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionEcases) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionE) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionRsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectI) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset5) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset3) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectER) =>
% 98.41/13.28 ((
% 98.41/13.28 (disjointsetsI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectRsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset4) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (bs114d) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusI) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusER) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusSubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusERneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusELneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusILneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusIRneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusSubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffE) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffIneg1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffIneg2) =>
% 98.41/13.28 ((
% 98.41/13.28 (secondinupair) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairiskpair) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairp) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletoninpowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletoninpowunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairset2E) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairsubunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairinpowunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem3) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairin) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempair1) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempair) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionE2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton1) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I2) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonsuniq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (theprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstin) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR11) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR12) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR1) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairequniteq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndin) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemER) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempaircEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrI) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrSub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setOfPairsIsBReln) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrERa) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrER) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcImageSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (apProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (app) =>
% 98.41/13.28 ((
% 98.41/13.28 (infuncsetfunc) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcinfuncset) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall1) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp3) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcextLem) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp4) =>
% 98.41/13.28 ((
% 98.41/13.28 (subbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq2) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2lamEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifp) =>
% 98.41/13.28 ((
% 98.41/13.28 (theeq) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrue) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueorfalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (setextT) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetTI) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetTI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetTE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectTELcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectTERcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT1) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT2) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT3) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementSub1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementSub2) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTnotintersectT) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementImpComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementSubsetComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementInPowersetComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (contraSubsetComplement) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTcontraSubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTILcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTIRcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInUnion) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInUnion2) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInIntersectUnions) =>
% 98.41/13.28 ((
% 98.41/13.28 (intersectInPowersetIntersectUnions) =>
% 98.41/13.28 ((
% 98.41/13.28 (inComplementUnionImpNotIn1) =>
% 98.41/13.28 ((
% 98.41/13.28 (inComplementUnionImpInComplement1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTE) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTEcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementUnionInPowersetComplement) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a2) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1a) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1b) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2b2) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2b) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule0) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule1) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule3) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule4) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_1) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_3) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_4) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_5) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1all2) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1SetBreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (choice2fnsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (setOfPairsIsBReln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1all1) =>
% 98.41/13.28 ((
% 98.41/13.28 (subbreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqbreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compEex) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionEcases) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionCommutes) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2Ex) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2W) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2A) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2B) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Ex) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Ex1) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Equiv) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1E) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1I) =>
% 98.41/13.28 ((
% 98.41/13.28 (injFuncInInjFuncSet) =>
% 98.41/13.28 ((
% 98.41/13.28 (!!) @ (
% 98.41/13.28 (('#B') @ (
% 98.41/13.28 !!) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 !!))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#S') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 '#S') @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 '#S'))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 =>))))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#C') @ in)))) @
% 98.41/13.28 injFuncSet)))))))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#C') @ in)))) @
% 98.41/13.28 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])).
% 98.41/13.28 thf(zip_derived_cl236, plain,
% 98.41/13.28 (~ (((noeltsimpempty) =>
% 98.41/13.28 (((setbeta) =>
% 98.41/13.28 (((nonemptyE1) =>
% 98.41/13.28 (((nonemptyI) =>
% 98.41/13.28 (((nonemptyI1) =>
% 98.41/13.28 (((setadjoinIL) =>
% 98.41/13.28 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 98.41/13.28 (((setadjoinIR) =>
% 98.41/13.28 (((setadjoinE) =>
% 98.41/13.28 (((setadjoinOr) =>
% 98.41/13.28 (((setoftrueEq) =>
% 98.41/13.28 (((powersetI) =>
% 98.41/13.28 (((emptyinPowerset) =>
% 98.41/13.28 (((emptyInPowerset) =>
% 98.41/13.28 (((powersetE) =>
% 98.41/13.28 (((setunionI) =>
% 98.41/13.28 (((setunionE) =>
% 98.41/13.28 (((subPowSU) =>
% 98.41/13.28 (((exuE2) =>
% 98.41/13.28 (((nonemptyImpWitness) =>
% 98.41/13.28 (((uniqinunit) =>
% 98.41/13.28 (((notinsingleton) =>
% 98.41/13.28 (((eqinunit) =>
% 98.41/13.28 (((singletonsswitch) =>
% 98.41/13.28 (((upairsetE) =>
% 98.41/13.28 (((upairsetIL) =>
% 98.41/13.28 (((upairsetIR) =>
% 98.41/13.28 (((emptyE1) =>
% 98.41/13.28 (((vacuousDall) =>
% 98.41/13.28 (((quantDeMorgan1) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan2) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan3) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan4) =>
% 98.41/13.28 ((
% 98.41/13.28 (prop2setI) =>
% 98.41/13.28 ((
% 98.41/13.28 (prop2set2propI) =>
% 98.41/13.28 ((
% 98.41/13.28 (notdexE) =>
% 98.41/13.28 ((
% 98.41/13.28 (notdallE) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI3) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (inCongP) =>
% 98.41/13.28 ((
% 98.41/13.28 (in__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuE3u) =>
% 98.41/13.28 ((
% 98.41/13.28 (exu__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoin__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (powerset__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunion__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuEu) =>
% 98.41/13.28 ((
% 98.41/13.28 (descr__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (dsetconstr__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqimpsubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqimpsubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (emptysetsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetE) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetE2) =>
% 98.41/13.28 ((
% 98.41/13.28 (notsubsetI) =>
% 98.41/13.28 ((
% 98.41/13.28 (notequalI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (notequalI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetRefl) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetTrans) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoinSub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoinSub2) =>
% 98.41/13.28 ((
% 98.41/13.28 (subset2powerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (setextsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetemptysetimpeq) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (inPowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (sepInPowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (sepSubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairset2IR) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionEcases) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionE) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionRsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectI) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset5) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset3) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectER) =>
% 98.41/13.28 ((
% 98.41/13.28 (disjointsetsI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectRsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset4) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (bs114d) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusI) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusER) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusSubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusERneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusELneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusILneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusIRneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusSubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffE) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffIneg1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffIneg2) =>
% 98.41/13.28 ((
% 98.41/13.28 (secondinupair) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairiskpair) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairp) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletoninpowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletoninpowunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairset2E) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairsubunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairinpowunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem3) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairin) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempair1) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempair) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionE2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton1) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I2) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonsuniq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (theprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstin) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR11) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR12) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR1) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairequniteq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndin) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemER) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempaircEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrI) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrSub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setOfPairsIsBReln) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrERa) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrER) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcImageSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (apProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (app) =>
% 98.41/13.28 ((
% 98.41/13.28 (infuncsetfunc) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcinfuncset) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall1) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp3) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcextLem) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp4) =>
% 98.41/13.28 ((
% 98.41/13.28 (subbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq2) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2lamEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifp) =>
% 98.41/13.28 ((
% 98.41/13.28 (theeq) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrue) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueorfalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (setextT) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetTI) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetTI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetTE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectTELcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectTERcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT1) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT2) =>
% 98.41/13.28 ((
% 98.41/13.28 (contrasubsetT3) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementSub1) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementSub2) =>
% 98.41/13.28 ((
% 98.41/13.28 (doubleComplementEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTnotintersectT) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementImpComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementSubsetComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementInPowersetComplementIntersect) =>
% 98.41/13.28 ((
% 98.41/13.28 (contraSubsetComplement) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementTcontraSubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTILcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTIRcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInUnion) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInUnion2) =>
% 98.41/13.28 ((
% 98.41/13.28 (inIntersectImpInIntersectUnions) =>
% 98.41/13.28 ((
% 98.41/13.28 (intersectInPowersetIntersectUnions) =>
% 98.41/13.28 ((
% 98.41/13.28 (inComplementUnionImpNotIn1) =>
% 98.41/13.28 ((
% 98.41/13.28 (inComplementUnionImpInComplement1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTE) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionTEcontra) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a1) =>
% 98.41/13.28 ((
% 98.41/13.28 (complementUnionInPowersetComplement) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a2) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1a) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1b) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan1) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2a) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2b2) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2b) =>
% 98.41/13.28 ((
% 98.41/13.28 (demorgan2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule0) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule1) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule3) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz13rule4) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_1) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_2) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_3) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_4) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz1_5) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1all2) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1SetBreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (choice2fnsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (setOfPairsIsBReln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1all1) =>
% 98.41/13.28 ((
% 98.41/13.28 (subbreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqbreln1) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1invE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1compEex) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionI) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionE) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionEcases) =>
% 98.41/13.28 ((
% 98.41/13.28 (breln1unionCommutes) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2Ex) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2W) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2A) =>
% 98.41/13.28 ((
% 98.41/13.28 (woz2B) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Ex) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Ex1) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1Equiv) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1E) =>
% 98.41/13.28 ((
% 98.41/13.28 (image1I) =>
% 98.41/13.28 ((
% 98.41/13.28 (injFuncInInjFuncSet) =>
% 98.41/13.28 ((
% 98.41/13.28 (!!) @ (
% 98.41/13.28 (('#B') @ (
% 98.41/13.28 !!) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 !!))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#S') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 '#S') @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 '#S'))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 =>))))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#C') @ in)))) @
% 98.41/13.28 injFuncSet)))))))) @
% 98.41/13.28 (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#B') @ (
% 98.41/13.28 (
% 98.41/13.28 ('#C') @ in)))) @
% 98.41/13.28 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl222])).
% 98.41/13.28 thf(zip_derived_cl251, plain,
% 98.41/13.28 (~ (((setbeta) =>
% 98.41/13.28 (((nonemptyE1) =>
% 98.41/13.28 (((nonemptyI) =>
% 98.41/13.28 (((nonemptyI1) =>
% 98.41/13.28 (((setadjoinIL) =>
% 98.41/13.28 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 98.41/13.28 (((setadjoinIR) =>
% 98.41/13.28 (((setadjoinE) =>
% 98.41/13.28 (((setadjoinOr) =>
% 98.41/13.28 (((setoftrueEq) =>
% 98.41/13.28 (((powersetI) =>
% 98.41/13.28 (((emptyinPowerset) =>
% 98.41/13.28 (((emptyInPowerset) =>
% 98.41/13.28 (((powersetE) =>
% 98.41/13.28 (((setunionI) =>
% 98.41/13.28 (((setunionE) =>
% 98.41/13.28 (((subPowSU) =>
% 98.41/13.28 (((exuE2) =>
% 98.41/13.28 (((nonemptyImpWitness) =>
% 98.41/13.28 (((uniqinunit) =>
% 98.41/13.28 (((notinsingleton) =>
% 98.41/13.28 (((eqinunit) =>
% 98.41/13.28 (((singletonsswitch) =>
% 98.41/13.28 (((upairsetE) =>
% 98.41/13.28 (((upairsetIL) =>
% 98.41/13.28 (((upairsetIR) =>
% 98.41/13.28 (((emptyE1) =>
% 98.41/13.28 (((vacuousDall) =>
% 98.41/13.28 (((quantDeMorgan1) =>
% 98.41/13.28 (((quantDeMorgan2) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan3) =>
% 98.41/13.28 ((
% 98.41/13.28 (quantDeMorgan4) =>
% 98.41/13.28 ((
% 98.41/13.28 (prop2setI) =>
% 98.41/13.28 ((
% 98.41/13.28 (prop2set2propI) =>
% 98.41/13.28 ((
% 98.41/13.28 (notdexE) =>
% 98.41/13.28 ((
% 98.41/13.28 (notdallE) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI3) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (inCongP) =>
% 98.41/13.28 ((
% 98.41/13.28 (in__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuE3u) =>
% 98.41/13.28 ((
% 98.41/13.28 (exu__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoin__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (powerset__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunion__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (exuEu) =>
% 98.41/13.28 ((
% 98.41/13.28 (descr__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (dsetconstr__Cong) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqimpsubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqimpsubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (emptysetsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetE) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetE2) =>
% 98.41/13.28 ((
% 98.41/13.28 (notsubsetI) =>
% 98.41/13.28 ((
% 98.41/13.28 (notequalI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (notequalI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetRefl) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetTrans) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoinSub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setadjoinSub2) =>
% 98.41/13.28 ((
% 98.41/13.28 (subset2powerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (setextsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (subsetemptysetimpeq) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetE1) =>
% 98.41/13.28 ((
% 98.41/13.28 (inPowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (sepInPowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (sepSubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairset2IR) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionEcases) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionE) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionRsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectI) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset5) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset3) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectER) =>
% 98.41/13.28 ((
% 98.41/13.28 (disjointsetsI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectRsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset4) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectSubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (bs114d) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusI) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusER) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusSubset2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusERneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusELneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusILneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusIRneg) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusLsub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setminusSubset1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffE) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffI1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffI2) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffIneg1) =>
% 98.41/13.28 ((
% 98.41/13.28 (symdiffIneg2) =>
% 98.41/13.28 ((
% 98.41/13.28 (secondinupair) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairIL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairIR) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairiskpair) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairp) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonsubset) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletoninpowerset) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletoninpowunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairset2E) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairsubunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairinpowunion) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ubforcartprodlem3) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairin) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempair1) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempair) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionE2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton1) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setunionsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1I2) =>
% 98.41/13.28 ((
% 98.41/13.28 (singletonsuniq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (theprop) =>
% 98.41/13.28 ((
% 98.41/13.28 (kfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstin) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjL) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR11) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR12) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR1) =>
% 98.41/13.28 ((
% 98.41/13.28 (upairequniteq) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR2) =>
% 98.41/13.28 ((
% 98.41/13.28 (setukpairinjR) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndsingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ksndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (kpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndin) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemEL) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairmemER) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodmempaircEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodfstpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodsndpairEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (cartprodpairsurjEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrI) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrSub) =>
% 98.41/13.28 ((
% 98.41/13.28 (setOfPairsIsBReln) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrERa) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL1) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrEL2) =>
% 98.41/13.28 ((
% 98.41/13.28 (dpsetconstrER) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcImageSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (apProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (app) =>
% 98.41/13.28 ((
% 98.41/13.28 (infuncsetfunc) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcinfuncset) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamProp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lamp) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2p) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall1) =>
% 98.41/13.28 ((
% 98.41/13.28 (brelnall2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ex1E2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp3) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcextLem) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcGraphProp4) =>
% 98.41/13.28 ((
% 98.41/13.28 (subbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (eqbreln) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext) =>
% 98.41/13.28 ((
% 98.41/13.28 (funcext2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq1) =>
% 98.41/13.28 ((
% 98.41/13.28 (ap2apEq2) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta1) =>
% 98.41/13.28 ((
% 98.41/13.28 (lam2lamEq) =>
% 98.41/13.28 ((
% 98.41/13.28 (beta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (eta2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalseProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp1) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueProp2) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifSingleton) =>
% 98.41/13.28 ((
% 98.41/13.28 (ifp) =>
% 98.41/13.28 ((
% 98.41/13.28 (theeq) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrue) =>
% 98.41/13.28 ((
% 98.41/13.28 (iffalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (iftrueorfalse) =>
% 98.41/13.28 ((
% 98.41/13.28 (binintersectT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (binunionT_lem) =>
% 98.41/13.28 ((
% 98.41/13.28 (powersetT_lem) =>
% 98.41/13.28 ((
% 98.41/13.29 (setminusT_lem) =>
% 98.41/13.29 ((
% 98.41/13.29 (complementT_lem) =>
% 98.41/13.29 ((
% 98.41/13.29 (setextT) =>
% 98.41/13.29 ((
% 98.41/13.29 (subsetTI) =>
% 98.41/13.29 ((
% 98.41/13.29 (powersetTI1) =>
% 98.41/13.29 ((
% 98.41/13.29 (powersetTE1) =>
% 98.41/13.29 ((
% 98.41/13.29 (complementTI1) =>
% 98.41/13.29 ((
% 98.41/13.29 (complementTE1) =>
% 98.41/13.29 ((
% 98.41/13.29 (binintersectTELcontra) =>
% 98.41/13.29 ((
% 98.41/13.29 (binintersectTERcontra) =>
% 98.41/13.29 ((
% 98.41/13.29 (contrasubsetT) =>
% 98.41/13.29 ((
% 98.41/13.29 (contrasubsetT1) =>
% 98.41/13.29 ((
% 98.41/13.29 (contrasubsetT2) =>
% 98.41/13.29 ((
% 98.41/13.29 (contrasubsetT3) =>
% 98.41/13.29 ((
% 98.41/13.29 (doubleComplementI1) =>
% 98.41/13.29 ((
% 98.41/13.29 (doubleComplementE1) =>
% 98.41/13.29 ((
% 98.41/13.29 (doubleComplementSub1) =>
% 98.41/13.29 ((
% 98.41/13.29 (doubleComplementSub2) =>
% 98.41/13.29 ((
% 98.41/13.29 (doubleComplementEq) =>
% 98.41/13.29 ((
% 98.41/13.29 (complementTnotintersectT) =>
% 98.41/13.29 ((
% 98.41/13.29 (complementImpComplementIntersect) =>
% 98.41/13.29 ((
% 98.41/13.29 (complementSubsetComplementIntersect) =>
% 98.41/13.29 ((
% 98.41/13.29 (complementInPowersetComplementIntersect) =>
% 98.41/13.29 ((
% 98.41/13.29 (contraSubsetComplement) =>
% 98.41/13.29 ((
% 98.41/13.29 (complementTcontraSubset) =>
% 98.41/13.29 ((
% 98.41/13.29 (binunionTILcontra) =>
% 98.41/13.29 ((
% 98.41/13.29 (binunionTIRcontra) =>
% 98.41/13.29 ((
% 98.41/13.29 (inIntersectImpInUnion) =>
% 98.41/13.29 ((
% 98.41/13.29 (inIntersectImpInUnion2) =>
% 98.41/13.29 ((
% 98.41/13.29 (inIntersectImpInIntersectUnions) =>
% 98.41/13.29 ((
% 98.41/13.29 (intersectInPowersetIntersectUnions) =>
% 98.41/13.29 ((
% 98.41/13.29 (inComplementUnionImpNotIn1) =>
% 98.41/13.29 ((
% 98.41/13.29 (inComplementUnionImpInComplement1) =>
% 98.41/13.29 ((
% 98.41/13.29 (binunionTE) =>
% 98.41/13.29 ((
% 98.41/13.29 (binunionTEcontra) =>
% 98.41/13.29 ((
% 98.41/13.29 (demorgan2a1) =>
% 98.41/13.29 ((
% 98.41/13.29 (complementUnionInPowersetComplement) =>
% 98.41/13.29 ((
% 98.41/13.29 (demorgan2a2) =>
% 98.41/13.29 ((
% 98.41/13.29 (demorgan1a) =>
% 98.41/13.29 ((
% 98.41/13.29 (demorgan1b) =>
% 98.41/13.29 ((
% 98.41/13.29 (demorgan1) =>
% 98.41/13.29 ((
% 98.41/13.29 (demorgan2a) =>
% 98.41/13.29 ((
% 98.41/13.29 (demorgan2b2) =>
% 98.41/13.29 ((
% 98.41/13.29 (demorgan2b) =>
% 98.41/13.29 ((
% 98.41/13.29 (demorgan2) =>
% 98.41/13.29 ((
% 98.41/13.29 (woz13rule0) =>
% 98.41/13.29 ((
% 98.41/13.29 (woz13rule1) =>
% 98.41/13.29 ((
% 98.41/13.29 (woz13rule2) =>
% 98.41/13.29 ((
% 98.41/13.29 (woz13rule3) =>
% 98.41/13.29 ((
% 98.41/13.29 (woz13rule4) =>
% 98.41/13.29 ((
% 98.41/13.29 (woz1_1) =>
% 98.41/13.29 ((
% 98.41/13.29 (woz1_2) =>
% 98.41/13.29 ((
% 98.41/13.29 (woz1_3) =>
% 98.41/13.29 ((
% 98.41/13.29 (woz1_4) =>
% 98.41/13.29 ((
% 98.41/13.29 (woz1_5) =>
% 98.41/13.29 ((
% 98.41/13.29 (breln1all2) =>
% 98.41/13.29 ((
% 98.41/13.29 (breln1SetBreln1) =>
% 98.41/13.29 ((
% 98.41/13.29 (choice2fnsingleton) =>
% 98.41/13.29 ((
% 98.41/13.29 (setOfPairsIsBReln1) =>
% 98.41/13.29 ((
% 98.41/13.29 (breln1all1) =>
% 98.41/13.29 ((
% 98.41/13.29 (subbreln1) =>
% 98.41/13.29 ((
% 98.41/13.29 (eqbreln1) =>
% 98.41/13.29 ((
% 98.41/13.29 (breln1invprop) =>
% 98.41/13.29 ((
% 98.41/13.29 (breln1invI) =>
% 98.41/13.29 ((
% 98.41/13.29 (breln1invE) =>
% 98.41/13.29 ((
% 98.41/13.29 (breln1compprop) =>
% 98.41/13.29 ((
% 98.41/13.29 (breln1compI) =>
% 98.41/13.29 ((
% 98.41/13.29 (breln1compE) =>
% 98.41/13.29 ((
% 98.41/13.29 (breln1compEex) =>
% 98.41/13.29 ((
% 98.41/13.29 (breln1unionprop) =>
% 98.41/13.29 ((
% 98.41/13.29 (breln1unionIL) =>
% 98.41/13.29 ((
% 98.41/13.29 (breln1unionIR) =>
% 98.41/13.29 ((
% 98.41/13.29 (breln1unionI) =>
% 98.41/13.29 ((
% 98.41/13.29 (breln1unionE) =>
% 98.41/13.29 ((
% 98.41/13.29 (breln1unionEcases) =>
% 98.41/13.29 ((
% 98.41/13.29 (breln1unionCommutes) =>
% 98.41/13.29 ((
% 98.41/13.29 (woz2Ex) =>
% 98.41/13.29 ((
% 98.41/13.29 (woz2W) =>
% 98.41/13.29 ((
% 98.41/13.29 (woz2A) =>
% 98.41/13.29 ((
% 98.41/13.29 (woz2B) =>
% 98.41/13.29 ((
% 98.41/13.29 (image1Ex) =>
% 98.41/13.29 ((
% 98.41/13.29 (image1Ex1) =>
% 98.41/13.29 ((
% 98.41/13.29 (image1Equiv) =>
% 98.41/13.29 ((
% 98.41/13.29 (image1E) =>
% 98.41/13.29 ((
% 98.41/13.29 (image1I) =>
% 98.41/13.29 ((
% 98.41/13.29 (injFuncInInjFuncSet) =>
% 98.41/13.29 ((
% 98.41/13.29 (!!) @ (
% 98.41/13.29 (('#B') @ (
% 98.41/13.29 !!) @
% 98.41/13.29 (
% 98.41/13.29 (
% 98.41/13.29 ('#B') @ (
% 98.41/13.29 (
% 98.41/13.29 ('#B') @ (
% 98.41/13.29 !!))) @
% 98.41/13.29 (
% 98.41/13.29 (
% 98.41/13.29 ('#S') @ (
% 98.41/13.29 (
% 98.41/13.29 ('#B') @ (
% 98.41/13.29 '#S') @
% 98.41/13.29 (
% 98.41/13.29 (
% 98.41/13.29 ('#B') @ (
% 98.41/13.29 (
% 98.41/13.29 ('#B') @ (
% 98.41/13.29 '#S'))) @
% 98.41/13.29 (
% 98.41/13.29 (
% 98.41/13.29 ('#B') @ (
% 98.41/13.29 (
% 98.41/13.29 ('#B') @ (
% 98.41/13.29 (
% 98.41/13.29 ('#B') @ (
% 98.41/13.29 =>))))) @
% 98.41/13.29 (
% 98.41/13.29 (
% 98.41/13.29 ('#B') @ (
% 98.41/13.29 (
% 98.41/13.29 ('#B') @ (
% 98.41/13.29 (
% 98.41/13.29 ('#C') @ in)))) @
% 98.41/13.29 injFuncSet)))))))) @
% 98.41/13.29 (
% 98.41/13.29 (
% 98.41/13.29 ('#B') @ (
% 98.41/13.29 (
% 98.41/13.29 ('#B') @ (
% 98.41/13.29 (
% 98.41/13.29 ('#C') @ in)))) @
% 98.41/13.29 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.41/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl236])).
% 98.41/13.29 thf(zip_derived_cl264, plain,
% 98.41/13.29 (~ (((nonemptyE1) =>
% 98.41/13.29 (((nonemptyI) =>
% 98.41/13.29 (((nonemptyI1) =>
% 98.41/13.29 (((setadjoinIL) =>
% 98.41/13.29 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 98.41/13.29 (((setadjoinIR) =>
% 98.41/13.29 (((setadjoinE) =>
% 98.41/13.29 (((setadjoinOr) =>
% 98.41/13.29 (((setoftrueEq) =>
% 98.41/13.29 (((powersetI) =>
% 98.41/13.29 (((emptyinPowerset) =>
% 98.41/13.29 (((emptyInPowerset) =>
% 98.41/13.29 (((powersetE) =>
% 98.41/13.29 (((setunionI) =>
% 98.41/13.29 (((setunionE) =>
% 98.41/13.29 (((subPowSU) =>
% 98.41/13.29 (((exuE2) =>
% 98.41/13.29 (((nonemptyImpWitness) =>
% 98.41/13.29 (((uniqinunit) =>
% 98.41/13.29 (((notinsingleton) =>
% 98.41/13.29 (((eqinunit) =>
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% 98.41/13.29 (((upairsetE) =>
% 98.41/13.29 (((upairsetIL) =>
% 98.41/13.29 (((upairsetIR) =>
% 98.41/13.29 (((emptyE1) =>
% 98.41/13.29 (((vacuousDall) =>
% 98.41/13.29 (((quantDeMorgan1) =>
% 98.41/13.29 (((quantDeMorgan2) =>
% 98.41/13.29 (((quantDeMorgan3) =>
% 98.41/13.29 ((
% 98.41/13.29 (quantDeMorgan4) =>
% 98.41/13.29 ((
% 98.41/13.29 (prop2setI) =>
% 98.41/13.29 ((
% 98.41/13.29 (prop2set2propI) =>
% 98.41/13.29 ((
% 98.41/13.29 (notdexE) =>
% 98.41/13.29 ((
% 98.41/13.29 (notdallE) =>
% 98.41/13.29 ((
% 98.41/13.29 (exuI1) =>
% 98.41/13.29 ((
% 98.41/13.29 (exuI3) =>
% 98.41/13.29 ((
% 98.41/13.29 (exuI2) =>
% 98.41/13.29 ((
% 98.41/13.29 (inCongP) =>
% 98.41/13.29 ((
% 98.41/13.29 (in__Cong) =>
% 98.41/13.29 ((
% 98.41/13.29 (exuE3u) =>
% 98.41/13.29 ((
% 98.41/13.29 (exu__Cong) =>
% 98.41/13.29 ((
% 98.41/13.29 (setadjoin__Cong) =>
% 98.41/13.29 ((
% 98.41/13.29 (powerset__Cong) =>
% 98.41/13.29 ((
% 98.41/13.29 (setunion__Cong) =>
% 98.41/13.29 ((
% 98.41/13.29 (exuEu) =>
% 98.41/13.29 ((
% 98.41/13.29 (descr__Cong) =>
% 98.41/13.29 ((
% 98.41/13.29 (dsetconstr__Cong) =>
% 98.41/13.29 ((
% 98.41/13.29 (subsetI1) =>
% 98.41/13.29 ((
% 98.41/13.29 (eqimpsubset2) =>
% 98.41/13.29 ((
% 98.41/13.29 (eqimpsubset1) =>
% 98.41/13.29 ((
% 98.41/13.29 (subsetI2) =>
% 98.41/13.29 ((
% 98.41/13.29 (emptysetsubset) =>
% 98.41/13.29 ((
% 98.41/13.29 (subsetE) =>
% 98.41/13.29 ((
% 98.41/13.29 (subsetE2) =>
% 98.41/13.29 ((
% 98.41/13.29 (notsubsetI) =>
% 98.41/13.29 ((
% 98.41/13.29 (notequalI1) =>
% 98.41/13.29 ((
% 98.41/13.29 (notequalI2) =>
% 98.41/13.29 ((
% 98.41/13.29 (subsetRefl) =>
% 98.41/13.29 ((
% 98.41/13.29 (subsetTrans) =>
% 98.41/13.29 ((
% 98.41/13.29 (setadjoinSub) =>
% 98.41/13.29 ((
% 98.41/13.29 (setadjoinSub2) =>
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% 98.41/13.29 (ubforcartprodlem3) =>
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% 98.41/13.29 ((
% 98.41/13.29 (cartprodmempair) =>
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% 98.41/13.29 (ex1I2) =>
% 98.41/13.29 ((
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% 98.41/13.29 (kfstpairEq) =>
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% 98.41/13.29 (cartprodfstin) =>
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% 98.41/13.29 (ksndpairEq) =>
% 98.41/13.29 ((
% 98.41/13.29 (kpairsurjEq) =>
% 98.41/13.29 ((
% 98.41/13.29 (cartprodsndin) =>
% 98.41/13.29 ((
% 98.41/13.29 (cartprodpairmemEL) =>
% 98.41/13.29 ((
% 98.41/13.29 (cartprodpairmemER) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodmempaircEq) =>
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% 99.02/13.29 (cartprodfstpairEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodsndpairEq) =>
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% 99.02/13.29 (cartprodpairsurjEq) =>
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% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrSub) =>
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% 99.02/13.29 (dpsetconstrEL2) =>
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% 99.02/13.29 (dpsetconstrER) =>
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% 99.02/13.29 (app) =>
% 99.02/13.29 ((
% 99.02/13.29 (infuncsetfunc) =>
% 99.02/13.29 ((
% 99.02/13.29 (ap2p) =>
% 99.02/13.29 ((
% 99.02/13.29 (funcinfuncset) =>
% 99.02/13.29 ((
% 99.02/13.29 (lamProp) =>
% 99.02/13.29 ((
% 99.02/13.29 (lamp) =>
% 99.02/13.29 ((
% 99.02/13.29 (lam2p) =>
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% 99.02/13.29 (brelnall2) =>
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% 99.02/13.29 (ex1E2) =>
% 99.02/13.29 ((
% 99.02/13.29 (funcGraphProp1) =>
% 99.02/13.29 ((
% 99.02/13.29 (funcGraphProp3) =>
% 99.02/13.29 ((
% 99.02/13.29 (funcGraphProp2) =>
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% 99.02/13.29 (eta1) =>
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% 99.02/13.29 (beta2) =>
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (binintersectTERcontra) =>
% 99.02/13.29 ((
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% 99.02/13.29 (contrasubsetT1) =>
% 99.02/13.29 ((
% 99.02/13.29 (contrasubsetT2) =>
% 99.02/13.29 ((
% 99.02/13.29 (contrasubsetT3) =>
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% 99.02/13.29 (doubleComplementSub2) =>
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% 99.02/13.29 (complementSubsetComplementIntersect) =>
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% 99.02/13.29 ((
% 99.02/13.29 (inIntersectImpInUnion2) =>
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% 99.02/13.29 (inIntersectImpInIntersectUnions) =>
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% 99.02/13.29 ((
% 99.02/13.29 (demorgan2a) =>
% 99.02/13.29 ((
% 99.02/13.29 (demorgan2b2) =>
% 99.02/13.29 ((
% 99.02/13.29 (demorgan2b) =>
% 99.02/13.29 ((
% 99.02/13.29 (demorgan2) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (woz13rule1) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 (woz1_5) =>
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% 99.02/13.29 ((
% 99.02/13.29 (breln1invE) =>
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% 99.02/13.29 ((
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% 99.02/13.29 (setadjoin__Cong) =>
% 99.02/13.29 ((
% 99.02/13.29 (powerset__Cong) =>
% 99.02/13.29 ((
% 99.02/13.29 (setunion__Cong) =>
% 99.02/13.29 ((
% 99.02/13.29 (exuEu) =>
% 99.02/13.29 ((
% 99.02/13.29 (descr__Cong) =>
% 99.02/13.29 ((
% 99.02/13.29 (dsetconstr__Cong) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (eqimpsubset2) =>
% 99.02/13.29 ((
% 99.02/13.29 (eqimpsubset1) =>
% 99.02/13.29 ((
% 99.02/13.29 (subsetI2) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (subsetE) =>
% 99.02/13.29 ((
% 99.02/13.29 (subsetE2) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (powersetE1) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (powersetsubset) =>
% 99.02/13.29 ((
% 99.02/13.29 (sepInPowerset) =>
% 99.02/13.29 ((
% 99.02/13.29 (sepSubset) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (upairset2IR) =>
% 99.02/13.29 ((
% 99.02/13.29 (binunionIR) =>
% 99.02/13.29 ((
% 99.02/13.29 (binunionEcases) =>
% 99.02/13.29 ((
% 99.02/13.29 (binunionE) =>
% 99.02/13.29 ((
% 99.02/13.29 (binunionLsub) =>
% 99.02/13.29 ((
% 99.02/13.29 (binunionRsub) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (binintersectSubset5) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (binintersectLsub) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectSubset2) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectSubset3) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectER) =>
% 99.02/13.29 ((
% 99.02/13.29 (disjointsetsI1) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectRsub) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectSubset4) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectSubset1) =>
% 99.02/13.29 ((
% 99.02/13.29 (bs114d) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusI) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusEL) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusER) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusSubset2) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusERneg) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusELneg) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusILneg) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusIRneg) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusLsub) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusSubset1) =>
% 99.02/13.29 ((
% 99.02/13.29 (symdiffE) =>
% 99.02/13.29 ((
% 99.02/13.29 (symdiffI1) =>
% 99.02/13.29 ((
% 99.02/13.29 (symdiffI2) =>
% 99.02/13.29 ((
% 99.02/13.29 (symdiffIneg1) =>
% 99.02/13.29 ((
% 99.02/13.29 (symdiffIneg2) =>
% 99.02/13.29 ((
% 99.02/13.29 (secondinupair) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairIL) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairIR) =>
% 99.02/13.29 ((
% 99.02/13.29 (kpairiskpair) =>
% 99.02/13.29 ((
% 99.02/13.29 (kpairp) =>
% 99.02/13.29 ((
% 99.02/13.29 (singletonsubset) =>
% 99.02/13.29 ((
% 99.02/13.29 (singletoninpowerset) =>
% 99.02/13.29 ((
% 99.02/13.29 (singletoninpowunion) =>
% 99.02/13.29 ((
% 99.02/13.29 (upairset2E) =>
% 99.02/13.29 ((
% 99.02/13.29 (upairsubunion) =>
% 99.02/13.29 ((
% 99.02/13.29 (upairinpowunion) =>
% 99.02/13.29 ((
% 99.02/13.29 (ubforcartprodlem1) =>
% 99.02/13.29 ((
% 99.02/13.29 (ubforcartprodlem2) =>
% 99.02/13.29 ((
% 99.02/13.29 (ubforcartprodlem3) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodpairin) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodmempair1) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodmempair) =>
% 99.02/13.29 ((
% 99.02/13.29 (setunionE2) =>
% 99.02/13.29 ((
% 99.02/13.29 (setunionsingleton1) =>
% 99.02/13.29 ((
% 99.02/13.29 (setunionsingleton2) =>
% 99.02/13.29 ((
% 99.02/13.29 (setunionsingleton) =>
% 99.02/13.29 ((
% 99.02/13.29 (singletonprop) =>
% 99.02/13.29 ((
% 99.02/13.29 (ex1E1) =>
% 99.02/13.29 ((
% 99.02/13.29 (ex1I) =>
% 99.02/13.29 ((
% 99.02/13.29 (ex1I2) =>
% 99.02/13.29 ((
% 99.02/13.29 (singletonsuniq) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjL1) =>
% 99.02/13.29 ((
% 99.02/13.29 (kfstsingleton) =>
% 99.02/13.29 ((
% 99.02/13.29 (theprop) =>
% 99.02/13.29 ((
% 99.02/13.29 (kfstpairEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodfstin) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjL2) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjL) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjR11) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjR12) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjR1) =>
% 99.02/13.29 ((
% 99.02/13.29 (upairequniteq) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjR2) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjR) =>
% 99.02/13.29 ((
% 99.02/13.29 (ksndsingleton) =>
% 99.02/13.29 ((
% 99.02/13.29 (ksndpairEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (kpairsurjEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodsndin) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodpairmemEL) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodpairmemER) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodmempaircEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodfstpairEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodsndpairEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodpairsurjEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrI) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrSub) =>
% 99.02/13.29 ((
% 99.02/13.29 (setOfPairsIsBReln) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrERa) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrEL1) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrEL2) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrER) =>
% 99.02/13.29 ((
% 99.02/13.29 (funcImageSingleton) =>
% 99.02/13.29 ((
% 99.02/13.29 (apProp) =>
% 99.02/13.29 ((
% 99.02/13.29 (app) =>
% 99.02/13.29 ((
% 99.02/13.29 (infuncsetfunc) =>
% 99.02/13.29 ((
% 99.02/13.29 (ap2p) =>
% 99.02/13.29 ((
% 99.02/13.29 (funcinfuncset) =>
% 99.02/13.29 ((
% 99.02/13.29 (lamProp) =>
% 99.02/13.29 ((
% 99.02/13.29 (lamp) =>
% 99.02/13.29 ((
% 99.02/13.29 (lam2p) =>
% 99.02/13.29 ((
% 99.02/13.29 (brelnall1) =>
% 99.02/13.29 ((
% 99.02/13.29 (brelnall2) =>
% 99.02/13.29 ((
% 99.02/13.29 (ex1E2) =>
% 99.02/13.29 ((
% 99.02/13.29 (funcGraphProp1) =>
% 99.02/13.29 ((
% 99.02/13.29 (funcGraphProp3) =>
% 99.02/13.29 ((
% 99.02/13.29 (funcGraphProp2) =>
% 99.02/13.29 ((
% 99.02/13.29 (funcextLem) =>
% 99.02/13.29 ((
% 99.02/13.29 (funcGraphProp4) =>
% 99.02/13.29 ((
% 99.02/13.29 (subbreln) =>
% 99.02/13.29 ((
% 99.02/13.29 (eqbreln) =>
% 99.02/13.29 ((
% 99.02/13.29 (funcext) =>
% 99.02/13.29 ((
% 99.02/13.29 (funcext2) =>
% 99.02/13.29 ((
% 99.02/13.29 (ap2apEq1) =>
% 99.02/13.29 ((
% 99.02/13.29 (ap2apEq2) =>
% 99.02/13.29 ((
% 99.02/13.29 (beta1) =>
% 99.02/13.29 ((
% 99.02/13.29 (eta1) =>
% 99.02/13.29 ((
% 99.02/13.29 (lam2lamEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (beta2) =>
% 99.02/13.29 ((
% 99.02/13.29 (eta2) =>
% 99.02/13.29 ((
% 99.02/13.29 (iffalseProp1) =>
% 99.02/13.29 ((
% 99.02/13.29 (iffalseProp2) =>
% 99.02/13.29 ((
% 99.02/13.29 (iftrueProp1) =>
% 99.02/13.29 ((
% 99.02/13.29 (iftrueProp2) =>
% 99.02/13.29 ((
% 99.02/13.29 (ifSingleton) =>
% 99.02/13.29 ((
% 99.02/13.29 (ifp) =>
% 99.02/13.29 ((
% 99.02/13.29 (theeq) =>
% 99.02/13.29 ((
% 99.02/13.29 (iftrue) =>
% 99.02/13.29 ((
% 99.02/13.29 (iffalse) =>
% 99.02/13.29 ((
% 99.02/13.29 (iftrueorfalse) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectT_lem) =>
% 99.02/13.29 ((
% 99.02/13.29 (binunionT_lem) =>
% 99.02/13.29 ((
% 99.02/13.29 (powersetT_lem) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusT_lem) =>
% 99.02/13.29 ((
% 99.02/13.29 (complementT_lem) =>
% 99.02/13.29 ((
% 99.02/13.29 (setextT) =>
% 99.02/13.29 ((
% 99.02/13.29 (subsetTI) =>
% 99.02/13.29 ((
% 99.02/13.29 (powersetTI1) =>
% 99.02/13.29 ((
% 99.02/13.29 (powersetTE1) =>
% 99.02/13.29 ((
% 99.02/13.29 (complementTI1) =>
% 99.02/13.29 ((
% 99.02/13.29 (complementTE1) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectTELcontra) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectTERcontra) =>
% 99.02/13.29 ((
% 99.02/13.29 (contrasubsetT) =>
% 99.02/13.29 ((
% 99.02/13.29 (contrasubsetT1) =>
% 99.02/13.29 ((
% 99.02/13.29 (contrasubsetT2) =>
% 99.02/13.29 ((
% 99.02/13.29 (contrasubsetT3) =>
% 99.02/13.29 ((
% 99.02/13.29 (doubleComplementI1) =>
% 99.02/13.29 ((
% 99.02/13.29 (doubleComplementE1) =>
% 99.02/13.29 ((
% 99.02/13.29 (doubleComplementSub1) =>
% 99.02/13.29 ((
% 99.02/13.29 (doubleComplementSub2) =>
% 99.02/13.29 ((
% 99.02/13.29 (doubleComplementEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (complementTnotintersectT) =>
% 99.02/13.29 ((
% 99.02/13.29 (complementImpComplementIntersect) =>
% 99.02/13.29 ((
% 99.02/13.29 (complementSubsetComplementIntersect) =>
% 99.02/13.29 ((
% 99.02/13.29 (complementInPowersetComplementIntersect) =>
% 99.02/13.29 ((
% 99.02/13.29 (contraSubsetComplement) =>
% 99.02/13.29 ((
% 99.02/13.29 (complementTcontraSubset) =>
% 99.02/13.29 ((
% 99.02/13.29 (binunionTILcontra) =>
% 99.02/13.29 ((
% 99.02/13.29 (binunionTIRcontra) =>
% 99.02/13.29 ((
% 99.02/13.29 (inIntersectImpInUnion) =>
% 99.02/13.29 ((
% 99.02/13.29 (inIntersectImpInUnion2) =>
% 99.02/13.29 ((
% 99.02/13.29 (inIntersectImpInIntersectUnions) =>
% 99.02/13.29 ((
% 99.02/13.29 (intersectInPowersetIntersectUnions) =>
% 99.02/13.29 ((
% 99.02/13.29 (inComplementUnionImpNotIn1) =>
% 99.02/13.29 ((
% 99.02/13.29 (inComplementUnionImpInComplement1) =>
% 99.02/13.29 ((
% 99.02/13.29 (binunionTE) =>
% 99.02/13.29 ((
% 99.02/13.29 (binunionTEcontra) =>
% 99.02/13.29 ((
% 99.02/13.29 (demorgan2a1) =>
% 99.02/13.29 ((
% 99.02/13.29 (complementUnionInPowersetComplement) =>
% 99.02/13.29 ((
% 99.02/13.29 (demorgan2a2) =>
% 99.02/13.29 ((
% 99.02/13.29 (demorgan1a) =>
% 99.02/13.29 ((
% 99.02/13.29 (demorgan1b) =>
% 99.02/13.29 ((
% 99.02/13.29 (demorgan1) =>
% 99.02/13.29 ((
% 99.02/13.29 (demorgan2a) =>
% 99.02/13.29 ((
% 99.02/13.29 (demorgan2b2) =>
% 99.02/13.29 ((
% 99.02/13.29 (demorgan2b) =>
% 99.02/13.29 ((
% 99.02/13.29 (demorgan2) =>
% 99.02/13.29 ((
% 99.02/13.29 (woz13rule0) =>
% 99.02/13.29 ((
% 99.02/13.29 (woz13rule1) =>
% 99.02/13.29 ((
% 99.02/13.29 (woz13rule2) =>
% 99.02/13.29 ((
% 99.02/13.29 (woz13rule3) =>
% 99.02/13.29 ((
% 99.02/13.29 (woz13rule4) =>
% 99.02/13.29 ((
% 99.02/13.29 (woz1_1) =>
% 99.02/13.29 ((
% 99.02/13.29 (woz1_2) =>
% 99.02/13.29 ((
% 99.02/13.29 (woz1_3) =>
% 99.02/13.29 ((
% 99.02/13.29 (woz1_4) =>
% 99.02/13.29 ((
% 99.02/13.29 (woz1_5) =>
% 99.02/13.29 ((
% 99.02/13.29 (breln1all2) =>
% 99.02/13.29 ((
% 99.02/13.29 (breln1SetBreln1) =>
% 99.02/13.29 ((
% 99.02/13.29 (choice2fnsingleton) =>
% 99.02/13.29 ((
% 99.02/13.29 (setOfPairsIsBReln1) =>
% 99.02/13.29 ((
% 99.02/13.29 (breln1all1) =>
% 99.02/13.29 ((
% 99.02/13.29 (subbreln1) =>
% 99.02/13.29 ((
% 99.02/13.29 (eqbreln1) =>
% 99.02/13.29 ((
% 99.02/13.29 (breln1invprop) =>
% 99.02/13.29 ((
% 99.02/13.29 (breln1invI) =>
% 99.02/13.29 ((
% 99.02/13.29 (breln1invE) =>
% 99.02/13.29 ((
% 99.02/13.29 (breln1compprop) =>
% 99.02/13.29 ((
% 99.02/13.29 (breln1compI) =>
% 99.02/13.29 ((
% 99.02/13.29 (breln1compE) =>
% 99.02/13.29 ((
% 99.02/13.29 (breln1compEex) =>
% 99.02/13.29 ((
% 99.02/13.29 (breln1unionprop) =>
% 99.02/13.29 ((
% 99.02/13.29 (breln1unionIL) =>
% 99.02/13.29 ((
% 99.02/13.29 (breln1unionIR) =>
% 99.02/13.29 ((
% 99.02/13.29 (breln1unionI) =>
% 99.02/13.29 ((
% 99.02/13.29 (breln1unionE) =>
% 99.02/13.29 ((
% 99.02/13.29 (breln1unionEcases) =>
% 99.02/13.29 ((
% 99.02/13.29 (breln1unionCommutes) =>
% 99.02/13.29 ((
% 99.02/13.29 (woz2Ex) =>
% 99.02/13.29 ((
% 99.02/13.29 (woz2W) =>
% 99.02/13.29 ((
% 99.02/13.29 (woz2A) =>
% 99.02/13.29 ((
% 99.02/13.29 (woz2B) =>
% 99.02/13.29 ((
% 99.02/13.29 (image1Ex) =>
% 99.02/13.29 ((
% 99.02/13.29 (image1Ex1) =>
% 99.02/13.29 ((
% 99.02/13.29 (image1Equiv) =>
% 99.02/13.29 ((
% 99.02/13.29 (image1E) =>
% 99.02/13.29 ((
% 99.02/13.29 (image1I) =>
% 99.02/13.29 ((
% 99.02/13.29 (injFuncInInjFuncSet) =>
% 99.02/13.29 ((
% 99.02/13.29 (!!) @ (
% 99.02/13.29 (('#B') @ (
% 99.02/13.29 !!) @
% 99.02/13.29 (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 !!))) @
% 99.02/13.29 (
% 99.02/13.29 (
% 99.02/13.29 ('#S') @ (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 '#S') @
% 99.02/13.29 (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
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% 99.02/13.29 (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 =>))))) @
% 99.02/13.29 (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 (
% 99.02/13.29 ('#C') @ in)))) @
% 99.02/13.29 injFuncSet)))))))) @
% 99.02/13.29 (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 (
% 99.02/13.29 ('#C') @ in)))) @
% 99.02/13.29 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl264])).
% 99.02/13.29 thf(zip_derived_cl293, plain,
% 99.02/13.29 (~ (((nonemptyI1) =>
% 99.02/13.29 (((setadjoinIL) =>
% 99.02/13.29 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 99.02/13.29 (((setadjoinIR) =>
% 99.02/13.29 (((setadjoinE) =>
% 99.02/13.29 (((setadjoinOr) =>
% 99.02/13.29 (((setoftrueEq) =>
% 99.02/13.29 (((powersetI) =>
% 99.02/13.29 (((emptyinPowerset) =>
% 99.02/13.29 (((emptyInPowerset) =>
% 99.02/13.29 (((powersetE) =>
% 99.02/13.29 (((setunionI) =>
% 99.02/13.29 (((setunionE) =>
% 99.02/13.29 (((subPowSU) =>
% 99.02/13.29 (((exuE2) =>
% 99.02/13.29 (((nonemptyImpWitness) =>
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% 99.02/13.29 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl280])).
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% 99.02/13.29 (((quantDeMorgan1) =>
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% 99.02/13.29 (((quantDeMorgan4) =>
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (exuI2) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (exu__Cong) =>
% 99.02/13.29 ((
% 99.02/13.29 (setadjoin__Cong) =>
% 99.02/13.29 ((
% 99.02/13.29 (powerset__Cong) =>
% 99.02/13.29 ((
% 99.02/13.29 (setunion__Cong) =>
% 99.02/13.29 ((
% 99.02/13.29 (exuEu) =>
% 99.02/13.29 ((
% 99.02/13.29 (descr__Cong) =>
% 99.02/13.29 ((
% 99.02/13.29 (dsetconstr__Cong) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (powersetE1) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (binunionEcases) =>
% 99.02/13.29 ((
% 99.02/13.29 (binunionE) =>
% 99.02/13.29 ((
% 99.02/13.29 (binunionLsub) =>
% 99.02/13.29 ((
% 99.02/13.29 (binunionRsub) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectI) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectSubset5) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectEL) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectLsub) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectSubset2) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectSubset3) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectER) =>
% 99.02/13.29 ((
% 99.02/13.29 (disjointsetsI1) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectRsub) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectSubset4) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectSubset1) =>
% 99.02/13.29 ((
% 99.02/13.29 (bs114d) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (setminusEL) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusER) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusSubset2) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (setminusELneg) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusILneg) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusIRneg) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusLsub) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusSubset1) =>
% 99.02/13.29 ((
% 99.02/13.29 (symdiffE) =>
% 99.02/13.29 ((
% 99.02/13.29 (symdiffI1) =>
% 99.02/13.29 ((
% 99.02/13.29 (symdiffI2) =>
% 99.02/13.29 ((
% 99.02/13.29 (symdiffIneg1) =>
% 99.02/13.29 ((
% 99.02/13.29 (symdiffIneg2) =>
% 99.02/13.29 ((
% 99.02/13.29 (secondinupair) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairIL) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairIR) =>
% 99.02/13.29 ((
% 99.02/13.29 (kpairiskpair) =>
% 99.02/13.29 ((
% 99.02/13.29 (kpairp) =>
% 99.02/13.29 ((
% 99.02/13.29 (singletonsubset) =>
% 99.02/13.29 ((
% 99.02/13.29 (singletoninpowerset) =>
% 99.02/13.29 ((
% 99.02/13.29 (singletoninpowunion) =>
% 99.02/13.29 ((
% 99.02/13.29 (upairset2E) =>
% 99.02/13.29 ((
% 99.02/13.29 (upairsubunion) =>
% 99.02/13.29 ((
% 99.02/13.29 (upairinpowunion) =>
% 99.02/13.29 ((
% 99.02/13.29 (ubforcartprodlem1) =>
% 99.02/13.29 ((
% 99.02/13.29 (ubforcartprodlem2) =>
% 99.02/13.29 ((
% 99.02/13.29 (ubforcartprodlem3) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodpairin) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodmempair1) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodmempair) =>
% 99.02/13.29 ((
% 99.02/13.29 (setunionE2) =>
% 99.02/13.29 ((
% 99.02/13.29 (setunionsingleton1) =>
% 99.02/13.29 ((
% 99.02/13.29 (setunionsingleton2) =>
% 99.02/13.29 ((
% 99.02/13.29 (setunionsingleton) =>
% 99.02/13.29 ((
% 99.02/13.29 (singletonprop) =>
% 99.02/13.29 ((
% 99.02/13.29 (ex1E1) =>
% 99.02/13.29 ((
% 99.02/13.29 (ex1I) =>
% 99.02/13.29 ((
% 99.02/13.29 (ex1I2) =>
% 99.02/13.29 ((
% 99.02/13.29 (singletonsuniq) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjL1) =>
% 99.02/13.29 ((
% 99.02/13.29 (kfstsingleton) =>
% 99.02/13.29 ((
% 99.02/13.29 (theprop) =>
% 99.02/13.29 ((
% 99.02/13.29 (kfstpairEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodfstin) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjL2) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjL) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjR11) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjR12) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjR1) =>
% 99.02/13.29 ((
% 99.02/13.29 (upairequniteq) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjR2) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjR) =>
% 99.02/13.29 ((
% 99.02/13.29 (ksndsingleton) =>
% 99.02/13.29 ((
% 99.02/13.29 (ksndpairEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (kpairsurjEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodsndin) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodpairmemEL) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodpairmemER) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodmempaircEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodfstpairEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodsndpairEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodpairsurjEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrI) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrSub) =>
% 99.02/13.29 ((
% 99.02/13.29 (setOfPairsIsBReln) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrERa) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrEL1) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrEL2) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrER) =>
% 99.02/13.29 ((
% 99.02/13.29 (funcImageSingleton) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (funcinfuncset) =>
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% 99.02/13.29 ((
% 99.02/13.29 (lamp) =>
% 99.02/13.29 ((
% 99.02/13.29 (lam2p) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (funcGraphProp3) =>
% 99.02/13.29 ((
% 99.02/13.29 (funcGraphProp2) =>
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% 99.02/13.29 ((
% 99.02/13.29 (funcGraphProp4) =>
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (ap2apEq2) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (eta1) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (intersectInPowersetIntersectUnions) =>
% 99.02/13.29 ((
% 99.02/13.29 (inComplementUnionImpNotIn1) =>
% 99.02/13.29 ((
% 99.02/13.29 (inComplementUnionImpInComplement1) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (complementUnionInPowersetComplement) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ('#B') @ (
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% 99.02/13.29 ('#B') @ (
% 99.02/13.29 !!))) @
% 99.02/13.29 (
% 99.02/13.29 (
% 99.02/13.29 ('#S') @ (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 '#S') @
% 99.02/13.29 (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
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% 99.02/13.29 (
% 99.02/13.29 (
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% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
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% 99.02/13.29 (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 (
% 99.02/13.29 ('#C') @ in)))) @
% 99.02/13.29 injFuncSet)))))))) @
% 99.02/13.29 (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 (
% 99.02/13.29 ('#B') @ (
% 99.02/13.29 (
% 99.02/13.29 ('#C') @ in)))) @
% 99.02/13.29 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl293])).
% 99.02/13.29 thf(zip_derived_cl322, plain,
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% 99.02/13.29 (((emptyInPowerset) =>
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% 99.02/13.29 (((setunionE) =>
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% 99.02/13.29 (((nonemptyImpWitness) =>
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% 99.02/13.29 (((quantDeMorgan1) =>
% 99.02/13.29 (((quantDeMorgan2) =>
% 99.02/13.29 (((quantDeMorgan3) =>
% 99.02/13.29 (((quantDeMorgan4) =>
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% 99.02/13.29 (((prop2set2propI) =>
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (exuI3) =>
% 99.02/13.29 ((
% 99.02/13.29 (exuI2) =>
% 99.02/13.29 ((
% 99.02/13.29 (inCongP) =>
% 99.02/13.29 ((
% 99.02/13.29 (in__Cong) =>
% 99.02/13.29 ((
% 99.02/13.29 (exuE3u) =>
% 99.02/13.29 ((
% 99.02/13.29 (exu__Cong) =>
% 99.02/13.29 ((
% 99.02/13.29 (setadjoin__Cong) =>
% 99.02/13.29 ((
% 99.02/13.29 (powerset__Cong) =>
% 99.02/13.29 ((
% 99.02/13.29 (setunion__Cong) =>
% 99.02/13.29 ((
% 99.02/13.29 (exuEu) =>
% 99.02/13.29 ((
% 99.02/13.29 (descr__Cong) =>
% 99.02/13.29 ((
% 99.02/13.29 (dsetconstr__Cong) =>
% 99.02/13.29 ((
% 99.02/13.29 (subsetI1) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (notequalI2) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (setadjoinSub2) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (powersetE1) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (powersetsubset) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (sepSubset) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (binunionE) =>
% 99.02/13.29 ((
% 99.02/13.29 (binunionLsub) =>
% 99.02/13.29 ((
% 99.02/13.29 (binunionRsub) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectI) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectSubset5) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectEL) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectLsub) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectSubset2) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectSubset3) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectER) =>
% 99.02/13.29 ((
% 99.02/13.29 (disjointsetsI1) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectRsub) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectSubset4) =>
% 99.02/13.29 ((
% 99.02/13.29 (binintersectSubset1) =>
% 99.02/13.29 ((
% 99.02/13.29 (bs114d) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusI) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusEL) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusER) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusSubset2) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusERneg) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusELneg) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusILneg) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusIRneg) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusLsub) =>
% 99.02/13.29 ((
% 99.02/13.29 (setminusSubset1) =>
% 99.02/13.29 ((
% 99.02/13.29 (symdiffE) =>
% 99.02/13.29 ((
% 99.02/13.29 (symdiffI1) =>
% 99.02/13.29 ((
% 99.02/13.29 (symdiffI2) =>
% 99.02/13.29 ((
% 99.02/13.29 (symdiffIneg1) =>
% 99.02/13.29 ((
% 99.02/13.29 (symdiffIneg2) =>
% 99.02/13.29 ((
% 99.02/13.29 (secondinupair) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairIL) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairIR) =>
% 99.02/13.29 ((
% 99.02/13.29 (kpairiskpair) =>
% 99.02/13.29 ((
% 99.02/13.29 (kpairp) =>
% 99.02/13.29 ((
% 99.02/13.29 (singletonsubset) =>
% 99.02/13.29 ((
% 99.02/13.29 (singletoninpowerset) =>
% 99.02/13.29 ((
% 99.02/13.29 (singletoninpowunion) =>
% 99.02/13.29 ((
% 99.02/13.29 (upairset2E) =>
% 99.02/13.29 ((
% 99.02/13.29 (upairsubunion) =>
% 99.02/13.29 ((
% 99.02/13.29 (upairinpowunion) =>
% 99.02/13.29 ((
% 99.02/13.29 (ubforcartprodlem1) =>
% 99.02/13.29 ((
% 99.02/13.29 (ubforcartprodlem2) =>
% 99.02/13.29 ((
% 99.02/13.29 (ubforcartprodlem3) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodpairin) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodmempair1) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodmempair) =>
% 99.02/13.29 ((
% 99.02/13.29 (setunionE2) =>
% 99.02/13.29 ((
% 99.02/13.29 (setunionsingleton1) =>
% 99.02/13.29 ((
% 99.02/13.29 (setunionsingleton2) =>
% 99.02/13.29 ((
% 99.02/13.29 (setunionsingleton) =>
% 99.02/13.29 ((
% 99.02/13.29 (singletonprop) =>
% 99.02/13.29 ((
% 99.02/13.29 (ex1E1) =>
% 99.02/13.29 ((
% 99.02/13.29 (ex1I) =>
% 99.02/13.29 ((
% 99.02/13.29 (ex1I2) =>
% 99.02/13.29 ((
% 99.02/13.29 (singletonsuniq) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjL1) =>
% 99.02/13.29 ((
% 99.02/13.29 (kfstsingleton) =>
% 99.02/13.29 ((
% 99.02/13.29 (theprop) =>
% 99.02/13.29 ((
% 99.02/13.29 (kfstpairEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodfstin) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjL2) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjL) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjR11) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjR12) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjR1) =>
% 99.02/13.29 ((
% 99.02/13.29 (upairequniteq) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjR2) =>
% 99.02/13.29 ((
% 99.02/13.29 (setukpairinjR) =>
% 99.02/13.29 ((
% 99.02/13.29 (ksndsingleton) =>
% 99.02/13.29 ((
% 99.02/13.29 (ksndpairEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (kpairsurjEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodsndin) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodpairmemEL) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodpairmemER) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodmempaircEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodfstpairEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodsndpairEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (cartprodpairsurjEq) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrI) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrSub) =>
% 99.02/13.29 ((
% 99.02/13.29 (setOfPairsIsBReln) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrERa) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrEL1) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrEL2) =>
% 99.02/13.29 ((
% 99.02/13.29 (dpsetconstrER) =>
% 99.02/13.29 ((
% 99.02/13.29 (funcImageSingleton) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (lam2p) =>
% 99.02/13.29 ((
% 99.02/13.29 (brelnall1) =>
% 99.02/13.29 ((
% 99.02/13.29 (brelnall2) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (funcGraphProp2) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
% 99.02/13.29 (inComplementUnionImpNotIn1) =>
% 99.02/13.29 ((
% 99.02/13.29 (inComplementUnionImpInComplement1) =>
% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.29 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 (ubforcartprodlem3) =>
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% 99.02/13.30 ((
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% 99.02/13.30 (demorgan2a) =>
% 99.02/13.30 ((
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% 99.02/13.30 (demorgan2b) =>
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% 99.02/13.30 ((
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% 99.02/13.30 (woz13rule2) =>
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% 99.02/13.30 (woz1_4) =>
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% 99.02/13.30 (woz1_5) =>
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% 99.02/13.30 (breln1invI) =>
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% 99.02/13.30 (breln1invE) =>
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% 99.02/13.30 (breln1compprop) =>
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% 99.02/13.30 (breln1compI) =>
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% 99.02/13.30 (breln1compE) =>
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% 99.02/13.30 (breln1compEex) =>
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% 99.02/13.30 (woz2W) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (woz2B) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (image1E) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (exu__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (setadjoin__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (powerset__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (setunion__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (exuEu) =>
% 99.02/13.30 ((
% 99.02/13.30 (descr__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (dsetconstr__Cong) =>
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (binintersectSubset3) =>
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 (kpairp) =>
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% 99.02/13.30 (ubforcartprodlem2) =>
% 99.02/13.30 ((
% 99.02/13.30 (ubforcartprodlem3) =>
% 99.02/13.30 ((
% 99.02/13.30 (cartprodpairin) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (cartprodmempair) =>
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 (complementInPowersetComplementIntersect) =>
% 99.02/13.30 ((
% 99.02/13.30 (contraSubsetComplement) =>
% 99.02/13.30 ((
% 99.02/13.30 (complementTcontraSubset) =>
% 99.02/13.30 ((
% 99.02/13.30 (binunionTILcontra) =>
% 99.02/13.30 ((
% 99.02/13.30 (binunionTIRcontra) =>
% 99.02/13.30 ((
% 99.02/13.30 (inIntersectImpInUnion) =>
% 99.02/13.30 ((
% 99.02/13.30 (inIntersectImpInUnion2) =>
% 99.02/13.30 ((
% 99.02/13.30 (inIntersectImpInIntersectUnions) =>
% 99.02/13.30 ((
% 99.02/13.30 (intersectInPowersetIntersectUnions) =>
% 99.02/13.30 ((
% 99.02/13.30 (inComplementUnionImpNotIn1) =>
% 99.02/13.30 ((
% 99.02/13.30 (inComplementUnionImpInComplement1) =>
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% 99.02/13.30 (binunionTE) =>
% 99.02/13.30 ((
% 99.02/13.30 (binunionTEcontra) =>
% 99.02/13.30 ((
% 99.02/13.30 (demorgan2a1) =>
% 99.02/13.30 ((
% 99.02/13.30 (complementUnionInPowersetComplement) =>
% 99.02/13.30 ((
% 99.02/13.30 (demorgan2a2) =>
% 99.02/13.30 ((
% 99.02/13.30 (demorgan1a) =>
% 99.02/13.30 ((
% 99.02/13.30 (demorgan1b) =>
% 99.02/13.30 ((
% 99.02/13.30 (demorgan1) =>
% 99.02/13.30 ((
% 99.02/13.30 (demorgan2a) =>
% 99.02/13.30 ((
% 99.02/13.30 (demorgan2b2) =>
% 99.02/13.30 ((
% 99.02/13.30 (demorgan2b) =>
% 99.02/13.30 ((
% 99.02/13.30 (demorgan2) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz13rule0) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz13rule1) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz13rule2) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz13rule3) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz13rule4) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz1_1) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz1_2) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz1_3) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz1_4) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz1_5) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1all2) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1SetBreln1) =>
% 99.02/13.30 ((
% 99.02/13.30 (choice2fnsingleton) =>
% 99.02/13.30 ((
% 99.02/13.30 (setOfPairsIsBReln1) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1all1) =>
% 99.02/13.30 ((
% 99.02/13.30 (subbreln1) =>
% 99.02/13.30 ((
% 99.02/13.30 (eqbreln1) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1invprop) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1invI) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1invE) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1compprop) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1compI) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1compE) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1compEex) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1unionprop) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1unionIL) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1unionIR) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1unionI) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1unionE) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1unionEcases) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1unionCommutes) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz2Ex) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz2W) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz2A) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz2B) =>
% 99.02/13.30 ((
% 99.02/13.30 (image1Ex) =>
% 99.02/13.30 ((
% 99.02/13.30 (image1Ex1) =>
% 99.02/13.30 ((
% 99.02/13.30 (image1Equiv) =>
% 99.02/13.30 ((
% 99.02/13.30 (image1E) =>
% 99.02/13.30 ((
% 99.02/13.30 (image1I) =>
% 99.02/13.30 ((
% 99.02/13.30 (injFuncInInjFuncSet) =>
% 99.02/13.30 ((
% 99.02/13.30 (!!) @ (
% 99.02/13.30 (('#B') @ (
% 99.02/13.30 !!) @
% 99.02/13.30 (
% 99.02/13.30 (
% 99.02/13.30 ('#B') @ (
% 99.02/13.30 (
% 99.02/13.30 ('#B') @ (
% 99.02/13.30 !!))) @
% 99.02/13.30 (
% 99.02/13.30 (
% 99.02/13.30 ('#S') @ (
% 99.02/13.30 (
% 99.02/13.30 ('#B') @ (
% 99.02/13.30 '#S') @
% 99.02/13.30 (
% 99.02/13.30 (
% 99.02/13.30 ('#B') @ (
% 99.02/13.30 (
% 99.02/13.30 ('#B') @ (
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% 99.02/13.30 (
% 99.02/13.30 (
% 99.02/13.30 ('#B') @ (
% 99.02/13.30 (
% 99.02/13.30 ('#B') @ (
% 99.02/13.30 (
% 99.02/13.30 ('#B') @ (
% 99.02/13.30 =>))))) @
% 99.02/13.30 (
% 99.02/13.30 (
% 99.02/13.30 ('#B') @ (
% 99.02/13.30 (
% 99.02/13.30 ('#B') @ (
% 99.02/13.30 (
% 99.02/13.30 ('#C') @ in)))) @
% 99.02/13.30 injFuncSet)))))))) @
% 99.02/13.30 (
% 99.02/13.30 (
% 99.02/13.30 ('#B') @ (
% 99.02/13.30 (
% 99.02/13.30 ('#B') @ (
% 99.02/13.30 (
% 99.02/13.30 ('#C') @ in)))) @
% 99.02/13.30 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl355])).
% 99.02/13.30 thf(zip_derived_cl369, plain,
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% 99.02/13.30 (((emptyinPowerset) =>
% 99.02/13.30 (((emptyInPowerset) =>
% 99.02/13.30 (((powersetE) =>
% 99.02/13.30 (((setunionI) =>
% 99.02/13.30 (((setunionE) =>
% 99.02/13.30 (((subPowSU) =>
% 99.02/13.30 (((exuE2) =>
% 99.02/13.30 (((nonemptyImpWitness) =>
% 99.02/13.30 (((uniqinunit) =>
% 99.02/13.30 (((notinsingleton) =>
% 99.02/13.30 (((eqinunit) =>
% 99.02/13.30 (((singletonsswitch) =>
% 99.02/13.30 (((upairsetE) =>
% 99.02/13.30 (((upairsetIL) =>
% 99.02/13.30 (((upairsetIR) =>
% 99.02/13.30 (((emptyE1) =>
% 99.02/13.30 (((vacuousDall) =>
% 99.02/13.30 (((quantDeMorgan1) =>
% 99.02/13.30 (((quantDeMorgan2) =>
% 99.02/13.30 (((quantDeMorgan3) =>
% 99.02/13.30 (((quantDeMorgan4) =>
% 99.02/13.30 (((prop2setI) =>
% 99.02/13.30 (((prop2set2propI) =>
% 99.02/13.30 (((notdexE) =>
% 99.02/13.30 (((notdallE) =>
% 99.02/13.30 (((exuI1) =>
% 99.02/13.30 (((exuI3) =>
% 99.02/13.30 (((exuI2) =>
% 99.02/13.30 (((inCongP) =>
% 99.02/13.30 ((
% 99.02/13.30 (in__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (exuE3u) =>
% 99.02/13.30 ((
% 99.02/13.30 (exu__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (setadjoin__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (powerset__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (setunion__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (exuEu) =>
% 99.02/13.30 ((
% 99.02/13.30 (descr__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (dsetconstr__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (subsetI1) =>
% 99.02/13.30 ((
% 99.02/13.30 (eqimpsubset2) =>
% 99.02/13.30 ((
% 99.02/13.30 (eqimpsubset1) =>
% 99.02/13.30 ((
% 99.02/13.30 (subsetI2) =>
% 99.02/13.30 ((
% 99.02/13.30 (emptysetsubset) =>
% 99.02/13.30 ((
% 99.02/13.30 (subsetE) =>
% 99.02/13.30 ((
% 99.02/13.30 (subsetE2) =>
% 99.02/13.30 ((
% 99.02/13.30 (notsubsetI) =>
% 99.02/13.30 ((
% 99.02/13.30 (notequalI1) =>
% 99.02/13.30 ((
% 99.02/13.30 (notequalI2) =>
% 99.02/13.30 ((
% 99.02/13.30 (subsetRefl) =>
% 99.02/13.30 ((
% 99.02/13.30 (subsetTrans) =>
% 99.02/13.30 ((
% 99.02/13.30 (setadjoinSub) =>
% 99.02/13.30 ((
% 99.02/13.30 (setadjoinSub2) =>
% 99.02/13.30 ((
% 99.02/13.30 (subset2powerset) =>
% 99.02/13.30 ((
% 99.02/13.30 (setextsub) =>
% 99.02/13.30 ((
% 99.02/13.30 (subsetemptysetimpeq) =>
% 99.02/13.30 ((
% 99.02/13.30 (powersetI1) =>
% 99.02/13.30 ((
% 99.02/13.30 (powersetE1) =>
% 99.02/13.30 ((
% 99.02/13.30 (inPowerset) =>
% 99.02/13.30 ((
% 99.02/13.30 (powersetsubset) =>
% 99.02/13.30 ((
% 99.02/13.30 (sepInPowerset) =>
% 99.02/13.30 ((
% 99.02/13.30 (sepSubset) =>
% 99.02/13.30 ((
% 99.02/13.30 (binunionIL) =>
% 99.02/13.30 ((
% 99.02/13.30 (upairset2IR) =>
% 99.02/13.30 ((
% 99.02/13.30 (binunionIR) =>
% 99.02/13.30 ((
% 99.02/13.30 (binunionEcases) =>
% 99.02/13.30 ((
% 99.02/13.30 (binunionE) =>
% 99.02/13.30 ((
% 99.02/13.30 (binunionLsub) =>
% 99.02/13.30 ((
% 99.02/13.30 (binunionRsub) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectI) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectSubset5) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectEL) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectLsub) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectSubset2) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectSubset3) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectER) =>
% 99.02/13.30 ((
% 99.02/13.30 (disjointsetsI1) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectRsub) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectSubset4) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectSubset1) =>
% 99.02/13.30 ((
% 99.02/13.30 (bs114d) =>
% 99.02/13.30 ((
% 99.02/13.30 (setminusI) =>
% 99.02/13.30 ((
% 99.02/13.30 (setminusEL) =>
% 99.02/13.30 ((
% 99.02/13.30 (setminusER) =>
% 99.02/13.30 ((
% 99.02/13.30 (setminusSubset2) =>
% 99.02/13.30 ((
% 99.02/13.30 (setminusERneg) =>
% 99.02/13.30 ((
% 99.02/13.30 (setminusELneg) =>
% 99.02/13.30 ((
% 99.02/13.30 (setminusILneg) =>
% 99.02/13.30 ((
% 99.02/13.30 (setminusIRneg) =>
% 99.02/13.30 ((
% 99.02/13.30 (setminusLsub) =>
% 99.02/13.30 ((
% 99.02/13.30 (setminusSubset1) =>
% 99.02/13.30 ((
% 99.02/13.30 (symdiffE) =>
% 99.02/13.30 ((
% 99.02/13.30 (symdiffI1) =>
% 99.02/13.30 ((
% 99.02/13.30 (symdiffI2) =>
% 99.02/13.30 ((
% 99.02/13.30 (symdiffIneg1) =>
% 99.02/13.30 ((
% 99.02/13.30 (symdiffIneg2) =>
% 99.02/13.30 ((
% 99.02/13.30 (secondinupair) =>
% 99.02/13.30 ((
% 99.02/13.30 (setukpairIL) =>
% 99.02/13.30 ((
% 99.02/13.30 (setukpairIR) =>
% 99.02/13.30 ((
% 99.02/13.30 (kpairiskpair) =>
% 99.02/13.30 ((
% 99.02/13.30 (kpairp) =>
% 99.02/13.30 ((
% 99.02/13.30 (singletonsubset) =>
% 99.02/13.30 ((
% 99.02/13.30 (singletoninpowerset) =>
% 99.02/13.30 ((
% 99.02/13.30 (singletoninpowunion) =>
% 99.02/13.30 ((
% 99.02/13.30 (upairset2E) =>
% 99.02/13.30 ((
% 99.02/13.30 (upairsubunion) =>
% 99.02/13.30 ((
% 99.02/13.30 (upairinpowunion) =>
% 99.02/13.30 ((
% 99.02/13.30 (ubforcartprodlem1) =>
% 99.02/13.30 ((
% 99.02/13.30 (ubforcartprodlem2) =>
% 99.02/13.30 ((
% 99.02/13.30 (ubforcartprodlem3) =>
% 99.02/13.30 ((
% 99.02/13.30 (cartprodpairin) =>
% 99.02/13.30 ((
% 99.02/13.30 (cartprodmempair1) =>
% 99.02/13.30 ((
% 99.02/13.30 (cartprodmempair) =>
% 99.02/13.30 ((
% 99.02/13.30 (setunionE2) =>
% 99.02/13.30 ((
% 99.02/13.30 (setunionsingleton1) =>
% 99.02/13.30 ((
% 99.02/13.30 (setunionsingleton2) =>
% 99.02/13.30 ((
% 99.02/13.30 (setunionsingleton) =>
% 99.02/13.30 ((
% 99.02/13.30 (singletonprop) =>
% 99.02/13.30 ((
% 99.02/13.30 (ex1E1) =>
% 99.02/13.30 ((
% 99.02/13.30 (ex1I) =>
% 99.02/13.30 ((
% 99.02/13.30 (ex1I2) =>
% 99.02/13.30 ((
% 99.02/13.30 (singletonsuniq) =>
% 99.02/13.30 ((
% 99.02/13.30 (setukpairinjL1) =>
% 99.02/13.30 ((
% 99.02/13.30 (kfstsingleton) =>
% 99.02/13.30 ((
% 99.02/13.30 (theprop) =>
% 99.02/13.30 ((
% 99.02/13.30 (kfstpairEq) =>
% 99.02/13.30 ((
% 99.02/13.30 (cartprodfstin) =>
% 99.02/13.30 ((
% 99.02/13.30 (setukpairinjL2) =>
% 99.02/13.30 ((
% 99.02/13.30 (setukpairinjL) =>
% 99.02/13.30 ((
% 99.02/13.30 (setukpairinjR11) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (ksndpairEq) =>
% 99.02/13.30 ((
% 99.02/13.30 (kpairsurjEq) =>
% 99.02/13.30 ((
% 99.02/13.30 (cartprodsndin) =>
% 99.02/13.30 ((
% 99.02/13.30 (cartprodpairmemEL) =>
% 99.02/13.30 ((
% 99.02/13.30 (cartprodpairmemER) =>
% 99.02/13.30 ((
% 99.02/13.30 (cartprodmempaircEq) =>
% 99.02/13.30 ((
% 99.02/13.30 (cartprodfstpairEq) =>
% 99.02/13.30 ((
% 99.02/13.30 (cartprodsndpairEq) =>
% 99.02/13.30 ((
% 99.02/13.30 (cartprodpairsurjEq) =>
% 99.02/13.30 ((
% 99.02/13.30 (dpsetconstrI) =>
% 99.02/13.30 ((
% 99.02/13.30 (dpsetconstrSub) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (funcinfuncset) =>
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 (contrasubsetT2) =>
% 99.02/13.30 ((
% 99.02/13.30 (contrasubsetT3) =>
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% 99.02/13.30 (doubleComplementI1) =>
% 99.02/13.30 ((
% 99.02/13.30 (doubleComplementE1) =>
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% 99.02/13.30 (doubleComplementSub1) =>
% 99.02/13.30 ((
% 99.02/13.30 (doubleComplementSub2) =>
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% 99.02/13.30 (doubleComplementEq) =>
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% 99.02/13.30 (complementImpComplementIntersect) =>
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% 99.02/13.30 (contraSubsetComplement) =>
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% 99.02/13.30 (complementTcontraSubset) =>
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% 99.02/13.30 (binunionTIRcontra) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (inIntersectImpInUnion2) =>
% 99.02/13.30 ((
% 99.02/13.30 (inIntersectImpInIntersectUnions) =>
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% 99.02/13.30 (inComplementUnionImpInComplement1) =>
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% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (complementUnionInPowersetComplement) =>
% 99.02/13.30 ((
% 99.02/13.30 (demorgan2a2) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (demorgan1b) =>
% 99.02/13.30 ((
% 99.02/13.30 (demorgan1) =>
% 99.02/13.30 ((
% 99.02/13.30 (demorgan2a) =>
% 99.02/13.30 ((
% 99.02/13.30 (demorgan2b2) =>
% 99.02/13.30 ((
% 99.02/13.30 (demorgan2b) =>
% 99.02/13.30 ((
% 99.02/13.30 (demorgan2) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz13rule0) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz13rule1) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz13rule2) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz13rule3) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz13rule4) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (woz1_2) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz1_3) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz1_4) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz1_5) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1all2) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (breln1invprop) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1invI) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1invE) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1compprop) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1compI) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1compE) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1compEex) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1unionprop) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1unionIL) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1unionIR) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1unionI) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1unionE) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1unionEcases) =>
% 99.02/13.30 ((
% 99.02/13.30 (breln1unionCommutes) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz2Ex) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz2W) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz2A) =>
% 99.02/13.30 ((
% 99.02/13.30 (woz2B) =>
% 99.02/13.30 ((
% 99.02/13.30 (image1Ex) =>
% 99.02/13.30 ((
% 99.02/13.30 (image1Ex1) =>
% 99.02/13.30 ((
% 99.02/13.30 (image1Equiv) =>
% 99.02/13.30 ((
% 99.02/13.30 (image1E) =>
% 99.02/13.30 ((
% 99.02/13.30 (image1I) =>
% 99.02/13.30 ((
% 99.02/13.30 (injFuncInInjFuncSet) =>
% 99.02/13.30 ((
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% 99.02/13.30 (
% 99.02/13.30 (
% 99.02/13.30 ('#B') @ (
% 99.02/13.30 (
% 99.02/13.30 ('#B') @ (
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% 99.02/13.30 (
% 99.02/13.30 (
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% 99.02/13.30 (
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% 99.02/13.30 ('#B') @ (
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% 99.02/13.30 (
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% 99.02/13.30 (
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% 99.02/13.30 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl362])).
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% 99.02/13.30 (((quantDeMorgan1) =>
% 99.02/13.30 (((quantDeMorgan2) =>
% 99.02/13.30 (((quantDeMorgan3) =>
% 99.02/13.30 (((quantDeMorgan4) =>
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% 99.02/13.30 ((
% 99.02/13.30 (exu__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (setadjoin__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (powerset__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (setunion__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (exuEu) =>
% 99.02/13.30 ((
% 99.02/13.30 (descr__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (dsetconstr__Cong) =>
% 99.02/13.30 ((
% 99.02/13.30 (subsetI1) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 (subsetE) =>
% 99.02/13.30 ((
% 99.02/13.30 (subsetE2) =>
% 99.02/13.30 ((
% 99.02/13.30 (notsubsetI) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (notequalI2) =>
% 99.02/13.30 ((
% 99.02/13.30 (subsetRefl) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (sepSubset) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (upairset2IR) =>
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (binintersectLsub) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectSubset2) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectSubset3) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectER) =>
% 99.02/13.30 ((
% 99.02/13.30 (disjointsetsI1) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectRsub) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectSubset4) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectSubset1) =>
% 99.02/13.30 ((
% 99.02/13.30 (bs114d) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (setminusEL) =>
% 99.02/13.30 ((
% 99.02/13.30 (setminusER) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 (kpairp) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (singletoninpowerset) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (ubforcartprodlem2) =>
% 99.02/13.30 ((
% 99.02/13.30 (ubforcartprodlem3) =>
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% 99.02/13.30 (cartprodpairin) =>
% 99.02/13.30 ((
% 99.02/13.30 (cartprodmempair1) =>
% 99.02/13.30 ((
% 99.02/13.30 (cartprodmempair) =>
% 99.02/13.30 ((
% 99.02/13.30 (setunionE2) =>
% 99.02/13.30 ((
% 99.02/13.30 (setunionsingleton1) =>
% 99.02/13.30 ((
% 99.02/13.30 (setunionsingleton2) =>
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% 99.02/13.30 (setunionsingleton) =>
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 (cartprodsndpairEq) =>
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 (descr__Cong) =>
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% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (lam2p) =>
% 99.02/13.30 ((
% 99.02/13.30 (brelnall1) =>
% 99.02/13.30 ((
% 99.02/13.30 (brelnall2) =>
% 99.02/13.30 ((
% 99.02/13.30 (ex1E2) =>
% 99.02/13.30 ((
% 99.02/13.30 (funcGraphProp1) =>
% 99.02/13.30 ((
% 99.02/13.30 (funcGraphProp3) =>
% 99.02/13.30 ((
% 99.02/13.30 (funcGraphProp2) =>
% 99.02/13.30 ((
% 99.02/13.30 (funcextLem) =>
% 99.02/13.30 ((
% 99.02/13.30 (funcGraphProp4) =>
% 99.02/13.30 ((
% 99.02/13.30 (subbreln) =>
% 99.02/13.30 ((
% 99.02/13.30 (eqbreln) =>
% 99.02/13.30 ((
% 99.02/13.30 (funcext) =>
% 99.02/13.30 ((
% 99.02/13.30 (funcext2) =>
% 99.02/13.30 ((
% 99.02/13.30 (ap2apEq1) =>
% 99.02/13.30 ((
% 99.02/13.30 (ap2apEq2) =>
% 99.02/13.30 ((
% 99.02/13.30 (beta1) =>
% 99.02/13.30 ((
% 99.02/13.30 (eta1) =>
% 99.02/13.30 ((
% 99.02/13.30 (lam2lamEq) =>
% 99.02/13.30 ((
% 99.02/13.30 (beta2) =>
% 99.02/13.30 ((
% 99.02/13.30 (eta2) =>
% 99.02/13.30 ((
% 99.02/13.30 (iffalseProp1) =>
% 99.02/13.30 ((
% 99.02/13.30 (iffalseProp2) =>
% 99.02/13.30 ((
% 99.02/13.30 (iftrueProp1) =>
% 99.02/13.30 ((
% 99.02/13.30 (iftrueProp2) =>
% 99.02/13.30 ((
% 99.02/13.30 (ifSingleton) =>
% 99.02/13.30 ((
% 99.02/13.30 (ifp) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (iftrue) =>
% 99.02/13.30 ((
% 99.02/13.30 (iffalse) =>
% 99.02/13.30 ((
% 99.02/13.30 (iftrueorfalse) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (binunionT_lem) =>
% 99.02/13.30 ((
% 99.02/13.30 (powersetT_lem) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (setextT) =>
% 99.02/13.30 ((
% 99.02/13.30 (subsetTI) =>
% 99.02/13.30 ((
% 99.02/13.30 (powersetTI1) =>
% 99.02/13.30 ((
% 99.02/13.30 (powersetTE1) =>
% 99.02/13.30 ((
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% 99.02/13.30 ((
% 99.02/13.30 (complementTE1) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectTELcontra) =>
% 99.02/13.30 ((
% 99.02/13.30 (binintersectTERcontra) =>
% 99.02/13.30 ((
% 99.02/13.30 (contrasubsetT) =>
% 99.02/13.30 ((
% 99.02/13.30 (contrasubsetT1) =>
% 99.02/13.30 ((
% 99.02/13.30 (contrasubsetT2) =>
% 99.02/13.30 ((
% 99.02/13.30 (contrasubsetT3) =>
% 99.02/13.30 ((
% 99.02/13.30 (doubleComplementI1) =>
% 99.02/13.30 ((
% 99.02/13.30 (doubleComplementE1) =>
% 99.02/13.30 ((
% 99.02/13.30 (doubleComplementSub1) =>
% 99.02/13.31 ((
% 99.02/13.31 (doubleComplementSub2) =>
% 99.02/13.31 ((
% 99.02/13.31 (doubleComplementEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (complementTnotintersectT) =>
% 99.02/13.31 ((
% 99.02/13.31 (complementImpComplementIntersect) =>
% 99.02/13.31 ((
% 99.02/13.31 (complementSubsetComplementIntersect) =>
% 99.02/13.31 ((
% 99.02/13.31 (complementInPowersetComplementIntersect) =>
% 99.02/13.31 ((
% 99.02/13.31 (contraSubsetComplement) =>
% 99.02/13.31 ((
% 99.02/13.31 (complementTcontraSubset) =>
% 99.02/13.31 ((
% 99.02/13.31 (binunionTILcontra) =>
% 99.02/13.31 ((
% 99.02/13.31 (binunionTIRcontra) =>
% 99.02/13.31 ((
% 99.02/13.31 (inIntersectImpInUnion) =>
% 99.02/13.31 ((
% 99.02/13.31 (inIntersectImpInUnion2) =>
% 99.02/13.31 ((
% 99.02/13.31 (inIntersectImpInIntersectUnions) =>
% 99.02/13.31 ((
% 99.02/13.31 (intersectInPowersetIntersectUnions) =>
% 99.02/13.31 ((
% 99.02/13.31 (inComplementUnionImpNotIn1) =>
% 99.02/13.31 ((
% 99.02/13.31 (inComplementUnionImpInComplement1) =>
% 99.02/13.31 ((
% 99.02/13.31 (binunionTE) =>
% 99.02/13.31 ((
% 99.02/13.31 (binunionTEcontra) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan2a1) =>
% 99.02/13.31 ((
% 99.02/13.31 (complementUnionInPowersetComplement) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan2a2) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan1a) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan1b) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan1) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan2a) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan2b2) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan2b) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan2) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz13rule0) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz13rule1) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz13rule2) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz13rule3) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz13rule4) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz1_1) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz1_2) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz1_3) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz1_4) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz1_5) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1all2) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1SetBreln1) =>
% 99.02/13.31 ((
% 99.02/13.31 (choice2fnsingleton) =>
% 99.02/13.31 ((
% 99.02/13.31 (setOfPairsIsBReln1) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1all1) =>
% 99.02/13.31 ((
% 99.02/13.31 (subbreln1) =>
% 99.02/13.31 ((
% 99.02/13.31 (eqbreln1) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1invprop) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1invI) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1invE) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1compprop) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1compI) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1compE) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1compEex) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionprop) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionIL) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionIR) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionI) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionE) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionEcases) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionCommutes) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz2Ex) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz2W) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz2A) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz2B) =>
% 99.02/13.31 ((
% 99.02/13.31 (image1Ex) =>
% 99.02/13.31 ((
% 99.02/13.31 (image1Ex1) =>
% 99.02/13.31 ((
% 99.02/13.31 (image1Equiv) =>
% 99.02/13.31 ((
% 99.02/13.31 (image1E) =>
% 99.02/13.31 ((
% 99.02/13.31 (image1I) =>
% 99.02/13.31 ((
% 99.02/13.31 (injFuncInInjFuncSet) =>
% 99.02/13.31 ((
% 99.02/13.31 (!!) @ (
% 99.02/13.31 (('#B') @ (
% 99.02/13.31 !!) @
% 99.02/13.31 (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 !!))) @
% 99.02/13.31 (
% 99.02/13.31 (
% 99.02/13.31 ('#S') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 '#S') @
% 99.02/13.31 (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
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% 99.02/13.31 (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 =>))))) @
% 99.02/13.31 (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#C') @ in)))) @
% 99.02/13.31 injFuncSet)))))))) @
% 99.02/13.31 (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#C') @ in)))) @
% 99.02/13.31 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl408])).
% 99.02/13.31 thf(zip_derived_cl428, plain,
% 99.02/13.31 (~ (((exuE2) =>
% 99.02/13.31 (((nonemptyImpWitness) =>
% 99.02/13.31 (((uniqinunit) =>
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% 99.02/13.31 (((eqinunit) =>
% 99.02/13.31 (((singletonsswitch) =>
% 99.02/13.31 (((upairsetE) =>
% 99.02/13.31 (((upairsetIL) =>
% 99.02/13.31 (((upairsetIR) =>
% 99.02/13.31 (((emptyE1) =>
% 99.02/13.31 (((vacuousDall) =>
% 99.02/13.31 (((quantDeMorgan1) =>
% 99.02/13.31 (((quantDeMorgan2) =>
% 99.02/13.31 (((quantDeMorgan3) =>
% 99.02/13.31 (((quantDeMorgan4) =>
% 99.02/13.31 (((prop2setI) =>
% 99.02/13.31 (((prop2set2propI) =>
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% 99.02/13.31 (((notdallE) =>
% 99.02/13.31 (((exuI1) =>
% 99.02/13.31 (((exuI3) =>
% 99.02/13.31 (((exuI2) =>
% 99.02/13.31 (((inCongP) =>
% 99.02/13.31 (((in__Cong) =>
% 99.02/13.31 (((exuE3u) =>
% 99.02/13.31 (((exu__Cong) =>
% 99.02/13.31 (((setadjoin__Cong) =>
% 99.02/13.31 (((powerset__Cong) =>
% 99.02/13.31 (((setunion__Cong) =>
% 99.02/13.31 (((exuEu) =>
% 99.02/13.31 ((
% 99.02/13.31 (descr__Cong) =>
% 99.02/13.31 ((
% 99.02/13.31 (dsetconstr__Cong) =>
% 99.02/13.31 ((
% 99.02/13.31 (subsetI1) =>
% 99.02/13.31 ((
% 99.02/13.31 (eqimpsubset2) =>
% 99.02/13.31 ((
% 99.02/13.31 (eqimpsubset1) =>
% 99.02/13.31 ((
% 99.02/13.31 (subsetI2) =>
% 99.02/13.31 ((
% 99.02/13.31 (emptysetsubset) =>
% 99.02/13.31 ((
% 99.02/13.31 (subsetE) =>
% 99.02/13.31 ((
% 99.02/13.31 (subsetE2) =>
% 99.02/13.31 ((
% 99.02/13.31 (notsubsetI) =>
% 99.02/13.31 ((
% 99.02/13.31 (notequalI1) =>
% 99.02/13.31 ((
% 99.02/13.31 (notequalI2) =>
% 99.02/13.31 ((
% 99.02/13.31 (subsetRefl) =>
% 99.02/13.31 ((
% 99.02/13.31 (subsetTrans) =>
% 99.02/13.31 ((
% 99.02/13.31 (setadjoinSub) =>
% 99.02/13.31 ((
% 99.02/13.31 (setadjoinSub2) =>
% 99.02/13.31 ((
% 99.02/13.31 (subset2powerset) =>
% 99.02/13.31 ((
% 99.02/13.31 (setextsub) =>
% 99.02/13.31 ((
% 99.02/13.31 (subsetemptysetimpeq) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (powersetE1) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (powersetsubset) =>
% 99.02/13.31 ((
% 99.02/13.31 (sepInPowerset) =>
% 99.02/13.31 ((
% 99.02/13.31 (sepSubset) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (upairset2IR) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (binunionEcases) =>
% 99.02/13.31 ((
% 99.02/13.31 (binunionE) =>
% 99.02/13.31 ((
% 99.02/13.31 (binunionLsub) =>
% 99.02/13.31 ((
% 99.02/13.31 (binunionRsub) =>
% 99.02/13.31 ((
% 99.02/13.31 (binintersectI) =>
% 99.02/13.31 ((
% 99.02/13.31 (binintersectSubset5) =>
% 99.02/13.31 ((
% 99.02/13.31 (binintersectEL) =>
% 99.02/13.31 ((
% 99.02/13.31 (binintersectLsub) =>
% 99.02/13.31 ((
% 99.02/13.31 (binintersectSubset2) =>
% 99.02/13.31 ((
% 99.02/13.31 (binintersectSubset3) =>
% 99.02/13.31 ((
% 99.02/13.31 (binintersectER) =>
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% 99.02/13.31 ((
% 99.02/13.31 (binintersectRsub) =>
% 99.02/13.31 ((
% 99.02/13.31 (binintersectSubset4) =>
% 99.02/13.31 ((
% 99.02/13.31 (binintersectSubset1) =>
% 99.02/13.31 ((
% 99.02/13.31 (bs114d) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (setminusEL) =>
% 99.02/13.31 ((
% 99.02/13.31 (setminusER) =>
% 99.02/13.31 ((
% 99.02/13.31 (setminusSubset2) =>
% 99.02/13.31 ((
% 99.02/13.31 (setminusERneg) =>
% 99.02/13.31 ((
% 99.02/13.31 (setminusELneg) =>
% 99.02/13.31 ((
% 99.02/13.31 (setminusILneg) =>
% 99.02/13.31 ((
% 99.02/13.31 (setminusIRneg) =>
% 99.02/13.31 ((
% 99.02/13.31 (setminusLsub) =>
% 99.02/13.31 ((
% 99.02/13.31 (setminusSubset1) =>
% 99.02/13.31 ((
% 99.02/13.31 (symdiffE) =>
% 99.02/13.31 ((
% 99.02/13.31 (symdiffI1) =>
% 99.02/13.31 ((
% 99.02/13.31 (symdiffI2) =>
% 99.02/13.31 ((
% 99.02/13.31 (symdiffIneg1) =>
% 99.02/13.31 ((
% 99.02/13.31 (symdiffIneg2) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (setukpairIR) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (kpairp) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (singletoninpowunion) =>
% 99.02/13.31 ((
% 99.02/13.31 (upairset2E) =>
% 99.02/13.31 ((
% 99.02/13.31 (upairsubunion) =>
% 99.02/13.31 ((
% 99.02/13.31 (upairinpowunion) =>
% 99.02/13.31 ((
% 99.02/13.31 (ubforcartprodlem1) =>
% 99.02/13.31 ((
% 99.02/13.31 (ubforcartprodlem2) =>
% 99.02/13.31 ((
% 99.02/13.31 (ubforcartprodlem3) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodpairin) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodmempair1) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodmempair) =>
% 99.02/13.31 ((
% 99.02/13.31 (setunionE2) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (setunionsingleton2) =>
% 99.02/13.31 ((
% 99.02/13.31 (setunionsingleton) =>
% 99.02/13.31 ((
% 99.02/13.31 (singletonprop) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (ex1I) =>
% 99.02/13.31 ((
% 99.02/13.31 (ex1I2) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjL1) =>
% 99.02/13.31 ((
% 99.02/13.31 (kfstsingleton) =>
% 99.02/13.31 ((
% 99.02/13.31 (theprop) =>
% 99.02/13.31 ((
% 99.02/13.31 (kfstpairEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodfstin) =>
% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjL2) =>
% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjL) =>
% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjR11) =>
% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjR12) =>
% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjR1) =>
% 99.02/13.31 ((
% 99.02/13.31 (upairequniteq) =>
% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjR2) =>
% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjR) =>
% 99.02/13.31 ((
% 99.02/13.31 (ksndsingleton) =>
% 99.02/13.31 ((
% 99.02/13.31 (ksndpairEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (kpairsurjEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodsndin) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodpairmemEL) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodpairmemER) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodmempaircEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodfstpairEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodsndpairEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodpairsurjEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (dpsetconstrI) =>
% 99.02/13.31 ((
% 99.02/13.31 (dpsetconstrSub) =>
% 99.02/13.31 ((
% 99.02/13.31 (setOfPairsIsBReln) =>
% 99.02/13.31 ((
% 99.02/13.31 (dpsetconstrERa) =>
% 99.02/13.31 ((
% 99.02/13.31 (dpsetconstrEL1) =>
% 99.02/13.31 ((
% 99.02/13.31 (dpsetconstrEL2) =>
% 99.02/13.31 ((
% 99.02/13.31 (dpsetconstrER) =>
% 99.02/13.31 ((
% 99.02/13.31 (funcImageSingleton) =>
% 99.02/13.31 ((
% 99.02/13.31 (apProp) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (infuncsetfunc) =>
% 99.02/13.31 ((
% 99.02/13.31 (ap2p) =>
% 99.02/13.31 ((
% 99.02/13.31 (funcinfuncset) =>
% 99.02/13.31 ((
% 99.02/13.31 (lamProp) =>
% 99.02/13.31 ((
% 99.02/13.31 (lamp) =>
% 99.02/13.31 ((
% 99.02/13.31 (lam2p) =>
% 99.02/13.31 ((
% 99.02/13.31 (brelnall1) =>
% 99.02/13.31 ((
% 99.02/13.31 (brelnall2) =>
% 99.02/13.31 ((
% 99.02/13.31 (ex1E2) =>
% 99.02/13.31 ((
% 99.02/13.31 (funcGraphProp1) =>
% 99.02/13.31 ((
% 99.02/13.31 (funcGraphProp3) =>
% 99.02/13.31 ((
% 99.02/13.31 (funcGraphProp2) =>
% 99.02/13.31 ((
% 99.02/13.31 (funcextLem) =>
% 99.02/13.31 ((
% 99.02/13.31 (funcGraphProp4) =>
% 99.02/13.31 ((
% 99.02/13.31 (subbreln) =>
% 99.02/13.31 ((
% 99.02/13.31 (eqbreln) =>
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% 99.02/13.31 (funcext) =>
% 99.02/13.31 ((
% 99.02/13.31 (funcext2) =>
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% 99.02/13.31 (ap2apEq1) =>
% 99.02/13.31 ((
% 99.02/13.31 (ap2apEq2) =>
% 99.02/13.31 ((
% 99.02/13.31 (beta1) =>
% 99.02/13.31 ((
% 99.02/13.31 (eta1) =>
% 99.02/13.31 ((
% 99.02/13.31 (lam2lamEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (beta2) =>
% 99.02/13.31 ((
% 99.02/13.31 (eta2) =>
% 99.02/13.31 ((
% 99.02/13.31 (iffalseProp1) =>
% 99.02/13.31 ((
% 99.02/13.31 (iffalseProp2) =>
% 99.02/13.31 ((
% 99.02/13.31 (iftrueProp1) =>
% 99.02/13.31 ((
% 99.02/13.31 (iftrueProp2) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (binunionT_lem) =>
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (powersetTI1) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (complementTE1) =>
% 99.02/13.31 ((
% 99.02/13.31 (binintersectTELcontra) =>
% 99.02/13.31 ((
% 99.02/13.31 (binintersectTERcontra) =>
% 99.02/13.31 ((
% 99.02/13.31 (contrasubsetT) =>
% 99.02/13.31 ((
% 99.02/13.31 (contrasubsetT1) =>
% 99.02/13.31 ((
% 99.02/13.31 (contrasubsetT2) =>
% 99.02/13.31 ((
% 99.02/13.31 (contrasubsetT3) =>
% 99.02/13.31 ((
% 99.02/13.31 (doubleComplementI1) =>
% 99.02/13.31 ((
% 99.02/13.31 (doubleComplementE1) =>
% 99.02/13.31 ((
% 99.02/13.31 (doubleComplementSub1) =>
% 99.02/13.31 ((
% 99.02/13.31 (doubleComplementSub2) =>
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% 99.02/13.31 (doubleComplementEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (complementTnotintersectT) =>
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% 99.02/13.31 (complementImpComplementIntersect) =>
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% 99.02/13.31 (complementSubsetComplementIntersect) =>
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% 99.02/13.31 (complementInPowersetComplementIntersect) =>
% 99.02/13.31 ((
% 99.02/13.31 (contraSubsetComplement) =>
% 99.02/13.31 ((
% 99.02/13.31 (complementTcontraSubset) =>
% 99.02/13.31 ((
% 99.02/13.31 (binunionTILcontra) =>
% 99.02/13.31 ((
% 99.02/13.31 (binunionTIRcontra) =>
% 99.02/13.31 ((
% 99.02/13.31 (inIntersectImpInUnion) =>
% 99.02/13.31 ((
% 99.02/13.31 (inIntersectImpInUnion2) =>
% 99.02/13.31 ((
% 99.02/13.31 (inIntersectImpInIntersectUnions) =>
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% 99.02/13.31 (intersectInPowersetIntersectUnions) =>
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% 99.02/13.31 (inComplementUnionImpInComplement1) =>
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% 99.02/13.31 (binunionTE) =>
% 99.02/13.31 ((
% 99.02/13.31 (binunionTEcontra) =>
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% 99.02/13.31 (demorgan2a1) =>
% 99.02/13.31 ((
% 99.02/13.31 (complementUnionInPowersetComplement) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan2a2) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan1a) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan1b) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan1) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan2a) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan2b2) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan2b) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan2) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz13rule0) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz13rule1) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz13rule2) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz13rule3) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz13rule4) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz1_1) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz1_2) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz1_3) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz1_4) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz1_5) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1all2) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1SetBreln1) =>
% 99.02/13.31 ((
% 99.02/13.31 (choice2fnsingleton) =>
% 99.02/13.31 ((
% 99.02/13.31 (setOfPairsIsBReln1) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1all1) =>
% 99.02/13.31 ((
% 99.02/13.31 (subbreln1) =>
% 99.02/13.31 ((
% 99.02/13.31 (eqbreln1) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1invprop) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1invI) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1invE) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1compprop) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1compI) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1compE) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1compEex) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionprop) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionIL) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionIR) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionI) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionE) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionEcases) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionCommutes) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz2Ex) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz2W) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz2A) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz2B) =>
% 99.02/13.31 ((
% 99.02/13.31 (image1Ex) =>
% 99.02/13.31 ((
% 99.02/13.31 (image1Ex1) =>
% 99.02/13.31 ((
% 99.02/13.31 (image1Equiv) =>
% 99.02/13.31 ((
% 99.02/13.31 (image1E) =>
% 99.02/13.31 ((
% 99.02/13.31 (image1I) =>
% 99.02/13.31 ((
% 99.02/13.31 (injFuncInInjFuncSet) =>
% 99.02/13.31 ((
% 99.02/13.31 (!!) @ (
% 99.02/13.31 (('#B') @ (
% 99.02/13.31 !!) @
% 99.02/13.31 (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 !!))) @
% 99.02/13.31 (
% 99.02/13.31 (
% 99.02/13.31 ('#S') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 '#S') @
% 99.02/13.31 (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
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% 99.02/13.31 (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
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% 99.02/13.31 (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#C') @ in)))) @
% 99.02/13.31 injFuncSet)))))))) @
% 99.02/13.31 (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#C') @ in)))) @
% 99.02/13.31 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl417])).
% 99.02/13.31 thf(zip_derived_cl439, plain,
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% 99.02/13.31 (((quantDeMorgan1) =>
% 99.02/13.31 (((quantDeMorgan2) =>
% 99.02/13.31 (((quantDeMorgan3) =>
% 99.02/13.31 (((quantDeMorgan4) =>
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% 99.02/13.31 (((exuI3) =>
% 99.02/13.31 (((exuI2) =>
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% 99.02/13.31 (((in__Cong) =>
% 99.02/13.31 (((exuE3u) =>
% 99.02/13.31 (((exu__Cong) =>
% 99.02/13.31 (((setadjoin__Cong) =>
% 99.02/13.31 (((powerset__Cong) =>
% 99.02/13.31 (((setunion__Cong) =>
% 99.02/13.31 (((exuEu) =>
% 99.02/13.31 (((descr__Cong) =>
% 99.02/13.31 ((
% 99.02/13.31 (dsetconstr__Cong) =>
% 99.02/13.31 ((
% 99.02/13.31 (subsetI1) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (eqimpsubset1) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (notequalI2) =>
% 99.02/13.31 ((
% 99.02/13.31 (subsetRefl) =>
% 99.02/13.31 ((
% 99.02/13.31 (subsetTrans) =>
% 99.02/13.31 ((
% 99.02/13.31 (setadjoinSub) =>
% 99.02/13.31 ((
% 99.02/13.31 (setadjoinSub2) =>
% 99.02/13.31 ((
% 99.02/13.31 (subset2powerset) =>
% 99.02/13.31 ((
% 99.02/13.31 (setextsub) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (sepSubset) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (binunionE) =>
% 99.02/13.31 ((
% 99.02/13.31 (binunionLsub) =>
% 99.02/13.31 ((
% 99.02/13.31 (binunionRsub) =>
% 99.02/13.31 ((
% 99.02/13.31 (binintersectI) =>
% 99.02/13.31 ((
% 99.02/13.31 (binintersectSubset5) =>
% 99.02/13.31 ((
% 99.02/13.31 (binintersectEL) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (binintersectSubset2) =>
% 99.02/13.31 ((
% 99.02/13.31 (binintersectSubset3) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (binintersectSubset1) =>
% 99.02/13.31 ((
% 99.02/13.31 (bs114d) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (setminusEL) =>
% 99.02/13.31 ((
% 99.02/13.31 (setminusER) =>
% 99.02/13.31 ((
% 99.02/13.31 (setminusSubset2) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (setminusELneg) =>
% 99.02/13.31 ((
% 99.02/13.31 (setminusILneg) =>
% 99.02/13.31 ((
% 99.02/13.31 (setminusIRneg) =>
% 99.02/13.31 ((
% 99.02/13.31 (setminusLsub) =>
% 99.02/13.31 ((
% 99.02/13.31 (setminusSubset1) =>
% 99.02/13.31 ((
% 99.02/13.31 (symdiffE) =>
% 99.02/13.31 ((
% 99.02/13.31 (symdiffI1) =>
% 99.02/13.31 ((
% 99.02/13.31 (symdiffI2) =>
% 99.02/13.31 ((
% 99.02/13.31 (symdiffIneg1) =>
% 99.02/13.31 ((
% 99.02/13.31 (symdiffIneg2) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (upairsubunion) =>
% 99.02/13.31 ((
% 99.02/13.31 (upairinpowunion) =>
% 99.02/13.31 ((
% 99.02/13.31 (ubforcartprodlem1) =>
% 99.02/13.31 ((
% 99.02/13.31 (ubforcartprodlem2) =>
% 99.02/13.31 ((
% 99.02/13.31 (ubforcartprodlem3) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodpairin) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodmempair1) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodmempair) =>
% 99.02/13.31 ((
% 99.02/13.31 (setunionE2) =>
% 99.02/13.31 ((
% 99.02/13.31 (setunionsingleton1) =>
% 99.02/13.31 ((
% 99.02/13.31 (setunionsingleton2) =>
% 99.02/13.31 ((
% 99.02/13.31 (setunionsingleton) =>
% 99.02/13.31 ((
% 99.02/13.31 (singletonprop) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (ex1I) =>
% 99.02/13.31 ((
% 99.02/13.31 (ex1I2) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjL1) =>
% 99.02/13.31 ((
% 99.02/13.31 (kfstsingleton) =>
% 99.02/13.31 ((
% 99.02/13.31 (theprop) =>
% 99.02/13.31 ((
% 99.02/13.31 (kfstpairEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodfstin) =>
% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjL2) =>
% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjL) =>
% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjR11) =>
% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjR12) =>
% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjR1) =>
% 99.02/13.31 ((
% 99.02/13.31 (upairequniteq) =>
% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjR2) =>
% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjR) =>
% 99.02/13.31 ((
% 99.02/13.31 (ksndsingleton) =>
% 99.02/13.31 ((
% 99.02/13.31 (ksndpairEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (kpairsurjEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodsndin) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodpairmemEL) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodpairmemER) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodmempaircEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodfstpairEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodsndpairEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodpairsurjEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (dpsetconstrI) =>
% 99.02/13.31 ((
% 99.02/13.31 (dpsetconstrSub) =>
% 99.02/13.31 ((
% 99.02/13.31 (setOfPairsIsBReln) =>
% 99.02/13.31 ((
% 99.02/13.31 (dpsetconstrERa) =>
% 99.02/13.31 ((
% 99.02/13.31 (dpsetconstrEL1) =>
% 99.02/13.31 ((
% 99.02/13.31 (dpsetconstrEL2) =>
% 99.02/13.31 ((
% 99.02/13.31 (dpsetconstrER) =>
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% 99.02/13.31 (ap2p) =>
% 99.02/13.31 ((
% 99.02/13.31 (funcinfuncset) =>
% 99.02/13.31 ((
% 99.02/13.31 (lamProp) =>
% 99.02/13.31 ((
% 99.02/13.31 (lamp) =>
% 99.02/13.31 ((
% 99.02/13.31 (lam2p) =>
% 99.02/13.31 ((
% 99.02/13.31 (brelnall1) =>
% 99.02/13.31 ((
% 99.02/13.31 (brelnall2) =>
% 99.02/13.31 ((
% 99.02/13.31 (ex1E2) =>
% 99.02/13.31 ((
% 99.02/13.31 (funcGraphProp1) =>
% 99.02/13.31 ((
% 99.02/13.31 (funcGraphProp3) =>
% 99.02/13.31 ((
% 99.02/13.31 (funcGraphProp2) =>
% 99.02/13.31 ((
% 99.02/13.31 (funcextLem) =>
% 99.02/13.31 ((
% 99.02/13.31 (funcGraphProp4) =>
% 99.02/13.31 ((
% 99.02/13.31 (subbreln) =>
% 99.02/13.31 ((
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% 99.02/13.31 (funcext2) =>
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% 99.02/13.31 (ap2apEq1) =>
% 99.02/13.31 ((
% 99.02/13.31 (ap2apEq2) =>
% 99.02/13.31 ((
% 99.02/13.31 (beta1) =>
% 99.02/13.31 ((
% 99.02/13.31 (eta1) =>
% 99.02/13.31 ((
% 99.02/13.31 (lam2lamEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (beta2) =>
% 99.02/13.31 ((
% 99.02/13.31 (eta2) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (iffalseProp2) =>
% 99.02/13.31 ((
% 99.02/13.31 (iftrueProp1) =>
% 99.02/13.31 ((
% 99.02/13.31 (iftrueProp2) =>
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (binintersectTELcontra) =>
% 99.02/13.31 ((
% 99.02/13.31 (binintersectTERcontra) =>
% 99.02/13.31 ((
% 99.02/13.31 (contrasubsetT) =>
% 99.02/13.31 ((
% 99.02/13.31 (contrasubsetT1) =>
% 99.02/13.31 ((
% 99.02/13.31 (contrasubsetT2) =>
% 99.02/13.31 ((
% 99.02/13.31 (contrasubsetT3) =>
% 99.02/13.31 ((
% 99.02/13.31 (doubleComplementI1) =>
% 99.02/13.31 ((
% 99.02/13.31 (doubleComplementE1) =>
% 99.02/13.31 ((
% 99.02/13.31 (doubleComplementSub1) =>
% 99.02/13.31 ((
% 99.02/13.31 (doubleComplementSub2) =>
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% 99.02/13.31 (doubleComplementEq) =>
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% 99.02/13.31 (complementSubsetComplementIntersect) =>
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% 99.02/13.31 (complementInPowersetComplementIntersect) =>
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% 99.02/13.31 (contraSubsetComplement) =>
% 99.02/13.31 ((
% 99.02/13.31 (complementTcontraSubset) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (binunionTIRcontra) =>
% 99.02/13.31 ((
% 99.02/13.31 (inIntersectImpInUnion) =>
% 99.02/13.31 ((
% 99.02/13.31 (inIntersectImpInUnion2) =>
% 99.02/13.31 ((
% 99.02/13.31 (inIntersectImpInIntersectUnions) =>
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% 99.02/13.31 (intersectInPowersetIntersectUnions) =>
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% 99.02/13.31 (binunionTEcontra) =>
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% 99.02/13.31 ((
% 99.02/13.31 (complementUnionInPowersetComplement) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan2a2) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan1a) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan1b) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan1) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan2a) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan2b2) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan2b) =>
% 99.02/13.31 ((
% 99.02/13.31 (demorgan2) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz13rule0) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz13rule1) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz13rule2) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz13rule3) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz13rule4) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz1_1) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz1_2) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz1_3) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz1_4) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz1_5) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1all2) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1SetBreln1) =>
% 99.02/13.31 ((
% 99.02/13.31 (choice2fnsingleton) =>
% 99.02/13.31 ((
% 99.02/13.31 (setOfPairsIsBReln1) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1all1) =>
% 99.02/13.31 ((
% 99.02/13.31 (subbreln1) =>
% 99.02/13.31 ((
% 99.02/13.31 (eqbreln1) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1invprop) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1invI) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1invE) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1compprop) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1compI) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1compE) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1compEex) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionprop) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionIL) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionIR) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionI) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionE) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionEcases) =>
% 99.02/13.31 ((
% 99.02/13.31 (breln1unionCommutes) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz2Ex) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz2W) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz2A) =>
% 99.02/13.31 ((
% 99.02/13.31 (woz2B) =>
% 99.02/13.31 ((
% 99.02/13.31 (image1Ex) =>
% 99.02/13.31 ((
% 99.02/13.31 (image1Ex1) =>
% 99.02/13.31 ((
% 99.02/13.31 (image1Equiv) =>
% 99.02/13.31 ((
% 99.02/13.31 (image1E) =>
% 99.02/13.31 ((
% 99.02/13.31 (image1I) =>
% 99.02/13.31 ((
% 99.02/13.31 (injFuncInInjFuncSet) =>
% 99.02/13.31 ((
% 99.02/13.31 (!!) @ (
% 99.02/13.31 (('#B') @ (
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% 99.02/13.31 (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 !!))) @
% 99.02/13.31 (
% 99.02/13.31 (
% 99.02/13.31 ('#S') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 '#S') @
% 99.02/13.31 (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
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% 99.02/13.31 (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
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% 99.02/13.31 (
% 99.02/13.31 (
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% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#C') @ in)))) @
% 99.02/13.31 injFuncSet)))))))) @
% 99.02/13.31 (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#B') @ (
% 99.02/13.31 (
% 99.02/13.31 ('#C') @ in)))) @
% 99.02/13.31 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl485])).
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% 99.02/13.31 (((vacuousDall) =>
% 99.02/13.31 (((quantDeMorgan1) =>
% 99.02/13.31 (((quantDeMorgan2) =>
% 99.02/13.31 (((quantDeMorgan3) =>
% 99.02/13.31 (((quantDeMorgan4) =>
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% 99.02/13.31 (((exuI2) =>
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% 99.02/13.31 (((in__Cong) =>
% 99.02/13.31 (((exuE3u) =>
% 99.02/13.31 (((exu__Cong) =>
% 99.02/13.31 (((setadjoin__Cong) =>
% 99.02/13.31 (((powerset__Cong) =>
% 99.02/13.31 (((setunion__Cong) =>
% 99.02/13.31 (((exuEu) =>
% 99.02/13.31 (((descr__Cong) =>
% 99.02/13.31 (((dsetconstr__Cong) =>
% 99.02/13.31 (((subsetI1) =>
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (binintersectSubset3) =>
% 99.02/13.31 ((
% 99.02/13.31 (binintersectER) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (setminusILneg) =>
% 99.02/13.31 ((
% 99.02/13.31 (setminusIRneg) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (symdiffI2) =>
% 99.02/13.31 ((
% 99.02/13.31 (symdiffIneg1) =>
% 99.02/13.31 ((
% 99.02/13.31 (symdiffIneg2) =>
% 99.02/13.31 ((
% 99.02/13.31 (secondinupair) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (kpairp) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (ubforcartprodlem2) =>
% 99.02/13.31 ((
% 99.02/13.31 (ubforcartprodlem3) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (cartprodmempair) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (setunionsingleton) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (kfstpairEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodfstin) =>
% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjL2) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjR11) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjR1) =>
% 99.02/13.31 ((
% 99.02/13.31 (upairequniteq) =>
% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjR2) =>
% 99.02/13.31 ((
% 99.02/13.31 (setukpairinjR) =>
% 99.02/13.31 ((
% 99.02/13.31 (ksndsingleton) =>
% 99.02/13.31 ((
% 99.02/13.31 (ksndpairEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (kpairsurjEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodsndin) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodpairmemEL) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodpairmemER) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodmempaircEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodfstpairEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodsndpairEq) =>
% 99.02/13.31 ((
% 99.02/13.31 (cartprodpairsurjEq) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (dpsetconstrEL2) =>
% 99.02/13.31 ((
% 99.02/13.31 (dpsetconstrER) =>
% 99.02/13.31 ((
% 99.02/13.31 (funcImageSingleton) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
% 99.02/13.31 (funcinfuncset) =>
% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.31 ((
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% 99.02/13.32 (funcGraphProp3) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcGraphProp2) =>
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% 99.02/13.32 ((
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% 99.02/13.32 (lam2lamEq) =>
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% 99.02/13.32 (demorgan2a) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2b2) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2b) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2) =>
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% 99.02/13.32 ((
% 99.02/13.32 (woz13rule1) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule2) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule3) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule4) =>
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% 99.02/13.32 (woz1_3) =>
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% 99.02/13.32 (woz1_4) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_5) =>
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (breln1invI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compI) =>
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% 99.02/13.32 (breln1compE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compEex) =>
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% 99.02/13.32 (breln1unionprop) =>
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% 99.02/13.32 ((
% 99.02/13.32 (woz2W) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (woz2B) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Ex) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Ex1) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Equiv) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1E) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1I) =>
% 99.02/13.32 ((
% 99.02/13.32 (injFuncInInjFuncSet) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (image1I) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (eta2) =>
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (binintersectTERcontra) =>
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% 99.02/13.32 (contrasubsetT3) =>
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% 99.02/13.32 (doubleComplementSub2) =>
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% 99.02/13.32 (complementTcontraSubset) =>
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% 99.02/13.32 (binunionTIRcontra) =>
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% 99.02/13.32 (inIntersectImpInUnion2) =>
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% 99.02/13.32 (inIntersectImpInIntersectUnions) =>
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% 99.02/13.32 ((
% 99.02/13.32 (demorgan2a) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2b2) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2b) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule0) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule1) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule2) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule3) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule4) =>
% 99.02/13.32 ((
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% 99.02/13.32 (woz1_2) =>
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% 99.02/13.32 (woz1_3) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_4) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_5) =>
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% 99.02/13.32 (setOfPairsIsBReln1) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1all1) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (eqbreln1) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compEex) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionprop) =>
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% 99.02/13.32 (breln1unionIL) =>
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% 99.02/13.32 (breln1unionIR) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionEcases) =>
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% 99.02/13.32 ((
% 99.02/13.32 (woz2W) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz2A) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz2B) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Ex) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Ex1) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Equiv) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1E) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1I) =>
% 99.02/13.32 ((
% 99.02/13.32 (injFuncInInjFuncSet) =>
% 99.02/13.32 ((
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% 99.02/13.32 (((powerset__Cong) =>
% 99.02/13.32 (((setunion__Cong) =>
% 99.02/13.32 (((exuEu) =>
% 99.02/13.32 (((descr__Cong) =>
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (kpairsurjEq) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairmemER) =>
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% 99.02/13.32 ((
% 99.02/13.32 (cartprodfstpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodsndpairEq) =>
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% 99.02/13.32 ((
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% 99.02/13.32 (contrasubsetT3) =>
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% 99.02/13.32 (demorgan1b) =>
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% 99.02/13.32 ((
% 99.02/13.32 (demorgan2a) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 (demorgan2) =>
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% 99.02/13.32 ((
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% 99.02/13.32 (woz13rule3) =>
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% 99.02/13.32 ((
% 99.02/13.32 (breln1invI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compE) =>
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% 99.02/13.32 (breln1compEex) =>
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% 99.02/13.32 ((
% 99.02/13.32 (breln1unionE) =>
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% 99.02/13.32 (breln1unionEcases) =>
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (woz2B) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (image1Ex1) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Equiv) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1E) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1I) =>
% 99.02/13.32 ((
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% 99.02/13.32 (
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% 99.02/13.32 (((powerset__Cong) =>
% 99.02/13.32 (((setunion__Cong) =>
% 99.02/13.32 (((exuEu) =>
% 99.02/13.32 (((descr__Cong) =>
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 (cartprodsndpairEq) =>
% 99.02/13.32 ((
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% 99.02/13.32 (contrasubsetT3) =>
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% 99.02/13.32 (doubleComplementSub2) =>
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% 99.02/13.32 (demorgan1b) =>
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% 99.02/13.32 ((
% 99.02/13.32 (demorgan2a) =>
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% 99.02/13.32 (demorgan2b2) =>
% 99.02/13.32 ((
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% 99.02/13.32 (demorgan2) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule0) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule1) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule2) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule3) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule4) =>
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% 99.02/13.32 (woz1_3) =>
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% 99.02/13.32 (woz1_5) =>
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% 99.02/13.32 ((
% 99.02/13.32 (breln1invI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invE) =>
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% 99.02/13.32 (breln1compprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compE) =>
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% 99.02/13.32 (breln1compEex) =>
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% 99.02/13.32 (breln1unionI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionEcases) =>
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% 99.02/13.32 (breln1unionCommutes) =>
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% 99.02/13.32 ((
% 99.02/13.32 (woz2W) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (woz2B) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (image1Equiv) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1E) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1I) =>
% 99.02/13.32 ((
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% 99.02/13.32 (
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% 99.02/13.32 (((powerset__Cong) =>
% 99.02/13.32 (((setunion__Cong) =>
% 99.02/13.32 (((exuEu) =>
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (upairset2IR) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (binunionEcases) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (binunionRsub) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 (symdiffI2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (symdiffIneg2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (kpairp) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (upairinpowunion) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairmemER) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodmempaircEq) =>
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% 99.02/13.32 (cartprodfstpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodsndpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairsurjEq) =>
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% 99.02/13.32 (contrasubsetT3) =>
% 99.02/13.32 ((
% 99.02/13.32 (doubleComplementI1) =>
% 99.02/13.32 ((
% 99.02/13.32 (doubleComplementE1) =>
% 99.02/13.32 ((
% 99.02/13.32 (doubleComplementSub1) =>
% 99.02/13.32 ((
% 99.02/13.32 (doubleComplementSub2) =>
% 99.02/13.32 ((
% 99.02/13.32 (doubleComplementEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (complementTnotintersectT) =>
% 99.02/13.32 ((
% 99.02/13.32 (complementImpComplementIntersect) =>
% 99.02/13.32 ((
% 99.02/13.32 (complementSubsetComplementIntersect) =>
% 99.02/13.32 ((
% 99.02/13.32 (complementInPowersetComplementIntersect) =>
% 99.02/13.32 ((
% 99.02/13.32 (contraSubsetComplement) =>
% 99.02/13.32 ((
% 99.02/13.32 (complementTcontraSubset) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionTILcontra) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionTIRcontra) =>
% 99.02/13.32 ((
% 99.02/13.32 (inIntersectImpInUnion) =>
% 99.02/13.32 ((
% 99.02/13.32 (inIntersectImpInUnion2) =>
% 99.02/13.32 ((
% 99.02/13.32 (inIntersectImpInIntersectUnions) =>
% 99.02/13.32 ((
% 99.02/13.32 (intersectInPowersetIntersectUnions) =>
% 99.02/13.32 ((
% 99.02/13.32 (inComplementUnionImpNotIn1) =>
% 99.02/13.32 ((
% 99.02/13.32 (inComplementUnionImpInComplement1) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionTE) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionTEcontra) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2a1) =>
% 99.02/13.32 ((
% 99.02/13.32 (complementUnionInPowersetComplement) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2a2) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan1a) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan1b) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan1) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2a) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2b2) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2b) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule0) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule1) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule2) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule3) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule4) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_1) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_2) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_3) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_4) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_5) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1all2) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1SetBreln1) =>
% 99.02/13.32 ((
% 99.02/13.32 (choice2fnsingleton) =>
% 99.02/13.32 ((
% 99.02/13.32 (setOfPairsIsBReln1) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1all1) =>
% 99.02/13.32 ((
% 99.02/13.32 (subbreln1) =>
% 99.02/13.32 ((
% 99.02/13.32 (eqbreln1) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compEex) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionIL) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionIR) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionEcases) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionCommutes) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz2Ex) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz2W) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz2A) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz2B) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Ex) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Ex1) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Equiv) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1E) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1I) =>
% 99.02/13.32 ((
% 99.02/13.32 (injFuncInInjFuncSet) =>
% 99.02/13.32 ((
% 99.02/13.32 (!!) @ (
% 99.02/13.32 (('#B') @ (
% 99.02/13.32 !!) @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 !!))) @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#S') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 '#S') @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 '#S'))) @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 =>))))) @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#C') @ in)))) @
% 99.02/13.32 injFuncSet)))))))) @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#C') @ in)))) @
% 99.02/13.32 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl553])).
% 99.02/13.32 thf(zip_derived_cl570, plain,
% 99.02/13.32 (~ (((prop2setI) =>
% 99.02/13.32 (((prop2set2propI) =>
% 99.02/13.32 (((notdexE) =>
% 99.02/13.32 (((notdallE) =>
% 99.02/13.32 (((exuI1) =>
% 99.02/13.32 (((exuI3) =>
% 99.02/13.32 (((exuI2) =>
% 99.02/13.32 (((inCongP) =>
% 99.02/13.32 (((in__Cong) =>
% 99.02/13.32 (((exuE3u) =>
% 99.02/13.32 (((exu__Cong) =>
% 99.02/13.32 (((setadjoin__Cong) =>
% 99.02/13.32 (((powerset__Cong) =>
% 99.02/13.32 (((setunion__Cong) =>
% 99.02/13.32 (((exuEu) =>
% 99.02/13.32 (((descr__Cong) =>
% 99.02/13.32 (((dsetconstr__Cong) =>
% 99.02/13.32 (((subsetI1) =>
% 99.02/13.32 (((eqimpsubset2) =>
% 99.02/13.32 (((eqimpsubset1) =>
% 99.02/13.32 (((subsetI2) =>
% 99.02/13.32 (((emptysetsubset) =>
% 99.02/13.32 (((subsetE) =>
% 99.02/13.32 (((subsetE2) =>
% 99.02/13.32 (((notsubsetI) =>
% 99.02/13.32 (((notequalI1) =>
% 99.02/13.32 (((notequalI2) =>
% 99.02/13.32 (((subsetRefl) =>
% 99.02/13.32 (((subsetTrans) =>
% 99.02/13.32 (((setadjoinSub) =>
% 99.02/13.32 ((
% 99.02/13.32 (setadjoinSub2) =>
% 99.02/13.32 ((
% 99.02/13.32 (subset2powerset) =>
% 99.02/13.32 ((
% 99.02/13.32 (setextsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (subsetemptysetimpeq) =>
% 99.02/13.32 ((
% 99.02/13.32 (powersetI1) =>
% 99.02/13.32 ((
% 99.02/13.32 (powersetE1) =>
% 99.02/13.32 ((
% 99.02/13.32 (inPowerset) =>
% 99.02/13.32 ((
% 99.02/13.32 (powersetsubset) =>
% 99.02/13.32 ((
% 99.02/13.32 (sepInPowerset) =>
% 99.02/13.32 ((
% 99.02/13.32 (sepSubset) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionIL) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairset2IR) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionIR) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionEcases) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionE) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionLsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionRsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectI) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset5) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectEL) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectLsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset2) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset3) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectER) =>
% 99.02/13.32 ((
% 99.02/13.32 (disjointsetsI1) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectRsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset4) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset1) =>
% 99.02/13.32 ((
% 99.02/13.32 (bs114d) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusI) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusEL) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusER) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusSubset2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusERneg) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusELneg) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusILneg) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusIRneg) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusLsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusSubset1) =>
% 99.02/13.32 ((
% 99.02/13.32 (symdiffE) =>
% 99.02/13.32 ((
% 99.02/13.32 (symdiffI1) =>
% 99.02/13.32 ((
% 99.02/13.32 (symdiffI2) =>
% 99.02/13.32 ((
% 99.02/13.32 (symdiffIneg1) =>
% 99.02/13.32 ((
% 99.02/13.32 (symdiffIneg2) =>
% 99.02/13.32 ((
% 99.02/13.32 (secondinupair) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairIL) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairIR) =>
% 99.02/13.32 ((
% 99.02/13.32 (kpairiskpair) =>
% 99.02/13.32 ((
% 99.02/13.32 (kpairp) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletonsubset) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletoninpowerset) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletoninpowunion) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairset2E) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairsubunion) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairinpowunion) =>
% 99.02/13.32 ((
% 99.02/13.32 (ubforcartprodlem1) =>
% 99.02/13.32 ((
% 99.02/13.32 (ubforcartprodlem2) =>
% 99.02/13.32 ((
% 99.02/13.32 (ubforcartprodlem3) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairin) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodmempair1) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodmempair) =>
% 99.02/13.32 ((
% 99.02/13.32 (setunionE2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setunionsingleton1) =>
% 99.02/13.32 ((
% 99.02/13.32 (setunionsingleton2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setunionsingleton) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletonprop) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (ex1I) =>
% 99.02/13.32 ((
% 99.02/13.32 (ex1I2) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletonsuniq) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjL1) =>
% 99.02/13.32 ((
% 99.02/13.32 (kfstsingleton) =>
% 99.02/13.32 ((
% 99.02/13.32 (theprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (kfstpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodfstin) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjL2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjL) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR11) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR12) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR1) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairequniteq) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR) =>
% 99.02/13.32 ((
% 99.02/13.32 (ksndsingleton) =>
% 99.02/13.32 ((
% 99.02/13.32 (ksndpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (kpairsurjEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodsndin) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairmemEL) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairmemER) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodmempaircEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodfstpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodsndpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairsurjEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrI) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrSub) =>
% 99.02/13.32 ((
% 99.02/13.32 (setOfPairsIsBReln) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrERa) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrEL1) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrEL2) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrER) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (apProp) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (ap2p) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcinfuncset) =>
% 99.02/13.32 ((
% 99.02/13.32 (lamProp) =>
% 99.02/13.32 ((
% 99.02/13.32 (lamp) =>
% 99.02/13.32 ((
% 99.02/13.32 (lam2p) =>
% 99.02/13.32 ((
% 99.02/13.32 (brelnall1) =>
% 99.02/13.32 ((
% 99.02/13.32 (brelnall2) =>
% 99.02/13.32 ((
% 99.02/13.32 (ex1E2) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcGraphProp1) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (funcGraphProp2) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcextLem) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcGraphProp4) =>
% 99.02/13.32 ((
% 99.02/13.32 (subbreln) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (funcext) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcext2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (ap2apEq2) =>
% 99.02/13.32 ((
% 99.02/13.32 (beta1) =>
% 99.02/13.32 ((
% 99.02/13.32 (eta1) =>
% 99.02/13.32 ((
% 99.02/13.32 (lam2lamEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (beta2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (iffalseProp2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (iftrueProp2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (iftrueorfalse) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (powersetTE1) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (contrasubsetT2) =>
% 99.02/13.32 ((
% 99.02/13.32 (contrasubsetT3) =>
% 99.02/13.32 ((
% 99.02/13.32 (doubleComplementI1) =>
% 99.02/13.32 ((
% 99.02/13.32 (doubleComplementE1) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (complementSubsetComplementIntersect) =>
% 99.02/13.32 ((
% 99.02/13.32 (complementInPowersetComplementIntersect) =>
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% 99.02/13.32 (demorgan1b) =>
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% 99.02/13.32 ((
% 99.02/13.32 (demorgan2a) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2b2) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2b) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (woz13rule1) =>
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% 99.02/13.32 (breln1compprop) =>
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% 99.02/13.32 (breln1compE) =>
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 (
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (symdiffIneg2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 (setukpairinjR) =>
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 (cartprodpairmemER) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodmempaircEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodfstpairEq) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (demorgan2a1) =>
% 99.02/13.32 ((
% 99.02/13.32 (complementUnionInPowersetComplement) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2a2) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan1a) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan1b) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan1) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2a) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2b2) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2b) =>
% 99.02/13.32 ((
% 99.02/13.32 (demorgan2) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule0) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule1) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule2) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule3) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule4) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_1) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_2) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_3) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_4) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_5) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1all2) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1SetBreln1) =>
% 99.02/13.32 ((
% 99.02/13.32 (choice2fnsingleton) =>
% 99.02/13.32 ((
% 99.02/13.32 (setOfPairsIsBReln1) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1all1) =>
% 99.02/13.32 ((
% 99.02/13.32 (subbreln1) =>
% 99.02/13.32 ((
% 99.02/13.32 (eqbreln1) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compEex) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionIL) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionIR) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionEcases) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionCommutes) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz2Ex) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz2W) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz2A) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz2B) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Ex) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Ex1) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Equiv) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1E) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1I) =>
% 99.02/13.32 ((
% 99.02/13.32 (injFuncInInjFuncSet) =>
% 99.02/13.32 ((
% 99.02/13.32 (!!) @ (
% 99.02/13.32 (('#B') @ (
% 99.02/13.32 !!) @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 !!))) @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#S') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 '#S') @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 '#S'))) @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 =>))))) @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#C') @ in)))) @
% 99.02/13.32 injFuncSet)))))))) @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#C') @ in)))) @
% 99.02/13.32 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl570])).
% 99.02/13.32 thf(zip_derived_cl586, plain,
% 99.02/13.32 (~ (((notdexE) =>
% 99.02/13.32 (((notdallE) =>
% 99.02/13.32 (((exuI1) =>
% 99.02/13.32 (((exuI3) =>
% 99.02/13.32 (((exuI2) =>
% 99.02/13.32 (((inCongP) =>
% 99.02/13.32 (((in__Cong) =>
% 99.02/13.32 (((exuE3u) =>
% 99.02/13.32 (((exu__Cong) =>
% 99.02/13.32 (((setadjoin__Cong) =>
% 99.02/13.32 (((powerset__Cong) =>
% 99.02/13.32 (((setunion__Cong) =>
% 99.02/13.32 (((exuEu) =>
% 99.02/13.32 (((descr__Cong) =>
% 99.02/13.32 (((dsetconstr__Cong) =>
% 99.02/13.32 (((subsetI1) =>
% 99.02/13.32 (((eqimpsubset2) =>
% 99.02/13.32 (((eqimpsubset1) =>
% 99.02/13.32 (((subsetI2) =>
% 99.02/13.32 (((emptysetsubset) =>
% 99.02/13.32 (((subsetE) =>
% 99.02/13.32 (((subsetE2) =>
% 99.02/13.32 (((notsubsetI) =>
% 99.02/13.32 (((notequalI1) =>
% 99.02/13.32 (((notequalI2) =>
% 99.02/13.32 (((subsetRefl) =>
% 99.02/13.32 (((subsetTrans) =>
% 99.02/13.32 (((setadjoinSub) =>
% 99.02/13.32 (((setadjoinSub2) =>
% 99.02/13.32 (((subset2powerset) =>
% 99.02/13.32 ((
% 99.02/13.32 (setextsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (subsetemptysetimpeq) =>
% 99.02/13.32 ((
% 99.02/13.32 (powersetI1) =>
% 99.02/13.32 ((
% 99.02/13.32 (powersetE1) =>
% 99.02/13.32 ((
% 99.02/13.32 (inPowerset) =>
% 99.02/13.32 ((
% 99.02/13.32 (powersetsubset) =>
% 99.02/13.32 ((
% 99.02/13.32 (sepInPowerset) =>
% 99.02/13.32 ((
% 99.02/13.32 (sepSubset) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionIL) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairset2IR) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionIR) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionEcases) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionE) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionLsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionRsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectI) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset5) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectEL) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectLsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset2) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset3) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectER) =>
% 99.02/13.32 ((
% 99.02/13.32 (disjointsetsI1) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectRsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset4) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset1) =>
% 99.02/13.32 ((
% 99.02/13.32 (bs114d) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusI) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusEL) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusER) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusSubset2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusERneg) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusELneg) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusILneg) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusIRneg) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusLsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusSubset1) =>
% 99.02/13.32 ((
% 99.02/13.32 (symdiffE) =>
% 99.02/13.32 ((
% 99.02/13.32 (symdiffI1) =>
% 99.02/13.32 ((
% 99.02/13.32 (symdiffI2) =>
% 99.02/13.32 ((
% 99.02/13.32 (symdiffIneg1) =>
% 99.02/13.32 ((
% 99.02/13.32 (symdiffIneg2) =>
% 99.02/13.32 ((
% 99.02/13.32 (secondinupair) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairIL) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairIR) =>
% 99.02/13.32 ((
% 99.02/13.32 (kpairiskpair) =>
% 99.02/13.32 ((
% 99.02/13.32 (kpairp) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletonsubset) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletoninpowerset) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletoninpowunion) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairset2E) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairsubunion) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairinpowunion) =>
% 99.02/13.32 ((
% 99.02/13.32 (ubforcartprodlem1) =>
% 99.02/13.32 ((
% 99.02/13.32 (ubforcartprodlem2) =>
% 99.02/13.32 ((
% 99.02/13.32 (ubforcartprodlem3) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairin) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodmempair1) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodmempair) =>
% 99.02/13.32 ((
% 99.02/13.32 (setunionE2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setunionsingleton1) =>
% 99.02/13.32 ((
% 99.02/13.32 (setunionsingleton2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setunionsingleton) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletonprop) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (ex1I) =>
% 99.02/13.32 ((
% 99.02/13.32 (ex1I2) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletonsuniq) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjL1) =>
% 99.02/13.32 ((
% 99.02/13.32 (kfstsingleton) =>
% 99.02/13.32 ((
% 99.02/13.32 (theprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (kfstpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodfstin) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjL2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjL) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR11) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR12) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR1) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairequniteq) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR) =>
% 99.02/13.32 ((
% 99.02/13.32 (ksndsingleton) =>
% 99.02/13.32 ((
% 99.02/13.32 (ksndpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (kpairsurjEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodsndin) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairmemEL) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairmemER) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodmempaircEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodfstpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodsndpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairsurjEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrI) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrSub) =>
% 99.02/13.32 ((
% 99.02/13.32 (setOfPairsIsBReln) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrERa) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrEL1) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrEL2) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrER) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcImageSingleton) =>
% 99.02/13.32 ((
% 99.02/13.32 (apProp) =>
% 99.02/13.32 ((
% 99.02/13.32 (app) =>
% 99.02/13.32 ((
% 99.02/13.32 (infuncsetfunc) =>
% 99.02/13.32 ((
% 99.02/13.32 (ap2p) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcinfuncset) =>
% 99.02/13.32 ((
% 99.02/13.32 (lamProp) =>
% 99.02/13.32 ((
% 99.02/13.32 (lamp) =>
% 99.02/13.32 ((
% 99.02/13.32 (lam2p) =>
% 99.02/13.32 ((
% 99.02/13.32 (brelnall1) =>
% 99.02/13.32 ((
% 99.02/13.32 (brelnall2) =>
% 99.02/13.32 ((
% 99.02/13.32 (ex1E2) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcGraphProp1) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcGraphProp3) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcGraphProp2) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcextLem) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcGraphProp4) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (eqbreln) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcext) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcext2) =>
% 99.02/13.32 ((
% 99.02/13.32 (ap2apEq1) =>
% 99.02/13.32 ((
% 99.02/13.32 (ap2apEq2) =>
% 99.02/13.32 ((
% 99.02/13.32 (beta1) =>
% 99.02/13.32 ((
% 99.02/13.32 (eta1) =>
% 99.02/13.32 ((
% 99.02/13.32 (lam2lamEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (beta2) =>
% 99.02/13.32 ((
% 99.02/13.32 (eta2) =>
% 99.02/13.32 ((
% 99.02/13.32 (iffalseProp1) =>
% 99.02/13.32 ((
% 99.02/13.32 (iffalseProp2) =>
% 99.02/13.32 ((
% 99.02/13.32 (iftrueProp1) =>
% 99.02/13.32 ((
% 99.02/13.32 (iftrueProp2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (iftrue) =>
% 99.02/13.32 ((
% 99.02/13.32 (iffalse) =>
% 99.02/13.32 ((
% 99.02/13.32 (iftrueorfalse) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectT_lem) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionT_lem) =>
% 99.02/13.32 ((
% 99.02/13.32 (powersetT_lem) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (complementTE1) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (binintersectTERcontra) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (contrasubsetT2) =>
% 99.02/13.32 ((
% 99.02/13.32 (contrasubsetT3) =>
% 99.02/13.32 ((
% 99.02/13.32 (doubleComplementI1) =>
% 99.02/13.32 ((
% 99.02/13.32 (doubleComplementE1) =>
% 99.02/13.32 ((
% 99.02/13.32 (doubleComplementSub1) =>
% 99.02/13.32 ((
% 99.02/13.32 (doubleComplementSub2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (contraSubsetComplement) =>
% 99.02/13.32 ((
% 99.02/13.32 (complementTcontraSubset) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionTILcontra) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionTIRcontra) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (inIntersectImpInUnion2) =>
% 99.02/13.32 ((
% 99.02/13.32 (inIntersectImpInIntersectUnions) =>
% 99.02/13.32 ((
% 99.02/13.32 (intersectInPowersetIntersectUnions) =>
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% 99.02/13.32 ((
% 99.02/13.32 (inComplementUnionImpInComplement1) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (demorgan2a) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (woz13rule3) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz13rule4) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_1) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_2) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_3) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_4) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz1_5) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (breln1SetBreln1) =>
% 99.02/13.32 ((
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% 99.02/13.32 (setOfPairsIsBReln1) =>
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% 99.02/13.32 (eqbreln1) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compEex) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionIL) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionIR) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionEcases) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionCommutes) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (woz2W) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz2A) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz2B) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Ex) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Ex1) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Equiv) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1E) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1I) =>
% 99.02/13.32 ((
% 99.02/13.32 (injFuncInInjFuncSet) =>
% 99.02/13.32 ((
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% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
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% 99.02/13.32 (
% 99.02/13.32 (
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% 99.02/13.32 (
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% 99.02/13.32 (
% 99.02/13.32 (
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% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
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% 99.02/13.32 (
% 99.02/13.32 (
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% 99.02/13.32 (
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% 99.02/13.32 injFuncSet)))))))) @
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% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#C') @ in)))) @
% 99.02/13.32 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
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% 99.02/13.32 (((exuE3u) =>
% 99.02/13.32 (((exu__Cong) =>
% 99.02/13.32 (((setadjoin__Cong) =>
% 99.02/13.32 (((powerset__Cong) =>
% 99.02/13.32 (((setunion__Cong) =>
% 99.02/13.32 (((exuEu) =>
% 99.02/13.32 (((descr__Cong) =>
% 99.02/13.32 (((dsetconstr__Cong) =>
% 99.02/13.32 (((subsetI1) =>
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% 99.02/13.32 (((eqimpsubset1) =>
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% 99.02/13.32 (((notequalI2) =>
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% 99.02/13.32 ((
% 99.02/13.32 (powersetE1) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (powersetsubset) =>
% 99.02/13.32 ((
% 99.02/13.32 (sepInPowerset) =>
% 99.02/13.32 ((
% 99.02/13.32 (sepSubset) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (upairset2IR) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (binunionEcases) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionE) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionLsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionRsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectI) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset5) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (binintersectLsub) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset3) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset4) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset1) =>
% 99.02/13.32 ((
% 99.02/13.32 (bs114d) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (setminusEL) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusER) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusSubset2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusERneg) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusELneg) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusILneg) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusIRneg) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusLsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusSubset1) =>
% 99.02/13.32 ((
% 99.02/13.32 (symdiffE) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (symdiffI2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (symdiffIneg2) =>
% 99.02/13.32 ((
% 99.02/13.32 (secondinupair) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairIL) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairIR) =>
% 99.02/13.32 ((
% 99.02/13.32 (kpairiskpair) =>
% 99.02/13.32 ((
% 99.02/13.32 (kpairp) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletonsubset) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletoninpowerset) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletoninpowunion) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairset2E) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairsubunion) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairinpowunion) =>
% 99.02/13.32 ((
% 99.02/13.32 (ubforcartprodlem1) =>
% 99.02/13.32 ((
% 99.02/13.32 (ubforcartprodlem2) =>
% 99.02/13.32 ((
% 99.02/13.32 (ubforcartprodlem3) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairin) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodmempair1) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodmempair) =>
% 99.02/13.32 ((
% 99.02/13.32 (setunionE2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (setunionsingleton) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjL1) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (kfstpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodfstin) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjL2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjL) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR11) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR12) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR1) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairequniteq) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR) =>
% 99.02/13.32 ((
% 99.02/13.32 (ksndsingleton) =>
% 99.02/13.32 ((
% 99.02/13.32 (ksndpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (kpairsurjEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodsndin) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairmemEL) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairmemER) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodmempaircEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodfstpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodsndpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairsurjEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrI) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrSub) =>
% 99.02/13.32 ((
% 99.02/13.32 (setOfPairsIsBReln) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrERa) =>
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% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrEL2) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrER) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcImageSingleton) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (lam2p) =>
% 99.02/13.32 ((
% 99.02/13.32 (brelnall1) =>
% 99.02/13.32 ((
% 99.02/13.32 (brelnall2) =>
% 99.02/13.32 ((
% 99.02/13.32 (ex1E2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (funcGraphProp3) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcGraphProp2) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcextLem) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcGraphProp4) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (funcext2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (ap2apEq2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (beta2) =>
% 99.02/13.32 ((
% 99.02/13.32 (eta2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (iffalseProp2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (contrasubsetT3) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (doubleComplementSub2) =>
% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
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% 99.02/13.32 ((
% 99.02/13.32 (eqbreln1) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1invE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1compEex) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionIL) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionIR) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionI) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionE) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionEcases) =>
% 99.02/13.32 ((
% 99.02/13.32 (breln1unionCommutes) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz2Ex) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz2W) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz2A) =>
% 99.02/13.32 ((
% 99.02/13.32 (woz2B) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Ex) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Ex1) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1Equiv) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1E) =>
% 99.02/13.32 ((
% 99.02/13.32 (image1I) =>
% 99.02/13.32 ((
% 99.02/13.32 (injFuncInInjFuncSet) =>
% 99.02/13.32 ((
% 99.02/13.32 (!!) @ (
% 99.02/13.32 (('#B') @ (
% 99.02/13.32 !!) @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 !!))) @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#S') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 '#S') @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 '#S'))) @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 =>))))) @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#C') @ in)))) @
% 99.02/13.32 injFuncSet)))))))) @
% 99.02/13.32 (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#B') @ (
% 99.02/13.32 (
% 99.02/13.32 ('#C') @ in)))) @
% 99.02/13.32 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl586])).
% 99.02/13.32 thf(zip_derived_cl606, plain,
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% 99.02/13.32 (((exuI3) =>
% 99.02/13.32 (((exuI2) =>
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% 99.02/13.32 (((in__Cong) =>
% 99.02/13.32 (((exuE3u) =>
% 99.02/13.32 (((exu__Cong) =>
% 99.02/13.32 (((setadjoin__Cong) =>
% 99.02/13.32 (((powerset__Cong) =>
% 99.02/13.32 (((setunion__Cong) =>
% 99.02/13.32 (((exuEu) =>
% 99.02/13.32 (((descr__Cong) =>
% 99.02/13.32 (((dsetconstr__Cong) =>
% 99.02/13.32 (((subsetI1) =>
% 99.02/13.32 (((eqimpsubset2) =>
% 99.02/13.32 (((eqimpsubset1) =>
% 99.02/13.32 (((subsetI2) =>
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% 99.02/13.32 (((subsetE) =>
% 99.02/13.32 (((subsetE2) =>
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% 99.02/13.32 (((notequalI1) =>
% 99.02/13.32 (((notequalI2) =>
% 99.02/13.32 (((subsetRefl) =>
% 99.02/13.32 (((subsetTrans) =>
% 99.02/13.32 (((setadjoinSub) =>
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% 99.02/13.32 (((setextsub) =>
% 99.02/13.32 (((subsetemptysetimpeq) =>
% 99.02/13.32 ((
% 99.02/13.32 (powersetI1) =>
% 99.02/13.32 ((
% 99.02/13.32 (powersetE1) =>
% 99.02/13.32 ((
% 99.02/13.32 (inPowerset) =>
% 99.02/13.32 ((
% 99.02/13.32 (powersetsubset) =>
% 99.02/13.32 ((
% 99.02/13.32 (sepInPowerset) =>
% 99.02/13.32 ((
% 99.02/13.32 (sepSubset) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionIL) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairset2IR) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionIR) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionEcases) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionE) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionLsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (binunionRsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectI) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset5) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectEL) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectLsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset2) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset3) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectER) =>
% 99.02/13.32 ((
% 99.02/13.32 (disjointsetsI1) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectRsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset4) =>
% 99.02/13.32 ((
% 99.02/13.32 (binintersectSubset1) =>
% 99.02/13.32 ((
% 99.02/13.32 (bs114d) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusI) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusEL) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusER) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusSubset2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusERneg) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusELneg) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusILneg) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusIRneg) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusLsub) =>
% 99.02/13.32 ((
% 99.02/13.32 (setminusSubset1) =>
% 99.02/13.32 ((
% 99.02/13.32 (symdiffE) =>
% 99.02/13.32 ((
% 99.02/13.32 (symdiffI1) =>
% 99.02/13.32 ((
% 99.02/13.32 (symdiffI2) =>
% 99.02/13.32 ((
% 99.02/13.32 (symdiffIneg1) =>
% 99.02/13.32 ((
% 99.02/13.32 (symdiffIneg2) =>
% 99.02/13.32 ((
% 99.02/13.32 (secondinupair) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairIL) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairIR) =>
% 99.02/13.32 ((
% 99.02/13.32 (kpairiskpair) =>
% 99.02/13.32 ((
% 99.02/13.32 (kpairp) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletonsubset) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletoninpowerset) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletoninpowunion) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairset2E) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairsubunion) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairinpowunion) =>
% 99.02/13.32 ((
% 99.02/13.32 (ubforcartprodlem1) =>
% 99.02/13.32 ((
% 99.02/13.32 (ubforcartprodlem2) =>
% 99.02/13.32 ((
% 99.02/13.32 (ubforcartprodlem3) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairin) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodmempair1) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodmempair) =>
% 99.02/13.32 ((
% 99.02/13.32 (setunionE2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setunionsingleton1) =>
% 99.02/13.32 ((
% 99.02/13.32 (setunionsingleton2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setunionsingleton) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletonprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (ex1E1) =>
% 99.02/13.32 ((
% 99.02/13.32 (ex1I) =>
% 99.02/13.32 ((
% 99.02/13.32 (ex1I2) =>
% 99.02/13.32 ((
% 99.02/13.32 (singletonsuniq) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjL1) =>
% 99.02/13.32 ((
% 99.02/13.32 (kfstsingleton) =>
% 99.02/13.32 ((
% 99.02/13.32 (theprop) =>
% 99.02/13.32 ((
% 99.02/13.32 (kfstpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodfstin) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjL2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjL) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR11) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR12) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR1) =>
% 99.02/13.32 ((
% 99.02/13.32 (upairequniteq) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR2) =>
% 99.02/13.32 ((
% 99.02/13.32 (setukpairinjR) =>
% 99.02/13.32 ((
% 99.02/13.32 (ksndsingleton) =>
% 99.02/13.32 ((
% 99.02/13.32 (ksndpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (kpairsurjEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodsndin) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairmemEL) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairmemER) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodmempaircEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodfstpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodsndpairEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (cartprodpairsurjEq) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrI) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrSub) =>
% 99.02/13.32 ((
% 99.02/13.32 (setOfPairsIsBReln) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrERa) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrEL1) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrEL2) =>
% 99.02/13.32 ((
% 99.02/13.32 (dpsetconstrER) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcImageSingleton) =>
% 99.02/13.32 ((
% 99.02/13.32 (apProp) =>
% 99.02/13.32 ((
% 99.02/13.32 (app) =>
% 99.02/13.32 ((
% 99.02/13.32 (infuncsetfunc) =>
% 99.02/13.32 ((
% 99.02/13.32 (ap2p) =>
% 99.02/13.32 ((
% 99.02/13.32 (funcinfuncset) =>
% 99.02/13.32 ((
% 99.02/13.32 (lamProp) =>
% 99.02/13.32 ((
% 99.02/13.32 (lamp) =>
% 99.02/13.32 ((
% 99.02/13.32 (lam2p) =>
% 99.02/13.32 ((
% 99.02/13.32 (brelnall1) =>
% 99.02/13.33 ((
% 99.02/13.33 (brelnall2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1E2) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp3) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcextLem) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp4) =>
% 99.02/13.33 ((
% 99.02/13.33 (subbreln) =>
% 99.02/13.33 ((
% 99.02/13.33 (eqbreln) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcext) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcext2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2apEq1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2apEq2) =>
% 99.02/13.33 ((
% 99.02/13.33 (beta1) =>
% 99.02/13.33 ((
% 99.02/13.33 (eta1) =>
% 99.02/13.33 ((
% 99.02/13.33 (lam2lamEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (beta2) =>
% 99.02/13.33 ((
% 99.02/13.33 (eta2) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalseProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalseProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ifSingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (ifp) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (iftrue) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalse) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueorfalse) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (setextT) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (powersetTE1) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (complementTE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectTELcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectTERcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT1) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT2) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT3) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub2) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTnotintersectT) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (complementInPowersetComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (contraSubsetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTcontraSubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTILcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTIRcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion2) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (intersectInPowersetIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (inComplementUnionImpNotIn1) =>
% 99.02/13.33 ((
% 99.02/13.33 (inComplementUnionImpInComplement1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTE) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTEcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementUnionInPowersetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (woz1_2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_4) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_5) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1all2) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1SetBreln1) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (eqbreln1) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (breln1invI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compEex) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 (breln1unionEcases) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionCommutes) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2Ex) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2W) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2A) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2B) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Ex) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Ex1) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Equiv) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1E) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1I) =>
% 99.02/13.33 ((
% 99.02/13.33 (injFuncInInjFuncSet) =>
% 99.02/13.33 ((
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% 99.02/13.33 (('#B') @ (
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% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
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% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#S') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 '#S') @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
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% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 =>))))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#C') @ in)))) @
% 99.02/13.33 injFuncSet)))))))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#C') @ in)))) @
% 99.02/13.33 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl595])).
% 99.02/13.33 thf(zip_derived_cl619, plain,
% 99.02/13.33 (~ (((exuI3) =>
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% 99.02/13.33 (((inCongP) =>
% 99.02/13.33 (((in__Cong) =>
% 99.02/13.33 (((exuE3u) =>
% 99.02/13.33 (((exu__Cong) =>
% 99.02/13.33 (((setadjoin__Cong) =>
% 99.02/13.33 (((powerset__Cong) =>
% 99.02/13.33 (((setunion__Cong) =>
% 99.02/13.33 (((exuEu) =>
% 99.02/13.33 (((descr__Cong) =>
% 99.02/13.33 (((dsetconstr__Cong) =>
% 99.02/13.33 (((subsetI1) =>
% 99.02/13.33 (((eqimpsubset2) =>
% 99.02/13.33 (((eqimpsubset1) =>
% 99.02/13.33 (((subsetI2) =>
% 99.02/13.33 (((emptysetsubset) =>
% 99.02/13.33 (((subsetE) =>
% 99.02/13.33 (((subsetE2) =>
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% 99.02/13.33 (((notequalI1) =>
% 99.02/13.33 (((notequalI2) =>
% 99.02/13.33 (((subsetRefl) =>
% 99.02/13.33 (((subsetTrans) =>
% 99.02/13.33 (((setadjoinSub) =>
% 99.02/13.33 (((setadjoinSub2) =>
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% 99.02/13.33 (((setextsub) =>
% 99.02/13.33 (((subsetemptysetimpeq) =>
% 99.02/13.33 (((powersetI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (inPowerset) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetsubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (sepInPowerset) =>
% 99.02/13.33 ((
% 99.02/13.33 (sepSubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairset2IR) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionEcases) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionE) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionRsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectI) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset5) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset2) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset3) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectER) =>
% 99.02/13.33 ((
% 99.02/13.33 (disjointsetsI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectRsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset4) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset1) =>
% 99.02/13.33 ((
% 99.02/13.33 (bs114d) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusI) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusER) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusSubset2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusERneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusELneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusILneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusIRneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusSubset1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffE) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffI2) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffIneg1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffIneg2) =>
% 99.02/13.33 ((
% 99.02/13.33 (secondinupair) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairiskpair) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairp) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonsubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletoninpowerset) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletoninpowunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairset2E) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairsubunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairinpowunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem3) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairin) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempair1) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempair) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionE2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton1) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1E1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1I) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1I2) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonsuniq) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL1) =>
% 99.02/13.33 ((
% 99.02/13.33 (kfstsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (theprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (kfstpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodfstin) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR11) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR12) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR1) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairequniteq) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR) =>
% 99.02/13.33 ((
% 99.02/13.33 (ksndsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (ksndpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairsurjEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodsndin) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairmemEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairmemER) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempaircEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodfstpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodsndpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairsurjEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrI) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrSub) =>
% 99.02/13.33 ((
% 99.02/13.33 (setOfPairsIsBReln) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrERa) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrEL1) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrEL2) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrER) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcImageSingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (apProp) =>
% 99.02/13.33 ((
% 99.02/13.33 (app) =>
% 99.02/13.33 ((
% 99.02/13.33 (infuncsetfunc) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2p) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcinfuncset) =>
% 99.02/13.33 ((
% 99.02/13.33 (lamProp) =>
% 99.02/13.33 ((
% 99.02/13.33 (lamp) =>
% 99.02/13.33 ((
% 99.02/13.33 (lam2p) =>
% 99.02/13.33 ((
% 99.02/13.33 (brelnall1) =>
% 99.02/13.33 ((
% 99.02/13.33 (brelnall2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1E2) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp3) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcextLem) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp4) =>
% 99.02/13.33 ((
% 99.02/13.33 (subbreln) =>
% 99.02/13.33 ((
% 99.02/13.33 (eqbreln) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcext) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcext2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2apEq1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2apEq2) =>
% 99.02/13.33 ((
% 99.02/13.33 (beta1) =>
% 99.02/13.33 ((
% 99.02/13.33 (eta1) =>
% 99.02/13.33 ((
% 99.02/13.33 (lam2lamEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (beta2) =>
% 99.02/13.33 ((
% 99.02/13.33 (eta2) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalseProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalseProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ifSingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (ifp) =>
% 99.02/13.33 ((
% 99.02/13.33 (theeq) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrue) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalse) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueorfalse) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (setextT) =>
% 99.02/13.33 ((
% 99.02/13.33 (subsetTI) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetTI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetTE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectTELcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectTERcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT1) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT2) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT3) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub2) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTnotintersectT) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementImpComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementSubsetComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementInPowersetComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (contraSubsetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTcontraSubset) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (binunionTIRcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion2) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (intersectInPowersetIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (inComplementUnionImpNotIn1) =>
% 99.02/13.33 ((
% 99.02/13.33 (inComplementUnionImpInComplement1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTE) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTEcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementUnionInPowersetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a2) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (demorgan1b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (woz1_3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_4) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_5) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (breln1invI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compprop) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (breln1compEex) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#S') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 '#S') @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 '#S'))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 =>))))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#C') @ in)))) @
% 99.02/13.33 injFuncSet)))))))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#C') @ in)))) @
% 99.02/13.33 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl606])).
% 99.02/13.33 thf(zip_derived_cl630, plain,
% 99.02/13.33 (~ (((exuI2) =>
% 99.02/13.33 (((inCongP) =>
% 99.02/13.33 (((in__Cong) =>
% 99.02/13.33 (((exuE3u) =>
% 99.02/13.33 (((exu__Cong) =>
% 99.02/13.33 (((setadjoin__Cong) =>
% 99.02/13.33 (((powerset__Cong) =>
% 99.02/13.33 (((setunion__Cong) =>
% 99.02/13.33 (((exuEu) =>
% 99.02/13.33 (((descr__Cong) =>
% 99.02/13.33 (((dsetconstr__Cong) =>
% 99.02/13.33 (((subsetI1) =>
% 99.02/13.33 (((eqimpsubset2) =>
% 99.02/13.33 (((eqimpsubset1) =>
% 99.02/13.33 (((subsetI2) =>
% 99.02/13.33 (((emptysetsubset) =>
% 99.02/13.33 (((subsetE) =>
% 99.02/13.33 (((subsetE2) =>
% 99.02/13.33 (((notsubsetI) =>
% 99.02/13.33 (((notequalI1) =>
% 99.02/13.33 (((notequalI2) =>
% 99.02/13.33 (((subsetRefl) =>
% 99.02/13.33 (((subsetTrans) =>
% 99.02/13.33 (((setadjoinSub) =>
% 99.02/13.33 (((setadjoinSub2) =>
% 99.02/13.33 (((subset2powerset) =>
% 99.02/13.33 (((setextsub) =>
% 99.02/13.33 (((subsetemptysetimpeq) =>
% 99.02/13.33 (((powersetI1) =>
% 99.02/13.33 (((powersetE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (inPowerset) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetsubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (sepInPowerset) =>
% 99.02/13.33 ((
% 99.02/13.33 (sepSubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairset2IR) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionEcases) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionE) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionRsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectI) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset5) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset2) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset3) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectER) =>
% 99.02/13.33 ((
% 99.02/13.33 (disjointsetsI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectRsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset4) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset1) =>
% 99.02/13.33 ((
% 99.02/13.33 (bs114d) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusI) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusER) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusSubset2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusERneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusELneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusILneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusIRneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusSubset1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffE) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffI2) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffIneg1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffIneg2) =>
% 99.02/13.33 ((
% 99.02/13.33 (secondinupair) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairiskpair) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairp) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonsubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletoninpowerset) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletoninpowunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairset2E) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairsubunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairinpowunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem3) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairin) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempair1) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempair) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionE2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton1) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1E1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1I) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1I2) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonsuniq) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL1) =>
% 99.02/13.33 ((
% 99.02/13.33 (kfstsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (theprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (kfstpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodfstin) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR11) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR12) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR1) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairequniteq) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR) =>
% 99.02/13.33 ((
% 99.02/13.33 (ksndsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (ksndpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairsurjEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodsndin) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairmemEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairmemER) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempaircEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodfstpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodsndpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairsurjEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrI) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrSub) =>
% 99.02/13.33 ((
% 99.02/13.33 (setOfPairsIsBReln) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrERa) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrEL1) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrEL2) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrER) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcImageSingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (apProp) =>
% 99.02/13.33 ((
% 99.02/13.33 (app) =>
% 99.02/13.33 ((
% 99.02/13.33 (infuncsetfunc) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2p) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcinfuncset) =>
% 99.02/13.33 ((
% 99.02/13.33 (lamProp) =>
% 99.02/13.33 ((
% 99.02/13.33 (lamp) =>
% 99.02/13.33 ((
% 99.02/13.33 (lam2p) =>
% 99.02/13.33 ((
% 99.02/13.33 (brelnall1) =>
% 99.02/13.33 ((
% 99.02/13.33 (brelnall2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1E2) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp3) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcextLem) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp4) =>
% 99.02/13.33 ((
% 99.02/13.33 (subbreln) =>
% 99.02/13.33 ((
% 99.02/13.33 (eqbreln) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcext) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcext2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2apEq1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2apEq2) =>
% 99.02/13.33 ((
% 99.02/13.33 (beta1) =>
% 99.02/13.33 ((
% 99.02/13.33 (eta1) =>
% 99.02/13.33 ((
% 99.02/13.33 (lam2lamEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (beta2) =>
% 99.02/13.33 ((
% 99.02/13.33 (eta2) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalseProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalseProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ifSingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (ifp) =>
% 99.02/13.33 ((
% 99.02/13.33 (theeq) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrue) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalse) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueorfalse) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (setextT) =>
% 99.02/13.33 ((
% 99.02/13.33 (subsetTI) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetTI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetTE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectTELcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectTERcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT1) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT2) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT3) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub2) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTnotintersectT) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementImpComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementSubsetComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementInPowersetComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (contraSubsetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTcontraSubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTILcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTIRcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion2) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (intersectInPowersetIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (inComplementUnionImpNotIn1) =>
% 99.02/13.33 ((
% 99.02/13.33 (inComplementUnionImpInComplement1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTE) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTEcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementUnionInPowersetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule0) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule1) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule2) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (woz1_2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_4) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_5) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1all2) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1SetBreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (choice2fnsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (setOfPairsIsBReln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1all1) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (breln1invprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compEex) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionEcases) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionCommutes) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (image1E) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1I) =>
% 99.02/13.33 ((
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% 99.02/13.33 (
% 99.02/13.33 ('#C') @ in)))) @
% 99.02/13.33 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl619])).
% 99.02/13.33 thf(zip_derived_cl640, plain,
% 99.02/13.33 (~ (((inCongP) =>
% 99.02/13.33 (((in__Cong) =>
% 99.02/13.33 (((exuE3u) =>
% 99.02/13.33 (((exu__Cong) =>
% 99.02/13.33 (((setadjoin__Cong) =>
% 99.02/13.33 (((powerset__Cong) =>
% 99.02/13.33 (((setunion__Cong) =>
% 99.02/13.33 (((exuEu) =>
% 99.02/13.33 (((descr__Cong) =>
% 99.02/13.33 (((dsetconstr__Cong) =>
% 99.02/13.33 (((subsetI1) =>
% 99.02/13.33 (((eqimpsubset2) =>
% 99.02/13.33 (((eqimpsubset1) =>
% 99.02/13.33 (((subsetI2) =>
% 99.02/13.33 (((emptysetsubset) =>
% 99.02/13.33 (((subsetE) =>
% 99.02/13.33 (((subsetE2) =>
% 99.02/13.33 (((notsubsetI) =>
% 99.02/13.33 (((notequalI1) =>
% 99.02/13.33 (((notequalI2) =>
% 99.02/13.33 (((subsetRefl) =>
% 99.02/13.33 (((subsetTrans) =>
% 99.02/13.33 (((setadjoinSub) =>
% 99.02/13.33 (((setadjoinSub2) =>
% 99.02/13.33 (((subset2powerset) =>
% 99.02/13.33 (((setextsub) =>
% 99.02/13.33 (((subsetemptysetimpeq) =>
% 99.02/13.33 (((powersetI1) =>
% 99.02/13.33 (((powersetE1) =>
% 99.02/13.33 (((inPowerset) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetsubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (sepInPowerset) =>
% 99.02/13.33 ((
% 99.02/13.33 (sepSubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairset2IR) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionEcases) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionE) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionRsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectI) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset5) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset2) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset3) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectER) =>
% 99.02/13.33 ((
% 99.02/13.33 (disjointsetsI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectRsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset4) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset1) =>
% 99.02/13.33 ((
% 99.02/13.33 (bs114d) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusI) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusER) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusSubset2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusERneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusELneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusILneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusIRneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusSubset1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffE) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffI2) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffIneg1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffIneg2) =>
% 99.02/13.33 ((
% 99.02/13.33 (secondinupair) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairiskpair) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairp) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonsubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletoninpowerset) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletoninpowunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairset2E) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairsubunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairinpowunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem3) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairin) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempair1) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempair) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionE2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton1) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1E1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1I) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1I2) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonsuniq) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL1) =>
% 99.02/13.33 ((
% 99.02/13.33 (kfstsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (theprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (kfstpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodfstin) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR11) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR12) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR1) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairequniteq) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR) =>
% 99.02/13.33 ((
% 99.02/13.33 (ksndsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (ksndpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairsurjEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodsndin) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairmemEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairmemER) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempaircEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodfstpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodsndpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairsurjEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrI) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrSub) =>
% 99.02/13.33 ((
% 99.02/13.33 (setOfPairsIsBReln) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrERa) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrEL1) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrEL2) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrER) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcImageSingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (apProp) =>
% 99.02/13.33 ((
% 99.02/13.33 (app) =>
% 99.02/13.33 ((
% 99.02/13.33 (infuncsetfunc) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2p) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcinfuncset) =>
% 99.02/13.33 ((
% 99.02/13.33 (lamProp) =>
% 99.02/13.33 ((
% 99.02/13.33 (lamp) =>
% 99.02/13.33 ((
% 99.02/13.33 (lam2p) =>
% 99.02/13.33 ((
% 99.02/13.33 (brelnall1) =>
% 99.02/13.33 ((
% 99.02/13.33 (brelnall2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1E2) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp3) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcextLem) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp4) =>
% 99.02/13.33 ((
% 99.02/13.33 (subbreln) =>
% 99.02/13.33 ((
% 99.02/13.33 (eqbreln) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcext) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcext2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2apEq1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2apEq2) =>
% 99.02/13.33 ((
% 99.02/13.33 (beta1) =>
% 99.02/13.33 ((
% 99.02/13.33 (eta1) =>
% 99.02/13.33 ((
% 99.02/13.33 (lam2lamEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (beta2) =>
% 99.02/13.33 ((
% 99.02/13.33 (eta2) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalseProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalseProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ifSingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (ifp) =>
% 99.02/13.33 ((
% 99.02/13.33 (theeq) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrue) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalse) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueorfalse) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (setextT) =>
% 99.02/13.33 ((
% 99.02/13.33 (subsetTI) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetTI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetTE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectTELcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectTERcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT1) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT2) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT3) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub2) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTnotintersectT) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementImpComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementSubsetComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementInPowersetComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (contraSubsetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTcontraSubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTILcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTIRcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion2) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (intersectInPowersetIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (inComplementUnionImpNotIn1) =>
% 99.02/13.33 ((
% 99.02/13.33 (inComplementUnionImpInComplement1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTE) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTEcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementUnionInPowersetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule0) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule1) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule4) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_1) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_4) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_5) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1all2) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1SetBreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (choice2fnsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (setOfPairsIsBReln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1all1) =>
% 99.02/13.33 ((
% 99.02/13.33 (subbreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (eqbreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compEex) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionEcases) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionCommutes) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2Ex) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2W) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2A) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2B) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Ex) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Ex1) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Equiv) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1E) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1I) =>
% 99.02/13.33 ((
% 99.02/13.33 (injFuncInInjFuncSet) =>
% 99.02/13.33 ((
% 99.02/13.33 (!!) @ (
% 99.02/13.33 (('#B') @ (
% 99.02/13.33 !!) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 !!))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#S') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 '#S') @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 '#S'))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 =>))))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#C') @ in)))) @
% 99.02/13.33 injFuncSet)))))))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#C') @ in)))) @
% 99.02/13.33 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl630])).
% 99.02/13.33 thf(zip_derived_cl650, plain,
% 99.02/13.33 (~ (((in__Cong) =>
% 99.02/13.33 (((exuE3u) =>
% 99.02/13.33 (((exu__Cong) =>
% 99.02/13.33 (((setadjoin__Cong) =>
% 99.02/13.33 (((powerset__Cong) =>
% 99.02/13.33 (((setunion__Cong) =>
% 99.02/13.33 (((exuEu) =>
% 99.02/13.33 (((descr__Cong) =>
% 99.02/13.33 (((dsetconstr__Cong) =>
% 99.02/13.33 (((subsetI1) =>
% 99.02/13.33 (((eqimpsubset2) =>
% 99.02/13.33 (((eqimpsubset1) =>
% 99.02/13.33 (((subsetI2) =>
% 99.02/13.33 (((emptysetsubset) =>
% 99.02/13.33 (((subsetE) =>
% 99.02/13.33 (((subsetE2) =>
% 99.02/13.33 (((notsubsetI) =>
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% 99.02/13.33 (((notequalI2) =>
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% 99.02/13.33 ((
% 99.02/13.33 (kpairsurjEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodsndin) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairmemEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairmemER) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempaircEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodfstpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodsndpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairsurjEq) =>
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% 99.02/13.33 ((
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% 99.02/13.33 (setOfPairsIsBReln) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrEL2) =>
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% 99.02/13.33 (dpsetconstrER) =>
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (app) =>
% 99.02/13.33 ((
% 99.02/13.33 (infuncsetfunc) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2p) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcinfuncset) =>
% 99.02/13.33 ((
% 99.02/13.33 (lamProp) =>
% 99.02/13.33 ((
% 99.02/13.33 (lamp) =>
% 99.02/13.33 ((
% 99.02/13.33 (lam2p) =>
% 99.02/13.33 ((
% 99.02/13.33 (brelnall1) =>
% 99.02/13.33 ((
% 99.02/13.33 (brelnall2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1E2) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp3) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcextLem) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp4) =>
% 99.02/13.33 ((
% 99.02/13.33 (subbreln) =>
% 99.02/13.33 ((
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% 99.02/13.33 (funcext2) =>
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% 99.02/13.33 ((
% 99.02/13.33 (ap2apEq2) =>
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% 99.02/13.33 (beta1) =>
% 99.02/13.33 ((
% 99.02/13.33 (eta1) =>
% 99.02/13.33 ((
% 99.02/13.33 (lam2lamEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (beta2) =>
% 99.02/13.33 ((
% 99.02/13.33 (eta2) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (iffalseProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueProp2) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (binintersectTERcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT1) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT2) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT3) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub2) =>
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% 99.02/13.33 (doubleComplementEq) =>
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% 99.02/13.33 (complementTnotintersectT) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementImpComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementSubsetComplementIntersect) =>
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% 99.02/13.33 (complementInPowersetComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (contraSubsetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTcontraSubset) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (binunionTIRcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion2) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (intersectInPowersetIntersectUnions) =>
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a2) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (demorgan1b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule0) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule1) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule4) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (woz1_2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_4) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_5) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (breln1SetBreln1) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (breln1invI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compEex) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (breln1unionEcases) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (woz2B) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (image1Ex1) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Equiv) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1E) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1I) =>
% 99.02/13.33 ((
% 99.02/13.33 (injFuncInInjFuncSet) =>
% 99.02/13.33 ((
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% 99.02/13.33 (
% 99.02/13.33 (
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% 99.02/13.33 injFuncSet)))))))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
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% 99.02/13.33 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl640])).
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% 99.02/13.33 (((powerset__Cong) =>
% 99.02/13.33 (((setunion__Cong) =>
% 99.02/13.33 (((exuEu) =>
% 99.02/13.33 (((descr__Cong) =>
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% 99.02/13.33 (((subsetI1) =>
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (binunionRsub) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset5) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (binintersectLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset2) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset3) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectER) =>
% 99.02/13.33 ((
% 99.02/13.33 (disjointsetsI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectRsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset4) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset1) =>
% 99.02/13.33 ((
% 99.02/13.33 (bs114d) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusI) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusER) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusSubset2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusERneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusELneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusILneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusIRneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusSubset1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffE) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffI2) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffIneg1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffIneg2) =>
% 99.02/13.33 ((
% 99.02/13.33 (secondinupair) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairiskpair) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairp) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonsubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletoninpowerset) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletoninpowunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairset2E) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairsubunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairinpowunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem3) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairin) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempair1) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempair) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionE2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton1) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1E1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1I) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1I2) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonsuniq) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL1) =>
% 99.02/13.33 ((
% 99.02/13.33 (kfstsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (theprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (kfstpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodfstin) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR11) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR12) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR1) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairequniteq) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR) =>
% 99.02/13.33 ((
% 99.02/13.33 (ksndsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (ksndpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairsurjEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodsndin) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairmemEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairmemER) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempaircEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodfstpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodsndpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairsurjEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrI) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrSub) =>
% 99.02/13.33 ((
% 99.02/13.33 (setOfPairsIsBReln) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrERa) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrEL1) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrEL2) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrER) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcImageSingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (apProp) =>
% 99.02/13.33 ((
% 99.02/13.33 (app) =>
% 99.02/13.33 ((
% 99.02/13.33 (infuncsetfunc) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2p) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcinfuncset) =>
% 99.02/13.33 ((
% 99.02/13.33 (lamProp) =>
% 99.02/13.33 ((
% 99.02/13.33 (lamp) =>
% 99.02/13.33 ((
% 99.02/13.33 (lam2p) =>
% 99.02/13.33 ((
% 99.02/13.33 (brelnall1) =>
% 99.02/13.33 ((
% 99.02/13.33 (brelnall2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1E2) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp3) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcextLem) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp4) =>
% 99.02/13.33 ((
% 99.02/13.33 (subbreln) =>
% 99.02/13.33 ((
% 99.02/13.33 (eqbreln) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcext) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcext2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2apEq1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2apEq2) =>
% 99.02/13.33 ((
% 99.02/13.33 (beta1) =>
% 99.02/13.33 ((
% 99.02/13.33 (eta1) =>
% 99.02/13.33 ((
% 99.02/13.33 (lam2lamEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (beta2) =>
% 99.02/13.33 ((
% 99.02/13.33 (eta2) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalseProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalseProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ifSingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (ifp) =>
% 99.02/13.33 ((
% 99.02/13.33 (theeq) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrue) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalse) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueorfalse) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (setextT) =>
% 99.02/13.33 ((
% 99.02/13.33 (subsetTI) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetTI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetTE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectTELcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectTERcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT1) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT2) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT3) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub2) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTnotintersectT) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementImpComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementSubsetComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementInPowersetComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (contraSubsetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTcontraSubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTILcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTIRcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion2) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (intersectInPowersetIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (inComplementUnionImpNotIn1) =>
% 99.02/13.33 ((
% 99.02/13.33 (inComplementUnionImpInComplement1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTE) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTEcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementUnionInPowersetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule0) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule1) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule4) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_1) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_4) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_5) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1all2) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1SetBreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (choice2fnsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (setOfPairsIsBReln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1all1) =>
% 99.02/13.33 ((
% 99.02/13.33 (subbreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (eqbreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compEex) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionEcases) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionCommutes) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2Ex) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2W) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2A) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2B) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Ex) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Ex1) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Equiv) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1E) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1I) =>
% 99.02/13.33 ((
% 99.02/13.33 (injFuncInInjFuncSet) =>
% 99.02/13.33 ((
% 99.02/13.33 (!!) @ (
% 99.02/13.33 (('#B') @ (
% 99.02/13.33 !!) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 !!))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#S') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 '#S') @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 '#S'))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 =>))))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#C') @ in)))) @
% 99.02/13.33 injFuncSet)))))))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#C') @ in)))) @
% 99.02/13.33 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl650])).
% 99.02/13.33 thf(zip_derived_cl672, plain,
% 99.02/13.33 (~ (((exu__Cong) =>
% 99.02/13.33 (((setadjoin__Cong) =>
% 99.02/13.33 (((powerset__Cong) =>
% 99.02/13.33 (((setunion__Cong) =>
% 99.02/13.33 (((exuEu) =>
% 99.02/13.33 (((descr__Cong) =>
% 99.02/13.33 (((dsetconstr__Cong) =>
% 99.02/13.33 (((subsetI1) =>
% 99.02/13.33 (((eqimpsubset2) =>
% 99.02/13.33 (((eqimpsubset1) =>
% 99.02/13.33 (((subsetI2) =>
% 99.02/13.33 (((emptysetsubset) =>
% 99.02/13.33 (((subsetE) =>
% 99.02/13.33 (((subsetE2) =>
% 99.02/13.33 (((notsubsetI) =>
% 99.02/13.33 (((notequalI1) =>
% 99.02/13.33 (((notequalI2) =>
% 99.02/13.33 (((subsetRefl) =>
% 99.02/13.33 (((subsetTrans) =>
% 99.02/13.33 (((setadjoinSub) =>
% 99.02/13.33 (((setadjoinSub2) =>
% 99.02/13.33 (((subset2powerset) =>
% 99.02/13.33 (((setextsub) =>
% 99.02/13.33 (((subsetemptysetimpeq) =>
% 99.02/13.33 (((powersetI1) =>
% 99.02/13.33 (((powersetE1) =>
% 99.02/13.33 (((inPowerset) =>
% 99.02/13.33 (((powersetsubset) =>
% 99.02/13.33 (((sepInPowerset) =>
% 99.02/13.33 (((sepSubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairset2IR) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionEcases) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionE) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionRsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectI) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset5) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset2) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset3) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectER) =>
% 99.02/13.33 ((
% 99.02/13.33 (disjointsetsI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectRsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset4) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset1) =>
% 99.02/13.33 ((
% 99.02/13.33 (bs114d) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusI) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusER) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusSubset2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusERneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusELneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusILneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusIRneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusSubset1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffE) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffI2) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffIneg1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffIneg2) =>
% 99.02/13.33 ((
% 99.02/13.33 (secondinupair) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairiskpair) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairp) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonsubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletoninpowerset) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletoninpowunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairset2E) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairsubunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairinpowunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem3) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairin) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempair1) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempair) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionE2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton1) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1E1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1I) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1I2) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonsuniq) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL1) =>
% 99.02/13.33 ((
% 99.02/13.33 (kfstsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (theprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (kfstpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodfstin) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR11) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR12) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR1) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairequniteq) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR) =>
% 99.02/13.33 ((
% 99.02/13.33 (ksndsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (ksndpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairsurjEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodsndin) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairmemEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairmemER) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempaircEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodfstpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodsndpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairsurjEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrI) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrSub) =>
% 99.02/13.33 ((
% 99.02/13.33 (setOfPairsIsBReln) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrERa) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrEL1) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrEL2) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrER) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcImageSingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (apProp) =>
% 99.02/13.33 ((
% 99.02/13.33 (app) =>
% 99.02/13.33 ((
% 99.02/13.33 (infuncsetfunc) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2p) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcinfuncset) =>
% 99.02/13.33 ((
% 99.02/13.33 (lamProp) =>
% 99.02/13.33 ((
% 99.02/13.33 (lamp) =>
% 99.02/13.33 ((
% 99.02/13.33 (lam2p) =>
% 99.02/13.33 ((
% 99.02/13.33 (brelnall1) =>
% 99.02/13.33 ((
% 99.02/13.33 (brelnall2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1E2) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp3) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcextLem) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp4) =>
% 99.02/13.33 ((
% 99.02/13.33 (subbreln) =>
% 99.02/13.33 ((
% 99.02/13.33 (eqbreln) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcext) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcext2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2apEq1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2apEq2) =>
% 99.02/13.33 ((
% 99.02/13.33 (beta1) =>
% 99.02/13.33 ((
% 99.02/13.33 (eta1) =>
% 99.02/13.33 ((
% 99.02/13.33 (lam2lamEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (beta2) =>
% 99.02/13.33 ((
% 99.02/13.33 (eta2) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalseProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalseProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ifSingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (ifp) =>
% 99.02/13.33 ((
% 99.02/13.33 (theeq) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrue) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalse) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueorfalse) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (setextT) =>
% 99.02/13.33 ((
% 99.02/13.33 (subsetTI) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetTI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetTE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectTELcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectTERcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT1) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT2) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT3) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub2) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTnotintersectT) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementImpComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementSubsetComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementInPowersetComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (contraSubsetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTcontraSubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTILcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTIRcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion2) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (intersectInPowersetIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (inComplementUnionImpNotIn1) =>
% 99.02/13.33 ((
% 99.02/13.33 (inComplementUnionImpInComplement1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTE) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTEcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementUnionInPowersetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule0) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule1) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule4) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_1) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_4) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_5) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1all2) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1SetBreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (choice2fnsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (setOfPairsIsBReln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1all1) =>
% 99.02/13.33 ((
% 99.02/13.33 (subbreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (eqbreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compEex) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionEcases) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionCommutes) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2Ex) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2W) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2A) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2B) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Ex) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Ex1) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Equiv) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1E) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1I) =>
% 99.02/13.33 ((
% 99.02/13.33 (injFuncInInjFuncSet) =>
% 99.02/13.33 ((
% 99.02/13.33 (!!) @ (
% 99.02/13.33 (('#B') @ (
% 99.02/13.33 !!) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 !!))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#S') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 '#S') @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 '#S'))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 =>))))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#C') @ in)))) @
% 99.02/13.33 injFuncSet)))))))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#C') @ in)))) @
% 99.02/13.33 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl660])).
% 99.02/13.33 thf(zip_derived_cl685, plain,
% 99.02/13.33 (~ (((setadjoin__Cong) =>
% 99.02/13.33 (((powerset__Cong) =>
% 99.02/13.33 (((setunion__Cong) =>
% 99.02/13.33 (((exuEu) =>
% 99.02/13.33 (((descr__Cong) =>
% 99.02/13.33 (((dsetconstr__Cong) =>
% 99.02/13.33 (((subsetI1) =>
% 99.02/13.33 (((eqimpsubset2) =>
% 99.02/13.33 (((eqimpsubset1) =>
% 99.02/13.33 (((subsetI2) =>
% 99.02/13.33 (((emptysetsubset) =>
% 99.02/13.33 (((subsetE) =>
% 99.02/13.33 (((subsetE2) =>
% 99.02/13.33 (((notsubsetI) =>
% 99.02/13.33 (((notequalI1) =>
% 99.02/13.33 (((notequalI2) =>
% 99.02/13.33 (((subsetRefl) =>
% 99.02/13.33 (((subsetTrans) =>
% 99.02/13.33 (((setadjoinSub) =>
% 99.02/13.33 (((setadjoinSub2) =>
% 99.02/13.33 (((subset2powerset) =>
% 99.02/13.33 (((setextsub) =>
% 99.02/13.33 (((subsetemptysetimpeq) =>
% 99.02/13.33 (((powersetI1) =>
% 99.02/13.33 (((powersetE1) =>
% 99.02/13.33 (((inPowerset) =>
% 99.02/13.33 (((powersetsubset) =>
% 99.02/13.33 (((sepInPowerset) =>
% 99.02/13.33 (((sepSubset) =>
% 99.02/13.33 (((binunionIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairset2IR) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionEcases) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionE) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionRsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectI) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset5) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset2) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset3) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectER) =>
% 99.02/13.33 ((
% 99.02/13.33 (disjointsetsI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectRsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset4) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset1) =>
% 99.02/13.33 ((
% 99.02/13.33 (bs114d) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusI) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusER) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusSubset2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusERneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusELneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusILneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusIRneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusSubset1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffE) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffI2) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffIneg1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffIneg2) =>
% 99.02/13.33 ((
% 99.02/13.33 (secondinupair) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairiskpair) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairp) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonsubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletoninpowerset) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletoninpowunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairset2E) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairsubunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairinpowunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem3) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairin) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempair1) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempair) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionE2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton1) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1E1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1I) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1I2) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonsuniq) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL1) =>
% 99.02/13.33 ((
% 99.02/13.33 (kfstsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (theprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (kfstpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodfstin) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL2) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR12) =>
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% 99.02/13.33 (setukpairinjR2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR) =>
% 99.02/13.33 ((
% 99.02/13.33 (ksndsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (ksndpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairsurjEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodsndin) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairmemEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairmemER) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempaircEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodfstpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodsndpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairsurjEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrI) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrSub) =>
% 99.02/13.33 ((
% 99.02/13.33 (setOfPairsIsBReln) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrERa) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrEL1) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrEL2) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrER) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcImageSingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (apProp) =>
% 99.02/13.33 ((
% 99.02/13.33 (app) =>
% 99.02/13.33 ((
% 99.02/13.33 (infuncsetfunc) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2p) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcinfuncset) =>
% 99.02/13.33 ((
% 99.02/13.33 (lamProp) =>
% 99.02/13.33 ((
% 99.02/13.33 (lamp) =>
% 99.02/13.33 ((
% 99.02/13.33 (lam2p) =>
% 99.02/13.33 ((
% 99.02/13.33 (brelnall1) =>
% 99.02/13.33 ((
% 99.02/13.33 (brelnall2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1E2) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp3) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcextLem) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp4) =>
% 99.02/13.33 ((
% 99.02/13.33 (subbreln) =>
% 99.02/13.33 ((
% 99.02/13.33 (eqbreln) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcext) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcext2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2apEq1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ap2apEq2) =>
% 99.02/13.33 ((
% 99.02/13.33 (beta1) =>
% 99.02/13.33 ((
% 99.02/13.33 (eta1) =>
% 99.02/13.33 ((
% 99.02/13.33 (lam2lamEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (beta2) =>
% 99.02/13.33 ((
% 99.02/13.33 (eta2) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalseProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalseProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueProp2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ifSingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (ifp) =>
% 99.02/13.33 ((
% 99.02/13.33 (theeq) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrue) =>
% 99.02/13.33 ((
% 99.02/13.33 (iffalse) =>
% 99.02/13.33 ((
% 99.02/13.33 (iftrueorfalse) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (setextT) =>
% 99.02/13.33 ((
% 99.02/13.33 (subsetTI) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetTI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetTE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectTELcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectTERcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT1) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT2) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT3) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub2) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTnotintersectT) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementImpComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementSubsetComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementInPowersetComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (contraSubsetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTcontraSubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTILcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTIRcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion2) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (intersectInPowersetIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (inComplementUnionImpNotIn1) =>
% 99.02/13.33 ((
% 99.02/13.33 (inComplementUnionImpInComplement1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTE) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTEcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementUnionInPowersetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule0) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule1) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule4) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_1) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_4) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_5) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1all2) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1SetBreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (choice2fnsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (setOfPairsIsBReln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1all1) =>
% 99.02/13.33 ((
% 99.02/13.33 (subbreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (eqbreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compEex) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionEcases) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionCommutes) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2Ex) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2W) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2A) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2B) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Ex) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Ex1) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Equiv) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1E) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1I) =>
% 99.02/13.33 ((
% 99.02/13.33 (injFuncInInjFuncSet) =>
% 99.02/13.33 ((
% 99.02/13.33 (!!) @ (
% 99.02/13.33 (('#B') @ (
% 99.02/13.33 !!) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 !!))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#S') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 '#S') @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 '#S'))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 =>))))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#C') @ in)))) @
% 99.02/13.33 injFuncSet)))))))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#C') @ in)))) @
% 99.02/13.33 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl672])).
% 99.02/13.33 thf(zip_derived_cl699, plain,
% 99.02/13.33 (~ (((powerset__Cong) =>
% 99.02/13.33 (((setunion__Cong) =>
% 99.02/13.33 (((exuEu) =>
% 99.02/13.33 (((descr__Cong) =>
% 99.02/13.33 (((dsetconstr__Cong) =>
% 99.02/13.33 (((subsetI1) =>
% 99.02/13.33 (((eqimpsubset2) =>
% 99.02/13.33 (((eqimpsubset1) =>
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% 99.02/13.33 (((subsetE) =>
% 99.02/13.33 (((subsetE2) =>
% 99.02/13.33 (((notsubsetI) =>
% 99.02/13.33 (((notequalI1) =>
% 99.02/13.33 (((notequalI2) =>
% 99.02/13.33 (((subsetRefl) =>
% 99.02/13.33 (((subsetTrans) =>
% 99.02/13.33 (((setadjoinSub) =>
% 99.02/13.33 (((setadjoinSub2) =>
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% 99.02/13.33 (((setextsub) =>
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% 99.02/13.33 (((powersetI1) =>
% 99.02/13.33 (((powersetE1) =>
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% 99.02/13.33 (((upairset2IR) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (binunionEcases) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionE) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionRsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectI) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset5) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset2) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset3) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectER) =>
% 99.02/13.33 ((
% 99.02/13.33 (disjointsetsI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectRsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset4) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset1) =>
% 99.02/13.33 ((
% 99.02/13.33 (bs114d) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusI) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusEL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusER) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusSubset2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusERneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusELneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusILneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusIRneg) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusLsub) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusSubset1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffE) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffI2) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffIneg1) =>
% 99.02/13.33 ((
% 99.02/13.33 (symdiffIneg2) =>
% 99.02/13.33 ((
% 99.02/13.33 (secondinupair) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairiskpair) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairp) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonsubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletoninpowerset) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletoninpowunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairset2E) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairsubunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairinpowunion) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem3) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairin) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempair1) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempair) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionE2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton1) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setunionsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1E1) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1I) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1I2) =>
% 99.02/13.33 ((
% 99.02/13.33 (singletonsuniq) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL1) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (kfstpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodfstin) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjL) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR11) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR12) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR1) =>
% 99.02/13.33 ((
% 99.02/13.33 (upairequniteq) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR2) =>
% 99.02/13.33 ((
% 99.02/13.33 (setukpairinjR) =>
% 99.02/13.33 ((
% 99.02/13.33 (ksndsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (ksndpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (kpairsurjEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodsndin) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairmemEL) =>
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% 99.02/13.33 (cartprodpairmemER) =>
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% 99.02/13.33 ((
% 99.02/13.33 (cartprodfstpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodsndpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairsurjEq) =>
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% 99.02/13.33 ((
% 99.02/13.33 (ap2p) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcinfuncset) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (lam2p) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (brelnall2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ex1E2) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp1) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp3) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp2) =>
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% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp4) =>
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% 99.02/13.33 (subbreln) =>
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% 99.02/13.33 (ap2apEq2) =>
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% 99.02/13.33 ((
% 99.02/13.33 (eta1) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 (complementTE1) =>
% 99.02/13.33 ((
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% 99.02/13.33 (binintersectTERcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT) =>
% 99.02/13.33 ((
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% 99.02/13.33 (contrasubsetT2) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT3) =>
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% 99.02/13.33 ((
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% 99.02/13.33 (complementInPowersetComplementIntersect) =>
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% 99.02/13.33 (contraSubsetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTcontraSubset) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (binunionTIRcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion2) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (intersectInPowersetIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (inComplementUnionImpNotIn1) =>
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% 99.02/13.33 (inComplementUnionImpInComplement1) =>
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% 99.02/13.33 (demorgan2a1) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a2) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (demorgan1b) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule0) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule1) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule4) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (woz1_2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_4) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_5) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (breln1SetBreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (choice2fnsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (setOfPairsIsBReln1) =>
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (eqbreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compEex) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionEcases) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionCommutes) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (woz2W) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (woz2B) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (image1Ex1) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Equiv) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1E) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1I) =>
% 99.02/13.33 ((
% 99.02/13.33 (injFuncInInjFuncSet) =>
% 99.02/13.33 ((
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% 99.02/13.33 (
% 99.02/13.33 (
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% 99.02/13.33 (
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% 99.02/13.33 ('#B') @ (
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% 99.02/13.33 (
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% 99.02/13.33 injFuncSet)))))))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
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% 99.02/13.33 (
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% 99.02/13.33 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl685])).
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (binintersectSubset3) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectER) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (binintersectRsub) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (symdiffIneg2) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem2) =>
% 99.02/13.33 ((
% 99.02/13.33 (ubforcartprodlem3) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairin) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (cartprodmempair) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (kpairsurjEq) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairmemER) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 (cartprodsndpairEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairsurjEq) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrSub) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrEL2) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrER) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcImageSingleton) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (ap2p) =>
% 99.02/13.33 ((
% 99.02/13.33 (funcinfuncset) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (funcGraphProp1) =>
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule0) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (woz13rule2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule4) =>
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% 99.02/13.33 (woz1_3) =>
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (breln1invI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compEex) =>
% 99.02/13.33 ((
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% 99.02/13.33 (breln1unionIL) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (breln1unionEcases) =>
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (woz2B) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (image1Ex1) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Equiv) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1E) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1I) =>
% 99.02/13.33 ((
% 99.02/13.33 (injFuncInInjFuncSet) =>
% 99.02/13.33 ((
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% 99.02/13.33 (
% 99.02/13.33 (
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% 99.02/13.33 (
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% 99.02/13.33 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl699])).
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (cartprodpairsurjEq) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrEL2) =>
% 99.02/13.33 ((
% 99.02/13.33 (dpsetconstrER) =>
% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
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% 99.02/13.33 ((
% 99.02/13.33 (binintersectT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (setminusT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementT_lem) =>
% 99.02/13.33 ((
% 99.02/13.33 (setextT) =>
% 99.02/13.33 ((
% 99.02/13.33 (subsetTI) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetTI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (powersetTE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectTELcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (binintersectTERcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT1) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT2) =>
% 99.02/13.33 ((
% 99.02/13.33 (contrasubsetT3) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementI1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementE1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub1) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementSub2) =>
% 99.02/13.33 ((
% 99.02/13.33 (doubleComplementEq) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTnotintersectT) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementImpComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementSubsetComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementInPowersetComplementIntersect) =>
% 99.02/13.33 ((
% 99.02/13.33 (contraSubsetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementTcontraSubset) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTILcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTIRcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInUnion2) =>
% 99.02/13.33 ((
% 99.02/13.33 (inIntersectImpInIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (intersectInPowersetIntersectUnions) =>
% 99.02/13.33 ((
% 99.02/13.33 (inComplementUnionImpNotIn1) =>
% 99.02/13.33 ((
% 99.02/13.33 (inComplementUnionImpInComplement1) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTE) =>
% 99.02/13.33 ((
% 99.02/13.33 (binunionTEcontra) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a1) =>
% 99.02/13.33 ((
% 99.02/13.33 (complementUnionInPowersetComplement) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan1) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2a) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b2) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2b) =>
% 99.02/13.33 ((
% 99.02/13.33 (demorgan2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule0) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule1) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz13rule4) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_1) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_2) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_3) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_4) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz1_5) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1all2) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1SetBreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (choice2fnsingleton) =>
% 99.02/13.33 ((
% 99.02/13.33 (setOfPairsIsBReln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1all1) =>
% 99.02/13.33 ((
% 99.02/13.33 (subbreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (eqbreln1) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1invE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1compEex) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionprop) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionIL) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionIR) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionI) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionE) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionEcases) =>
% 99.02/13.33 ((
% 99.02/13.33 (breln1unionCommutes) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2Ex) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2W) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2A) =>
% 99.02/13.33 ((
% 99.02/13.33 (woz2B) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Ex) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Ex1) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1Equiv) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1E) =>
% 99.02/13.33 ((
% 99.02/13.33 (image1I) =>
% 99.02/13.33 ((
% 99.02/13.33 (injFuncInInjFuncSet) =>
% 99.02/13.33 ((
% 99.02/13.33 (!!) @ (
% 99.02/13.33 (('#B') @ (
% 99.02/13.33 !!) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 !!))) @
% 99.02/13.33 (
% 99.02/13.33 (
% 99.02/13.33 ('#S') @ (
% 99.02/13.33 (
% 99.02/13.33 ('#B') @ (
% 99.02/13.33 '#S') @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 '#S'))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 =>))))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#C') @ in)))) @
% 99.02/13.34 injFuncSet)))))))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#C') @ in)))) @
% 99.02/13.34 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl714])).
% 99.02/13.34 thf(zip_derived_cl749, plain,
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% 99.02/13.34 (((dsetconstr__Cong) =>
% 99.02/13.34 (((subsetI1) =>
% 99.02/13.34 (((eqimpsubset2) =>
% 99.02/13.34 (((eqimpsubset1) =>
% 99.02/13.34 (((subsetI2) =>
% 99.02/13.34 (((emptysetsubset) =>
% 99.02/13.34 (((subsetE) =>
% 99.02/13.34 (((subsetE2) =>
% 99.02/13.34 (((notsubsetI) =>
% 99.02/13.34 (((notequalI1) =>
% 99.02/13.34 (((notequalI2) =>
% 99.02/13.34 (((subsetRefl) =>
% 99.02/13.34 (((subsetTrans) =>
% 99.02/13.34 (((setadjoinSub) =>
% 99.02/13.34 (((setadjoinSub2) =>
% 99.02/13.34 (((subset2powerset) =>
% 99.02/13.34 (((setextsub) =>
% 99.02/13.34 (((subsetemptysetimpeq) =>
% 99.02/13.34 (((powersetI1) =>
% 99.02/13.34 (((powersetE1) =>
% 99.02/13.34 (((inPowerset) =>
% 99.02/13.34 (((powersetsubset) =>
% 99.02/13.34 (((sepInPowerset) =>
% 99.02/13.34 (((sepSubset) =>
% 99.02/13.34 (((binunionIL) =>
% 99.02/13.34 (((upairset2IR) =>
% 99.02/13.34 (((binunionIR) =>
% 99.02/13.34 (((binunionEcases) =>
% 99.02/13.34 (((binunionE) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionLsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionRsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectI) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset5) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectLsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset2) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset3) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectER) =>
% 99.02/13.34 ((
% 99.02/13.34 (disjointsetsI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectRsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset4) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (bs114d) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusI) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusER) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusERneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusELneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusILneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusIRneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusLsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffE) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI2) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg2) =>
% 99.02/13.34 ((
% 99.02/13.34 (secondinupair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIR) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairiskpair) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairp) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowerset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairset2E) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairsubunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairinpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem3) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair1) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionE2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton1) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I2) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsuniq) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (theprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstin) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR11) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR12) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR1) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairequniteq) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR) =>
% 99.02/13.34 ((
% 99.02/13.34 (ksndsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (ksndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemER) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempaircEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrI) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrSub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setOfPairsIsBReln) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrERa) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrER) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcImageSingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (apProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (app) =>
% 99.02/13.34 ((
% 99.02/13.34 (infuncsetfunc) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcinfuncset) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall1) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp3) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcextLem) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp4) =>
% 99.02/13.34 ((
% 99.02/13.34 (subbreln) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (funcext) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcext2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq2) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (eta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2lamEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta2) =>
% 99.02/13.34 ((
% 99.02/13.34 (eta2) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalseProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalseProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ifSingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (ifp) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (binunionT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (setextT) =>
% 99.02/13.34 ((
% 99.02/13.34 (subsetTI) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetTI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetTE1) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (complementTE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectTELcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectTERcontra) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT2) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT3) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub2) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTnotintersectT) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementImpComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementSubsetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementInPowersetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (contraSubsetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTcontraSubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTILcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTIRcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion2) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInIntersectUnions) =>
% 99.02/13.34 ((
% 99.02/13.34 (intersectInPowersetIntersectUnions) =>
% 99.02/13.34 ((
% 99.02/13.34 (inComplementUnionImpNotIn1) =>
% 99.02/13.34 ((
% 99.02/13.34 (inComplementUnionImpInComplement1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTE) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTEcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementUnionInPowersetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule0) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule1) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule3) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule4) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_1) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_3) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_4) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_5) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1all2) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1SetBreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (choice2fnsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (setOfPairsIsBReln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1all1) =>
% 99.02/13.34 ((
% 99.02/13.34 (subbreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (eqbreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compEex) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionIL) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionIR) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionEcases) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionCommutes) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2Ex) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2W) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2A) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2B) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex1) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Equiv) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1E) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (injFuncInInjFuncSet) =>
% 99.02/13.34 ((
% 99.02/13.34 (!!) @ (
% 99.02/13.34 (('#B') @ (
% 99.02/13.34 !!) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 !!))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#S') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 '#S') @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 '#S'))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 =>))))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#C') @ in)))) @
% 99.02/13.34 injFuncSet)))))))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#C') @ in)))) @
% 99.02/13.34 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl731])).
% 99.02/13.34 thf(zip_derived_cl769, plain,
% 99.02/13.34 (~ (((dsetconstr__Cong) =>
% 99.02/13.34 (((subsetI1) =>
% 99.02/13.34 (((eqimpsubset2) =>
% 99.02/13.34 (((eqimpsubset1) =>
% 99.02/13.34 (((subsetI2) =>
% 99.02/13.34 (((emptysetsubset) =>
% 99.02/13.34 (((subsetE) =>
% 99.02/13.34 (((subsetE2) =>
% 99.02/13.34 (((notsubsetI) =>
% 99.02/13.34 (((notequalI1) =>
% 99.02/13.34 (((notequalI2) =>
% 99.02/13.34 (((subsetRefl) =>
% 99.02/13.34 (((subsetTrans) =>
% 99.02/13.34 (((setadjoinSub) =>
% 99.02/13.34 (((setadjoinSub2) =>
% 99.02/13.34 (((subset2powerset) =>
% 99.02/13.34 (((setextsub) =>
% 99.02/13.34 (((subsetemptysetimpeq) =>
% 99.02/13.34 (((powersetI1) =>
% 99.02/13.34 (((powersetE1) =>
% 99.02/13.34 (((inPowerset) =>
% 99.02/13.34 (((powersetsubset) =>
% 99.02/13.34 (((sepInPowerset) =>
% 99.02/13.34 (((sepSubset) =>
% 99.02/13.34 (((binunionIL) =>
% 99.02/13.34 (((upairset2IR) =>
% 99.02/13.34 (((binunionIR) =>
% 99.02/13.34 (((binunionEcases) =>
% 99.02/13.34 (((binunionE) =>
% 99.02/13.34 (((binunionLsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionRsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectI) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset5) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectLsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset2) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset3) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectER) =>
% 99.02/13.34 ((
% 99.02/13.34 (disjointsetsI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectRsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset4) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (bs114d) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusI) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusER) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusERneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusELneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusILneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusIRneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusLsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffE) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI2) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg2) =>
% 99.02/13.34 ((
% 99.02/13.34 (secondinupair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIR) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairiskpair) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairp) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowerset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairset2E) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairsubunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairinpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem3) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair1) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionE2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton1) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I2) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsuniq) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (theprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstin) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR11) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR12) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR1) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairequniteq) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR) =>
% 99.02/13.34 ((
% 99.02/13.34 (ksndsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (ksndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemER) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempaircEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrI) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrSub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setOfPairsIsBReln) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrERa) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrER) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcImageSingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (apProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (app) =>
% 99.02/13.34 ((
% 99.02/13.34 (infuncsetfunc) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcinfuncset) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall1) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp3) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcextLem) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp4) =>
% 99.02/13.34 ((
% 99.02/13.34 (subbreln) =>
% 99.02/13.34 ((
% 99.02/13.34 (eqbreln) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcext) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcext2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq2) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (eta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2lamEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta2) =>
% 99.02/13.34 ((
% 99.02/13.34 (eta2) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalseProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalseProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ifSingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (ifp) =>
% 99.02/13.34 ((
% 99.02/13.34 (theeq) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrue) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalse) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueorfalse) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (setextT) =>
% 99.02/13.34 ((
% 99.02/13.34 (subsetTI) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetTI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetTE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectTELcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectTERcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT1) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT2) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT3) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub2) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTnotintersectT) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementImpComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementSubsetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementInPowersetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (contraSubsetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTcontraSubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTILcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTIRcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion2) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInIntersectUnions) =>
% 99.02/13.34 ((
% 99.02/13.34 (intersectInPowersetIntersectUnions) =>
% 99.02/13.34 ((
% 99.02/13.34 (inComplementUnionImpNotIn1) =>
% 99.02/13.34 ((
% 99.02/13.34 (inComplementUnionImpInComplement1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTE) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTEcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementUnionInPowersetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule0) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule1) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule3) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule4) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_1) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_3) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_4) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_5) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1all2) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1SetBreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (choice2fnsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (setOfPairsIsBReln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1all1) =>
% 99.02/13.34 ((
% 99.02/13.34 (subbreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (eqbreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compEex) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionIL) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionIR) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionEcases) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionCommutes) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2Ex) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2W) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2A) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2B) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex1) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Equiv) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1E) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (injFuncInInjFuncSet) =>
% 99.02/13.34 ((
% 99.02/13.34 (!!) @ (
% 99.02/13.34 (('#B') @ (
% 99.02/13.34 !!) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
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% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#S') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
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% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
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% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 =>))))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#C') @ in)))) @
% 99.02/13.34 injFuncSet)))))))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#C') @ in)))) @
% 99.02/13.34 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl749])).
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% 99.02/13.34 (((subsetE2) =>
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% 99.02/13.34 (((notequalI1) =>
% 99.02/13.34 (((notequalI2) =>
% 99.02/13.34 (((subsetRefl) =>
% 99.02/13.34 (((subsetTrans) =>
% 99.02/13.34 (((setadjoinSub) =>
% 99.02/13.34 (((setadjoinSub2) =>
% 99.02/13.34 (((subset2powerset) =>
% 99.02/13.34 (((setextsub) =>
% 99.02/13.34 (((subsetemptysetimpeq) =>
% 99.02/13.34 (((powersetI1) =>
% 99.02/13.34 (((powersetE1) =>
% 99.02/13.34 (((inPowerset) =>
% 99.02/13.34 (((powersetsubset) =>
% 99.02/13.34 (((sepInPowerset) =>
% 99.02/13.34 (((sepSubset) =>
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% 99.02/13.34 (((upairset2IR) =>
% 99.02/13.34 (((binunionIR) =>
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% 99.02/13.34 (((binunionE) =>
% 99.02/13.34 (((binunionLsub) =>
% 99.02/13.34 (((binunionRsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectI) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset5) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectLsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset2) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset3) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectER) =>
% 99.02/13.34 ((
% 99.02/13.34 (disjointsetsI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectRsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset4) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (bs114d) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusI) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusER) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusERneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusELneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusILneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusIRneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusLsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffE) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI2) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg2) =>
% 99.02/13.34 ((
% 99.02/13.34 (secondinupair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIR) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairiskpair) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairp) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowerset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairset2E) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairsubunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairinpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem3) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair1) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionE2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton1) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I2) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsuniq) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (theprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstin) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR11) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR12) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR1) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairequniteq) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR) =>
% 99.02/13.34 ((
% 99.02/13.34 (ksndsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (ksndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemER) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempaircEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrI) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrSub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setOfPairsIsBReln) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrERa) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrER) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcImageSingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (apProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (app) =>
% 99.02/13.34 ((
% 99.02/13.34 (infuncsetfunc) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcinfuncset) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall1) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp3) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcextLem) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp4) =>
% 99.02/13.34 ((
% 99.02/13.34 (subbreln) =>
% 99.02/13.34 ((
% 99.02/13.34 (eqbreln) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcext) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcext2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq2) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (eta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2lamEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta2) =>
% 99.02/13.34 ((
% 99.02/13.34 (eta2) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalseProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalseProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ifSingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (ifp) =>
% 99.02/13.34 ((
% 99.02/13.34 (theeq) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrue) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalse) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueorfalse) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (binunionT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (setextT) =>
% 99.02/13.34 ((
% 99.02/13.34 (subsetTI) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetTI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetTE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectTELcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectTERcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT1) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT2) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT3) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub2) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTnotintersectT) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementImpComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementSubsetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementInPowersetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (contraSubsetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTcontraSubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTILcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTIRcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion2) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInIntersectUnions) =>
% 99.02/13.34 ((
% 99.02/13.34 (intersectInPowersetIntersectUnions) =>
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% 99.02/13.34 (inComplementUnionImpNotIn1) =>
% 99.02/13.34 ((
% 99.02/13.34 (inComplementUnionImpInComplement1) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (binunionTEcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementUnionInPowersetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (breln1invI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invE) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (breln1compI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compE) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (breln1unionI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionEcases) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionCommutes) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2Ex) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2W) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2A) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2B) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex1) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Equiv) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1E) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (injFuncInInjFuncSet) =>
% 99.02/13.34 ((
% 99.02/13.34 (!!) @ (
% 99.02/13.34 (('#B') @ (
% 99.02/13.34 !!) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 !!))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#S') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 '#S') @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 '#S'))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 =>))))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#C') @ in)))) @
% 99.02/13.34 injFuncSet)))))))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#C') @ in)))) @
% 99.02/13.34 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl769])).
% 99.02/13.34 thf(zip_derived_cl807, plain,
% 99.02/13.34 (~ (((eqimpsubset2) =>
% 99.02/13.34 (((eqimpsubset1) =>
% 99.02/13.34 (((subsetI2) =>
% 99.02/13.34 (((emptysetsubset) =>
% 99.02/13.34 (((subsetE) =>
% 99.02/13.34 (((subsetE2) =>
% 99.02/13.34 (((notsubsetI) =>
% 99.02/13.34 (((notequalI1) =>
% 99.02/13.34 (((notequalI2) =>
% 99.02/13.34 (((subsetRefl) =>
% 99.02/13.34 (((subsetTrans) =>
% 99.02/13.34 (((setadjoinSub) =>
% 99.02/13.34 (((setadjoinSub2) =>
% 99.02/13.34 (((subset2powerset) =>
% 99.02/13.34 (((setextsub) =>
% 99.02/13.34 (((subsetemptysetimpeq) =>
% 99.02/13.34 (((powersetI1) =>
% 99.02/13.34 (((powersetE1) =>
% 99.02/13.34 (((inPowerset) =>
% 99.02/13.34 (((powersetsubset) =>
% 99.02/13.34 (((sepInPowerset) =>
% 99.02/13.34 (((sepSubset) =>
% 99.02/13.34 (((binunionIL) =>
% 99.02/13.34 (((upairset2IR) =>
% 99.02/13.34 (((binunionIR) =>
% 99.02/13.34 (((binunionEcases) =>
% 99.02/13.34 (((binunionE) =>
% 99.02/13.34 (((binunionLsub) =>
% 99.02/13.34 (((binunionRsub) =>
% 99.02/13.34 (((binintersectI) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset5) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectLsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset2) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset3) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectER) =>
% 99.02/13.34 ((
% 99.02/13.34 (disjointsetsI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectRsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset4) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (bs114d) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusI) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusER) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusERneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusELneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusILneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusIRneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusLsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffE) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI2) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg2) =>
% 99.02/13.34 ((
% 99.02/13.34 (secondinupair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIR) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairiskpair) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairp) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowerset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairset2E) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairsubunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairinpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem3) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair1) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionE2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton1) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I2) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsuniq) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (theprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstin) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR11) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR12) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR1) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairequniteq) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR) =>
% 99.02/13.34 ((
% 99.02/13.34 (ksndsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (ksndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemER) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempaircEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrI) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrSub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setOfPairsIsBReln) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrERa) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrER) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcImageSingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (apProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (app) =>
% 99.02/13.34 ((
% 99.02/13.34 (infuncsetfunc) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcinfuncset) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall1) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp3) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcextLem) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp4) =>
% 99.02/13.34 ((
% 99.02/13.34 (subbreln) =>
% 99.02/13.34 ((
% 99.02/13.34 (eqbreln) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcext) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcext2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq2) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (eta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2lamEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta2) =>
% 99.02/13.34 ((
% 99.02/13.34 (eta2) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalseProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalseProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ifSingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (ifp) =>
% 99.02/13.34 ((
% 99.02/13.34 (theeq) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrue) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalse) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueorfalse) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (setextT) =>
% 99.02/13.34 ((
% 99.02/13.34 (subsetTI) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetTI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetTE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectTELcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectTERcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT1) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT2) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT3) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub2) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTnotintersectT) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementImpComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementSubsetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementInPowersetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (contraSubsetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTcontraSubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTILcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTIRcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion2) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInIntersectUnions) =>
% 99.02/13.34 ((
% 99.02/13.34 (intersectInPowersetIntersectUnions) =>
% 99.02/13.34 ((
% 99.02/13.34 (inComplementUnionImpNotIn1) =>
% 99.02/13.34 ((
% 99.02/13.34 (inComplementUnionImpInComplement1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTE) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTEcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementUnionInPowersetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule0) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule1) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule3) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule4) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_1) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_3) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_4) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_5) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1all2) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1SetBreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (choice2fnsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (setOfPairsIsBReln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1all1) =>
% 99.02/13.34 ((
% 99.02/13.34 (subbreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (eqbreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compEex) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionIL) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionIR) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionEcases) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionCommutes) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2Ex) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2W) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2A) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2B) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex1) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Equiv) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1E) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (injFuncInInjFuncSet) =>
% 99.02/13.34 ((
% 99.02/13.34 (!!) @ (
% 99.02/13.34 (('#B') @ (
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% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
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% 99.02/13.34 (
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% 99.02/13.34 (
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% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
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% 99.02/13.34 ('#B') @ (
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% 99.02/13.34 (
% 99.02/13.34 (
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% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
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% 99.02/13.34 (binintersectLsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset2) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset3) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectER) =>
% 99.02/13.34 ((
% 99.02/13.34 (disjointsetsI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectRsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset4) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (bs114d) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusI) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusER) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusERneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusELneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusILneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusIRneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusLsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffE) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI2) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg2) =>
% 99.02/13.34 ((
% 99.02/13.34 (secondinupair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIR) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairiskpair) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairp) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowerset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairset2E) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairsubunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairinpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem3) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair1) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionE2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton1) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I2) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsuniq) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (theprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstin) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR11) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR12) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR1) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairequniteq) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR) =>
% 99.02/13.34 ((
% 99.02/13.34 (ksndsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (ksndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemER) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempaircEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrI) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrSub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setOfPairsIsBReln) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrERa) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrER) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcImageSingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (apProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (app) =>
% 99.02/13.34 ((
% 99.02/13.34 (infuncsetfunc) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcinfuncset) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall1) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp3) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcextLem) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp4) =>
% 99.02/13.34 ((
% 99.02/13.34 (subbreln) =>
% 99.02/13.34 ((
% 99.02/13.34 (eqbreln) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcext) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcext2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq2) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (eta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2lamEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta2) =>
% 99.02/13.34 ((
% 99.02/13.34 (eta2) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalseProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalseProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ifSingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (ifp) =>
% 99.02/13.34 ((
% 99.02/13.34 (theeq) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrue) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalse) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueorfalse) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (setextT) =>
% 99.02/13.34 ((
% 99.02/13.34 (subsetTI) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetTI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetTE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectTELcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectTERcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT1) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT2) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT3) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub2) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTnotintersectT) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementImpComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementSubsetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementInPowersetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (contraSubsetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTcontraSubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTILcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTIRcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion2) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInIntersectUnions) =>
% 99.02/13.34 ((
% 99.02/13.34 (intersectInPowersetIntersectUnions) =>
% 99.02/13.34 ((
% 99.02/13.34 (inComplementUnionImpNotIn1) =>
% 99.02/13.34 ((
% 99.02/13.34 (inComplementUnionImpInComplement1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTE) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTEcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementUnionInPowersetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule0) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule1) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule3) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule4) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_1) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_3) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_4) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_5) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1all2) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1SetBreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (choice2fnsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (setOfPairsIsBReln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1all1) =>
% 99.02/13.34 ((
% 99.02/13.34 (subbreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (eqbreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compEex) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionIL) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionIR) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionEcases) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionCommutes) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2Ex) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2W) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2A) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2B) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex1) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Equiv) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1E) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (injFuncInInjFuncSet) =>
% 99.02/13.34 ((
% 99.02/13.34 (!!) @ (
% 99.02/13.34 (('#B') @ (
% 99.02/13.34 !!) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 !!))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#S') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 '#S') @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 '#S'))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 =>))))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#C') @ in)))) @
% 99.02/13.34 injFuncSet)))))))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#C') @ in)))) @
% 99.02/13.34 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl824])).
% 99.02/13.34 thf(zip_derived_cl850, plain,
% 99.02/13.34 (~ (((emptysetsubset) =>
% 99.02/13.34 (((subsetE) =>
% 99.02/13.34 (((subsetE2) =>
% 99.02/13.34 (((notsubsetI) =>
% 99.02/13.34 (((notequalI1) =>
% 99.02/13.34 (((notequalI2) =>
% 99.02/13.34 (((subsetRefl) =>
% 99.02/13.34 (((subsetTrans) =>
% 99.02/13.34 (((setadjoinSub) =>
% 99.02/13.34 (((setadjoinSub2) =>
% 99.02/13.34 (((subset2powerset) =>
% 99.02/13.34 (((setextsub) =>
% 99.02/13.34 (((subsetemptysetimpeq) =>
% 99.02/13.34 (((powersetI1) =>
% 99.02/13.34 (((powersetE1) =>
% 99.02/13.34 (((inPowerset) =>
% 99.02/13.34 (((powersetsubset) =>
% 99.02/13.34 (((sepInPowerset) =>
% 99.02/13.34 (((sepSubset) =>
% 99.02/13.34 (((binunionIL) =>
% 99.02/13.34 (((upairset2IR) =>
% 99.02/13.34 (((binunionIR) =>
% 99.02/13.34 (((binunionEcases) =>
% 99.02/13.34 (((binunionE) =>
% 99.02/13.34 (((binunionLsub) =>
% 99.02/13.34 (((binunionRsub) =>
% 99.02/13.34 (((binintersectI) =>
% 99.02/13.34 (((binintersectSubset5) =>
% 99.02/13.34 (((binintersectEL) =>
% 99.02/13.34 (((binintersectLsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset2) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset3) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectER) =>
% 99.02/13.34 ((
% 99.02/13.34 (disjointsetsI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectRsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset4) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (bs114d) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusI) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusER) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusERneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusELneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusILneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusIRneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusLsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffE) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI2) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg2) =>
% 99.02/13.34 ((
% 99.02/13.34 (secondinupair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIR) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairiskpair) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairp) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowerset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairset2E) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairsubunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairinpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem3) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair1) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionE2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton1) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I2) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsuniq) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (theprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstin) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR11) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR12) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR1) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairequniteq) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR) =>
% 99.02/13.34 ((
% 99.02/13.34 (ksndsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (ksndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemER) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempaircEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrI) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrSub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setOfPairsIsBReln) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrERa) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrER) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcImageSingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (apProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (app) =>
% 99.02/13.34 ((
% 99.02/13.34 (infuncsetfunc) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcinfuncset) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall1) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp3) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcextLem) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp4) =>
% 99.02/13.34 ((
% 99.02/13.34 (subbreln) =>
% 99.02/13.34 ((
% 99.02/13.34 (eqbreln) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcext) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcext2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq2) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (eta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2lamEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta2) =>
% 99.02/13.34 ((
% 99.02/13.34 (eta2) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalseProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalseProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ifSingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (ifp) =>
% 99.02/13.34 ((
% 99.02/13.34 (theeq) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrue) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalse) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueorfalse) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (setextT) =>
% 99.02/13.34 ((
% 99.02/13.34 (subsetTI) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetTI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetTE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectTELcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectTERcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT1) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT2) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT3) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub2) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTnotintersectT) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementImpComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementSubsetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementInPowersetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (contraSubsetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTcontraSubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTILcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTIRcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion2) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInIntersectUnions) =>
% 99.02/13.34 ((
% 99.02/13.34 (intersectInPowersetIntersectUnions) =>
% 99.02/13.34 ((
% 99.02/13.34 (inComplementUnionImpNotIn1) =>
% 99.02/13.34 ((
% 99.02/13.34 (inComplementUnionImpInComplement1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTE) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTEcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementUnionInPowersetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule0) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule1) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule3) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule4) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_1) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_3) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_4) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_5) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1all2) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1SetBreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (choice2fnsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (setOfPairsIsBReln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1all1) =>
% 99.02/13.34 ((
% 99.02/13.34 (subbreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (eqbreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compEex) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionIL) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionIR) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionEcases) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionCommutes) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2Ex) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2W) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2A) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2B) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex1) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Equiv) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1E) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (injFuncInInjFuncSet) =>
% 99.02/13.34 ((
% 99.02/13.34 (!!) @ (
% 99.02/13.34 (('#B') @ (
% 99.02/13.34 !!) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 !!))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#S') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 '#S') @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 '#S'))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 =>))))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#C') @ in)))) @
% 99.02/13.34 injFuncSet)))))))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#C') @ in)))) @
% 99.02/13.34 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl838])).
% 99.02/13.34 thf(zip_derived_cl863, plain,
% 99.02/13.34 (~ (((subsetE) =>
% 99.02/13.34 (((subsetE2) =>
% 99.02/13.34 (((notsubsetI) =>
% 99.02/13.34 (((notequalI1) =>
% 99.02/13.34 (((notequalI2) =>
% 99.02/13.34 (((subsetRefl) =>
% 99.02/13.34 (((subsetTrans) =>
% 99.02/13.34 (((setadjoinSub) =>
% 99.02/13.34 (((setadjoinSub2) =>
% 99.02/13.34 (((subset2powerset) =>
% 99.02/13.34 (((setextsub) =>
% 99.02/13.34 (((subsetemptysetimpeq) =>
% 99.02/13.34 (((powersetI1) =>
% 99.02/13.34 (((powersetE1) =>
% 99.02/13.34 (((inPowerset) =>
% 99.02/13.34 (((powersetsubset) =>
% 99.02/13.34 (((sepInPowerset) =>
% 99.02/13.34 (((sepSubset) =>
% 99.02/13.34 (((binunionIL) =>
% 99.02/13.34 (((upairset2IR) =>
% 99.02/13.34 (((binunionIR) =>
% 99.02/13.34 (((binunionEcases) =>
% 99.02/13.34 (((binunionE) =>
% 99.02/13.34 (((binunionLsub) =>
% 99.02/13.34 (((binunionRsub) =>
% 99.02/13.34 (((binintersectI) =>
% 99.02/13.34 (((binintersectSubset5) =>
% 99.02/13.34 (((binintersectEL) =>
% 99.02/13.34 (((binintersectLsub) =>
% 99.02/13.34 (((binintersectSubset2) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset3) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectER) =>
% 99.02/13.34 ((
% 99.02/13.34 (disjointsetsI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectRsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset4) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (bs114d) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusI) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusER) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusERneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusELneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusILneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusIRneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusLsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffE) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI2) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg2) =>
% 99.02/13.34 ((
% 99.02/13.34 (secondinupair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIR) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairiskpair) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairp) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowerset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairset2E) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairsubunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairinpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem3) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair1) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionE2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton1) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I2) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsuniq) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (theprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstin) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR11) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR12) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR1) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairequniteq) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR) =>
% 99.02/13.34 ((
% 99.02/13.34 (ksndsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (ksndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemER) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempaircEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrI) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrSub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setOfPairsIsBReln) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrERa) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrER) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcImageSingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (apProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (app) =>
% 99.02/13.34 ((
% 99.02/13.34 (infuncsetfunc) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcinfuncset) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall1) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp3) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcextLem) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp4) =>
% 99.02/13.34 ((
% 99.02/13.34 (subbreln) =>
% 99.02/13.34 ((
% 99.02/13.34 (eqbreln) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcext) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcext2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq2) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (eta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2lamEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta2) =>
% 99.02/13.34 ((
% 99.02/13.34 (eta2) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalseProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalseProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ifSingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (ifp) =>
% 99.02/13.34 ((
% 99.02/13.34 (theeq) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrue) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalse) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueorfalse) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (setextT) =>
% 99.02/13.34 ((
% 99.02/13.34 (subsetTI) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetTI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetTE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectTELcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectTERcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT1) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT2) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT3) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub2) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTnotintersectT) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementImpComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementSubsetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementInPowersetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (contraSubsetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTcontraSubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTILcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTIRcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion2) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInIntersectUnions) =>
% 99.02/13.34 ((
% 99.02/13.34 (intersectInPowersetIntersectUnions) =>
% 99.02/13.34 ((
% 99.02/13.34 (inComplementUnionImpNotIn1) =>
% 99.02/13.34 ((
% 99.02/13.34 (inComplementUnionImpInComplement1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTE) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTEcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementUnionInPowersetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule0) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule1) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule3) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule4) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_1) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_3) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_4) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_5) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1all2) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1SetBreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (choice2fnsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (setOfPairsIsBReln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1all1) =>
% 99.02/13.34 ((
% 99.02/13.34 (subbreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (eqbreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compEex) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionIL) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionIR) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionEcases) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionCommutes) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2Ex) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2W) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2A) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2B) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex1) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Equiv) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1E) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (injFuncInInjFuncSet) =>
% 99.02/13.34 ((
% 99.02/13.34 (!!) @ (
% 99.02/13.34 (('#B') @ (
% 99.02/13.34 !!) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 !!))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#S') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 '#S') @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 '#S'))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 =>))))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#C') @ in)))) @
% 99.02/13.34 injFuncSet)))))))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#C') @ in)))) @
% 99.02/13.34 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl850])).
% 99.02/13.34 thf(zip_derived_cl878, plain,
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% 99.02/13.34 (((notsubsetI) =>
% 99.02/13.34 (((notequalI1) =>
% 99.02/13.34 (((notequalI2) =>
% 99.02/13.34 (((subsetRefl) =>
% 99.02/13.34 (((subsetTrans) =>
% 99.02/13.34 (((setadjoinSub) =>
% 99.02/13.34 (((setadjoinSub2) =>
% 99.02/13.34 (((subset2powerset) =>
% 99.02/13.34 (((setextsub) =>
% 99.02/13.34 (((subsetemptysetimpeq) =>
% 99.02/13.34 (((powersetI1) =>
% 99.02/13.34 (((powersetE1) =>
% 99.02/13.34 (((inPowerset) =>
% 99.02/13.34 (((powersetsubset) =>
% 99.02/13.34 (((sepInPowerset) =>
% 99.02/13.34 (((sepSubset) =>
% 99.02/13.34 (((binunionIL) =>
% 99.02/13.34 (((upairset2IR) =>
% 99.02/13.34 (((binunionIR) =>
% 99.02/13.34 (((binunionEcases) =>
% 99.02/13.34 (((binunionE) =>
% 99.02/13.34 (((binunionLsub) =>
% 99.02/13.34 (((binunionRsub) =>
% 99.02/13.34 (((binintersectI) =>
% 99.02/13.34 (((binintersectSubset5) =>
% 99.02/13.34 (((binintersectEL) =>
% 99.02/13.34 (((binintersectLsub) =>
% 99.02/13.34 (((binintersectSubset2) =>
% 99.02/13.34 (((binintersectSubset3) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectER) =>
% 99.02/13.34 ((
% 99.02/13.34 (disjointsetsI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectRsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset4) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (bs114d) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusI) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusER) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusERneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusELneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusILneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusIRneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusLsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffE) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI2) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg2) =>
% 99.02/13.34 ((
% 99.02/13.34 (secondinupair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIR) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairiskpair) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairp) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowerset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairset2E) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairsubunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairinpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem3) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair1) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionE2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton1) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I2) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsuniq) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (theprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstin) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR11) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR12) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR1) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairequniteq) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (ksndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemER) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempaircEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrI) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrSub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setOfPairsIsBReln) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrERa) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrER) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcImageSingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (apProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (app) =>
% 99.02/13.34 ((
% 99.02/13.34 (infuncsetfunc) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcinfuncset) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall1) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp3) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcextLem) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp4) =>
% 99.02/13.34 ((
% 99.02/13.34 (subbreln) =>
% 99.02/13.34 ((
% 99.02/13.34 (eqbreln) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcext) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcext2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq2) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (eta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2lamEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta2) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (iffalseProp2) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (binintersectTERcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT2) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT3) =>
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% 99.02/13.34 (contraSubsetComplement) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (binunionTIRcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion2) =>
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% 99.02/13.34 (demorgan1a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule0) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule1) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule3) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule4) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_1) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_3) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_4) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_5) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1all2) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1SetBreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (choice2fnsingleton) =>
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% 99.02/13.34 (setOfPairsIsBReln1) =>
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% 99.02/13.34 ((
% 99.02/13.34 (subbreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (eqbreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compEex) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionIL) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionIR) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionEcases) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionCommutes) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (woz2W) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2A) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2B) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex1) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Equiv) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1E) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (injFuncInInjFuncSet) =>
% 99.02/13.34 ((
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% 99.02/13.34 (
% 99.02/13.34 (
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% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
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% 99.02/13.34 (
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% 99.02/13.34 (
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% 99.02/13.34 injFuncSet)))))))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#C') @ in)))) @
% 99.02/13.34 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (upairinpowunion) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem3) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair) =>
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (brelnall2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E2) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp3) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp2) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp4) =>
% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
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% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT2) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT3) =>
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% 99.02/13.34 (doubleComplementI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub2) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTnotintersectT) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementImpComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementSubsetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementInPowersetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (contraSubsetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTcontraSubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTILcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTIRcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion2) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInIntersectUnions) =>
% 99.02/13.34 ((
% 99.02/13.34 (intersectInPowersetIntersectUnions) =>
% 99.02/13.34 ((
% 99.02/13.34 (inComplementUnionImpNotIn1) =>
% 99.02/13.34 ((
% 99.02/13.34 (inComplementUnionImpInComplement1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTE) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTEcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementUnionInPowersetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule0) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule1) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule3) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule4) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_1) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_3) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_4) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz1_5) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1all2) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1SetBreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (choice2fnsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (setOfPairsIsBReln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1all1) =>
% 99.02/13.34 ((
% 99.02/13.34 (subbreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (eqbreln1) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1invE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1compEex) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionIL) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionIR) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionI) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionE) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionEcases) =>
% 99.02/13.34 ((
% 99.02/13.34 (breln1unionCommutes) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2Ex) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2W) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2A) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz2B) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Ex1) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1Equiv) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1E) =>
% 99.02/13.34 ((
% 99.02/13.34 (image1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (injFuncInInjFuncSet) =>
% 99.02/13.34 ((
% 99.02/13.34 (!!) @ (
% 99.02/13.34 (('#B') @ (
% 99.02/13.34 !!) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 !!))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#S') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 '#S') @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 '#S'))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 =>))))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#C') @ in)))) @
% 99.02/13.34 injFuncSet)))))))) @
% 99.02/13.34 (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#B') @ (
% 99.02/13.34 (
% 99.02/13.34 ('#C') @ in)))) @
% 99.02/13.34 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl878])).
% 99.02/13.34 thf(zip_derived_cl909, plain,
% 99.02/13.34 (~ (((notequalI1) =>
% 99.02/13.34 (((notequalI2) =>
% 99.02/13.34 (((subsetRefl) =>
% 99.02/13.34 (((subsetTrans) =>
% 99.02/13.34 (((setadjoinSub) =>
% 99.02/13.34 (((setadjoinSub2) =>
% 99.02/13.34 (((subset2powerset) =>
% 99.02/13.34 (((setextsub) =>
% 99.02/13.34 (((subsetemptysetimpeq) =>
% 99.02/13.34 (((powersetI1) =>
% 99.02/13.34 (((powersetE1) =>
% 99.02/13.34 (((inPowerset) =>
% 99.02/13.34 (((powersetsubset) =>
% 99.02/13.34 (((sepInPowerset) =>
% 99.02/13.34 (((sepSubset) =>
% 99.02/13.34 (((binunionIL) =>
% 99.02/13.34 (((upairset2IR) =>
% 99.02/13.34 (((binunionIR) =>
% 99.02/13.34 (((binunionEcases) =>
% 99.02/13.34 (((binunionE) =>
% 99.02/13.34 (((binunionLsub) =>
% 99.02/13.34 (((binunionRsub) =>
% 99.02/13.34 (((binintersectI) =>
% 99.02/13.34 (((binintersectSubset5) =>
% 99.02/13.34 (((binintersectEL) =>
% 99.02/13.34 (((binintersectLsub) =>
% 99.02/13.34 (((binintersectSubset2) =>
% 99.02/13.34 (((binintersectSubset3) =>
% 99.02/13.34 (((binintersectER) =>
% 99.02/13.34 (((disjointsetsI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectRsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset4) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (bs114d) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusI) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusER) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusERneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusELneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusILneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusIRneg) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusLsub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusSubset1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffE) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffI2) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg1) =>
% 99.02/13.34 ((
% 99.02/13.34 (symdiffIneg2) =>
% 99.02/13.34 ((
% 99.02/13.34 (secondinupair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairIR) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairiskpair) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairp) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowerset) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletoninpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairset2E) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairsubunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairinpowunion) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ubforcartprodlem3) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair1) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempair) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionE2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton1) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setunionsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1I2) =>
% 99.02/13.34 ((
% 99.02/13.34 (singletonsuniq) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (theprop) =>
% 99.02/13.34 ((
% 99.02/13.34 (kfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstin) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjL) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR11) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR12) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR1) =>
% 99.02/13.34 ((
% 99.02/13.34 (upairequniteq) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR2) =>
% 99.02/13.34 ((
% 99.02/13.34 (setukpairinjR) =>
% 99.02/13.34 ((
% 99.02/13.34 (ksndsingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (ksndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (kpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndin) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemEL) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairmemER) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodmempaircEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodfstpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodsndpairEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (cartprodpairsurjEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrI) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrSub) =>
% 99.02/13.34 ((
% 99.02/13.34 (setOfPairsIsBReln) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrERa) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL1) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrEL2) =>
% 99.02/13.34 ((
% 99.02/13.34 (dpsetconstrER) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcImageSingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (apProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (app) =>
% 99.02/13.34 ((
% 99.02/13.34 (infuncsetfunc) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcinfuncset) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamProp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lamp) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2p) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall1) =>
% 99.02/13.34 ((
% 99.02/13.34 (brelnall2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ex1E2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp3) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcextLem) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcGraphProp4) =>
% 99.02/13.34 ((
% 99.02/13.34 (subbreln) =>
% 99.02/13.34 ((
% 99.02/13.34 (eqbreln) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcext) =>
% 99.02/13.34 ((
% 99.02/13.34 (funcext2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq1) =>
% 99.02/13.34 ((
% 99.02/13.34 (ap2apEq2) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (eta1) =>
% 99.02/13.34 ((
% 99.02/13.34 (lam2lamEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (beta2) =>
% 99.02/13.34 ((
% 99.02/13.34 (eta2) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalseProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalseProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueProp1) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueProp2) =>
% 99.02/13.34 ((
% 99.02/13.34 (ifSingleton) =>
% 99.02/13.34 ((
% 99.02/13.34 (ifp) =>
% 99.02/13.34 ((
% 99.02/13.34 (theeq) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrue) =>
% 99.02/13.34 ((
% 99.02/13.34 (iffalse) =>
% 99.02/13.34 ((
% 99.02/13.34 (iftrueorfalse) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (setminusT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementT_lem) =>
% 99.02/13.34 ((
% 99.02/13.34 (setextT) =>
% 99.02/13.34 ((
% 99.02/13.34 (subsetTI) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetTI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (powersetTE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectTELcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (binintersectTERcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT1) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT2) =>
% 99.02/13.34 ((
% 99.02/13.34 (contrasubsetT3) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementI1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementE1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub1) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementSub2) =>
% 99.02/13.34 ((
% 99.02/13.34 (doubleComplementEq) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTnotintersectT) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementImpComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementSubsetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementInPowersetComplementIntersect) =>
% 99.02/13.34 ((
% 99.02/13.34 (contraSubsetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementTcontraSubset) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTILcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTIRcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInUnion2) =>
% 99.02/13.34 ((
% 99.02/13.34 (inIntersectImpInIntersectUnions) =>
% 99.02/13.34 ((
% 99.02/13.34 (intersectInPowersetIntersectUnions) =>
% 99.02/13.34 ((
% 99.02/13.34 (inComplementUnionImpNotIn1) =>
% 99.02/13.34 ((
% 99.02/13.34 (inComplementUnionImpInComplement1) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTE) =>
% 99.02/13.34 ((
% 99.02/13.34 (binunionTEcontra) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a1) =>
% 99.02/13.34 ((
% 99.02/13.34 (complementUnionInPowersetComplement) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan1) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2a) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b2) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2b) =>
% 99.02/13.34 ((
% 99.02/13.34 (demorgan2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule0) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule1) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule2) =>
% 99.02/13.34 ((
% 99.02/13.34 (woz13rule3) =>
% 99.02/13.34 ((
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% 99.02/13.35 (symdiffIneg2) =>
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% 99.02/13.35 (setukpairIR) =>
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% 99.02/13.35 (ubforcartprodlem3) =>
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% 99.02/13.35 (cartprodmempair) =>
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% 99.02/13.35 (setunionsingleton2) =>
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% 99.02/13.35 (setunionsingleton) =>
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (ex1I2) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 (kfstpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodfstin) =>
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% 99.02/13.35 (setukpairinjR12) =>
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% 99.02/13.35 (setukpairinjR1) =>
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% 99.02/13.35 (setukpairinjR) =>
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% 99.02/13.35 (ksndsingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (ksndpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (kpairsurjEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodsndin) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairmemEL) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairmemER) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodmempaircEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodfstpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodsndpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairsurjEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrI) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrSub) =>
% 99.02/13.35 ((
% 99.02/13.35 (setOfPairsIsBReln) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrERa) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrEL1) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrEL2) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrER) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcImageSingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (apProp) =>
% 99.02/13.35 ((
% 99.02/13.35 (app) =>
% 99.02/13.35 ((
% 99.02/13.35 (infuncsetfunc) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2p) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcinfuncset) =>
% 99.02/13.35 ((
% 99.02/13.35 (lamProp) =>
% 99.02/13.35 ((
% 99.02/13.35 (lamp) =>
% 99.02/13.35 ((
% 99.02/13.35 (lam2p) =>
% 99.02/13.35 ((
% 99.02/13.35 (brelnall1) =>
% 99.02/13.35 ((
% 99.02/13.35 (brelnall2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ex1E2) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp1) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp3) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp2) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcextLem) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp4) =>
% 99.02/13.35 ((
% 99.02/13.35 (subbreln) =>
% 99.02/13.35 ((
% 99.02/13.35 (eqbreln) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcext) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcext2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2apEq1) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2apEq2) =>
% 99.02/13.35 ((
% 99.02/13.35 (beta1) =>
% 99.02/13.35 ((
% 99.02/13.35 (eta1) =>
% 99.02/13.35 ((
% 99.02/13.35 (lam2lamEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (beta2) =>
% 99.02/13.35 ((
% 99.02/13.35 (eta2) =>
% 99.02/13.35 ((
% 99.02/13.35 (iffalseProp1) =>
% 99.02/13.35 ((
% 99.02/13.35 (iffalseProp2) =>
% 99.02/13.35 ((
% 99.02/13.35 (iftrueProp1) =>
% 99.02/13.35 ((
% 99.02/13.35 (iftrueProp2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ifSingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (ifp) =>
% 99.02/13.35 ((
% 99.02/13.35 (theeq) =>
% 99.02/13.35 ((
% 99.02/13.35 (iftrue) =>
% 99.02/13.35 ((
% 99.02/13.35 (iffalse) =>
% 99.02/13.35 ((
% 99.02/13.35 (iftrueorfalse) =>
% 99.02/13.35 ((
% 99.02/13.35 (binintersectT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (binunionT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (powersetT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (setextT) =>
% 99.02/13.35 ((
% 99.02/13.35 (subsetTI) =>
% 99.02/13.35 ((
% 99.02/13.35 (powersetTI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (powersetTE1) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTE1) =>
% 99.02/13.35 ((
% 99.02/13.35 (binintersectTELcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (binintersectTERcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT1) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT2) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT3) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementE1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementSub1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementSub2) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTnotintersectT) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementImpComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementSubsetComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementInPowersetComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (contraSubsetComplement) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTcontraSubset) =>
% 99.02/13.35 ((
% 99.02/13.35 (binunionTILcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (binunionTIRcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (inIntersectImpInUnion) =>
% 99.02/13.35 ((
% 99.02/13.35 (inIntersectImpInUnion2) =>
% 99.02/13.35 ((
% 99.02/13.35 (inIntersectImpInIntersectUnions) =>
% 99.02/13.35 ((
% 99.02/13.35 (intersectInPowersetIntersectUnions) =>
% 99.02/13.35 ((
% 99.02/13.35 (inComplementUnionImpNotIn1) =>
% 99.02/13.35 ((
% 99.02/13.35 (inComplementUnionImpInComplement1) =>
% 99.02/13.35 ((
% 99.02/13.35 (binunionTE) =>
% 99.02/13.35 ((
% 99.02/13.35 (binunionTEcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2a1) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementUnionInPowersetComplement) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2a2) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan1a) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan1b) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan1) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2a) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2b2) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2b) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule0) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule1) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule3) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule4) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_1) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_3) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_4) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_5) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1all2) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1SetBreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (choice2fnsingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (setOfPairsIsBReln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1all1) =>
% 99.02/13.35 ((
% 99.02/13.35 (subbreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (eqbreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invI) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compI) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compEex) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (breln1unionIL) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionIR) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionI) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionEcases) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionCommutes) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2Ex) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2W) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2A) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2B) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (image1Ex1) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1Equiv) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1E) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1I) =>
% 99.02/13.35 ((
% 99.02/13.35 (injFuncInInjFuncSet) =>
% 99.02/13.35 ((
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% 99.02/13.35 (('#B') @ (
% 99.02/13.35 !!) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
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% 99.02/13.35 (
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% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
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% 99.02/13.35 (
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% 99.02/13.35 (
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% 99.02/13.35 (
% 99.02/13.35 (
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% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
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% 99.02/13.35 injFuncSet)))))))) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#C') @ in)))) @
% 99.02/13.35 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.02/13.35 (((binintersectSubset3) =>
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% 99.02/13.35 (((binintersectSubset1) =>
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (setminusER) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (setminusILneg) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusIRneg) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusLsub) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusSubset1) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffE) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffI2) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffIneg1) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffIneg2) =>
% 99.02/13.35 ((
% 99.02/13.35 (secondinupair) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairIL) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairIR) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (kpairp) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (upairset2E) =>
% 99.02/13.35 ((
% 99.02/13.35 (upairsubunion) =>
% 99.02/13.35 ((
% 99.02/13.35 (upairinpowunion) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (ubforcartprodlem2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ubforcartprodlem3) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairin) =>
% 99.02/13.35 ((
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% 99.02/13.35 (cartprodmempaircEq) =>
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% 99.02/13.35 (cartprodsndpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairsurjEq) =>
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% 99.02/13.35 (dpsetconstrEL2) =>
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% 99.02/13.35 (dpsetconstrER) =>
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% 99.02/13.35 (app) =>
% 99.02/13.35 ((
% 99.02/13.35 (infuncsetfunc) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2p) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcinfuncset) =>
% 99.02/13.35 ((
% 99.02/13.35 (lamProp) =>
% 99.02/13.35 ((
% 99.02/13.35 (lamp) =>
% 99.02/13.35 ((
% 99.02/13.35 (lam2p) =>
% 99.02/13.35 ((
% 99.02/13.35 (brelnall1) =>
% 99.02/13.35 ((
% 99.02/13.35 (brelnall2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ex1E2) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp1) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp3) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp2) =>
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% 99.02/13.35 (funcGraphProp4) =>
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% 99.02/13.35 ((
% 99.02/13.35 (funcext2) =>
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% 99.02/13.35 (ap2apEq1) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2apEq2) =>
% 99.02/13.35 ((
% 99.02/13.35 (beta1) =>
% 99.02/13.35 ((
% 99.02/13.35 (eta1) =>
% 99.02/13.35 ((
% 99.02/13.35 (lam2lamEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (beta2) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (iffalseProp2) =>
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (binintersectTELcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (binintersectTERcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT2) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT3) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementE1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementSub1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementSub2) =>
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% 99.02/13.35 (doubleComplementEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTnotintersectT) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementImpComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementSubsetComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementInPowersetComplementIntersect) =>
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% 99.02/13.35 (contraSubsetComplement) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTcontraSubset) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (binunionTIRcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (inIntersectImpInUnion) =>
% 99.02/13.35 ((
% 99.02/13.35 (inIntersectImpInUnion2) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (complementUnionInPowersetComplement) =>
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% 99.02/13.35 (demorgan1a) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan1b) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan1) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2a) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2b2) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2b) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule0) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule1) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule3) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule4) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (woz1_2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_3) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_4) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_5) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1all2) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1SetBreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (choice2fnsingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (setOfPairsIsBReln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1all1) =>
% 99.02/13.35 ((
% 99.02/13.35 (subbreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (eqbreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invI) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compI) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compEex) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (breln1unionIR) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (breln1unionE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionEcases) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (woz2W) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (woz2B) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (image1Ex1) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1Equiv) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1E) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1I) =>
% 99.02/13.35 ((
% 99.02/13.35 (injFuncInInjFuncSet) =>
% 99.02/13.35 ((
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% 99.02/13.35 (
% 99.02/13.35 (
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% 99.02/13.35 injFuncSet)))))))) @
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% 99.02/13.35 (
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% 99.02/13.35 (
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% 99.02/13.35 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 (dpsetconstrER) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcImageSingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (apProp) =>
% 99.02/13.35 ((
% 99.02/13.35 (app) =>
% 99.02/13.35 ((
% 99.02/13.35 (infuncsetfunc) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2p) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcinfuncset) =>
% 99.02/13.35 ((
% 99.02/13.35 (lamProp) =>
% 99.02/13.35 ((
% 99.02/13.35 (lamp) =>
% 99.02/13.35 ((
% 99.02/13.35 (lam2p) =>
% 99.02/13.35 ((
% 99.02/13.35 (brelnall1) =>
% 99.02/13.35 ((
% 99.02/13.35 (brelnall2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ex1E2) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp1) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp3) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp2) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcextLem) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp4) =>
% 99.02/13.35 ((
% 99.02/13.35 (subbreln) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (funcext2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2apEq1) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2apEq2) =>
% 99.02/13.35 ((
% 99.02/13.35 (beta1) =>
% 99.02/13.35 ((
% 99.02/13.35 (eta1) =>
% 99.02/13.35 ((
% 99.02/13.35 (lam2lamEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (beta2) =>
% 99.02/13.35 ((
% 99.02/13.35 (eta2) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (iffalseProp2) =>
% 99.02/13.35 ((
% 99.02/13.35 (iftrueProp1) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (complementT_lem) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (complementTI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTE1) =>
% 99.02/13.35 ((
% 99.02/13.35 (binintersectTELcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (binintersectTERcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT1) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT2) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT3) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementE1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementSub1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementSub2) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTnotintersectT) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementImpComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementSubsetComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementInPowersetComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (contraSubsetComplement) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTcontraSubset) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (binunionTIRcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (inIntersectImpInUnion) =>
% 99.02/13.35 ((
% 99.02/13.35 (inIntersectImpInUnion2) =>
% 99.02/13.35 ((
% 99.02/13.35 (inIntersectImpInIntersectUnions) =>
% 99.02/13.35 ((
% 99.02/13.35 (intersectInPowersetIntersectUnions) =>
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% 99.02/13.35 (inComplementUnionImpNotIn1) =>
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% 99.02/13.35 (inComplementUnionImpInComplement1) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (binunionTEcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2a1) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementUnionInPowersetComplement) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2a2) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan1a) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan1b) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan1) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2a) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2b2) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2b) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule0) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule1) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule3) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule4) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_1) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_3) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_4) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_5) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1all2) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1SetBreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (choice2fnsingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (setOfPairsIsBReln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1all1) =>
% 99.02/13.35 ((
% 99.02/13.35 (subbreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (eqbreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invI) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compI) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compEex) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionIL) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionIR) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionI) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionEcases) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionCommutes) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2Ex) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2W) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2A) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2B) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1Ex) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1Ex1) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1Equiv) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1E) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1I) =>
% 99.02/13.35 ((
% 99.02/13.35 (injFuncInInjFuncSet) =>
% 99.02/13.35 ((
% 99.02/13.35 (!!) @ (
% 99.02/13.35 (('#B') @ (
% 99.02/13.35 !!) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 !!))) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#S') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
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% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
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% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 =>))))) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
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% 99.02/13.35 injFuncSet)))))))) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#C') @ in)))) @
% 99.02/13.35 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.35 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl967])).
% 99.02/13.35 thf(zip_derived_cl1000, plain,
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% 99.02/13.35 (((powersetE1) =>
% 99.02/13.35 (((inPowerset) =>
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% 99.02/13.35 (((sepSubset) =>
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% 99.02/13.35 (((upairset2IR) =>
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% 99.02/13.35 (((binunionE) =>
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% 99.02/13.35 (((binintersectEL) =>
% 99.02/13.35 (((binintersectLsub) =>
% 99.02/13.35 (((binintersectSubset2) =>
% 99.02/13.35 (((binintersectSubset3) =>
% 99.02/13.35 (((binintersectER) =>
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% 99.02/13.35 (((binintersectRsub) =>
% 99.02/13.35 (((binintersectSubset4) =>
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (setminusIRneg) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusLsub) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusSubset1) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (symdiffI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffI2) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffIneg1) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffIneg2) =>
% 99.02/13.35 ((
% 99.02/13.35 (secondinupair) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairIL) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairIR) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (kpairp) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (ubforcartprodlem2) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (cartprodmempair) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (cartprodfstin) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjL2) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR11) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR1) =>
% 99.02/13.35 ((
% 99.02/13.35 (upairequniteq) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR2) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR) =>
% 99.02/13.35 ((
% 99.02/13.35 (ksndsingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (ksndpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (kpairsurjEq) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrER) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (brelnall2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ex1E2) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp1) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp3) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp2) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp4) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (eqbreln) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcext) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcext2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2apEq1) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2apEq2) =>
% 99.02/13.35 ((
% 99.02/13.35 (beta1) =>
% 99.02/13.35 ((
% 99.02/13.35 (eta1) =>
% 99.02/13.35 ((
% 99.02/13.35 (lam2lamEq) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (binunionT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (powersetT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementT_lem) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (complementTE1) =>
% 99.02/13.35 ((
% 99.02/13.35 (binintersectTELcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (binintersectTERcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT1) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT2) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT3) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementE1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementSub1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementSub2) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTnotintersectT) =>
% 99.02/13.35 ((
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% 99.02/13.35 (complementSubsetComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementInPowersetComplementIntersect) =>
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% 99.02/13.35 (contraSubsetComplement) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTcontraSubset) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (binunionTIRcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (inIntersectImpInUnion) =>
% 99.02/13.35 ((
% 99.02/13.35 (inIntersectImpInUnion2) =>
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (complementUnionInPowersetComplement) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2a2) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan1a) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan1b) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan1) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2a) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2b2) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2b) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule0) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule1) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule3) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule4) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_1) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_3) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_4) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_5) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1all2) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1SetBreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (choice2fnsingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (setOfPairsIsBReln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1all1) =>
% 99.02/13.35 ((
% 99.02/13.35 (subbreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (eqbreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invI) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compI) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compEex) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionIL) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionIR) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionI) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionEcases) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionCommutes) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2Ex) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2W) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2A) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2B) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1Ex) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1Ex1) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1Equiv) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1E) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1I) =>
% 99.02/13.35 ((
% 99.02/13.35 (injFuncInInjFuncSet) =>
% 99.02/13.35 ((
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% 99.02/13.35 (('#B') @ (
% 99.02/13.35 !!) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 !!))) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#S') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
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% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 '#S'))) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 =>))))) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#C') @ in)))) @
% 99.02/13.35 injFuncSet)))))))) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#C') @ in)))) @
% 99.02/13.35 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.35 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl984])).
% 99.02/13.35 thf(zip_derived_cl1015, plain,
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% 99.02/13.35 (((powersetE1) =>
% 99.02/13.35 (((inPowerset) =>
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% 99.02/13.35 (((sepInPowerset) =>
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% 99.02/13.35 (((upairset2IR) =>
% 99.02/13.35 (((binunionIR) =>
% 99.02/13.35 (((binunionEcases) =>
% 99.02/13.35 (((binunionE) =>
% 99.02/13.35 (((binunionLsub) =>
% 99.02/13.35 (((binunionRsub) =>
% 99.02/13.35 (((binintersectI) =>
% 99.02/13.35 (((binintersectSubset5) =>
% 99.02/13.35 (((binintersectEL) =>
% 99.02/13.35 (((binintersectLsub) =>
% 99.02/13.35 (((binintersectSubset2) =>
% 99.02/13.35 (((binintersectSubset3) =>
% 99.02/13.35 (((binintersectER) =>
% 99.02/13.35 (((disjointsetsI1) =>
% 99.02/13.35 (((binintersectRsub) =>
% 99.02/13.35 (((binintersectSubset4) =>
% 99.02/13.35 (((binintersectSubset1) =>
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% 99.02/13.35 (((setminusEL) =>
% 99.02/13.35 (((setminusER) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusSubset2) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusERneg) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusELneg) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusILneg) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusIRneg) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusLsub) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusSubset1) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffE) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffI2) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffIneg1) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffIneg2) =>
% 99.02/13.35 ((
% 99.02/13.35 (secondinupair) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairIL) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairIR) =>
% 99.02/13.35 ((
% 99.02/13.35 (kpairiskpair) =>
% 99.02/13.35 ((
% 99.02/13.35 (kpairp) =>
% 99.02/13.35 ((
% 99.02/13.35 (singletonsubset) =>
% 99.02/13.35 ((
% 99.02/13.35 (singletoninpowerset) =>
% 99.02/13.35 ((
% 99.02/13.35 (singletoninpowunion) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (upairsubunion) =>
% 99.02/13.35 ((
% 99.02/13.35 (upairinpowunion) =>
% 99.02/13.35 ((
% 99.02/13.35 (ubforcartprodlem1) =>
% 99.02/13.35 ((
% 99.02/13.35 (ubforcartprodlem2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ubforcartprodlem3) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairin) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodmempair1) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodmempair) =>
% 99.02/13.35 ((
% 99.02/13.35 (setunionE2) =>
% 99.02/13.35 ((
% 99.02/13.35 (setunionsingleton1) =>
% 99.02/13.35 ((
% 99.02/13.35 (setunionsingleton2) =>
% 99.02/13.35 ((
% 99.02/13.35 (setunionsingleton) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (kfstpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodfstin) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjL2) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjL) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR11) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR12) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR1) =>
% 99.02/13.35 ((
% 99.02/13.35 (upairequniteq) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR2) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR) =>
% 99.02/13.35 ((
% 99.02/13.35 (ksndsingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (ksndpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (kpairsurjEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodsndin) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairmemEL) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairmemER) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodmempaircEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodfstpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodsndpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairsurjEq) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrEL2) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrER) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcImageSingleton) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (app) =>
% 99.02/13.35 ((
% 99.02/13.35 (infuncsetfunc) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2p) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcinfuncset) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (lam2p) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (brelnall2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ex1E2) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp1) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp3) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp2) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcextLem) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp4) =>
% 99.02/13.35 ((
% 99.02/13.35 (subbreln) =>
% 99.02/13.35 ((
% 99.02/13.35 (eqbreln) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcext) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcext2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2apEq1) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2apEq2) =>
% 99.02/13.35 ((
% 99.02/13.35 (beta1) =>
% 99.02/13.35 ((
% 99.02/13.35 (eta1) =>
% 99.02/13.35 ((
% 99.02/13.35 (lam2lamEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (beta2) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (iffalseProp2) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (iftrueProp2) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (binintersectT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (binunionT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (powersetT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (setextT) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (powersetTE1) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (binintersectTERcontra) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT2) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT3) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementE1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementSub1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementSub2) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTnotintersectT) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementImpComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementSubsetComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementInPowersetComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (contraSubsetComplement) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTcontraSubset) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (binunionTIRcontra) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (inIntersectImpInUnion2) =>
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% 99.02/13.35 (intersectInPowersetIntersectUnions) =>
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% 99.02/13.35 (inComplementUnionImpNotIn1) =>
% 99.02/13.35 ((
% 99.02/13.35 (inComplementUnionImpInComplement1) =>
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (complementUnionInPowersetComplement) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (demorgan2b) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule0) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule1) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule3) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule4) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_1) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_3) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_4) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_5) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1all2) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1SetBreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (choice2fnsingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (setOfPairsIsBReln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1all1) =>
% 99.02/13.35 ((
% 99.02/13.35 (subbreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (eqbreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invI) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compI) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compEex) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionIL) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionIR) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionI) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionEcases) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionCommutes) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2Ex) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2W) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2A) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2B) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1Ex) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1Ex1) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1Equiv) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1E) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1I) =>
% 99.02/13.35 ((
% 99.02/13.35 (injFuncInInjFuncSet) =>
% 99.02/13.35 ((
% 99.02/13.35 (!!) @ (
% 99.02/13.35 (('#B') @ (
% 99.02/13.35 !!) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 !!))) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#S') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 '#S') @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 '#S'))) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 =>))))) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#C') @ in)))) @
% 99.02/13.35 injFuncSet)))))))) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#C') @ in)))) @
% 99.02/13.35 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.35 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1000])).
% 99.02/13.35 thf(zip_derived_cl1027, plain,
% 99.02/13.35 (~ (((subsetemptysetimpeq) =>
% 99.02/13.35 (((powersetI1) =>
% 99.02/13.35 (((powersetE1) =>
% 99.02/13.35 (((inPowerset) =>
% 99.02/13.35 (((powersetsubset) =>
% 99.02/13.35 (((sepInPowerset) =>
% 99.02/13.35 (((sepSubset) =>
% 99.02/13.35 (((binunionIL) =>
% 99.02/13.35 (((upairset2IR) =>
% 99.02/13.35 (((binunionIR) =>
% 99.02/13.35 (((binunionEcases) =>
% 99.02/13.35 (((binunionE) =>
% 99.02/13.35 (((binunionLsub) =>
% 99.02/13.35 (((binunionRsub) =>
% 99.02/13.35 (((binintersectI) =>
% 99.02/13.35 (((binintersectSubset5) =>
% 99.02/13.35 (((binintersectEL) =>
% 99.02/13.35 (((binintersectLsub) =>
% 99.02/13.35 (((binintersectSubset2) =>
% 99.02/13.35 (((binintersectSubset3) =>
% 99.02/13.35 (((binintersectER) =>
% 99.02/13.35 (((disjointsetsI1) =>
% 99.02/13.35 (((binintersectRsub) =>
% 99.02/13.35 (((binintersectSubset4) =>
% 99.02/13.35 (((binintersectSubset1) =>
% 99.02/13.35 (((bs114d) =>
% 99.02/13.35 (((setminusI) =>
% 99.02/13.35 (((setminusEL) =>
% 99.02/13.35 (((setminusER) =>
% 99.02/13.35 (((setminusSubset2) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusERneg) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusELneg) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusILneg) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusIRneg) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusLsub) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusSubset1) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffE) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffI2) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffIneg1) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffIneg2) =>
% 99.02/13.35 ((
% 99.02/13.35 (secondinupair) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairIL) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairIR) =>
% 99.02/13.35 ((
% 99.02/13.35 (kpairiskpair) =>
% 99.02/13.35 ((
% 99.02/13.35 (kpairp) =>
% 99.02/13.35 ((
% 99.02/13.35 (singletonsubset) =>
% 99.02/13.35 ((
% 99.02/13.35 (singletoninpowerset) =>
% 99.02/13.35 ((
% 99.02/13.35 (singletoninpowunion) =>
% 99.02/13.35 ((
% 99.02/13.35 (upairset2E) =>
% 99.02/13.35 ((
% 99.02/13.35 (upairsubunion) =>
% 99.02/13.35 ((
% 99.02/13.35 (upairinpowunion) =>
% 99.02/13.35 ((
% 99.02/13.35 (ubforcartprodlem1) =>
% 99.02/13.35 ((
% 99.02/13.35 (ubforcartprodlem2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ubforcartprodlem3) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairin) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodmempair1) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodmempair) =>
% 99.02/13.35 ((
% 99.02/13.35 (setunionE2) =>
% 99.02/13.35 ((
% 99.02/13.35 (setunionsingleton1) =>
% 99.02/13.35 ((
% 99.02/13.35 (setunionsingleton2) =>
% 99.02/13.35 ((
% 99.02/13.35 (setunionsingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (singletonprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (ex1E1) =>
% 99.02/13.35 ((
% 99.02/13.35 (ex1I) =>
% 99.02/13.35 ((
% 99.02/13.35 (ex1I2) =>
% 99.02/13.35 ((
% 99.02/13.35 (singletonsuniq) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjL1) =>
% 99.02/13.35 ((
% 99.02/13.35 (kfstsingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (theprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (kfstpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodfstin) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjL2) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjL) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR11) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR12) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR1) =>
% 99.02/13.35 ((
% 99.02/13.35 (upairequniteq) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR2) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR) =>
% 99.02/13.35 ((
% 99.02/13.35 (ksndsingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (ksndpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (kpairsurjEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodsndin) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairmemEL) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairmemER) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodmempaircEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodfstpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodsndpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairsurjEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrI) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrSub) =>
% 99.02/13.35 ((
% 99.02/13.35 (setOfPairsIsBReln) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrERa) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrEL1) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrEL2) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrER) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcImageSingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (apProp) =>
% 99.02/13.35 ((
% 99.02/13.35 (app) =>
% 99.02/13.35 ((
% 99.02/13.35 (infuncsetfunc) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2p) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcinfuncset) =>
% 99.02/13.35 ((
% 99.02/13.35 (lamProp) =>
% 99.02/13.35 ((
% 99.02/13.35 (lamp) =>
% 99.02/13.35 ((
% 99.02/13.35 (lam2p) =>
% 99.02/13.35 ((
% 99.02/13.35 (brelnall1) =>
% 99.02/13.35 ((
% 99.02/13.35 (brelnall2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ex1E2) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp1) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp3) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp2) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcextLem) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp4) =>
% 99.02/13.35 ((
% 99.02/13.35 (subbreln) =>
% 99.02/13.35 ((
% 99.02/13.35 (eqbreln) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcext) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcext2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2apEq1) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2apEq2) =>
% 99.02/13.35 ((
% 99.02/13.35 (beta1) =>
% 99.02/13.35 ((
% 99.02/13.35 (eta1) =>
% 99.02/13.35 ((
% 99.02/13.35 (lam2lamEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (beta2) =>
% 99.02/13.35 ((
% 99.02/13.35 (eta2) =>
% 99.02/13.35 ((
% 99.02/13.35 (iffalseProp1) =>
% 99.02/13.35 ((
% 99.02/13.35 (iffalseProp2) =>
% 99.02/13.35 ((
% 99.02/13.35 (iftrueProp1) =>
% 99.02/13.35 ((
% 99.02/13.35 (iftrueProp2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ifSingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (ifp) =>
% 99.02/13.35 ((
% 99.02/13.35 (theeq) =>
% 99.02/13.35 ((
% 99.02/13.35 (iftrue) =>
% 99.02/13.35 ((
% 99.02/13.35 (iffalse) =>
% 99.02/13.35 ((
% 99.02/13.35 (iftrueorfalse) =>
% 99.02/13.35 ((
% 99.02/13.35 (binintersectT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (binunionT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (powersetT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (setextT) =>
% 99.02/13.35 ((
% 99.02/13.35 (subsetTI) =>
% 99.02/13.35 ((
% 99.02/13.35 (powersetTI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (powersetTE1) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTE1) =>
% 99.02/13.35 ((
% 99.02/13.35 (binintersectTELcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (binintersectTERcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT1) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT2) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT3) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementE1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementSub1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementSub2) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTnotintersectT) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementImpComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementSubsetComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementInPowersetComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (contraSubsetComplement) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTcontraSubset) =>
% 99.02/13.35 ((
% 99.02/13.35 (binunionTILcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (binunionTIRcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (inIntersectImpInUnion) =>
% 99.02/13.35 ((
% 99.02/13.35 (inIntersectImpInUnion2) =>
% 99.02/13.35 ((
% 99.02/13.35 (inIntersectImpInIntersectUnions) =>
% 99.02/13.35 ((
% 99.02/13.35 (intersectInPowersetIntersectUnions) =>
% 99.02/13.35 ((
% 99.02/13.35 (inComplementUnionImpNotIn1) =>
% 99.02/13.35 ((
% 99.02/13.35 (inComplementUnionImpInComplement1) =>
% 99.02/13.35 ((
% 99.02/13.35 (binunionTE) =>
% 99.02/13.35 ((
% 99.02/13.35 (binunionTEcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2a1) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementUnionInPowersetComplement) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2a2) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan1a) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan1b) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan1) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2a) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2b2) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (demorgan2) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (breln1unionEcases) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (woz2B) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (image1Ex1) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1Equiv) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1E) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1I) =>
% 99.02/13.35 ((
% 99.02/13.35 (injFuncInInjFuncSet) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (setminusIRneg) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (setminusSubset1) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (symdiffI2) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (symdiffIneg2) =>
% 99.02/13.35 ((
% 99.02/13.35 (secondinupair) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairIL) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairIR) =>
% 99.02/13.35 ((
% 99.02/13.35 (kpairiskpair) =>
% 99.02/13.35 ((
% 99.02/13.35 (kpairp) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (singletoninpowerset) =>
% 99.02/13.35 ((
% 99.02/13.35 (singletoninpowunion) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (upairsubunion) =>
% 99.02/13.35 ((
% 99.02/13.35 (upairinpowunion) =>
% 99.02/13.35 ((
% 99.02/13.35 (ubforcartprodlem1) =>
% 99.02/13.35 ((
% 99.02/13.35 (ubforcartprodlem2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ubforcartprodlem3) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairin) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodmempair1) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodmempair) =>
% 99.02/13.35 ((
% 99.02/13.35 (setunionE2) =>
% 99.02/13.35 ((
% 99.02/13.35 (setunionsingleton1) =>
% 99.02/13.35 ((
% 99.02/13.35 (setunionsingleton2) =>
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% 99.02/13.35 (setunionsingleton) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (ex1E1) =>
% 99.02/13.35 ((
% 99.02/13.35 (ex1I) =>
% 99.02/13.35 ((
% 99.02/13.35 (ex1I2) =>
% 99.02/13.35 ((
% 99.02/13.35 (singletonsuniq) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjL1) =>
% 99.02/13.35 ((
% 99.02/13.35 (kfstsingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (theprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (kfstpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodfstin) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjL2) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjL) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR11) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR12) =>
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% 99.02/13.35 (setukpairinjR1) =>
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% 99.02/13.35 (upairequniteq) =>
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% 99.02/13.35 (setukpairinjR2) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR) =>
% 99.02/13.35 ((
% 99.02/13.35 (ksndsingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (ksndpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (kpairsurjEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodsndin) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairmemEL) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairmemER) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodmempaircEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodfstpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodsndpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairsurjEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrI) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrSub) =>
% 99.02/13.35 ((
% 99.02/13.35 (setOfPairsIsBReln) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrERa) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrEL1) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrEL2) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrER) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcImageSingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (apProp) =>
% 99.02/13.35 ((
% 99.02/13.35 (app) =>
% 99.02/13.35 ((
% 99.02/13.35 (infuncsetfunc) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2p) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcinfuncset) =>
% 99.02/13.35 ((
% 99.02/13.35 (lamProp) =>
% 99.02/13.35 ((
% 99.02/13.35 (lamp) =>
% 99.02/13.35 ((
% 99.02/13.35 (lam2p) =>
% 99.02/13.35 ((
% 99.02/13.35 (brelnall1) =>
% 99.02/13.35 ((
% 99.02/13.35 (brelnall2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ex1E2) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp1) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp3) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp2) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcextLem) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp4) =>
% 99.02/13.35 ((
% 99.02/13.35 (subbreln) =>
% 99.02/13.35 ((
% 99.02/13.35 (eqbreln) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcext) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcext2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2apEq1) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2apEq2) =>
% 99.02/13.35 ((
% 99.02/13.35 (beta1) =>
% 99.02/13.35 ((
% 99.02/13.35 (eta1) =>
% 99.02/13.35 ((
% 99.02/13.35 (lam2lamEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (beta2) =>
% 99.02/13.35 ((
% 99.02/13.35 (eta2) =>
% 99.02/13.35 ((
% 99.02/13.35 (iffalseProp1) =>
% 99.02/13.35 ((
% 99.02/13.35 (iffalseProp2) =>
% 99.02/13.35 ((
% 99.02/13.35 (iftrueProp1) =>
% 99.02/13.35 ((
% 99.02/13.35 (iftrueProp2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ifSingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (ifp) =>
% 99.02/13.35 ((
% 99.02/13.35 (theeq) =>
% 99.02/13.35 ((
% 99.02/13.35 (iftrue) =>
% 99.02/13.35 ((
% 99.02/13.35 (iffalse) =>
% 99.02/13.35 ((
% 99.02/13.35 (iftrueorfalse) =>
% 99.02/13.35 ((
% 99.02/13.35 (binintersectT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (binunionT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (powersetT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (setextT) =>
% 99.02/13.35 ((
% 99.02/13.35 (subsetTI) =>
% 99.02/13.35 ((
% 99.02/13.35 (powersetTI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (powersetTE1) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTE1) =>
% 99.02/13.35 ((
% 99.02/13.35 (binintersectTELcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (binintersectTERcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT1) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT2) =>
% 99.02/13.35 ((
% 99.02/13.35 (contrasubsetT3) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementE1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementSub1) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementSub2) =>
% 99.02/13.35 ((
% 99.02/13.35 (doubleComplementEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTnotintersectT) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementImpComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementSubsetComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementInPowersetComplementIntersect) =>
% 99.02/13.35 ((
% 99.02/13.35 (contraSubsetComplement) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementTcontraSubset) =>
% 99.02/13.35 ((
% 99.02/13.35 (binunionTILcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (binunionTIRcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (inIntersectImpInUnion) =>
% 99.02/13.35 ((
% 99.02/13.35 (inIntersectImpInUnion2) =>
% 99.02/13.35 ((
% 99.02/13.35 (inIntersectImpInIntersectUnions) =>
% 99.02/13.35 ((
% 99.02/13.35 (intersectInPowersetIntersectUnions) =>
% 99.02/13.35 ((
% 99.02/13.35 (inComplementUnionImpNotIn1) =>
% 99.02/13.35 ((
% 99.02/13.35 (inComplementUnionImpInComplement1) =>
% 99.02/13.35 ((
% 99.02/13.35 (binunionTE) =>
% 99.02/13.35 ((
% 99.02/13.35 (binunionTEcontra) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2a1) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementUnionInPowersetComplement) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2a2) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan1a) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan1b) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan1) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2a) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2b2) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2b) =>
% 99.02/13.35 ((
% 99.02/13.35 (demorgan2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule0) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule1) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule3) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz13rule4) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_1) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_2) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_3) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_4) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz1_5) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1all2) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1SetBreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (choice2fnsingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (setOfPairsIsBReln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1all1) =>
% 99.02/13.35 ((
% 99.02/13.35 (subbreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (eqbreln1) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invI) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1invE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compI) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1compEex) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionIL) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionIR) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionI) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionE) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionEcases) =>
% 99.02/13.35 ((
% 99.02/13.35 (breln1unionCommutes) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2Ex) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2W) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2A) =>
% 99.02/13.35 ((
% 99.02/13.35 (woz2B) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1Ex) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1Ex1) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1Equiv) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1E) =>
% 99.02/13.35 ((
% 99.02/13.35 (image1I) =>
% 99.02/13.35 ((
% 99.02/13.35 (injFuncInInjFuncSet) =>
% 99.02/13.35 ((
% 99.02/13.35 (!!) @ (
% 99.02/13.35 (('#B') @ (
% 99.02/13.35 !!) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 !!))) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#S') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 '#S') @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 '#S'))) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 =>))))) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#C') @ in)))) @
% 99.02/13.35 injFuncSet)))))))) @
% 99.02/13.35 (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#B') @ (
% 99.02/13.35 (
% 99.02/13.35 ('#C') @ in)))) @
% 99.02/13.35 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.35 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1039])).
% 99.02/13.35 thf(zip_derived_cl1067, plain,
% 99.02/13.35 (~ (((inPowerset) =>
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% 99.02/13.35 (((upairset2IR) =>
% 99.02/13.35 (((binunionIR) =>
% 99.02/13.35 (((binunionEcases) =>
% 99.02/13.35 (((binunionE) =>
% 99.02/13.35 (((binunionLsub) =>
% 99.02/13.35 (((binunionRsub) =>
% 99.02/13.35 (((binintersectI) =>
% 99.02/13.35 (((binintersectSubset5) =>
% 99.02/13.35 (((binintersectEL) =>
% 99.02/13.35 (((binintersectLsub) =>
% 99.02/13.35 (((binintersectSubset2) =>
% 99.02/13.35 (((binintersectSubset3) =>
% 99.02/13.35 (((binintersectER) =>
% 99.02/13.35 (((disjointsetsI1) =>
% 99.02/13.35 (((binintersectRsub) =>
% 99.02/13.35 (((binintersectSubset4) =>
% 99.02/13.35 (((binintersectSubset1) =>
% 99.02/13.35 (((bs114d) =>
% 99.02/13.35 (((setminusI) =>
% 99.02/13.35 (((setminusEL) =>
% 99.02/13.35 (((setminusER) =>
% 99.02/13.35 (((setminusSubset2) =>
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% 99.02/13.35 (((setminusELneg) =>
% 99.02/13.35 (((setminusILneg) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusIRneg) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusLsub) =>
% 99.02/13.35 ((
% 99.02/13.35 (setminusSubset1) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffE) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffI1) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffI2) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffIneg1) =>
% 99.02/13.35 ((
% 99.02/13.35 (symdiffIneg2) =>
% 99.02/13.35 ((
% 99.02/13.35 (secondinupair) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairIL) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairIR) =>
% 99.02/13.35 ((
% 99.02/13.35 (kpairiskpair) =>
% 99.02/13.35 ((
% 99.02/13.35 (kpairp) =>
% 99.02/13.35 ((
% 99.02/13.35 (singletonsubset) =>
% 99.02/13.35 ((
% 99.02/13.35 (singletoninpowerset) =>
% 99.02/13.35 ((
% 99.02/13.35 (singletoninpowunion) =>
% 99.02/13.35 ((
% 99.02/13.35 (upairset2E) =>
% 99.02/13.35 ((
% 99.02/13.35 (upairsubunion) =>
% 99.02/13.35 ((
% 99.02/13.35 (upairinpowunion) =>
% 99.02/13.35 ((
% 99.02/13.35 (ubforcartprodlem1) =>
% 99.02/13.35 ((
% 99.02/13.35 (ubforcartprodlem2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ubforcartprodlem3) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairin) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodmempair1) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodmempair) =>
% 99.02/13.35 ((
% 99.02/13.35 (setunionE2) =>
% 99.02/13.35 ((
% 99.02/13.35 (setunionsingleton1) =>
% 99.02/13.35 ((
% 99.02/13.35 (setunionsingleton2) =>
% 99.02/13.35 ((
% 99.02/13.35 (setunionsingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (singletonprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (ex1E1) =>
% 99.02/13.35 ((
% 99.02/13.35 (ex1I) =>
% 99.02/13.35 ((
% 99.02/13.35 (ex1I2) =>
% 99.02/13.35 ((
% 99.02/13.35 (singletonsuniq) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjL1) =>
% 99.02/13.35 ((
% 99.02/13.35 (kfstsingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (theprop) =>
% 99.02/13.35 ((
% 99.02/13.35 (kfstpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodfstin) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjL2) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjL) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR11) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR12) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR1) =>
% 99.02/13.35 ((
% 99.02/13.35 (upairequniteq) =>
% 99.02/13.35 ((
% 99.02/13.35 (setukpairinjR2) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (ksndpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (kpairsurjEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodsndin) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairmemEL) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairmemER) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodmempaircEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodfstpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodsndpairEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (cartprodpairsurjEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrI) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrSub) =>
% 99.02/13.35 ((
% 99.02/13.35 (setOfPairsIsBReln) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrEL1) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrEL2) =>
% 99.02/13.35 ((
% 99.02/13.35 (dpsetconstrER) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcImageSingleton) =>
% 99.02/13.35 ((
% 99.02/13.35 (apProp) =>
% 99.02/13.35 ((
% 99.02/13.35 (app) =>
% 99.02/13.35 ((
% 99.02/13.35 (infuncsetfunc) =>
% 99.02/13.35 ((
% 99.02/13.35 (ap2p) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcinfuncset) =>
% 99.02/13.35 ((
% 99.02/13.35 (lamProp) =>
% 99.02/13.35 ((
% 99.02/13.35 (lamp) =>
% 99.02/13.35 ((
% 99.02/13.35 (lam2p) =>
% 99.02/13.35 ((
% 99.02/13.35 (brelnall1) =>
% 99.02/13.35 ((
% 99.02/13.35 (brelnall2) =>
% 99.02/13.35 ((
% 99.02/13.35 (ex1E2) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp1) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp3) =>
% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp2) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (funcGraphProp4) =>
% 99.02/13.35 ((
% 99.02/13.35 (subbreln) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (funcext2) =>
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% 99.02/13.35 ((
% 99.02/13.35 (ap2apEq2) =>
% 99.02/13.35 ((
% 99.02/13.35 (beta1) =>
% 99.02/13.35 ((
% 99.02/13.35 (eta1) =>
% 99.02/13.35 ((
% 99.02/13.35 (lam2lamEq) =>
% 99.02/13.35 ((
% 99.02/13.35 (beta2) =>
% 99.02/13.35 ((
% 99.02/13.35 (eta2) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (iffalseProp2) =>
% 99.02/13.35 ((
% 99.02/13.35 (iftrueProp1) =>
% 99.02/13.35 ((
% 99.02/13.35 (iftrueProp2) =>
% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 (iftrue) =>
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% 99.02/13.35 ((
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% 99.02/13.35 ((
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% 99.02/13.35 ((
% 99.02/13.35 (setminusT_lem) =>
% 99.02/13.35 ((
% 99.02/13.35 (complementT_lem) =>
% 99.02/13.35 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (complementTE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectTELcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectTERcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT1) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT2) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT3) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementI1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementSub1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementSub2) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTnotintersectT) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementImpComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementSubsetComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementInPowersetComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (contraSubsetComplement) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTcontraSubset) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTILcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTIRcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInUnion) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInUnion2) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInIntersectUnions) =>
% 99.02/13.36 ((
% 99.02/13.36 (intersectInPowersetIntersectUnions) =>
% 99.02/13.36 ((
% 99.02/13.36 (inComplementUnionImpNotIn1) =>
% 99.02/13.36 ((
% 99.02/13.36 (inComplementUnionImpInComplement1) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTE) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTEcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a1) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementUnionInPowersetComplement) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a2) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1a) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1b) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2b2) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2b) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule0) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule1) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule3) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule4) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_1) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_3) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_4) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_5) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1all2) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1SetBreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (choice2fnsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (setOfPairsIsBReln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1all1) =>
% 99.02/13.36 ((
% 99.02/13.36 (subbreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (eqbreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compEex) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionIL) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionIR) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionEcases) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionCommutes) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2Ex) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2W) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2A) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2B) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Ex) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Ex1) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Equiv) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1E) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1I) =>
% 99.02/13.36 ((
% 99.02/13.36 (injFuncInInjFuncSet) =>
% 99.02/13.36 ((
% 99.02/13.36 (!!) @ (
% 99.02/13.36 (('#B') @ (
% 99.02/13.36 !!) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 !!))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#S') @ (
% 99.02/13.36 (
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% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
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% 99.02/13.36 ('#B') @ (
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% 99.02/13.36 (
% 99.02/13.36 (
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% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 =>))))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
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% 99.02/13.36 injFuncSet)))))))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#C') @ in)))) @
% 99.02/13.36 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1055])).
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% 99.02/13.36 (((binunionRsub) =>
% 99.02/13.36 (((binintersectI) =>
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% 99.02/13.36 (((binintersectEL) =>
% 99.02/13.36 (((binintersectLsub) =>
% 99.02/13.36 (((binintersectSubset2) =>
% 99.02/13.36 (((binintersectSubset3) =>
% 99.02/13.36 (((binintersectER) =>
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% 99.02/13.36 (((binintersectRsub) =>
% 99.02/13.36 (((binintersectSubset4) =>
% 99.02/13.36 (((binintersectSubset1) =>
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (symdiffI2) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (symdiffIneg2) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (kpairp) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletonsubset) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletoninpowerset) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletoninpowunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairset2E) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairsubunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairinpowunion) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempair) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (ex1I2) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL1) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR12) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR1) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairequniteq) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (ksndpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (kpairsurjEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodsndin) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairmemEL) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairmemER) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempaircEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodfstpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodsndpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairsurjEq) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (funcinfuncset) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (lam2p) =>
% 99.02/13.36 ((
% 99.02/13.36 (brelnall1) =>
% 99.02/13.36 ((
% 99.02/13.36 (brelnall2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1E2) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (funcextLem) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp4) =>
% 99.02/13.36 ((
% 99.02/13.36 (subbreln) =>
% 99.02/13.36 ((
% 99.02/13.36 (eqbreln) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcext) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcext2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2apEq1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2apEq2) =>
% 99.02/13.36 ((
% 99.02/13.36 (beta1) =>
% 99.02/13.36 ((
% 99.02/13.36 (eta1) =>
% 99.02/13.36 ((
% 99.02/13.36 (lam2lamEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (beta2) =>
% 99.02/13.36 ((
% 99.02/13.36 (eta2) =>
% 99.02/13.36 ((
% 99.02/13.36 (iffalseProp1) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a2) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1a) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1b) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2b2) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2b) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule0) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule1) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule3) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule4) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_1) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_3) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_4) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_5) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1all2) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1SetBreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (choice2fnsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (setOfPairsIsBReln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1all1) =>
% 99.02/13.36 ((
% 99.02/13.36 (subbreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (eqbreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compEex) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionIL) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionIR) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionEcases) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionCommutes) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2Ex) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2W) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2A) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2B) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Ex) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Ex1) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Equiv) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1E) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1I) =>
% 99.02/13.36 ((
% 99.02/13.36 (injFuncInInjFuncSet) =>
% 99.02/13.36 ((
% 99.02/13.36 (!!) @ (
% 99.02/13.36 (('#B') @ (
% 99.02/13.36 !!) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 !!))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#S') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 '#S') @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 '#S'))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 =>))))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#C') @ in)))) @
% 99.02/13.36 injFuncSet)))))))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#C') @ in)))) @
% 99.02/13.36 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1074])).
% 99.02/13.36 thf(zip_derived_cl1090, plain,
% 99.02/13.36 (~ (((sepSubset) =>
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% 99.02/13.36 (((upairset2IR) =>
% 99.02/13.36 (((binunionIR) =>
% 99.02/13.36 (((binunionEcases) =>
% 99.02/13.36 (((binunionE) =>
% 99.02/13.36 (((binunionLsub) =>
% 99.02/13.36 (((binunionRsub) =>
% 99.02/13.36 (((binintersectI) =>
% 99.02/13.36 (((binintersectSubset5) =>
% 99.02/13.36 (((binintersectEL) =>
% 99.02/13.36 (((binintersectLsub) =>
% 99.02/13.36 (((binintersectSubset2) =>
% 99.02/13.36 (((binintersectSubset3) =>
% 99.02/13.36 (((binintersectER) =>
% 99.02/13.36 (((disjointsetsI1) =>
% 99.02/13.36 (((binintersectRsub) =>
% 99.02/13.36 (((binintersectSubset4) =>
% 99.02/13.36 (((binintersectSubset1) =>
% 99.02/13.36 (((bs114d) =>
% 99.02/13.36 (((setminusI) =>
% 99.02/13.36 (((setminusEL) =>
% 99.02/13.36 (((setminusER) =>
% 99.02/13.36 (((setminusSubset2) =>
% 99.02/13.36 (((setminusERneg) =>
% 99.02/13.36 (((setminusELneg) =>
% 99.02/13.36 (((setminusILneg) =>
% 99.02/13.36 (((setminusIRneg) =>
% 99.02/13.36 (((setminusLsub) =>
% 99.02/13.36 (((setminusSubset1) =>
% 99.02/13.36 ((
% 99.02/13.36 (symdiffE) =>
% 99.02/13.36 ((
% 99.02/13.36 (symdiffI1) =>
% 99.02/13.36 ((
% 99.02/13.36 (symdiffI2) =>
% 99.02/13.36 ((
% 99.02/13.36 (symdiffIneg1) =>
% 99.02/13.36 ((
% 99.02/13.36 (symdiffIneg2) =>
% 99.02/13.36 ((
% 99.02/13.36 (secondinupair) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairIL) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairIR) =>
% 99.02/13.36 ((
% 99.02/13.36 (kpairiskpair) =>
% 99.02/13.36 ((
% 99.02/13.36 (kpairp) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletonsubset) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletoninpowerset) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletoninpowunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairset2E) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairsubunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairinpowunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem3) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairin) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempair1) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempair) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionE2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionsingleton1) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionsingleton2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletonprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1E1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1I) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1I2) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletonsuniq) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL1) =>
% 99.02/13.36 ((
% 99.02/13.36 (kfstsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (theprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (kfstpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodfstin) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR11) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR12) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR1) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairequniteq) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR) =>
% 99.02/13.36 ((
% 99.02/13.36 (ksndsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (ksndpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (kpairsurjEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodsndin) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairmemEL) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairmemER) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempaircEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodfstpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodsndpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairsurjEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrI) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrSub) =>
% 99.02/13.36 ((
% 99.02/13.36 (setOfPairsIsBReln) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrERa) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrEL1) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrEL2) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrER) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcImageSingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (apProp) =>
% 99.02/13.36 ((
% 99.02/13.36 (app) =>
% 99.02/13.36 ((
% 99.02/13.36 (infuncsetfunc) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2p) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcinfuncset) =>
% 99.02/13.36 ((
% 99.02/13.36 (lamProp) =>
% 99.02/13.36 ((
% 99.02/13.36 (lamp) =>
% 99.02/13.36 ((
% 99.02/13.36 (lam2p) =>
% 99.02/13.36 ((
% 99.02/13.36 (brelnall1) =>
% 99.02/13.36 ((
% 99.02/13.36 (brelnall2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1E2) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp1) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp3) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp2) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcextLem) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp4) =>
% 99.02/13.36 ((
% 99.02/13.36 (subbreln) =>
% 99.02/13.36 ((
% 99.02/13.36 (eqbreln) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcext) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcext2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2apEq1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2apEq2) =>
% 99.02/13.36 ((
% 99.02/13.36 (beta1) =>
% 99.02/13.36 ((
% 99.02/13.36 (eta1) =>
% 99.02/13.36 ((
% 99.02/13.36 (lam2lamEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (beta2) =>
% 99.02/13.36 ((
% 99.02/13.36 (eta2) =>
% 99.02/13.36 ((
% 99.02/13.36 (iffalseProp1) =>
% 99.02/13.36 ((
% 99.02/13.36 (iffalseProp2) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrueProp1) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrueProp2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ifSingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (ifp) =>
% 99.02/13.36 ((
% 99.02/13.36 (theeq) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrue) =>
% 99.02/13.36 ((
% 99.02/13.36 (iffalse) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrueorfalse) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (powersetT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (setminusT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (setextT) =>
% 99.02/13.36 ((
% 99.02/13.36 (subsetTI) =>
% 99.02/13.36 ((
% 99.02/13.36 (powersetTI1) =>
% 99.02/13.36 ((
% 99.02/13.36 (powersetTE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTI1) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectTELcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectTERcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT1) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT2) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT3) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementI1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementSub1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementSub2) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTnotintersectT) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementImpComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementSubsetComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementInPowersetComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (contraSubsetComplement) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTcontraSubset) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTILcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTIRcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInUnion) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInUnion2) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInIntersectUnions) =>
% 99.02/13.36 ((
% 99.02/13.36 (intersectInPowersetIntersectUnions) =>
% 99.02/13.36 ((
% 99.02/13.36 (inComplementUnionImpNotIn1) =>
% 99.02/13.36 ((
% 99.02/13.36 (inComplementUnionImpInComplement1) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTE) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTEcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a1) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementUnionInPowersetComplement) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a2) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1a) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1b) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2b2) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2b) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (breln1invE) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (breln1compE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compEex) =>
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1090])).
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% 99.02/13.36 ((
% 99.02/13.36 (setukpairIR) =>
% 99.02/13.36 ((
% 99.02/13.36 (kpairiskpair) =>
% 99.02/13.36 ((
% 99.02/13.36 (kpairp) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletonsubset) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletoninpowerset) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletoninpowunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairset2E) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairsubunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairinpowunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem3) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairin) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempair1) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempair) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionE2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionsingleton1) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionsingleton2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletonprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1E1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1I) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1I2) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletonsuniq) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL1) =>
% 99.02/13.36 ((
% 99.02/13.36 (kfstsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (theprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (kfstpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodfstin) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR11) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR12) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR1) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairequniteq) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR) =>
% 99.02/13.36 ((
% 99.02/13.36 (ksndsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (ksndpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (kpairsurjEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodsndin) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairmemEL) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairmemER) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempaircEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodfstpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodsndpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairsurjEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrI) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrSub) =>
% 99.02/13.36 ((
% 99.02/13.36 (setOfPairsIsBReln) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrERa) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrEL1) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrEL2) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrER) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcImageSingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (apProp) =>
% 99.02/13.36 ((
% 99.02/13.36 (app) =>
% 99.02/13.36 ((
% 99.02/13.36 (infuncsetfunc) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2p) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcinfuncset) =>
% 99.02/13.36 ((
% 99.02/13.36 (lamProp) =>
% 99.02/13.36 ((
% 99.02/13.36 (lamp) =>
% 99.02/13.36 ((
% 99.02/13.36 (lam2p) =>
% 99.02/13.36 ((
% 99.02/13.36 (brelnall1) =>
% 99.02/13.36 ((
% 99.02/13.36 (brelnall2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1E2) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp1) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp3) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp2) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcextLem) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp4) =>
% 99.02/13.36 ((
% 99.02/13.36 (subbreln) =>
% 99.02/13.36 ((
% 99.02/13.36 (eqbreln) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcext) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcext2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2apEq1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2apEq2) =>
% 99.02/13.36 ((
% 99.02/13.36 (beta1) =>
% 99.02/13.36 ((
% 99.02/13.36 (eta1) =>
% 99.02/13.36 ((
% 99.02/13.36 (lam2lamEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (beta2) =>
% 99.02/13.36 ((
% 99.02/13.36 (eta2) =>
% 99.02/13.36 ((
% 99.02/13.36 (iffalseProp1) =>
% 99.02/13.36 ((
% 99.02/13.36 (iffalseProp2) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrueProp1) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrueProp2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ifSingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (ifp) =>
% 99.02/13.36 ((
% 99.02/13.36 (theeq) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrue) =>
% 99.02/13.36 ((
% 99.02/13.36 (iffalse) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrueorfalse) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (powersetT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (setminusT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (setextT) =>
% 99.02/13.36 ((
% 99.02/13.36 (subsetTI) =>
% 99.02/13.36 ((
% 99.02/13.36 (powersetTI1) =>
% 99.02/13.36 ((
% 99.02/13.36 (powersetTE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTI1) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectTELcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectTERcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT1) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT2) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT3) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementI1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementSub1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementSub2) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTnotintersectT) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementImpComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementSubsetComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementInPowersetComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (contraSubsetComplement) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTcontraSubset) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTILcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTIRcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInUnion) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInUnion2) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInIntersectUnions) =>
% 99.02/13.36 ((
% 99.02/13.36 (intersectInPowersetIntersectUnions) =>
% 99.02/13.36 ((
% 99.02/13.36 (inComplementUnionImpNotIn1) =>
% 99.02/13.36 ((
% 99.02/13.36 (inComplementUnionImpInComplement1) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTE) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTEcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a1) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementUnionInPowersetComplement) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a2) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1a) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1b) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2b2) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2b) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule0) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule1) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule3) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule4) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_1) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_3) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_4) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_5) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1all2) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1SetBreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (choice2fnsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (setOfPairsIsBReln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1all1) =>
% 99.02/13.36 ((
% 99.02/13.36 (subbreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (eqbreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compEex) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionIL) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionIR) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionEcases) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionCommutes) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2Ex) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2W) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2A) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2B) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Ex) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Ex1) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Equiv) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1E) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1I) =>
% 99.02/13.36 ((
% 99.02/13.36 (injFuncInInjFuncSet) =>
% 99.02/13.36 ((
% 99.02/13.36 (!!) @ (
% 99.02/13.36 (('#B') @ (
% 99.02/13.36 !!) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 !!))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#S') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 '#S') @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 '#S'))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 =>))))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#C') @ in)))) @
% 99.02/13.36 injFuncSet)))))))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#C') @ in)))) @
% 99.02/13.36 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1096])).
% 99.02/13.36 thf(zip_derived_cl1109, plain,
% 99.02/13.36 (~ (((binunionIR) =>
% 99.02/13.36 (((binunionEcases) =>
% 99.02/13.36 (((binunionE) =>
% 99.02/13.36 (((binunionLsub) =>
% 99.02/13.36 (((binunionRsub) =>
% 99.02/13.36 (((binintersectI) =>
% 99.02/13.36 (((binintersectSubset5) =>
% 99.02/13.36 (((binintersectEL) =>
% 99.02/13.36 (((binintersectLsub) =>
% 99.02/13.36 (((binintersectSubset2) =>
% 99.02/13.36 (((binintersectSubset3) =>
% 99.02/13.36 (((binintersectER) =>
% 99.02/13.36 (((disjointsetsI1) =>
% 99.02/13.36 (((binintersectRsub) =>
% 99.02/13.36 (((binintersectSubset4) =>
% 99.02/13.36 (((binintersectSubset1) =>
% 99.02/13.36 (((bs114d) =>
% 99.02/13.36 (((setminusI) =>
% 99.02/13.36 (((setminusEL) =>
% 99.02/13.36 (((setminusER) =>
% 99.02/13.36 (((setminusSubset2) =>
% 99.02/13.36 (((setminusERneg) =>
% 99.02/13.36 (((setminusELneg) =>
% 99.02/13.36 (((setminusILneg) =>
% 99.02/13.36 (((setminusIRneg) =>
% 99.02/13.36 (((setminusLsub) =>
% 99.02/13.36 (((setminusSubset1) =>
% 99.02/13.36 (((symdiffE) =>
% 99.02/13.36 (((symdiffI1) =>
% 99.02/13.36 (((symdiffI2) =>
% 99.02/13.36 ((
% 99.02/13.36 (symdiffIneg1) =>
% 99.02/13.36 ((
% 99.02/13.36 (symdiffIneg2) =>
% 99.02/13.36 ((
% 99.02/13.36 (secondinupair) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairIL) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairIR) =>
% 99.02/13.36 ((
% 99.02/13.36 (kpairiskpair) =>
% 99.02/13.36 ((
% 99.02/13.36 (kpairp) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletonsubset) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletoninpowerset) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletoninpowunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairset2E) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairsubunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairinpowunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem3) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairin) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempair1) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempair) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionE2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionsingleton1) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionsingleton2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletonprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1E1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1I) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1I2) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletonsuniq) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL1) =>
% 99.02/13.36 ((
% 99.02/13.36 (kfstsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (theprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (kfstpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodfstin) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR11) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR12) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR1) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairequniteq) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR) =>
% 99.02/13.36 ((
% 99.02/13.36 (ksndsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (ksndpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (kpairsurjEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodsndin) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairmemEL) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairmemER) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempaircEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodfstpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodsndpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairsurjEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrI) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrSub) =>
% 99.02/13.36 ((
% 99.02/13.36 (setOfPairsIsBReln) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrERa) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrEL1) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrEL2) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrER) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcImageSingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (apProp) =>
% 99.02/13.36 ((
% 99.02/13.36 (app) =>
% 99.02/13.36 ((
% 99.02/13.36 (infuncsetfunc) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2p) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcinfuncset) =>
% 99.02/13.36 ((
% 99.02/13.36 (lamProp) =>
% 99.02/13.36 ((
% 99.02/13.36 (lamp) =>
% 99.02/13.36 ((
% 99.02/13.36 (lam2p) =>
% 99.02/13.36 ((
% 99.02/13.36 (brelnall1) =>
% 99.02/13.36 ((
% 99.02/13.36 (brelnall2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1E2) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp1) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp3) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp2) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcextLem) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp4) =>
% 99.02/13.36 ((
% 99.02/13.36 (subbreln) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (funcext) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcext2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2apEq1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2apEq2) =>
% 99.02/13.36 ((
% 99.02/13.36 (beta1) =>
% 99.02/13.36 ((
% 99.02/13.36 (eta1) =>
% 99.02/13.36 ((
% 99.02/13.36 (lam2lamEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (beta2) =>
% 99.02/13.36 ((
% 99.02/13.36 (eta2) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (iffalseProp2) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrueProp1) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (iftrue) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (binunionT_lem) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (setminusT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (setextT) =>
% 99.02/13.36 ((
% 99.02/13.36 (subsetTI) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (powersetTE1) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (complementTE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectTELcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectTERcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT1) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT2) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT3) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementI1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementSub1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementSub2) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTnotintersectT) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementImpComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementSubsetComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementInPowersetComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (contraSubsetComplement) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTcontraSubset) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTILcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTIRcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInUnion) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInUnion2) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInIntersectUnions) =>
% 99.02/13.36 ((
% 99.02/13.36 (intersectInPowersetIntersectUnions) =>
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% 99.02/13.36 (inComplementUnionImpNotIn1) =>
% 99.02/13.36 ((
% 99.02/13.36 (inComplementUnionImpInComplement1) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTE) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTEcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a1) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementUnionInPowersetComplement) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a2) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1a) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1b) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2b2) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2b) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule0) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule1) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule3) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule4) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_1) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_3) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_4) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_5) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1all2) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1SetBreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (choice2fnsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (setOfPairsIsBReln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1all1) =>
% 99.02/13.36 ((
% 99.02/13.36 (subbreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (eqbreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compEex) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionIL) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionIR) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionEcases) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionCommutes) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2Ex) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2W) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2A) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2B) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Ex) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Ex1) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Equiv) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1E) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1I) =>
% 99.02/13.36 ((
% 99.02/13.36 (injFuncInInjFuncSet) =>
% 99.02/13.36 ((
% 99.02/13.36 (!!) @ (
% 99.02/13.36 (('#B') @ (
% 99.02/13.36 !!) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 !!))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#S') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
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% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
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% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 =>))))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#C') @ in)))) @
% 99.02/13.36 injFuncSet)))))))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#C') @ in)))) @
% 99.02/13.36 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1102])).
% 99.02/13.36 thf(zip_derived_cl1115, plain,
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% 99.02/13.36 (((binunionLsub) =>
% 99.02/13.36 (((binunionRsub) =>
% 99.02/13.36 (((binintersectI) =>
% 99.02/13.36 (((binintersectSubset5) =>
% 99.02/13.36 (((binintersectEL) =>
% 99.02/13.36 (((binintersectLsub) =>
% 99.02/13.36 (((binintersectSubset2) =>
% 99.02/13.36 (((binintersectSubset3) =>
% 99.02/13.36 (((binintersectER) =>
% 99.02/13.36 (((disjointsetsI1) =>
% 99.02/13.36 (((binintersectRsub) =>
% 99.02/13.36 (((binintersectSubset4) =>
% 99.02/13.36 (((binintersectSubset1) =>
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% 99.02/13.36 (((setminusI) =>
% 99.02/13.36 (((setminusEL) =>
% 99.02/13.36 (((setminusER) =>
% 99.02/13.36 (((setminusSubset2) =>
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% 99.02/13.36 (((setminusELneg) =>
% 99.02/13.36 (((setminusILneg) =>
% 99.02/13.36 (((setminusIRneg) =>
% 99.02/13.36 (((setminusLsub) =>
% 99.02/13.36 (((setminusSubset1) =>
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% 99.02/13.36 (((symdiffI1) =>
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% 99.02/13.36 ((
% 99.02/13.36 (symdiffIneg2) =>
% 99.02/13.36 ((
% 99.02/13.36 (secondinupair) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairIL) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairIR) =>
% 99.02/13.36 ((
% 99.02/13.36 (kpairiskpair) =>
% 99.02/13.36 ((
% 99.02/13.36 (kpairp) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletonsubset) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletoninpowerset) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletoninpowunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairset2E) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairsubunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairinpowunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem3) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairin) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempair1) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempair) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionE2) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL1) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (kfstpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodfstin) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR11) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR12) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR1) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairequniteq) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR) =>
% 99.02/13.36 ((
% 99.02/13.36 (ksndsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (ksndpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (kpairsurjEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodsndin) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairmemEL) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairmemER) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempaircEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodfstpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodsndpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairsurjEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrI) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrSub) =>
% 99.02/13.36 ((
% 99.02/13.36 (setOfPairsIsBReln) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrERa) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrEL2) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrER) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (funcinfuncset) =>
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (brelnall1) =>
% 99.02/13.36 ((
% 99.02/13.36 (brelnall2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1E2) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp1) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp3) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp2) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcextLem) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp4) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (funcext2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2apEq1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2apEq2) =>
% 99.02/13.36 ((
% 99.02/13.36 (beta1) =>
% 99.02/13.36 ((
% 99.02/13.36 (eta1) =>
% 99.02/13.36 ((
% 99.02/13.36 (lam2lamEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (beta2) =>
% 99.02/13.36 ((
% 99.02/13.36 (eta2) =>
% 99.02/13.36 ((
% 99.02/13.36 (iffalseProp1) =>
% 99.02/13.36 ((
% 99.02/13.36 (iffalseProp2) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrueProp1) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrueProp2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ifSingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (ifp) =>
% 99.02/13.36 ((
% 99.02/13.36 (theeq) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrue) =>
% 99.02/13.36 ((
% 99.02/13.36 (iffalse) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrueorfalse) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (powersetT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (setminusT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (setextT) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (powersetTI1) =>
% 99.02/13.36 ((
% 99.02/13.36 (powersetTE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTI1) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectTELcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectTERcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT2) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT3) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementI1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementSub1) =>
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% 99.02/13.36 (doubleComplementSub2) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementEq) =>
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% 99.02/13.36 (complementTnotintersectT) =>
% 99.02/13.36 ((
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% 99.02/13.36 (complementSubsetComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementInPowersetComplementIntersect) =>
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% 99.02/13.36 (contraSubsetComplement) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTcontraSubset) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (binunionTIRcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInUnion) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInUnion2) =>
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% 99.02/13.36 (inIntersectImpInIntersectUnions) =>
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% 99.02/13.36 (inComplementUnionImpInComplement1) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a1) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementUnionInPowersetComplement) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a2) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1a) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1b) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2b2) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2b) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule0) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule1) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule3) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule4) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_1) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_3) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_4) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_5) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1all2) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1SetBreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (choice2fnsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (setOfPairsIsBReln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1all1) =>
% 99.02/13.36 ((
% 99.02/13.36 (subbreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (eqbreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compEex) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionIL) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionIR) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionEcases) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionCommutes) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2Ex) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2W) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2A) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2B) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Ex) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Ex1) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Equiv) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1E) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1I) =>
% 99.02/13.36 ((
% 99.02/13.36 (injFuncInInjFuncSet) =>
% 99.02/13.36 ((
% 99.02/13.36 (!!) @ (
% 99.02/13.36 (('#B') @ (
% 99.02/13.36 !!) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 !!))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#S') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
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% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 '#S'))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 =>))))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#C') @ in)))) @
% 99.02/13.36 injFuncSet)))))))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#C') @ in)))) @
% 99.02/13.36 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1109])).
% 99.02/13.36 thf(zip_derived_cl1121, plain,
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% 99.02/13.36 (((binunionRsub) =>
% 99.02/13.36 (((binintersectI) =>
% 99.02/13.36 (((binintersectSubset5) =>
% 99.02/13.36 (((binintersectEL) =>
% 99.02/13.36 (((binintersectLsub) =>
% 99.02/13.36 (((binintersectSubset2) =>
% 99.02/13.36 (((binintersectSubset3) =>
% 99.02/13.36 (((binintersectER) =>
% 99.02/13.36 (((disjointsetsI1) =>
% 99.02/13.36 (((binintersectRsub) =>
% 99.02/13.36 (((binintersectSubset4) =>
% 99.02/13.36 (((binintersectSubset1) =>
% 99.02/13.36 (((bs114d) =>
% 99.02/13.36 (((setminusI) =>
% 99.02/13.36 (((setminusEL) =>
% 99.02/13.36 (((setminusER) =>
% 99.02/13.36 (((setminusSubset2) =>
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% 99.02/13.36 (((setminusELneg) =>
% 99.02/13.36 (((setminusILneg) =>
% 99.02/13.36 (((setminusIRneg) =>
% 99.02/13.36 (((setminusLsub) =>
% 99.02/13.36 (((setminusSubset1) =>
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% 99.02/13.36 (((symdiffI1) =>
% 99.02/13.36 (((symdiffI2) =>
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% 99.02/13.36 (((symdiffIneg2) =>
% 99.02/13.36 ((
% 99.02/13.36 (secondinupair) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairIL) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairIR) =>
% 99.02/13.36 ((
% 99.02/13.36 (kpairiskpair) =>
% 99.02/13.36 ((
% 99.02/13.36 (kpairp) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletonsubset) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletoninpowerset) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletoninpowunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairset2E) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairsubunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairinpowunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem3) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairin) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempair1) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempair) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionE2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionsingleton1) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionsingleton2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionsingleton) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (ex1E1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1I) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1I2) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletonsuniq) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL1) =>
% 99.02/13.36 ((
% 99.02/13.36 (kfstsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (theprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (kfstpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodfstin) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR11) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR12) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR1) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairequniteq) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR) =>
% 99.02/13.36 ((
% 99.02/13.36 (ksndsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (ksndpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (kpairsurjEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodsndin) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairmemEL) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairmemER) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempaircEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodfstpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodsndpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairsurjEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrI) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrSub) =>
% 99.02/13.36 ((
% 99.02/13.36 (setOfPairsIsBReln) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrERa) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrEL1) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrEL2) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrER) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (funcinfuncset) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (brelnall2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1E2) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp1) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp3) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp2) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcextLem) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp4) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (funcext2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2apEq1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2apEq2) =>
% 99.02/13.36 ((
% 99.02/13.36 (beta1) =>
% 99.02/13.36 ((
% 99.02/13.36 (eta1) =>
% 99.02/13.36 ((
% 99.02/13.36 (lam2lamEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (beta2) =>
% 99.02/13.36 ((
% 99.02/13.36 (eta2) =>
% 99.02/13.36 ((
% 99.02/13.36 (iffalseProp1) =>
% 99.02/13.36 ((
% 99.02/13.36 (iffalseProp2) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrueProp1) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrueProp2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ifSingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (ifp) =>
% 99.02/13.36 ((
% 99.02/13.36 (theeq) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrue) =>
% 99.02/13.36 ((
% 99.02/13.36 (iffalse) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrueorfalse) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (powersetT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (setminusT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (setextT) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (binintersectTERcontra) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT1) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT2) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT3) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementI1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementSub1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementSub2) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTnotintersectT) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementImpComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementSubsetComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementInPowersetComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (contraSubsetComplement) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTcontraSubset) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (binunionTIRcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInUnion) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInUnion2) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInIntersectUnions) =>
% 99.02/13.36 ((
% 99.02/13.36 (intersectInPowersetIntersectUnions) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (inComplementUnionImpInComplement1) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (eta1) =>
% 99.02/13.36 ((
% 99.02/13.36 (lam2lamEq) =>
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 (doubleComplementSub2) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (demorgan2b) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 injFuncSet)))))))) @
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% 99.02/13.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1121])).
% 99.02/13.36 thf(zip_derived_cl1135, plain,
% 99.02/13.36 (~ (((binunionRsub) =>
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% 99.02/13.36 (ksndpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (kpairsurjEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodsndin) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairmemEL) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairmemER) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempaircEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodfstpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodsndpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairsurjEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrI) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrSub) =>
% 99.02/13.36 ((
% 99.02/13.36 (setOfPairsIsBReln) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrERa) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrEL1) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrEL2) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrER) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcImageSingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (apProp) =>
% 99.02/13.36 ((
% 99.02/13.36 (app) =>
% 99.02/13.36 ((
% 99.02/13.36 (infuncsetfunc) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2p) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcinfuncset) =>
% 99.02/13.36 ((
% 99.02/13.36 (lamProp) =>
% 99.02/13.36 ((
% 99.02/13.36 (lamp) =>
% 99.02/13.36 ((
% 99.02/13.36 (lam2p) =>
% 99.02/13.36 ((
% 99.02/13.36 (brelnall1) =>
% 99.02/13.36 ((
% 99.02/13.36 (brelnall2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1E2) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp1) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp3) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp2) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcextLem) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp4) =>
% 99.02/13.36 ((
% 99.02/13.36 (subbreln) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (funcext) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcext2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2apEq1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2apEq2) =>
% 99.02/13.36 ((
% 99.02/13.36 (beta1) =>
% 99.02/13.36 ((
% 99.02/13.36 (eta1) =>
% 99.02/13.36 ((
% 99.02/13.36 (lam2lamEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (beta2) =>
% 99.02/13.36 ((
% 99.02/13.36 (eta2) =>
% 99.02/13.36 ((
% 99.02/13.36 (iffalseProp1) =>
% 99.02/13.36 ((
% 99.02/13.36 (iffalseProp2) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrueProp1) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrueProp2) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (ifp) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (iftrue) =>
% 99.02/13.36 ((
% 99.02/13.36 (iffalse) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrueorfalse) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (powersetT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (setminusT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (setextT) =>
% 99.02/13.36 ((
% 99.02/13.36 (subsetTI) =>
% 99.02/13.36 ((
% 99.02/13.36 (powersetTI1) =>
% 99.02/13.36 ((
% 99.02/13.36 (powersetTE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTI1) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectTELcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectTERcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT1) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT2) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT3) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementI1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementSub1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementSub2) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTnotintersectT) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementImpComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementSubsetComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementInPowersetComplementIntersect) =>
% 99.02/13.36 ((
% 99.02/13.36 (contraSubsetComplement) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTcontraSubset) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTILcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTIRcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInUnion) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInUnion2) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInIntersectUnions) =>
% 99.02/13.36 ((
% 99.02/13.36 (intersectInPowersetIntersectUnions) =>
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% 99.02/13.36 (inComplementUnionImpNotIn1) =>
% 99.02/13.36 ((
% 99.02/13.36 (inComplementUnionImpInComplement1) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTE) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTEcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a1) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementUnionInPowersetComplement) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a2) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1a) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1b) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2b2) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2b) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule0) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule1) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule3) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule4) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_1) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_3) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_4) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_5) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1all2) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1SetBreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (choice2fnsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (setOfPairsIsBReln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1all1) =>
% 99.02/13.36 ((
% 99.02/13.36 (subbreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (eqbreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compEex) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionIL) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionIR) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionEcases) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionCommutes) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2Ex) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2W) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2A) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2B) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Ex) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Ex1) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Equiv) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1E) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1I) =>
% 99.02/13.36 ((
% 99.02/13.36 (injFuncInInjFuncSet) =>
% 99.02/13.36 ((
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% 99.02/13.36 (('#B') @ (
% 99.02/13.36 !!) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
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% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#S') @ (
% 99.02/13.36 (
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% 99.02/13.36 (
% 99.02/13.36 (
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% 99.02/13.36 (
% 99.02/13.36 (
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% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 =>))))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
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% 99.02/13.36 injFuncSet)))))))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#C') @ in)))) @
% 99.02/13.36 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1128])).
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% 99.02/13.36 (((binintersectRsub) =>
% 99.02/13.36 (((binintersectSubset4) =>
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% 99.02/13.36 (((setminusEL) =>
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (singletoninpowunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairset2E) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairsubunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairinpowunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem3) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairin) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempair1) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempair) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionE2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionsingleton1) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (kfstpairEq) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjL) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR11) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR12) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR1) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairequniteq) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (kpairsurjEq) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairmemEL) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairmemER) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempaircEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodfstpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodsndpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairsurjEq) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrSub) =>
% 99.02/13.36 ((
% 99.02/13.36 (setOfPairsIsBReln) =>
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% 99.02/13.36 (dpsetconstrEL1) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrEL2) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrER) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (app) =>
% 99.02/13.36 ((
% 99.02/13.36 (infuncsetfunc) =>
% 99.02/13.36 ((
% 99.02/13.36 (ap2p) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcinfuncset) =>
% 99.02/13.36 ((
% 99.02/13.36 (lamProp) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (lam2p) =>
% 99.02/13.36 ((
% 99.02/13.36 (brelnall1) =>
% 99.02/13.36 ((
% 99.02/13.36 (brelnall2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ex1E2) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp1) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp3) =>
% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp2) =>
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% 99.02/13.36 ((
% 99.02/13.36 (funcGraphProp4) =>
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% 99.02/13.36 (funcext2) =>
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% 99.02/13.36 ((
% 99.02/13.36 (ap2apEq2) =>
% 99.02/13.36 ((
% 99.02/13.36 (beta1) =>
% 99.02/13.36 ((
% 99.02/13.36 (eta1) =>
% 99.02/13.36 ((
% 99.02/13.36 (lam2lamEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (beta2) =>
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% 99.02/13.36 (iffalseProp2) =>
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 (complementTE1) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (binintersectTERcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT) =>
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% 99.02/13.36 (contrasubsetT1) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT2) =>
% 99.02/13.36 ((
% 99.02/13.36 (contrasubsetT3) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementI1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementE1) =>
% 99.02/13.36 ((
% 99.02/13.36 (doubleComplementSub1) =>
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% 99.02/13.36 (doubleComplementSub2) =>
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% 99.02/13.36 (complementSubsetComplementIntersect) =>
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% 99.02/13.36 (complementInPowersetComplementIntersect) =>
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% 99.02/13.36 (contraSubsetComplement) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementTcontraSubset) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTILcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionTIRcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInUnion) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInUnion2) =>
% 99.02/13.36 ((
% 99.02/13.36 (inIntersectImpInIntersectUnions) =>
% 99.02/13.36 ((
% 99.02/13.36 (intersectInPowersetIntersectUnions) =>
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% 99.02/13.36 (inComplementUnionImpInComplement1) =>
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% 99.02/13.36 (binunionTEcontra) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a1) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementUnionInPowersetComplement) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a2) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1a) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1b) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan1) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2a) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2b2) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2b) =>
% 99.02/13.36 ((
% 99.02/13.36 (demorgan2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule0) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule1) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule3) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz13rule4) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_1) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_2) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_3) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_4) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz1_5) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1all2) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1SetBreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (choice2fnsingleton) =>
% 99.02/13.36 ((
% 99.02/13.36 (setOfPairsIsBReln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1all1) =>
% 99.02/13.36 ((
% 99.02/13.36 (subbreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (eqbreln1) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1invE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1compEex) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionprop) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionIL) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionIR) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionI) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionE) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionEcases) =>
% 99.02/13.36 ((
% 99.02/13.36 (breln1unionCommutes) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2Ex) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2W) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2A) =>
% 99.02/13.36 ((
% 99.02/13.36 (woz2B) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Ex) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Ex1) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1Equiv) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1E) =>
% 99.02/13.36 ((
% 99.02/13.36 (image1I) =>
% 99.02/13.36 ((
% 99.02/13.36 (injFuncInInjFuncSet) =>
% 99.02/13.36 ((
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% 99.02/13.36 (('#B') @ (
% 99.02/13.36 !!) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
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% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#S') @ (
% 99.02/13.36 (
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% 99.02/13.36 (
% 99.02/13.36 (
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% 99.02/13.36 (
% 99.02/13.36 (
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% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 =>))))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
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% 99.02/13.36 injFuncSet)))))))) @
% 99.02/13.36 (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#B') @ (
% 99.02/13.36 (
% 99.02/13.36 ('#C') @ in)))) @
% 99.02/13.36 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1135])).
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% 99.02/13.36 (((binintersectSubset4) =>
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% 99.02/13.36 ((
% 99.02/13.36 (singletoninpowerset) =>
% 99.02/13.36 ((
% 99.02/13.36 (singletoninpowunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairset2E) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairsubunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairinpowunion) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem1) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem2) =>
% 99.02/13.36 ((
% 99.02/13.36 (ubforcartprodlem3) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairin) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempair1) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempair) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionE2) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionsingleton1) =>
% 99.02/13.36 ((
% 99.02/13.36 (setunionsingleton2) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR12) =>
% 99.02/13.36 ((
% 99.02/13.36 (setukpairinjR1) =>
% 99.02/13.36 ((
% 99.02/13.36 (upairequniteq) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairmemER) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodmempaircEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodfstpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodsndpairEq) =>
% 99.02/13.36 ((
% 99.02/13.36 (cartprodpairsurjEq) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrSub) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrEL2) =>
% 99.02/13.36 ((
% 99.02/13.36 (dpsetconstrER) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (beta2) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (iffalseProp2) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (iftrueProp2) =>
% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
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% 99.02/13.36 ((
% 99.02/13.36 (iftrue) =>
% 99.02/13.36 ((
% 99.02/13.36 (iffalse) =>
% 99.02/13.36 ((
% 99.02/13.36 (iftrueorfalse) =>
% 99.02/13.36 ((
% 99.02/13.36 (binintersectT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (binunionT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (powersetT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (setminusT_lem) =>
% 99.02/13.36 ((
% 99.02/13.36 (complementT_lem) =>
% 99.02/13.36 ((
% 99.02/13.37 (setextT) =>
% 99.02/13.37 ((
% 99.02/13.37 (subsetTI) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTE1) =>
% 99.02/13.37 ((
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% 99.02/13.37 ((
% 99.02/13.37 (complementTE1) =>
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% 99.02/13.37 ((
% 99.02/13.37 (binintersectTERcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT1) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT2) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT3) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub2) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTnotintersectT) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementImpComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementSubsetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementInPowersetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (contraSubsetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTcontraSubset) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTILcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTIRcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion2) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (intersectInPowersetIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpNotIn1) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpInComplement1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTE) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTEcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementUnionInPowersetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule0) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_5) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all2) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1SetBreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (choice2fnsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all1) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compEex) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIL) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIR) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionEcases) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionCommutes) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2Ex) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2W) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2A) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2B) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Ex) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Ex1) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Equiv) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1E) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1I) =>
% 99.02/13.37 ((
% 99.02/13.37 (injFuncInInjFuncSet) =>
% 99.02/13.37 ((
% 99.02/13.37 (!!) @ (
% 99.02/13.37 (('#B') @ (
% 99.02/13.37 !!) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 !!))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#S') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 '#S') @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 '#S'))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 =>))))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#C') @ in)))) @
% 99.02/13.37 injFuncSet)))))))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#C') @ in)))) @
% 99.02/13.37 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1142])).
% 99.02/13.37 thf(zip_derived_cl1158, plain,
% 99.02/13.37 (~ (((binintersectEL) =>
% 99.02/13.37 (((binintersectLsub) =>
% 99.02/13.37 (((binintersectSubset2) =>
% 99.02/13.37 (((binintersectSubset3) =>
% 99.02/13.37 (((binintersectER) =>
% 99.02/13.37 (((disjointsetsI1) =>
% 99.02/13.37 (((binintersectRsub) =>
% 99.02/13.37 (((binintersectSubset4) =>
% 99.02/13.37 (((binintersectSubset1) =>
% 99.02/13.37 (((bs114d) =>
% 99.02/13.37 (((setminusI) =>
% 99.02/13.37 (((setminusEL) =>
% 99.02/13.37 (((setminusER) =>
% 99.02/13.37 (((setminusSubset2) =>
% 99.02/13.37 (((setminusERneg) =>
% 99.02/13.37 (((setminusELneg) =>
% 99.02/13.37 (((setminusILneg) =>
% 99.02/13.37 (((setminusIRneg) =>
% 99.02/13.37 (((setminusLsub) =>
% 99.02/13.37 (((setminusSubset1) =>
% 99.02/13.37 (((symdiffE) =>
% 99.02/13.37 (((symdiffI1) =>
% 99.02/13.37 (((symdiffI2) =>
% 99.02/13.37 (((symdiffIneg1) =>
% 99.02/13.37 (((symdiffIneg2) =>
% 99.02/13.37 (((secondinupair) =>
% 99.02/13.37 (((setukpairIL) =>
% 99.02/13.37 (((setukpairIR) =>
% 99.02/13.37 (((kpairiskpair) =>
% 99.02/13.37 (((kpairp) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletonsubset) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletoninpowerset) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletoninpowunion) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairset2E) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairsubunion) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairinpowunion) =>
% 99.02/13.37 ((
% 99.02/13.37 (ubforcartprodlem1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ubforcartprodlem2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ubforcartprodlem3) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairin) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempair1) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempair) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionE2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton1) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletonprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1E1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1I) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1I2) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletonsuniq) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL1) =>
% 99.02/13.37 ((
% 99.02/13.37 (kfstsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (theprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (kfstpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodfstin) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR11) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR12) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR1) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairequniteq) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR) =>
% 99.02/13.37 ((
% 99.02/13.37 (ksndsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (ksndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (kpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndin) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemEL) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemER) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempaircEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodfstpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrI) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrSub) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrERa) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL1) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL2) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrER) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcImageSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (apProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (app) =>
% 99.02/13.37 ((
% 99.02/13.37 (infuncsetfunc) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcinfuncset) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall1) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1E2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp3) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcextLem) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp4) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq2) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2lamEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifp) =>
% 99.02/13.37 ((
% 99.02/13.37 (theeq) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrue) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueorfalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setminusT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setextT) =>
% 99.02/13.37 ((
% 99.02/13.37 (subsetTI) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTELcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTERcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT1) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT2) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT3) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub2) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTnotintersectT) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementImpComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementSubsetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementInPowersetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (contraSubsetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTcontraSubset) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTILcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTIRcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion2) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (intersectInPowersetIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpNotIn1) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpInComplement1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTE) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTEcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementUnionInPowersetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule0) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_5) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all2) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1SetBreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (choice2fnsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all1) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compprop) =>
% 99.02/13.37 ((
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% 99.02/13.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1158])).
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% 99.02/13.37 (((symdiffIneg2) =>
% 99.02/13.37 (((secondinupair) =>
% 99.02/13.37 (((setukpairIL) =>
% 99.02/13.37 (((setukpairIR) =>
% 99.02/13.37 (((kpairiskpair) =>
% 99.02/13.37 (((kpairp) =>
% 99.02/13.37 (((singletonsubset) =>
% 99.02/13.37 (((singletoninpowerset) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletoninpowunion) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairset2E) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairsubunion) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairinpowunion) =>
% 99.02/13.37 ((
% 99.02/13.37 (ubforcartprodlem1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ubforcartprodlem2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ubforcartprodlem3) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairin) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempair1) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempair) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionE2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton1) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletonprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1E1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1I) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1I2) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletonsuniq) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL1) =>
% 99.02/13.37 ((
% 99.02/13.37 (kfstsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (theprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (kfstpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodfstin) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR11) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR12) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR1) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairequniteq) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR) =>
% 99.02/13.37 ((
% 99.02/13.37 (ksndsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (ksndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (kpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndin) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemEL) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemER) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempaircEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodfstpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrI) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrSub) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrERa) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL1) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL2) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrER) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcImageSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (apProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (app) =>
% 99.02/13.37 ((
% 99.02/13.37 (infuncsetfunc) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcinfuncset) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall1) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1E2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp3) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcextLem) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp4) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq2) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2lamEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifp) =>
% 99.02/13.37 ((
% 99.02/13.37 (theeq) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrue) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueorfalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setminusT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setextT) =>
% 99.02/13.37 ((
% 99.02/13.37 (subsetTI) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTELcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTERcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT1) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT2) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT3) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub2) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTnotintersectT) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementImpComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementSubsetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementInPowersetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (contraSubsetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTcontraSubset) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTILcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTIRcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion2) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (intersectInPowersetIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpNotIn1) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpInComplement1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTE) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTEcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementUnionInPowersetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule0) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_5) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all2) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1SetBreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (choice2fnsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all1) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compEex) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIL) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIR) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionEcases) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionCommutes) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2Ex) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2W) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2A) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2B) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Ex) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Ex1) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Equiv) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1E) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1I) =>
% 99.02/13.37 ((
% 99.02/13.37 (injFuncInInjFuncSet) =>
% 99.02/13.37 ((
% 99.02/13.37 (!!) @ (
% 99.02/13.37 (('#B') @ (
% 99.02/13.37 !!) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 !!))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#S') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 '#S') @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 '#S'))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 =>))))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#C') @ in)))) @
% 99.02/13.37 injFuncSet)))))))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#C') @ in)))) @
% 99.02/13.37 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1166])).
% 99.02/13.37 thf(zip_derived_cl1183, plain,
% 99.02/13.37 (~ (((binintersectSubset3) =>
% 99.02/13.37 (((binintersectER) =>
% 99.02/13.37 (((disjointsetsI1) =>
% 99.02/13.37 (((binintersectRsub) =>
% 99.02/13.37 (((binintersectSubset4) =>
% 99.02/13.37 (((binintersectSubset1) =>
% 99.02/13.37 (((bs114d) =>
% 99.02/13.37 (((setminusI) =>
% 99.02/13.37 (((setminusEL) =>
% 99.02/13.37 (((setminusER) =>
% 99.02/13.37 (((setminusSubset2) =>
% 99.02/13.37 (((setminusERneg) =>
% 99.02/13.37 (((setminusELneg) =>
% 99.02/13.37 (((setminusILneg) =>
% 99.02/13.37 (((setminusIRneg) =>
% 99.02/13.37 (((setminusLsub) =>
% 99.02/13.37 (((setminusSubset1) =>
% 99.02/13.37 (((symdiffE) =>
% 99.02/13.37 (((symdiffI1) =>
% 99.02/13.37 (((symdiffI2) =>
% 99.02/13.37 (((symdiffIneg1) =>
% 99.02/13.37 (((symdiffIneg2) =>
% 99.02/13.37 (((secondinupair) =>
% 99.02/13.37 (((setukpairIL) =>
% 99.02/13.37 (((setukpairIR) =>
% 99.02/13.37 (((kpairiskpair) =>
% 99.02/13.37 (((kpairp) =>
% 99.02/13.37 (((singletonsubset) =>
% 99.02/13.37 (((singletoninpowerset) =>
% 99.02/13.37 (((singletoninpowunion) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairset2E) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairsubunion) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairinpowunion) =>
% 99.02/13.37 ((
% 99.02/13.37 (ubforcartprodlem1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ubforcartprodlem2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ubforcartprodlem3) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairin) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempair1) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempair) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionE2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton1) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletonprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1E1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1I) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1I2) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletonsuniq) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL1) =>
% 99.02/13.37 ((
% 99.02/13.37 (kfstsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (theprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (kfstpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodfstin) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR11) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR12) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR1) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairequniteq) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR) =>
% 99.02/13.37 ((
% 99.02/13.37 (ksndsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (ksndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (kpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndin) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemEL) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemER) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempaircEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodfstpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrI) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrSub) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrERa) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL1) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL2) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrER) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcImageSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (apProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (app) =>
% 99.02/13.37 ((
% 99.02/13.37 (infuncsetfunc) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcinfuncset) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall1) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1E2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp3) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcextLem) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp4) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq2) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2lamEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifp) =>
% 99.02/13.37 ((
% 99.02/13.37 (theeq) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrue) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueorfalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setminusT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setextT) =>
% 99.02/13.37 ((
% 99.02/13.37 (subsetTI) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTELcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTERcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT1) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT2) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT3) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub2) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTnotintersectT) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementImpComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementSubsetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementInPowersetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (contraSubsetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTcontraSubset) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTILcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTIRcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion2) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (intersectInPowersetIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpNotIn1) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpInComplement1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTE) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTEcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementUnionInPowersetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule0) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_5) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all2) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1SetBreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (choice2fnsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all1) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compEex) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIL) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIR) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionEcases) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionCommutes) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2Ex) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2W) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2A) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2B) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Ex) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Ex1) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Equiv) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1E) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1I) =>
% 99.02/13.37 ((
% 99.02/13.37 (injFuncInInjFuncSet) =>
% 99.02/13.37 ((
% 99.02/13.37 (!!) @ (
% 99.02/13.37 (('#B') @ (
% 99.02/13.37 !!) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 !!))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#S') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 '#S') @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 '#S'))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 =>))))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#C') @ in)))) @
% 99.02/13.37 injFuncSet)))))))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#C') @ in)))) @
% 99.02/13.37 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1174])).
% 99.02/13.37 thf(zip_derived_cl1193, plain,
% 99.02/13.37 (~ (((binintersectER) =>
% 99.02/13.37 (((disjointsetsI1) =>
% 99.02/13.37 (((binintersectRsub) =>
% 99.02/13.37 (((binintersectSubset4) =>
% 99.02/13.37 (((binintersectSubset1) =>
% 99.02/13.37 (((bs114d) =>
% 99.02/13.37 (((setminusI) =>
% 99.02/13.37 (((setminusEL) =>
% 99.02/13.37 (((setminusER) =>
% 99.02/13.37 (((setminusSubset2) =>
% 99.02/13.37 (((setminusERneg) =>
% 99.02/13.37 (((setminusELneg) =>
% 99.02/13.37 (((setminusILneg) =>
% 99.02/13.37 (((setminusIRneg) =>
% 99.02/13.37 (((setminusLsub) =>
% 99.02/13.37 (((setminusSubset1) =>
% 99.02/13.37 (((symdiffE) =>
% 99.02/13.37 (((symdiffI1) =>
% 99.02/13.37 (((symdiffI2) =>
% 99.02/13.37 (((symdiffIneg1) =>
% 99.02/13.37 (((symdiffIneg2) =>
% 99.02/13.37 (((secondinupair) =>
% 99.02/13.37 (((setukpairIL) =>
% 99.02/13.37 (((setukpairIR) =>
% 99.02/13.37 (((kpairiskpair) =>
% 99.02/13.37 (((kpairp) =>
% 99.02/13.37 (((singletonsubset) =>
% 99.02/13.37 (((singletoninpowerset) =>
% 99.02/13.37 (((singletoninpowunion) =>
% 99.02/13.37 (((upairset2E) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairsubunion) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairinpowunion) =>
% 99.02/13.37 ((
% 99.02/13.37 (ubforcartprodlem1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ubforcartprodlem2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ubforcartprodlem3) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairin) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempair1) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempair) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionE2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton1) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletonprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1E1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1I) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1I2) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletonsuniq) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL1) =>
% 99.02/13.37 ((
% 99.02/13.37 (kfstsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (theprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (kfstpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodfstin) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR11) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR12) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR1) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairequniteq) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR) =>
% 99.02/13.37 ((
% 99.02/13.37 (ksndsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (ksndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (kpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndin) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemEL) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemER) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempaircEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodfstpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrI) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrSub) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrERa) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL1) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL2) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrER) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcImageSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (apProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (app) =>
% 99.02/13.37 ((
% 99.02/13.37 (infuncsetfunc) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcinfuncset) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall1) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1E2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp3) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcextLem) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp4) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq2) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2lamEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifp) =>
% 99.02/13.37 ((
% 99.02/13.37 (theeq) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrue) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueorfalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setminusT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setextT) =>
% 99.02/13.37 ((
% 99.02/13.37 (subsetTI) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTELcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTERcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT1) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT2) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT3) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub2) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTnotintersectT) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementImpComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementSubsetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementInPowersetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (contraSubsetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTcontraSubset) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTILcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTIRcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion2) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (intersectInPowersetIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpNotIn1) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpInComplement1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTE) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTEcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementUnionInPowersetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule0) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_5) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all2) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1SetBreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (choice2fnsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all1) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compEex) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIL) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIR) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionEcases) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionCommutes) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2Ex) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2W) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2A) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2B) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Ex) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Ex1) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Equiv) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1E) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1I) =>
% 99.02/13.37 ((
% 99.02/13.37 (injFuncInInjFuncSet) =>
% 99.02/13.37 ((
% 99.02/13.37 (!!) @ (
% 99.02/13.37 (('#B') @ (
% 99.02/13.37 !!) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 !!))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#S') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 '#S') @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 '#S'))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 =>))))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#C') @ in)))) @
% 99.02/13.37 injFuncSet)))))))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#C') @ in)))) @
% 99.02/13.37 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1183])).
% 99.02/13.37 thf(zip_derived_cl1206, plain,
% 99.02/13.37 (~ (((disjointsetsI1) =>
% 99.02/13.37 (((binintersectRsub) =>
% 99.02/13.37 (((binintersectSubset4) =>
% 99.02/13.37 (((binintersectSubset1) =>
% 99.02/13.37 (((bs114d) =>
% 99.02/13.37 (((setminusI) =>
% 99.02/13.37 (((setminusEL) =>
% 99.02/13.37 (((setminusER) =>
% 99.02/13.37 (((setminusSubset2) =>
% 99.02/13.37 (((setminusERneg) =>
% 99.02/13.37 (((setminusELneg) =>
% 99.02/13.37 (((setminusILneg) =>
% 99.02/13.37 (((setminusIRneg) =>
% 99.02/13.37 (((setminusLsub) =>
% 99.02/13.37 (((setminusSubset1) =>
% 99.02/13.37 (((symdiffE) =>
% 99.02/13.37 (((symdiffI1) =>
% 99.02/13.37 (((symdiffI2) =>
% 99.02/13.37 (((symdiffIneg1) =>
% 99.02/13.37 (((symdiffIneg2) =>
% 99.02/13.37 (((secondinupair) =>
% 99.02/13.37 (((setukpairIL) =>
% 99.02/13.37 (((setukpairIR) =>
% 99.02/13.37 (((kpairiskpair) =>
% 99.02/13.37 (((kpairp) =>
% 99.02/13.37 (((singletonsubset) =>
% 99.02/13.37 (((singletoninpowerset) =>
% 99.02/13.37 (((singletoninpowunion) =>
% 99.02/13.37 (((upairset2E) =>
% 99.02/13.37 (((upairsubunion) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairinpowunion) =>
% 99.02/13.37 ((
% 99.02/13.37 (ubforcartprodlem1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ubforcartprodlem2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ubforcartprodlem3) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairin) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempair1) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempair) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionE2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton1) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletonprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1E1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1I) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1I2) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletonsuniq) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL1) =>
% 99.02/13.37 ((
% 99.02/13.37 (kfstsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (theprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (kfstpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodfstin) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR11) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR12) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR1) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairequniteq) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR) =>
% 99.02/13.37 ((
% 99.02/13.37 (ksndsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (ksndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (kpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndin) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemEL) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemER) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempaircEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodfstpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrI) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrSub) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrERa) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL1) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL2) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrER) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcImageSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (apProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (app) =>
% 99.02/13.37 ((
% 99.02/13.37 (infuncsetfunc) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcinfuncset) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall1) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1E2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp3) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcextLem) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp4) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq2) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2lamEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifp) =>
% 99.02/13.37 ((
% 99.02/13.37 (theeq) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrue) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueorfalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setminusT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setextT) =>
% 99.02/13.37 ((
% 99.02/13.37 (subsetTI) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTELcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTERcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT1) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT2) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT3) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub2) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTnotintersectT) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementImpComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementSubsetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementInPowersetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (contraSubsetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTcontraSubset) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTILcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTIRcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion2) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (intersectInPowersetIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpNotIn1) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpInComplement1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTE) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTEcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementUnionInPowersetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule0) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_5) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all2) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1SetBreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (choice2fnsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all1) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compEex) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIL) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIR) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionEcases) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionCommutes) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2Ex) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2W) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2A) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2B) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Ex) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Ex1) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Equiv) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1E) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1I) =>
% 99.02/13.37 ((
% 99.02/13.37 (injFuncInInjFuncSet) =>
% 99.02/13.37 ((
% 99.02/13.37 (!!) @ (
% 99.02/13.37 (('#B') @ (
% 99.02/13.37 !!) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 !!))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#S') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 '#S') @
% 99.02/13.37 (
% 99.02/13.37 (
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% 99.02/13.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1193])).
% 99.02/13.37 thf(zip_derived_cl1216, plain,
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% 99.02/13.37 (ubforcartprodlem3) =>
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 (cartprodpairmemEL) =>
% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
% 99.02/13.37 (cartprodfstpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndpairEq) =>
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% 99.02/13.37 ((
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% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL2) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrER) =>
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
% 99.02/13.37 (brelnall2) =>
% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 (beta2) =>
% 99.02/13.37 ((
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% 99.02/13.37 ((
% 99.02/13.37 (iftrue) =>
% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 (contrasubsetT3) =>
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% 99.02/13.37 (doubleComplementE1) =>
% 99.02/13.37 ((
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% 99.02/13.37 (doubleComplementSub2) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementEq) =>
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% 99.02/13.37 (complementTnotintersectT) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementImpComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementSubsetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementInPowersetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (contraSubsetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTcontraSubset) =>
% 99.02/13.37 ((
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% 99.02/13.37 ((
% 99.02/13.37 (binunionTIRcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion2) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (intersectInPowersetIntersectUnions) =>
% 99.02/13.37 ((
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% 99.02/13.37 (inComplementUnionImpInComplement1) =>
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% 99.02/13.37 ((
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% 99.02/13.37 ((
% 99.02/13.37 (complementUnionInPowersetComplement) =>
% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
% 99.02/13.37 (demorgan1b) =>
% 99.02/13.37 ((
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% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a) =>
% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 ((
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% 99.02/13.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1206])).
% 99.02/13.37 thf(zip_derived_cl1223, plain,
% 99.02/13.37 (~ (((binintersectSubset4) =>
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% 99.02/13.37 (ksndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (kpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndin) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemEL) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemER) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempaircEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodfstpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrI) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrSub) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrERa) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL1) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL2) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrER) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcImageSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (apProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (app) =>
% 99.02/13.37 ((
% 99.02/13.37 (infuncsetfunc) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcinfuncset) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall1) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1E2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp3) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcextLem) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp4) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq2) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2lamEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifp) =>
% 99.02/13.37 ((
% 99.02/13.37 (theeq) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrue) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueorfalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setminusT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setextT) =>
% 99.02/13.37 ((
% 99.02/13.37 (subsetTI) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTELcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTERcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT1) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT2) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT3) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub2) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTnotintersectT) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementImpComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementSubsetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementInPowersetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (contraSubsetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTcontraSubset) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTILcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTIRcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion2) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (intersectInPowersetIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpNotIn1) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpInComplement1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTE) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTEcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementUnionInPowersetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule0) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_5) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all2) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1SetBreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (choice2fnsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all1) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compEex) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIL) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIR) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionEcases) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionCommutes) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2Ex) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2W) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2A) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2B) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Ex) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Ex1) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Equiv) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1E) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1I) =>
% 99.02/13.37 ((
% 99.02/13.37 (injFuncInInjFuncSet) =>
% 99.02/13.37 ((
% 99.02/13.37 (!!) @ (
% 99.02/13.37 (('#B') @ (
% 99.02/13.37 !!) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 !!))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#S') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 '#S') @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 '#S'))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 =>))))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#C') @ in)))) @
% 99.02/13.37 injFuncSet)))))))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#C') @ in)))) @
% 99.02/13.37 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1216])).
% 99.02/13.37 thf(zip_derived_cl1231, plain,
% 99.02/13.37 (~ (((binintersectSubset1) =>
% 99.02/13.37 (((bs114d) =>
% 99.02/13.37 (((setminusI) =>
% 99.02/13.37 (((setminusEL) =>
% 99.02/13.37 (((setminusER) =>
% 99.02/13.37 (((setminusSubset2) =>
% 99.02/13.37 (((setminusERneg) =>
% 99.02/13.37 (((setminusELneg) =>
% 99.02/13.37 (((setminusILneg) =>
% 99.02/13.37 (((setminusIRneg) =>
% 99.02/13.37 (((setminusLsub) =>
% 99.02/13.37 (((setminusSubset1) =>
% 99.02/13.37 (((symdiffE) =>
% 99.02/13.37 (((symdiffI1) =>
% 99.02/13.37 (((symdiffI2) =>
% 99.02/13.37 (((symdiffIneg1) =>
% 99.02/13.37 (((symdiffIneg2) =>
% 99.02/13.37 (((secondinupair) =>
% 99.02/13.37 (((setukpairIL) =>
% 99.02/13.37 (((setukpairIR) =>
% 99.02/13.37 (((kpairiskpair) =>
% 99.02/13.37 (((kpairp) =>
% 99.02/13.37 (((singletonsubset) =>
% 99.02/13.37 (((singletoninpowerset) =>
% 99.02/13.37 (((singletoninpowunion) =>
% 99.02/13.37 (((upairset2E) =>
% 99.02/13.37 (((upairsubunion) =>
% 99.02/13.37 (((upairinpowunion) =>
% 99.02/13.37 (((ubforcartprodlem1) =>
% 99.02/13.37 (((ubforcartprodlem2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ubforcartprodlem3) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairin) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempair1) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempair) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionE2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton1) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletonprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1E1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1I) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1I2) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletonsuniq) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL1) =>
% 99.02/13.37 ((
% 99.02/13.37 (kfstsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (theprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (kfstpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodfstin) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR11) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR12) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR1) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairequniteq) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR) =>
% 99.02/13.37 ((
% 99.02/13.37 (ksndsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (ksndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (kpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndin) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemEL) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemER) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempaircEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodfstpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrI) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrSub) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrERa) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL1) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL2) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrER) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcImageSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (apProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (app) =>
% 99.02/13.37 ((
% 99.02/13.37 (infuncsetfunc) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcinfuncset) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall1) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1E2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp3) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcextLem) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp4) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq2) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2lamEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifp) =>
% 99.02/13.37 ((
% 99.02/13.37 (theeq) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrue) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueorfalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setminusT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setextT) =>
% 99.02/13.37 ((
% 99.02/13.37 (subsetTI) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTELcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTERcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT1) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT2) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT3) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub2) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTnotintersectT) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementImpComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementSubsetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementInPowersetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (contraSubsetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTcontraSubset) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTILcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTIRcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion2) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (intersectInPowersetIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpNotIn1) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpInComplement1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTE) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTEcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementUnionInPowersetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule0) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_5) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all2) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1SetBreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (choice2fnsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all1) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compEex) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIL) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIR) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionEcases) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionCommutes) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2Ex) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2W) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2A) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2B) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Ex) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Ex1) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Equiv) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1E) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1I) =>
% 99.02/13.37 ((
% 99.02/13.37 (injFuncInInjFuncSet) =>
% 99.02/13.37 ((
% 99.02/13.37 (!!) @ (
% 99.02/13.37 (('#B') @ (
% 99.02/13.37 !!) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 !!))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#S') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 '#S') @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 '#S'))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 =>))))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#C') @ in)))) @
% 99.02/13.37 injFuncSet)))))))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#C') @ in)))) @
% 99.02/13.37 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1223])).
% 99.02/13.37 thf(zip_derived_cl1239, plain,
% 99.02/13.37 (~ (((bs114d) =>
% 99.02/13.37 (((setminusI) =>
% 99.02/13.37 (((setminusEL) =>
% 99.02/13.37 (((setminusER) =>
% 99.02/13.37 (((setminusSubset2) =>
% 99.02/13.37 (((setminusERneg) =>
% 99.02/13.37 (((setminusELneg) =>
% 99.02/13.37 (((setminusILneg) =>
% 99.02/13.37 (((setminusIRneg) =>
% 99.02/13.37 (((setminusLsub) =>
% 99.02/13.37 (((setminusSubset1) =>
% 99.02/13.37 (((symdiffE) =>
% 99.02/13.37 (((symdiffI1) =>
% 99.02/13.37 (((symdiffI2) =>
% 99.02/13.37 (((symdiffIneg1) =>
% 99.02/13.37 (((symdiffIneg2) =>
% 99.02/13.37 (((secondinupair) =>
% 99.02/13.37 (((setukpairIL) =>
% 99.02/13.37 (((setukpairIR) =>
% 99.02/13.37 (((kpairiskpair) =>
% 99.02/13.37 (((kpairp) =>
% 99.02/13.37 (((singletonsubset) =>
% 99.02/13.37 (((singletoninpowerset) =>
% 99.02/13.37 (((singletoninpowunion) =>
% 99.02/13.37 (((upairset2E) =>
% 99.02/13.37 (((upairsubunion) =>
% 99.02/13.37 (((upairinpowunion) =>
% 99.02/13.37 (((ubforcartprodlem1) =>
% 99.02/13.37 (((ubforcartprodlem2) =>
% 99.02/13.37 (((ubforcartprodlem3) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairin) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempair1) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempair) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionE2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton1) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletonprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1E1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1I) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1I2) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletonsuniq) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL1) =>
% 99.02/13.37 ((
% 99.02/13.37 (kfstsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (theprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (kfstpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodfstin) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR11) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR12) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR1) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairequniteq) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR) =>
% 99.02/13.37 ((
% 99.02/13.37 (ksndsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (ksndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (kpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndin) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemEL) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemER) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempaircEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodfstpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrI) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrSub) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrERa) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL1) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL2) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrER) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcImageSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (apProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (app) =>
% 99.02/13.37 ((
% 99.02/13.37 (infuncsetfunc) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcinfuncset) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall1) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1E2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp3) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcextLem) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp4) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq2) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2lamEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifp) =>
% 99.02/13.37 ((
% 99.02/13.37 (theeq) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrue) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueorfalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setminusT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setextT) =>
% 99.02/13.37 ((
% 99.02/13.37 (subsetTI) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTELcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTERcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT1) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT2) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT3) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub2) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTnotintersectT) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementImpComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementSubsetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementInPowersetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (contraSubsetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTcontraSubset) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTILcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTIRcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion2) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (intersectInPowersetIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpNotIn1) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpInComplement1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTE) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTEcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementUnionInPowersetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule0) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_5) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all2) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1SetBreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (choice2fnsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all1) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compEex) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIL) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIR) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionEcases) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionCommutes) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2Ex) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2W) =>
% 99.02/13.37 ((
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% 99.02/13.37 (setukpairinjR12) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR1) =>
% 99.02/13.37 ((
% 99.02/13.37 (upairequniteq) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjR) =>
% 99.02/13.37 ((
% 99.02/13.37 (ksndsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (ksndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (kpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndin) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemEL) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairmemER) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodmempaircEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodfstpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodsndpairEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (cartprodpairsurjEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrI) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrSub) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrERa) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL1) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrEL2) =>
% 99.02/13.37 ((
% 99.02/13.37 (dpsetconstrER) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcImageSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (apProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (app) =>
% 99.02/13.37 ((
% 99.02/13.37 (infuncsetfunc) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcinfuncset) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamProp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lamp) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2p) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall1) =>
% 99.02/13.37 ((
% 99.02/13.37 (brelnall2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1E2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp3) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcextLem) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcGraphProp4) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext) =>
% 99.02/13.37 ((
% 99.02/13.37 (funcext2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ap2apEq2) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta1) =>
% 99.02/13.37 ((
% 99.02/13.37 (lam2lamEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (beta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (eta2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalseProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp1) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueProp2) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifSingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (ifp) =>
% 99.02/13.37 ((
% 99.02/13.37 (theeq) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrue) =>
% 99.02/13.37 ((
% 99.02/13.37 (iffalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (iftrueorfalse) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setminusT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementT_lem) =>
% 99.02/13.37 ((
% 99.02/13.37 (setextT) =>
% 99.02/13.37 ((
% 99.02/13.37 (subsetTI) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (powersetTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTELcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binintersectTERcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT1) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT2) =>
% 99.02/13.37 ((
% 99.02/13.37 (contrasubsetT3) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementI1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementE1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub1) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementSub2) =>
% 99.02/13.37 ((
% 99.02/13.37 (doubleComplementEq) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTnotintersectT) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementImpComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementSubsetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementInPowersetComplementIntersect) =>
% 99.02/13.37 ((
% 99.02/13.37 (contraSubsetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementTcontraSubset) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTILcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTIRcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInUnion2) =>
% 99.02/13.37 ((
% 99.02/13.37 (inIntersectImpInIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (intersectInPowersetIntersectUnions) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpNotIn1) =>
% 99.02/13.37 ((
% 99.02/13.37 (inComplementUnionImpInComplement1) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTE) =>
% 99.02/13.37 ((
% 99.02/13.37 (binunionTEcontra) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a1) =>
% 99.02/13.37 ((
% 99.02/13.37 (complementUnionInPowersetComplement) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan1) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2a) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b2) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2b) =>
% 99.02/13.37 ((
% 99.02/13.37 (demorgan2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule0) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz13rule4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_1) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_2) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_3) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_4) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz1_5) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all2) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1SetBreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (choice2fnsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (setOfPairsIsBReln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1all1) =>
% 99.02/13.37 ((
% 99.02/13.37 (subbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (eqbreln1) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1invE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1compEex) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIL) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionIR) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionI) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionE) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionEcases) =>
% 99.02/13.37 ((
% 99.02/13.37 (breln1unionCommutes) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2Ex) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2W) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2A) =>
% 99.02/13.37 ((
% 99.02/13.37 (woz2B) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Ex) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Ex1) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1Equiv) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1E) =>
% 99.02/13.37 ((
% 99.02/13.37 (image1I) =>
% 99.02/13.37 ((
% 99.02/13.37 (injFuncInInjFuncSet) =>
% 99.02/13.37 ((
% 99.02/13.37 (!!) @ (
% 99.02/13.37 (('#B') @ (
% 99.02/13.37 !!) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 !!))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#S') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 '#S') @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 '#S'))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 =>))))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#C') @ in)))) @
% 99.02/13.37 injFuncSet)))))))) @
% 99.02/13.37 (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#B') @ (
% 99.02/13.37 (
% 99.02/13.37 ('#C') @ in)))) @
% 99.02/13.37 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1247])).
% 99.02/13.37 thf(zip_derived_cl1264, plain,
% 99.02/13.37 (~ (((setminusER) =>
% 99.02/13.37 (((setminusSubset2) =>
% 99.02/13.37 (((setminusERneg) =>
% 99.02/13.37 (((setminusELneg) =>
% 99.02/13.37 (((setminusILneg) =>
% 99.02/13.37 (((setminusIRneg) =>
% 99.02/13.37 (((setminusLsub) =>
% 99.02/13.37 (((setminusSubset1) =>
% 99.02/13.37 (((symdiffE) =>
% 99.02/13.37 (((symdiffI1) =>
% 99.02/13.37 (((symdiffI2) =>
% 99.02/13.37 (((symdiffIneg1) =>
% 99.02/13.37 (((symdiffIneg2) =>
% 99.02/13.37 (((secondinupair) =>
% 99.02/13.37 (((setukpairIL) =>
% 99.02/13.37 (((setukpairIR) =>
% 99.02/13.37 (((kpairiskpair) =>
% 99.02/13.37 (((kpairp) =>
% 99.02/13.37 (((singletonsubset) =>
% 99.02/13.37 (((singletoninpowerset) =>
% 99.02/13.37 (((singletoninpowunion) =>
% 99.02/13.37 (((upairset2E) =>
% 99.02/13.37 (((upairsubunion) =>
% 99.02/13.37 (((upairinpowunion) =>
% 99.02/13.37 (((ubforcartprodlem1) =>
% 99.02/13.37 (((ubforcartprodlem2) =>
% 99.02/13.37 (((ubforcartprodlem3) =>
% 99.02/13.37 (((cartprodpairin) =>
% 99.02/13.37 (((cartprodmempair1) =>
% 99.02/13.37 (((cartprodmempair) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionE2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton1) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton2) =>
% 99.02/13.37 ((
% 99.02/13.37 (setunionsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletonprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1E1) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1I) =>
% 99.02/13.37 ((
% 99.02/13.37 (ex1I2) =>
% 99.02/13.37 ((
% 99.02/13.37 (singletonsuniq) =>
% 99.02/13.37 ((
% 99.02/13.37 (setukpairinjL1) =>
% 99.02/13.37 ((
% 99.02/13.37 (kfstsingleton) =>
% 99.02/13.37 ((
% 99.02/13.37 (theprop) =>
% 99.02/13.37 ((
% 99.02/13.37 (kfstpairEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodfstin) =>
% 99.02/13.38 ((
% 99.02/13.38 (setukpairinjL2) =>
% 99.02/13.38 ((
% 99.02/13.38 (setukpairinjL) =>
% 99.02/13.38 ((
% 99.02/13.38 (setukpairinjR11) =>
% 99.02/13.38 ((
% 99.02/13.38 (setukpairinjR12) =>
% 99.02/13.38 ((
% 99.02/13.38 (setukpairinjR1) =>
% 99.02/13.38 ((
% 99.02/13.38 (upairequniteq) =>
% 99.02/13.38 ((
% 99.02/13.38 (setukpairinjR2) =>
% 99.02/13.38 ((
% 99.02/13.38 (setukpairinjR) =>
% 99.02/13.38 ((
% 99.02/13.38 (ksndsingleton) =>
% 99.02/13.38 ((
% 99.02/13.38 (ksndpairEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (kpairsurjEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodsndin) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodpairmemEL) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodpairmemER) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodmempaircEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodfstpairEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodsndpairEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodpairsurjEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrI) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrSub) =>
% 99.02/13.38 ((
% 99.02/13.38 (setOfPairsIsBReln) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrERa) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrEL1) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrEL2) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrER) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcImageSingleton) =>
% 99.02/13.38 ((
% 99.02/13.38 (apProp) =>
% 99.02/13.38 ((
% 99.02/13.38 (app) =>
% 99.02/13.38 ((
% 99.02/13.38 (infuncsetfunc) =>
% 99.02/13.38 ((
% 99.02/13.38 (ap2p) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcinfuncset) =>
% 99.02/13.38 ((
% 99.02/13.38 (lamProp) =>
% 99.02/13.38 ((
% 99.02/13.38 (lamp) =>
% 99.02/13.38 ((
% 99.02/13.38 (lam2p) =>
% 99.02/13.38 ((
% 99.02/13.38 (brelnall1) =>
% 99.02/13.38 ((
% 99.02/13.38 (brelnall2) =>
% 99.02/13.38 ((
% 99.02/13.38 (ex1E2) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcGraphProp1) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcGraphProp3) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcGraphProp2) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcextLem) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcGraphProp4) =>
% 99.02/13.38 ((
% 99.02/13.38 (subbreln) =>
% 99.02/13.38 ((
% 99.02/13.38 (eqbreln) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcext) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcext2) =>
% 99.02/13.38 ((
% 99.02/13.38 (ap2apEq1) =>
% 99.02/13.38 ((
% 99.02/13.38 (ap2apEq2) =>
% 99.02/13.38 ((
% 99.02/13.38 (beta1) =>
% 99.02/13.38 ((
% 99.02/13.38 (eta1) =>
% 99.02/13.38 ((
% 99.02/13.38 (lam2lamEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (beta2) =>
% 99.02/13.38 ((
% 99.02/13.38 (eta2) =>
% 99.02/13.38 ((
% 99.02/13.38 (iffalseProp1) =>
% 99.02/13.38 ((
% 99.02/13.38 (iffalseProp2) =>
% 99.02/13.38 ((
% 99.02/13.38 (iftrueProp1) =>
% 99.02/13.38 ((
% 99.02/13.38 (iftrueProp2) =>
% 99.02/13.38 ((
% 99.02/13.38 (ifSingleton) =>
% 99.02/13.38 ((
% 99.02/13.38 (ifp) =>
% 99.02/13.38 ((
% 99.02/13.38 (theeq) =>
% 99.02/13.38 ((
% 99.02/13.38 (iftrue) =>
% 99.02/13.38 ((
% 99.02/13.38 (iffalse) =>
% 99.02/13.38 ((
% 99.02/13.38 (iftrueorfalse) =>
% 99.02/13.38 ((
% 99.02/13.38 (binintersectT_lem) =>
% 99.02/13.38 ((
% 99.02/13.38 (binunionT_lem) =>
% 99.02/13.38 ((
% 99.02/13.38 (powersetT_lem) =>
% 99.02/13.38 ((
% 99.02/13.38 (setminusT_lem) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementT_lem) =>
% 99.02/13.38 ((
% 99.02/13.38 (setextT) =>
% 99.02/13.38 ((
% 99.02/13.38 (subsetTI) =>
% 99.02/13.38 ((
% 99.02/13.38 (powersetTI1) =>
% 99.02/13.38 ((
% 99.02/13.38 (powersetTE1) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementTI1) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementTE1) =>
% 99.02/13.38 ((
% 99.02/13.38 (binintersectTELcontra) =>
% 99.02/13.38 ((
% 99.02/13.38 (binintersectTERcontra) =>
% 99.02/13.38 ((
% 99.02/13.38 (contrasubsetT) =>
% 99.02/13.38 ((
% 99.02/13.38 (contrasubsetT1) =>
% 99.02/13.38 ((
% 99.02/13.38 (contrasubsetT2) =>
% 99.02/13.38 ((
% 99.02/13.38 (contrasubsetT3) =>
% 99.02/13.38 ((
% 99.02/13.38 (doubleComplementI1) =>
% 99.02/13.38 ((
% 99.02/13.38 (doubleComplementE1) =>
% 99.02/13.38 ((
% 99.02/13.38 (doubleComplementSub1) =>
% 99.02/13.38 ((
% 99.02/13.38 (doubleComplementSub2) =>
% 99.02/13.38 ((
% 99.02/13.38 (doubleComplementEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementTnotintersectT) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementImpComplementIntersect) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementSubsetComplementIntersect) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementInPowersetComplementIntersect) =>
% 99.02/13.38 ((
% 99.02/13.38 (contraSubsetComplement) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementTcontraSubset) =>
% 99.02/13.38 ((
% 99.02/13.38 (binunionTILcontra) =>
% 99.02/13.38 ((
% 99.02/13.38 (binunionTIRcontra) =>
% 99.02/13.38 ((
% 99.02/13.38 (inIntersectImpInUnion) =>
% 99.02/13.38 ((
% 99.02/13.38 (inIntersectImpInUnion2) =>
% 99.02/13.38 ((
% 99.02/13.38 (inIntersectImpInIntersectUnions) =>
% 99.02/13.38 ((
% 99.02/13.38 (intersectInPowersetIntersectUnions) =>
% 99.02/13.38 ((
% 99.02/13.38 (inComplementUnionImpNotIn1) =>
% 99.02/13.38 ((
% 99.02/13.38 (inComplementUnionImpInComplement1) =>
% 99.02/13.38 ((
% 99.02/13.38 (binunionTE) =>
% 99.02/13.38 ((
% 99.02/13.38 (binunionTEcontra) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2a1) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementUnionInPowersetComplement) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2a2) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan1a) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan1b) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan1) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2a) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2b2) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2b) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz13rule0) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz13rule1) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz13rule2) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz13rule3) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz13rule4) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz1_1) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz1_2) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz1_3) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz1_4) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz1_5) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1all2) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1SetBreln1) =>
% 99.02/13.38 ((
% 99.02/13.38 (choice2fnsingleton) =>
% 99.02/13.38 ((
% 99.02/13.38 (setOfPairsIsBReln1) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1all1) =>
% 99.02/13.38 ((
% 99.02/13.38 (subbreln1) =>
% 99.02/13.38 ((
% 99.02/13.38 (eqbreln1) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1invprop) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1invI) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1invE) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1compprop) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1compI) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1compE) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1compEex) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionprop) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionIL) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionIR) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionI) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionE) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionEcases) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionCommutes) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz2Ex) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz2W) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz2A) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz2B) =>
% 99.02/13.38 ((
% 99.02/13.38 (image1Ex) =>
% 99.02/13.38 ((
% 99.02/13.38 (image1Ex1) =>
% 99.02/13.38 ((
% 99.02/13.38 (image1Equiv) =>
% 99.02/13.38 ((
% 99.02/13.38 (image1E) =>
% 99.02/13.38 ((
% 99.02/13.38 (image1I) =>
% 99.02/13.38 ((
% 99.02/13.38 (injFuncInInjFuncSet) =>
% 99.02/13.38 ((
% 99.02/13.38 (!!) @ (
% 99.02/13.38 (('#B') @ (
% 99.02/13.38 !!) @
% 99.02/13.38 (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 !!))) @
% 99.02/13.38 (
% 99.02/13.38 (
% 99.02/13.38 ('#S') @ (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 '#S') @
% 99.02/13.38 (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 '#S'))) @
% 99.02/13.38 (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 =>))))) @
% 99.02/13.38 (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 (
% 99.02/13.38 ('#C') @ in)))) @
% 99.02/13.38 injFuncSet)))))))) @
% 99.02/13.38 (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 (
% 99.02/13.38 ('#C') @ in)))) @
% 99.02/13.38 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.02/13.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1255])).
% 99.02/13.38 thf(zip_derived_cl1272, plain,
% 99.02/13.38 (~ (((setminusSubset2) =>
% 99.02/13.38 (((setminusERneg) =>
% 99.02/13.38 (((setminusELneg) =>
% 99.02/13.38 (((setminusILneg) =>
% 99.02/13.38 (((setminusIRneg) =>
% 99.02/13.38 (((setminusLsub) =>
% 99.02/13.38 (((setminusSubset1) =>
% 99.02/13.38 (((symdiffE) =>
% 99.02/13.38 (((symdiffI1) =>
% 99.02/13.38 (((symdiffI2) =>
% 99.02/13.38 (((symdiffIneg1) =>
% 99.02/13.38 (((symdiffIneg2) =>
% 99.02/13.38 (((secondinupair) =>
% 99.02/13.38 (((setukpairIL) =>
% 99.02/13.38 (((setukpairIR) =>
% 99.02/13.38 (((kpairiskpair) =>
% 99.02/13.38 (((kpairp) =>
% 99.02/13.38 (((singletonsubset) =>
% 99.02/13.38 (((singletoninpowerset) =>
% 99.02/13.38 (((singletoninpowunion) =>
% 99.02/13.38 (((upairset2E) =>
% 99.02/13.38 (((upairsubunion) =>
% 99.02/13.38 (((upairinpowunion) =>
% 99.02/13.38 (((ubforcartprodlem1) =>
% 99.02/13.38 (((ubforcartprodlem2) =>
% 99.02/13.38 (((ubforcartprodlem3) =>
% 99.02/13.38 (((cartprodpairin) =>
% 99.02/13.38 (((cartprodmempair1) =>
% 99.02/13.38 (((cartprodmempair) =>
% 99.02/13.38 (((setunionE2) =>
% 99.02/13.38 ((
% 99.02/13.38 (setunionsingleton1) =>
% 99.02/13.38 ((
% 99.02/13.38 (setunionsingleton2) =>
% 99.02/13.38 ((
% 99.02/13.38 (setunionsingleton) =>
% 99.02/13.38 ((
% 99.02/13.38 (singletonprop) =>
% 99.02/13.38 ((
% 99.02/13.38 (ex1E1) =>
% 99.02/13.38 ((
% 99.02/13.38 (ex1I) =>
% 99.02/13.38 ((
% 99.02/13.38 (ex1I2) =>
% 99.02/13.38 ((
% 99.02/13.38 (singletonsuniq) =>
% 99.02/13.38 ((
% 99.02/13.38 (setukpairinjL1) =>
% 99.02/13.38 ((
% 99.02/13.38 (kfstsingleton) =>
% 99.02/13.38 ((
% 99.02/13.38 (theprop) =>
% 99.02/13.38 ((
% 99.02/13.38 (kfstpairEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodfstin) =>
% 99.02/13.38 ((
% 99.02/13.38 (setukpairinjL2) =>
% 99.02/13.38 ((
% 99.02/13.38 (setukpairinjL) =>
% 99.02/13.38 ((
% 99.02/13.38 (setukpairinjR11) =>
% 99.02/13.38 ((
% 99.02/13.38 (setukpairinjR12) =>
% 99.02/13.38 ((
% 99.02/13.38 (setukpairinjR1) =>
% 99.02/13.38 ((
% 99.02/13.38 (upairequniteq) =>
% 99.02/13.38 ((
% 99.02/13.38 (setukpairinjR2) =>
% 99.02/13.38 ((
% 99.02/13.38 (setukpairinjR) =>
% 99.02/13.38 ((
% 99.02/13.38 (ksndsingleton) =>
% 99.02/13.38 ((
% 99.02/13.38 (ksndpairEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (kpairsurjEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodsndin) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodpairmemEL) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodpairmemER) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodmempaircEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodfstpairEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodsndpairEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodpairsurjEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrI) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrSub) =>
% 99.02/13.38 ((
% 99.02/13.38 (setOfPairsIsBReln) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrERa) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrEL1) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrEL2) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrER) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcImageSingleton) =>
% 99.02/13.38 ((
% 99.02/13.38 (apProp) =>
% 99.02/13.38 ((
% 99.02/13.38 (app) =>
% 99.02/13.38 ((
% 99.02/13.38 (infuncsetfunc) =>
% 99.02/13.38 ((
% 99.02/13.38 (ap2p) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcinfuncset) =>
% 99.02/13.38 ((
% 99.02/13.38 (lamProp) =>
% 99.02/13.38 ((
% 99.02/13.38 (lamp) =>
% 99.02/13.38 ((
% 99.02/13.38 (lam2p) =>
% 99.02/13.38 ((
% 99.02/13.38 (brelnall1) =>
% 99.02/13.38 ((
% 99.02/13.38 (brelnall2) =>
% 99.02/13.38 ((
% 99.02/13.38 (ex1E2) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcGraphProp1) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcGraphProp3) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcGraphProp2) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcextLem) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcGraphProp4) =>
% 99.02/13.38 ((
% 99.02/13.38 (subbreln) =>
% 99.02/13.38 ((
% 99.02/13.38 (eqbreln) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcext) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcext2) =>
% 99.02/13.38 ((
% 99.02/13.38 (ap2apEq1) =>
% 99.02/13.38 ((
% 99.02/13.38 (ap2apEq2) =>
% 99.02/13.38 ((
% 99.02/13.38 (beta1) =>
% 99.02/13.38 ((
% 99.02/13.38 (eta1) =>
% 99.02/13.38 ((
% 99.02/13.38 (lam2lamEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (beta2) =>
% 99.02/13.38 ((
% 99.02/13.38 (eta2) =>
% 99.02/13.38 ((
% 99.02/13.38 (iffalseProp1) =>
% 99.02/13.38 ((
% 99.02/13.38 (iffalseProp2) =>
% 99.02/13.38 ((
% 99.02/13.38 (iftrueProp1) =>
% 99.02/13.38 ((
% 99.02/13.38 (iftrueProp2) =>
% 99.02/13.38 ((
% 99.02/13.38 (ifSingleton) =>
% 99.02/13.38 ((
% 99.02/13.38 (ifp) =>
% 99.02/13.38 ((
% 99.02/13.38 (theeq) =>
% 99.02/13.38 ((
% 99.02/13.38 (iftrue) =>
% 99.02/13.38 ((
% 99.02/13.38 (iffalse) =>
% 99.02/13.38 ((
% 99.02/13.38 (iftrueorfalse) =>
% 99.02/13.38 ((
% 99.02/13.38 (binintersectT_lem) =>
% 99.02/13.38 ((
% 99.02/13.38 (binunionT_lem) =>
% 99.02/13.38 ((
% 99.02/13.38 (powersetT_lem) =>
% 99.02/13.38 ((
% 99.02/13.38 (setminusT_lem) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementT_lem) =>
% 99.02/13.38 ((
% 99.02/13.38 (setextT) =>
% 99.02/13.38 ((
% 99.02/13.38 (subsetTI) =>
% 99.02/13.38 ((
% 99.02/13.38 (powersetTI1) =>
% 99.02/13.38 ((
% 99.02/13.38 (powersetTE1) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementTI1) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementTE1) =>
% 99.02/13.38 ((
% 99.02/13.38 (binintersectTELcontra) =>
% 99.02/13.38 ((
% 99.02/13.38 (binintersectTERcontra) =>
% 99.02/13.38 ((
% 99.02/13.38 (contrasubsetT) =>
% 99.02/13.38 ((
% 99.02/13.38 (contrasubsetT1) =>
% 99.02/13.38 ((
% 99.02/13.38 (contrasubsetT2) =>
% 99.02/13.38 ((
% 99.02/13.38 (contrasubsetT3) =>
% 99.02/13.38 ((
% 99.02/13.38 (doubleComplementI1) =>
% 99.02/13.38 ((
% 99.02/13.38 (doubleComplementE1) =>
% 99.02/13.38 ((
% 99.02/13.38 (doubleComplementSub1) =>
% 99.02/13.38 ((
% 99.02/13.38 (doubleComplementSub2) =>
% 99.02/13.38 ((
% 99.02/13.38 (doubleComplementEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementTnotintersectT) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementImpComplementIntersect) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementSubsetComplementIntersect) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementInPowersetComplementIntersect) =>
% 99.02/13.38 ((
% 99.02/13.38 (contraSubsetComplement) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementTcontraSubset) =>
% 99.02/13.38 ((
% 99.02/13.38 (binunionTILcontra) =>
% 99.02/13.38 ((
% 99.02/13.38 (binunionTIRcontra) =>
% 99.02/13.38 ((
% 99.02/13.38 (inIntersectImpInUnion) =>
% 99.02/13.38 ((
% 99.02/13.38 (inIntersectImpInUnion2) =>
% 99.02/13.38 ((
% 99.02/13.38 (inIntersectImpInIntersectUnions) =>
% 99.02/13.38 ((
% 99.02/13.38 (intersectInPowersetIntersectUnions) =>
% 99.02/13.38 ((
% 99.02/13.38 (inComplementUnionImpNotIn1) =>
% 99.02/13.38 ((
% 99.02/13.38 (inComplementUnionImpInComplement1) =>
% 99.02/13.38 ((
% 99.02/13.38 (binunionTE) =>
% 99.02/13.38 ((
% 99.02/13.38 (binunionTEcontra) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2a1) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementUnionInPowersetComplement) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2a2) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan1a) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan1b) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan1) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2a) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2b2) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2b) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz13rule0) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz13rule1) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz13rule2) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz13rule3) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz13rule4) =>
% 99.02/13.38 ((
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% 99.02/13.38 ((
% 99.02/13.38 (woz1_2) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz1_3) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz1_4) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz1_5) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1all2) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1SetBreln1) =>
% 99.02/13.38 ((
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% 99.02/13.38 ((
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% 99.02/13.38 ((
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% 99.02/13.38 ((
% 99.02/13.38 (subbreln1) =>
% 99.02/13.38 ((
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% 99.02/13.38 ((
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% 99.02/13.38 ((
% 99.02/13.38 (breln1invI) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1invE) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1compprop) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1compI) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1compE) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1compEex) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionprop) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionIL) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionIR) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionI) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionE) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionEcases) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionCommutes) =>
% 99.02/13.38 ((
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% 99.02/13.38 ((
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% 99.02/13.38 ((
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% 99.02/13.38 (cartprodsndin) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodpairmemEL) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodpairmemER) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodmempaircEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodfstpairEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodsndpairEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (cartprodpairsurjEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrI) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrSub) =>
% 99.02/13.38 ((
% 99.02/13.38 (setOfPairsIsBReln) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrERa) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrEL1) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrEL2) =>
% 99.02/13.38 ((
% 99.02/13.38 (dpsetconstrER) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcImageSingleton) =>
% 99.02/13.38 ((
% 99.02/13.38 (apProp) =>
% 99.02/13.38 ((
% 99.02/13.38 (app) =>
% 99.02/13.38 ((
% 99.02/13.38 (infuncsetfunc) =>
% 99.02/13.38 ((
% 99.02/13.38 (ap2p) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcinfuncset) =>
% 99.02/13.38 ((
% 99.02/13.38 (lamProp) =>
% 99.02/13.38 ((
% 99.02/13.38 (lamp) =>
% 99.02/13.38 ((
% 99.02/13.38 (lam2p) =>
% 99.02/13.38 ((
% 99.02/13.38 (brelnall1) =>
% 99.02/13.38 ((
% 99.02/13.38 (brelnall2) =>
% 99.02/13.38 ((
% 99.02/13.38 (ex1E2) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcGraphProp1) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcGraphProp3) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcGraphProp2) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcextLem) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcGraphProp4) =>
% 99.02/13.38 ((
% 99.02/13.38 (subbreln) =>
% 99.02/13.38 ((
% 99.02/13.38 (eqbreln) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcext) =>
% 99.02/13.38 ((
% 99.02/13.38 (funcext2) =>
% 99.02/13.38 ((
% 99.02/13.38 (ap2apEq1) =>
% 99.02/13.38 ((
% 99.02/13.38 (ap2apEq2) =>
% 99.02/13.38 ((
% 99.02/13.38 (beta1) =>
% 99.02/13.38 ((
% 99.02/13.38 (eta1) =>
% 99.02/13.38 ((
% 99.02/13.38 (lam2lamEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (beta2) =>
% 99.02/13.38 ((
% 99.02/13.38 (eta2) =>
% 99.02/13.38 ((
% 99.02/13.38 (iffalseProp1) =>
% 99.02/13.38 ((
% 99.02/13.38 (iffalseProp2) =>
% 99.02/13.38 ((
% 99.02/13.38 (iftrueProp1) =>
% 99.02/13.38 ((
% 99.02/13.38 (iftrueProp2) =>
% 99.02/13.38 ((
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% 99.02/13.38 ((
% 99.02/13.38 (ifp) =>
% 99.02/13.38 ((
% 99.02/13.38 (theeq) =>
% 99.02/13.38 ((
% 99.02/13.38 (iftrue) =>
% 99.02/13.38 ((
% 99.02/13.38 (iffalse) =>
% 99.02/13.38 ((
% 99.02/13.38 (iftrueorfalse) =>
% 99.02/13.38 ((
% 99.02/13.38 (binintersectT_lem) =>
% 99.02/13.38 ((
% 99.02/13.38 (binunionT_lem) =>
% 99.02/13.38 ((
% 99.02/13.38 (powersetT_lem) =>
% 99.02/13.38 ((
% 99.02/13.38 (setminusT_lem) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementT_lem) =>
% 99.02/13.38 ((
% 99.02/13.38 (setextT) =>
% 99.02/13.38 ((
% 99.02/13.38 (subsetTI) =>
% 99.02/13.38 ((
% 99.02/13.38 (powersetTI1) =>
% 99.02/13.38 ((
% 99.02/13.38 (powersetTE1) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementTI1) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementTE1) =>
% 99.02/13.38 ((
% 99.02/13.38 (binintersectTELcontra) =>
% 99.02/13.38 ((
% 99.02/13.38 (binintersectTERcontra) =>
% 99.02/13.38 ((
% 99.02/13.38 (contrasubsetT) =>
% 99.02/13.38 ((
% 99.02/13.38 (contrasubsetT1) =>
% 99.02/13.38 ((
% 99.02/13.38 (contrasubsetT2) =>
% 99.02/13.38 ((
% 99.02/13.38 (contrasubsetT3) =>
% 99.02/13.38 ((
% 99.02/13.38 (doubleComplementI1) =>
% 99.02/13.38 ((
% 99.02/13.38 (doubleComplementE1) =>
% 99.02/13.38 ((
% 99.02/13.38 (doubleComplementSub1) =>
% 99.02/13.38 ((
% 99.02/13.38 (doubleComplementSub2) =>
% 99.02/13.38 ((
% 99.02/13.38 (doubleComplementEq) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementTnotintersectT) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementImpComplementIntersect) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementSubsetComplementIntersect) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementInPowersetComplementIntersect) =>
% 99.02/13.38 ((
% 99.02/13.38 (contraSubsetComplement) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementTcontraSubset) =>
% 99.02/13.38 ((
% 99.02/13.38 (binunionTILcontra) =>
% 99.02/13.38 ((
% 99.02/13.38 (binunionTIRcontra) =>
% 99.02/13.38 ((
% 99.02/13.38 (inIntersectImpInUnion) =>
% 99.02/13.38 ((
% 99.02/13.38 (inIntersectImpInUnion2) =>
% 99.02/13.38 ((
% 99.02/13.38 (inIntersectImpInIntersectUnions) =>
% 99.02/13.38 ((
% 99.02/13.38 (intersectInPowersetIntersectUnions) =>
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% 99.02/13.38 (inComplementUnionImpNotIn1) =>
% 99.02/13.38 ((
% 99.02/13.38 (inComplementUnionImpInComplement1) =>
% 99.02/13.38 ((
% 99.02/13.38 (binunionTE) =>
% 99.02/13.38 ((
% 99.02/13.38 (binunionTEcontra) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2a1) =>
% 99.02/13.38 ((
% 99.02/13.38 (complementUnionInPowersetComplement) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2a2) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan1a) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan1b) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan1) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2a) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2b2) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2b) =>
% 99.02/13.38 ((
% 99.02/13.38 (demorgan2) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz13rule0) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz13rule1) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz13rule2) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz13rule3) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz13rule4) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz1_1) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz1_2) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz1_3) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz1_4) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz1_5) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1all2) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1SetBreln1) =>
% 99.02/13.38 ((
% 99.02/13.38 (choice2fnsingleton) =>
% 99.02/13.38 ((
% 99.02/13.38 (setOfPairsIsBReln1) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1all1) =>
% 99.02/13.38 ((
% 99.02/13.38 (subbreln1) =>
% 99.02/13.38 ((
% 99.02/13.38 (eqbreln1) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1invprop) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1invI) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1invE) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1compprop) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1compI) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1compE) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1compEex) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionprop) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionIL) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionIR) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionI) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionE) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionEcases) =>
% 99.02/13.38 ((
% 99.02/13.38 (breln1unionCommutes) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz2Ex) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz2W) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz2A) =>
% 99.02/13.38 ((
% 99.02/13.38 (woz2B) =>
% 99.02/13.38 ((
% 99.02/13.38 (image1Ex) =>
% 99.02/13.38 ((
% 99.02/13.38 (image1Ex1) =>
% 99.02/13.38 ((
% 99.02/13.38 (image1Equiv) =>
% 99.02/13.38 ((
% 99.02/13.38 (image1E) =>
% 99.02/13.38 ((
% 99.02/13.38 (image1I) =>
% 99.02/13.38 ((
% 99.02/13.38 (injFuncInInjFuncSet) =>
% 99.02/13.38 ((
% 99.02/13.38 (!!) @ (
% 99.02/13.38 (('#B') @ (
% 99.02/13.38 !!) @
% 99.02/13.38 (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 !!))) @
% 99.02/13.38 (
% 99.02/13.38 (
% 99.02/13.38 ('#S') @ (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 '#S') @
% 99.02/13.38 (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 '#S'))) @
% 99.02/13.38 (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 (
% 99.02/13.38 ('#B') @ (
% 99.02/13.38 =>))))) @
% 99.67/13.38 (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#C') @ in)))) @
% 99.67/13.38 injFuncSet)))))))) @
% 99.67/13.38 (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#C') @ in)))) @
% 99.67/13.38 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.67/13.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1280])).
% 99.67/13.38 thf(zip_derived_cl1296, plain,
% 99.67/13.38 (~ (((setminusILneg) =>
% 99.67/13.38 (((setminusIRneg) =>
% 99.67/13.38 (((setminusLsub) =>
% 99.67/13.38 (((setminusSubset1) =>
% 99.67/13.38 (((symdiffE) =>
% 99.67/13.38 (((symdiffI1) =>
% 99.67/13.38 (((symdiffI2) =>
% 99.67/13.38 (((symdiffIneg1) =>
% 99.67/13.38 (((symdiffIneg2) =>
% 99.67/13.38 (((secondinupair) =>
% 99.67/13.38 (((setukpairIL) =>
% 99.67/13.38 (((setukpairIR) =>
% 99.67/13.38 (((kpairiskpair) =>
% 99.67/13.38 (((kpairp) =>
% 99.67/13.38 (((singletonsubset) =>
% 99.67/13.38 (((singletoninpowerset) =>
% 99.67/13.38 (((singletoninpowunion) =>
% 99.67/13.38 (((upairset2E) =>
% 99.67/13.38 (((upairsubunion) =>
% 99.67/13.38 (((upairinpowunion) =>
% 99.67/13.38 (((ubforcartprodlem1) =>
% 99.67/13.38 (((ubforcartprodlem2) =>
% 99.67/13.38 (((ubforcartprodlem3) =>
% 99.67/13.38 (((cartprodpairin) =>
% 99.67/13.38 (((cartprodmempair1) =>
% 99.67/13.38 (((cartprodmempair) =>
% 99.67/13.38 (((setunionE2) =>
% 99.67/13.38 (((setunionsingleton1) =>
% 99.67/13.38 (((setunionsingleton2) =>
% 99.67/13.38 (((setunionsingleton) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (ex1I) =>
% 99.67/13.38 ((
% 99.67/13.38 (ex1I2) =>
% 99.67/13.38 ((
% 99.67/13.38 (singletonsuniq) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjL1) =>
% 99.67/13.38 ((
% 99.67/13.38 (kfstsingleton) =>
% 99.67/13.38 ((
% 99.67/13.38 (theprop) =>
% 99.67/13.38 ((
% 99.67/13.38 (kfstpairEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodfstin) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjL2) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjL) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR11) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR12) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR1) =>
% 99.67/13.38 ((
% 99.67/13.38 (upairequniteq) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR2) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR) =>
% 99.67/13.38 ((
% 99.67/13.38 (ksndsingleton) =>
% 99.67/13.38 ((
% 99.67/13.38 (ksndpairEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (kpairsurjEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodsndin) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodpairmemEL) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodpairmemER) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodmempaircEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodfstpairEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodsndpairEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodpairsurjEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrI) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrSub) =>
% 99.67/13.38 ((
% 99.67/13.38 (setOfPairsIsBReln) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrERa) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrEL1) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrEL2) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrER) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcImageSingleton) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (app) =>
% 99.67/13.38 ((
% 99.67/13.38 (infuncsetfunc) =>
% 99.67/13.38 ((
% 99.67/13.38 (ap2p) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcinfuncset) =>
% 99.67/13.38 ((
% 99.67/13.38 (lamProp) =>
% 99.67/13.38 ((
% 99.67/13.38 (lamp) =>
% 99.67/13.38 ((
% 99.67/13.38 (lam2p) =>
% 99.67/13.38 ((
% 99.67/13.38 (brelnall1) =>
% 99.67/13.38 ((
% 99.67/13.38 (brelnall2) =>
% 99.67/13.38 ((
% 99.67/13.38 (ex1E2) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp1) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp3) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp2) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcextLem) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp4) =>
% 99.67/13.38 ((
% 99.67/13.38 (subbreln) =>
% 99.67/13.38 ((
% 99.67/13.38 (eqbreln) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcext) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcext2) =>
% 99.67/13.38 ((
% 99.67/13.38 (ap2apEq1) =>
% 99.67/13.38 ((
% 99.67/13.38 (ap2apEq2) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (eta1) =>
% 99.67/13.38 ((
% 99.67/13.38 (lam2lamEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (beta2) =>
% 99.67/13.38 ((
% 99.67/13.38 (eta2) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (iftrueProp2) =>
% 99.67/13.38 ((
% 99.67/13.38 (ifSingleton) =>
% 99.67/13.38 ((
% 99.67/13.38 (ifp) =>
% 99.67/13.38 ((
% 99.67/13.38 (theeq) =>
% 99.67/13.38 ((
% 99.67/13.38 (iftrue) =>
% 99.67/13.38 ((
% 99.67/13.38 (iffalse) =>
% 99.67/13.38 ((
% 99.67/13.38 (iftrueorfalse) =>
% 99.67/13.38 ((
% 99.67/13.38 (binintersectT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (binunionT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (powersetT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (setminusT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (setextT) =>
% 99.67/13.38 ((
% 99.67/13.38 (subsetTI) =>
% 99.67/13.38 ((
% 99.67/13.38 (powersetTI1) =>
% 99.67/13.38 ((
% 99.67/13.38 (powersetTE1) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementTI1) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementTE1) =>
% 99.67/13.38 ((
% 99.67/13.38 (binintersectTELcontra) =>
% 99.67/13.38 ((
% 99.67/13.38 (binintersectTERcontra) =>
% 99.67/13.38 ((
% 99.67/13.38 (contrasubsetT) =>
% 99.67/13.38 ((
% 99.67/13.38 (contrasubsetT1) =>
% 99.67/13.38 ((
% 99.67/13.38 (contrasubsetT2) =>
% 99.67/13.38 ((
% 99.67/13.38 (contrasubsetT3) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementI1) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementE1) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementSub1) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementSub2) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementTnotintersectT) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (demorgan2b) =>
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 (breln1unionI) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1unionE) =>
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (cartprodmempaircEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodfstpairEq) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (cartprodpairsurjEq) =>
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (powersetTE1) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (contrasubsetT2) =>
% 99.67/13.38 ((
% 99.67/13.38 (contrasubsetT3) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementE1) =>
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% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementSub2) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementEq) =>
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% 99.67/13.38 ((
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% 99.67/13.38 (brelnall1) =>
% 99.67/13.38 ((
% 99.67/13.38 (brelnall2) =>
% 99.67/13.38 ((
% 99.67/13.38 (ex1E2) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp1) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp3) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp2) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcextLem) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp4) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (funcext2) =>
% 99.67/13.38 ((
% 99.67/13.38 (ap2apEq1) =>
% 99.67/13.38 ((
% 99.67/13.38 (ap2apEq2) =>
% 99.67/13.38 ((
% 99.67/13.38 (beta1) =>
% 99.67/13.38 ((
% 99.67/13.38 (eta1) =>
% 99.67/13.38 ((
% 99.67/13.38 (lam2lamEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (beta2) =>
% 99.67/13.38 ((
% 99.67/13.38 (eta2) =>
% 99.67/13.38 ((
% 99.67/13.38 (iffalseProp1) =>
% 99.67/13.38 ((
% 99.67/13.38 (iffalseProp2) =>
% 99.67/13.38 ((
% 99.67/13.38 (iftrueProp1) =>
% 99.67/13.38 ((
% 99.67/13.38 (iftrueProp2) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (iftrue) =>
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% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (powersetT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (setminusT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (setextT) =>
% 99.67/13.38 ((
% 99.67/13.38 (subsetTI) =>
% 99.67/13.38 ((
% 99.67/13.38 (powersetTI1) =>
% 99.67/13.38 ((
% 99.67/13.38 (powersetTE1) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementTI1) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementTE1) =>
% 99.67/13.38 ((
% 99.67/13.38 (binintersectTELcontra) =>
% 99.67/13.38 ((
% 99.67/13.38 (binintersectTERcontra) =>
% 99.67/13.38 ((
% 99.67/13.38 (contrasubsetT) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (contrasubsetT2) =>
% 99.67/13.38 ((
% 99.67/13.38 (contrasubsetT3) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementI1) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementE1) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementSub1) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementSub2) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementTnotintersectT) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementImpComplementIntersect) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementSubsetComplementIntersect) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementInPowersetComplementIntersect) =>
% 99.67/13.38 ((
% 99.67/13.38 (contraSubsetComplement) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementTcontraSubset) =>
% 99.67/13.38 ((
% 99.67/13.38 (binunionTILcontra) =>
% 99.67/13.38 ((
% 99.67/13.38 (binunionTIRcontra) =>
% 99.67/13.38 ((
% 99.67/13.38 (inIntersectImpInUnion) =>
% 99.67/13.38 ((
% 99.67/13.38 (inIntersectImpInUnion2) =>
% 99.67/13.38 ((
% 99.67/13.38 (inIntersectImpInIntersectUnions) =>
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% 99.67/13.38 ((
% 99.67/13.38 (inComplementUnionImpInComplement1) =>
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% 99.67/13.38 ((
% 99.67/13.38 (binunionTEcontra) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (complementUnionInPowersetComplement) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan2a2) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan1a) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan1b) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan1) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan2a) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan2b2) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan2b) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan2) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz13rule0) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz13rule1) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz13rule2) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz13rule3) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz13rule4) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz1_1) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz1_2) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz1_3) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz1_4) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz1_5) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1all2) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1SetBreln1) =>
% 99.67/13.38 ((
% 99.67/13.38 (choice2fnsingleton) =>
% 99.67/13.38 ((
% 99.67/13.38 (setOfPairsIsBReln1) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1all1) =>
% 99.67/13.38 ((
% 99.67/13.38 (subbreln1) =>
% 99.67/13.38 ((
% 99.67/13.38 (eqbreln1) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1invprop) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1invI) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1invE) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1compprop) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1compI) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1compE) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1compEex) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1unionprop) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1unionIL) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1unionIR) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1unionI) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1unionE) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1unionEcases) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1unionCommutes) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz2Ex) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz2W) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz2A) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz2B) =>
% 99.67/13.38 ((
% 99.67/13.38 (image1Ex) =>
% 99.67/13.38 ((
% 99.67/13.38 (image1Ex1) =>
% 99.67/13.38 ((
% 99.67/13.38 (image1Equiv) =>
% 99.67/13.38 ((
% 99.67/13.38 (image1E) =>
% 99.67/13.38 ((
% 99.67/13.38 (image1I) =>
% 99.67/13.38 ((
% 99.67/13.38 (injFuncInInjFuncSet) =>
% 99.67/13.38 ((
% 99.67/13.38 (!!) @ (
% 99.67/13.38 (('#B') @ (
% 99.67/13.38 !!) @
% 99.67/13.38 (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 !!))) @
% 99.67/13.38 (
% 99.67/13.38 (
% 99.67/13.38 ('#S') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 '#S') @
% 99.67/13.38 (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 '#S'))) @
% 99.67/13.38 (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 =>))))) @
% 99.67/13.38 (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#C') @ in)))) @
% 99.67/13.38 injFuncSet)))))))) @
% 99.67/13.38 (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#C') @ in)))) @
% 99.67/13.38 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.67/13.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1313])).
% 99.67/13.38 thf(zip_derived_cl1329, plain,
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% 99.67/13.38 (((symdiffIneg2) =>
% 99.67/13.38 (((secondinupair) =>
% 99.67/13.38 (((setukpairIL) =>
% 99.67/13.38 (((setukpairIR) =>
% 99.67/13.38 (((kpairiskpair) =>
% 99.67/13.38 (((kpairp) =>
% 99.67/13.38 (((singletonsubset) =>
% 99.67/13.38 (((singletoninpowerset) =>
% 99.67/13.38 (((singletoninpowunion) =>
% 99.67/13.38 (((upairset2E) =>
% 99.67/13.38 (((upairsubunion) =>
% 99.67/13.38 (((upairinpowunion) =>
% 99.67/13.38 (((ubforcartprodlem1) =>
% 99.67/13.38 (((ubforcartprodlem2) =>
% 99.67/13.38 (((ubforcartprodlem3) =>
% 99.67/13.38 (((cartprodpairin) =>
% 99.67/13.38 (((cartprodmempair1) =>
% 99.67/13.38 (((cartprodmempair) =>
% 99.67/13.38 (((setunionE2) =>
% 99.67/13.38 (((setunionsingleton1) =>
% 99.67/13.38 (((setunionsingleton2) =>
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% 99.67/13.38 (((singletonprop) =>
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% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (kfstsingleton) =>
% 99.67/13.38 ((
% 99.67/13.38 (theprop) =>
% 99.67/13.38 ((
% 99.67/13.38 (kfstpairEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodfstin) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjL2) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjL) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR11) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR12) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR1) =>
% 99.67/13.38 ((
% 99.67/13.38 (upairequniteq) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR2) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR) =>
% 99.67/13.38 ((
% 99.67/13.38 (ksndsingleton) =>
% 99.67/13.38 ((
% 99.67/13.38 (ksndpairEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (kpairsurjEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodsndin) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodpairmemEL) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodpairmemER) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodmempaircEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodfstpairEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodsndpairEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodpairsurjEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrI) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrSub) =>
% 99.67/13.38 ((
% 99.67/13.38 (setOfPairsIsBReln) =>
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% 99.67/13.38 (dpsetconstrERa) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrEL1) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrEL2) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrER) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcImageSingleton) =>
% 99.67/13.38 ((
% 99.67/13.38 (apProp) =>
% 99.67/13.38 ((
% 99.67/13.38 (app) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (ap2p) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (lamp) =>
% 99.67/13.38 ((
% 99.67/13.38 (lam2p) =>
% 99.67/13.38 ((
% 99.67/13.38 (brelnall1) =>
% 99.67/13.38 ((
% 99.67/13.38 (brelnall2) =>
% 99.67/13.38 ((
% 99.67/13.38 (ex1E2) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp3) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp4) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (funcext) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcext2) =>
% 99.67/13.38 ((
% 99.67/13.38 (ap2apEq1) =>
% 99.67/13.38 ((
% 99.67/13.38 (ap2apEq2) =>
% 99.67/13.38 ((
% 99.67/13.38 (beta1) =>
% 99.67/13.38 ((
% 99.67/13.38 (eta1) =>
% 99.67/13.38 ((
% 99.67/13.38 (lam2lamEq) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (iftrueorfalse) =>
% 99.67/13.38 ((
% 99.67/13.38 (binintersectT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (binunionT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (powersetT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (setminusT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (setextT) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (powersetTE1) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (complementTE1) =>
% 99.67/13.38 ((
% 99.67/13.38 (binintersectTELcontra) =>
% 99.67/13.38 ((
% 99.67/13.38 (binintersectTERcontra) =>
% 99.67/13.38 ((
% 99.67/13.38 (contrasubsetT) =>
% 99.67/13.38 ((
% 99.67/13.38 (contrasubsetT1) =>
% 99.67/13.38 ((
% 99.67/13.38 (contrasubsetT2) =>
% 99.67/13.38 ((
% 99.67/13.38 (contrasubsetT3) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementI1) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementE1) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementSub1) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementSub2) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementTnotintersectT) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementImpComplementIntersect) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementSubsetComplementIntersect) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementInPowersetComplementIntersect) =>
% 99.67/13.38 ((
% 99.67/13.38 (contraSubsetComplement) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementTcontraSubset) =>
% 99.67/13.38 ((
% 99.67/13.38 (binunionTILcontra) =>
% 99.67/13.38 ((
% 99.67/13.38 (binunionTIRcontra) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
% 99.67/13.38 (inIntersectImpInUnion2) =>
% 99.67/13.38 ((
% 99.67/13.38 (inIntersectImpInIntersectUnions) =>
% 99.67/13.38 ((
% 99.67/13.38 (intersectInPowersetIntersectUnions) =>
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% 99.67/13.38 (inComplementUnionImpNotIn1) =>
% 99.67/13.38 ((
% 99.67/13.38 (inComplementUnionImpInComplement1) =>
% 99.67/13.38 ((
% 99.67/13.38 (binunionTE) =>
% 99.67/13.38 ((
% 99.67/13.38 (binunionTEcontra) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan2a1) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementUnionInPowersetComplement) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan2a2) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan1a) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan1b) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan1) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan2a) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan2b2) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan2b) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan2) =>
% 99.67/13.38 ((
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% 99.67/13.38 ((
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% 99.67/13.38 (((setunionsingleton2) =>
% 99.67/13.38 (((setunionsingleton) =>
% 99.67/13.38 (((singletonprop) =>
% 99.67/13.38 (((ex1E1) =>
% 99.67/13.38 (((ex1I) =>
% 99.67/13.38 (((ex1I2) =>
% 99.67/13.38 (((singletonsuniq) =>
% 99.67/13.38 (((setukpairinjL1) =>
% 99.67/13.38 ((
% 99.67/13.38 (kfstsingleton) =>
% 99.67/13.38 ((
% 99.67/13.38 (theprop) =>
% 99.67/13.38 ((
% 99.67/13.38 (kfstpairEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodfstin) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjL2) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjL) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR11) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR12) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR1) =>
% 99.67/13.38 ((
% 99.67/13.38 (upairequniteq) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR2) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR) =>
% 99.67/13.38 ((
% 99.67/13.38 (ksndsingleton) =>
% 99.67/13.38 ((
% 99.67/13.38 (ksndpairEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (kpairsurjEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodsndin) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodpairmemEL) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodpairmemER) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodmempaircEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodfstpairEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodsndpairEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodpairsurjEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrI) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrSub) =>
% 99.67/13.38 ((
% 99.67/13.38 (setOfPairsIsBReln) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrERa) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrEL1) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrEL2) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrER) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcImageSingleton) =>
% 99.67/13.38 ((
% 99.67/13.38 (apProp) =>
% 99.67/13.38 ((
% 99.67/13.38 (app) =>
% 99.67/13.38 ((
% 99.67/13.38 (infuncsetfunc) =>
% 99.67/13.38 ((
% 99.67/13.38 (ap2p) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcinfuncset) =>
% 99.67/13.38 ((
% 99.67/13.38 (lamProp) =>
% 99.67/13.38 ((
% 99.67/13.38 (lamp) =>
% 99.67/13.38 ((
% 99.67/13.38 (lam2p) =>
% 99.67/13.38 ((
% 99.67/13.38 (brelnall1) =>
% 99.67/13.38 ((
% 99.67/13.38 (brelnall2) =>
% 99.67/13.38 ((
% 99.67/13.38 (ex1E2) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp1) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp3) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp2) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcextLem) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp4) =>
% 99.67/13.38 ((
% 99.67/13.38 (subbreln) =>
% 99.67/13.38 ((
% 99.67/13.38 (eqbreln) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcext) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcext2) =>
% 99.67/13.38 ((
% 99.67/13.38 (ap2apEq1) =>
% 99.67/13.38 ((
% 99.67/13.38 (ap2apEq2) =>
% 99.67/13.38 ((
% 99.67/13.38 (beta1) =>
% 99.67/13.38 ((
% 99.67/13.38 (eta1) =>
% 99.67/13.38 ((
% 99.67/13.38 (lam2lamEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (beta2) =>
% 99.67/13.38 ((
% 99.67/13.38 (eta2) =>
% 99.67/13.38 ((
% 99.67/13.38 (iffalseProp1) =>
% 99.67/13.38 ((
% 99.67/13.38 (iffalseProp2) =>
% 99.67/13.38 ((
% 99.67/13.38 (iftrueProp1) =>
% 99.67/13.38 ((
% 99.67/13.38 (iftrueProp2) =>
% 99.67/13.38 ((
% 99.67/13.38 (ifSingleton) =>
% 99.67/13.38 ((
% 99.67/13.38 (ifp) =>
% 99.67/13.38 ((
% 99.67/13.38 (theeq) =>
% 99.67/13.38 ((
% 99.67/13.38 (iftrue) =>
% 99.67/13.38 ((
% 99.67/13.38 (iffalse) =>
% 99.67/13.38 ((
% 99.67/13.38 (iftrueorfalse) =>
% 99.67/13.38 ((
% 99.67/13.38 (binintersectT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (binunionT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (powersetT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (setminusT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (setextT) =>
% 99.67/13.38 ((
% 99.67/13.38 (subsetTI) =>
% 99.67/13.38 ((
% 99.67/13.38 (powersetTI1) =>
% 99.67/13.38 ((
% 99.67/13.38 (powersetTE1) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementTI1) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementTE1) =>
% 99.67/13.38 ((
% 99.67/13.38 (binintersectTELcontra) =>
% 99.67/13.38 ((
% 99.67/13.38 (binintersectTERcontra) =>
% 99.67/13.38 ((
% 99.67/13.38 (contrasubsetT) =>
% 99.67/13.38 ((
% 99.67/13.38 (contrasubsetT1) =>
% 99.67/13.38 ((
% 99.67/13.38 (contrasubsetT2) =>
% 99.67/13.38 ((
% 99.67/13.38 (contrasubsetT3) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementI1) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementE1) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementSub1) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementSub2) =>
% 99.67/13.38 ((
% 99.67/13.38 (doubleComplementEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementTnotintersectT) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementImpComplementIntersect) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementSubsetComplementIntersect) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementInPowersetComplementIntersect) =>
% 99.67/13.38 ((
% 99.67/13.38 (contraSubsetComplement) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementTcontraSubset) =>
% 99.67/13.38 ((
% 99.67/13.38 (binunionTILcontra) =>
% 99.67/13.38 ((
% 99.67/13.38 (binunionTIRcontra) =>
% 99.67/13.38 ((
% 99.67/13.38 (inIntersectImpInUnion) =>
% 99.67/13.38 ((
% 99.67/13.38 (inIntersectImpInUnion2) =>
% 99.67/13.38 ((
% 99.67/13.38 (inIntersectImpInIntersectUnions) =>
% 99.67/13.38 ((
% 99.67/13.38 (intersectInPowersetIntersectUnions) =>
% 99.67/13.38 ((
% 99.67/13.38 (inComplementUnionImpNotIn1) =>
% 99.67/13.38 ((
% 99.67/13.38 (inComplementUnionImpInComplement1) =>
% 99.67/13.38 ((
% 99.67/13.38 (binunionTE) =>
% 99.67/13.38 ((
% 99.67/13.38 (binunionTEcontra) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan2a1) =>
% 99.67/13.38 ((
% 99.67/13.38 (complementUnionInPowersetComplement) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan2a2) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan1a) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan1b) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan1) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan2a) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan2b2) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan2b) =>
% 99.67/13.38 ((
% 99.67/13.38 (demorgan2) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz13rule0) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz13rule1) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz13rule2) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz13rule3) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz13rule4) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz1_1) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz1_2) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz1_3) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz1_4) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz1_5) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1all2) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1SetBreln1) =>
% 99.67/13.38 ((
% 99.67/13.38 (choice2fnsingleton) =>
% 99.67/13.38 ((
% 99.67/13.38 (setOfPairsIsBReln1) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1all1) =>
% 99.67/13.38 ((
% 99.67/13.38 (subbreln1) =>
% 99.67/13.38 ((
% 99.67/13.38 (eqbreln1) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1invprop) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1invI) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1invE) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1compprop) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1compI) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1compE) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1compEex) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1unionprop) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1unionIL) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1unionIR) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1unionI) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1unionE) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1unionEcases) =>
% 99.67/13.38 ((
% 99.67/13.38 (breln1unionCommutes) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz2Ex) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz2W) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz2A) =>
% 99.67/13.38 ((
% 99.67/13.38 (woz2B) =>
% 99.67/13.38 ((
% 99.67/13.38 (image1Ex) =>
% 99.67/13.38 ((
% 99.67/13.38 (image1Ex1) =>
% 99.67/13.38 ((
% 99.67/13.38 (image1Equiv) =>
% 99.67/13.38 ((
% 99.67/13.38 (image1E) =>
% 99.67/13.38 ((
% 99.67/13.38 (image1I) =>
% 99.67/13.38 ((
% 99.67/13.38 (injFuncInInjFuncSet) =>
% 99.67/13.38 ((
% 99.67/13.38 (!!) @ (
% 99.67/13.38 (('#B') @ (
% 99.67/13.38 !!) @
% 99.67/13.38 (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 !!))) @
% 99.67/13.38 (
% 99.67/13.38 (
% 99.67/13.38 ('#S') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 '#S') @
% 99.67/13.38 (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 '#S'))) @
% 99.67/13.38 (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 =>))))) @
% 99.67/13.38 (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#C') @ in)))) @
% 99.67/13.38 injFuncSet)))))))) @
% 99.67/13.38 (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#B') @ (
% 99.67/13.38 (
% 99.67/13.38 ('#C') @ in)))) @
% 99.67/13.38 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.67/13.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1338])).
% 99.67/13.38 thf(zip_derived_cl1354, plain,
% 99.67/13.38 (~ (((symdiffIneg1) =>
% 99.67/13.38 (((symdiffIneg2) =>
% 99.67/13.38 (((secondinupair) =>
% 99.67/13.38 (((setukpairIL) =>
% 99.67/13.38 (((setukpairIR) =>
% 99.67/13.38 (((kpairiskpair) =>
% 99.67/13.38 (((kpairp) =>
% 99.67/13.38 (((singletonsubset) =>
% 99.67/13.38 (((singletoninpowerset) =>
% 99.67/13.38 (((singletoninpowunion) =>
% 99.67/13.38 (((upairset2E) =>
% 99.67/13.38 (((upairsubunion) =>
% 99.67/13.38 (((upairinpowunion) =>
% 99.67/13.38 (((ubforcartprodlem1) =>
% 99.67/13.38 (((ubforcartprodlem2) =>
% 99.67/13.38 (((ubforcartprodlem3) =>
% 99.67/13.38 (((cartprodpairin) =>
% 99.67/13.38 (((cartprodmempair1) =>
% 99.67/13.38 (((cartprodmempair) =>
% 99.67/13.38 (((setunionE2) =>
% 99.67/13.38 (((setunionsingleton1) =>
% 99.67/13.38 (((setunionsingleton2) =>
% 99.67/13.38 (((setunionsingleton) =>
% 99.67/13.38 (((singletonprop) =>
% 99.67/13.38 (((ex1E1) =>
% 99.67/13.38 (((ex1I) =>
% 99.67/13.38 (((ex1I2) =>
% 99.67/13.38 (((singletonsuniq) =>
% 99.67/13.38 (((setukpairinjL1) =>
% 99.67/13.38 (((kfstsingleton) =>
% 99.67/13.38 ((
% 99.67/13.38 (theprop) =>
% 99.67/13.38 ((
% 99.67/13.38 (kfstpairEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodfstin) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjL2) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjL) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR11) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR12) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR1) =>
% 99.67/13.38 ((
% 99.67/13.38 (upairequniteq) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR2) =>
% 99.67/13.38 ((
% 99.67/13.38 (setukpairinjR) =>
% 99.67/13.38 ((
% 99.67/13.38 (ksndsingleton) =>
% 99.67/13.38 ((
% 99.67/13.38 (ksndpairEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (kpairsurjEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodsndin) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodpairmemEL) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodpairmemER) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodmempaircEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodfstpairEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodsndpairEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (cartprodpairsurjEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrI) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrSub) =>
% 99.67/13.38 ((
% 99.67/13.38 (setOfPairsIsBReln) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrERa) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrEL1) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrEL2) =>
% 99.67/13.38 ((
% 99.67/13.38 (dpsetconstrER) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcImageSingleton) =>
% 99.67/13.38 ((
% 99.67/13.38 (apProp) =>
% 99.67/13.38 ((
% 99.67/13.38 (app) =>
% 99.67/13.38 ((
% 99.67/13.38 (infuncsetfunc) =>
% 99.67/13.38 ((
% 99.67/13.38 (ap2p) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcinfuncset) =>
% 99.67/13.38 ((
% 99.67/13.38 (lamProp) =>
% 99.67/13.38 ((
% 99.67/13.38 (lamp) =>
% 99.67/13.38 ((
% 99.67/13.38 (lam2p) =>
% 99.67/13.38 ((
% 99.67/13.38 (brelnall1) =>
% 99.67/13.38 ((
% 99.67/13.38 (brelnall2) =>
% 99.67/13.38 ((
% 99.67/13.38 (ex1E2) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp1) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp3) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp2) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcextLem) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcGraphProp4) =>
% 99.67/13.38 ((
% 99.67/13.38 (subbreln) =>
% 99.67/13.38 ((
% 99.67/13.38 (eqbreln) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcext) =>
% 99.67/13.38 ((
% 99.67/13.38 (funcext2) =>
% 99.67/13.38 ((
% 99.67/13.38 (ap2apEq1) =>
% 99.67/13.38 ((
% 99.67/13.38 (ap2apEq2) =>
% 99.67/13.38 ((
% 99.67/13.38 (beta1) =>
% 99.67/13.38 ((
% 99.67/13.38 (eta1) =>
% 99.67/13.38 ((
% 99.67/13.38 (lam2lamEq) =>
% 99.67/13.38 ((
% 99.67/13.38 (beta2) =>
% 99.67/13.38 ((
% 99.67/13.38 (eta2) =>
% 99.67/13.38 ((
% 99.67/13.38 (iffalseProp1) =>
% 99.67/13.38 ((
% 99.67/13.38 (iffalseProp2) =>
% 99.67/13.38 ((
% 99.67/13.38 (iftrueProp1) =>
% 99.67/13.38 ((
% 99.67/13.38 (iftrueProp2) =>
% 99.67/13.38 ((
% 99.67/13.38 (ifSingleton) =>
% 99.67/13.38 ((
% 99.67/13.38 (ifp) =>
% 99.67/13.38 ((
% 99.67/13.38 (theeq) =>
% 99.67/13.38 ((
% 99.67/13.38 (iftrue) =>
% 99.67/13.38 ((
% 99.67/13.38 (iffalse) =>
% 99.67/13.38 ((
% 99.67/13.38 (iftrueorfalse) =>
% 99.67/13.38 ((
% 99.67/13.38 (binintersectT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (binunionT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (powersetT_lem) =>
% 99.67/13.38 ((
% 99.67/13.38 (setminusT_lem) =>
% 99.67/13.38 ((
% 99.67/13.39 (complementT_lem) =>
% 99.67/13.39 ((
% 99.67/13.39 (setextT) =>
% 99.67/13.39 ((
% 99.67/13.39 (subsetTI) =>
% 99.67/13.39 ((
% 99.67/13.39 (powersetTI1) =>
% 99.67/13.39 ((
% 99.67/13.39 (powersetTE1) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementTI1) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementTE1) =>
% 99.67/13.39 ((
% 99.67/13.39 (binintersectTELcontra) =>
% 99.67/13.39 ((
% 99.67/13.39 (binintersectTERcontra) =>
% 99.67/13.39 ((
% 99.67/13.39 (contrasubsetT) =>
% 99.67/13.39 ((
% 99.67/13.39 (contrasubsetT1) =>
% 99.67/13.39 ((
% 99.67/13.39 (contrasubsetT2) =>
% 99.67/13.39 ((
% 99.67/13.39 (contrasubsetT3) =>
% 99.67/13.39 ((
% 99.67/13.39 (doubleComplementI1) =>
% 99.67/13.39 ((
% 99.67/13.39 (doubleComplementE1) =>
% 99.67/13.39 ((
% 99.67/13.39 (doubleComplementSub1) =>
% 99.67/13.39 ((
% 99.67/13.39 (doubleComplementSub2) =>
% 99.67/13.39 ((
% 99.67/13.39 (doubleComplementEq) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementTnotintersectT) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementImpComplementIntersect) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementSubsetComplementIntersect) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementInPowersetComplementIntersect) =>
% 99.67/13.39 ((
% 99.67/13.39 (contraSubsetComplement) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementTcontraSubset) =>
% 99.67/13.39 ((
% 99.67/13.39 (binunionTILcontra) =>
% 99.67/13.39 ((
% 99.67/13.39 (binunionTIRcontra) =>
% 99.67/13.39 ((
% 99.67/13.39 (inIntersectImpInUnion) =>
% 99.67/13.39 ((
% 99.67/13.39 (inIntersectImpInUnion2) =>
% 99.67/13.39 ((
% 99.67/13.39 (inIntersectImpInIntersectUnions) =>
% 99.67/13.39 ((
% 99.67/13.39 (intersectInPowersetIntersectUnions) =>
% 99.67/13.39 ((
% 99.67/13.39 (inComplementUnionImpNotIn1) =>
% 99.67/13.39 ((
% 99.67/13.39 (inComplementUnionImpInComplement1) =>
% 99.67/13.39 ((
% 99.67/13.39 (binunionTE) =>
% 99.67/13.39 ((
% 99.67/13.39 (binunionTEcontra) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan2a1) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementUnionInPowersetComplement) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan2a2) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan1a) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan1b) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan1) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan2a) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan2b2) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan2b) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan2) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz13rule0) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz13rule1) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz13rule2) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz13rule3) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz13rule4) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz1_1) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz1_2) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz1_3) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz1_4) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz1_5) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1all2) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1SetBreln1) =>
% 99.67/13.39 ((
% 99.67/13.39 (choice2fnsingleton) =>
% 99.67/13.39 ((
% 99.67/13.39 (setOfPairsIsBReln1) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1all1) =>
% 99.67/13.39 ((
% 99.67/13.39 (subbreln1) =>
% 99.67/13.39 ((
% 99.67/13.39 (eqbreln1) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1invprop) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1invI) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1invE) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1compprop) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1compI) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1compE) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1compEex) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1unionprop) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1unionIL) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1unionIR) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1unionI) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1unionE) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1unionEcases) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1unionCommutes) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz2Ex) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz2W) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz2A) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz2B) =>
% 99.67/13.39 ((
% 99.67/13.39 (image1Ex) =>
% 99.67/13.39 ((
% 99.67/13.39 (image1Ex1) =>
% 99.67/13.39 ((
% 99.67/13.39 (image1Equiv) =>
% 99.67/13.39 ((
% 99.67/13.39 (image1E) =>
% 99.67/13.39 ((
% 99.67/13.39 (image1I) =>
% 99.67/13.39 ((
% 99.67/13.39 (injFuncInInjFuncSet) =>
% 99.67/13.39 ((
% 99.67/13.39 (!!) @ (
% 99.67/13.39 (('#B') @ (
% 99.67/13.39 !!) @
% 99.67/13.39 (
% 99.67/13.39 (
% 99.67/13.39 ('#B') @ (
% 99.67/13.39 (
% 99.67/13.39 ('#B') @ (
% 99.67/13.39 !!))) @
% 99.67/13.39 (
% 99.67/13.39 (
% 99.67/13.39 ('#S') @ (
% 99.67/13.39 (
% 99.67/13.39 ('#B') @ (
% 99.67/13.39 '#S') @
% 99.67/13.39 (
% 99.67/13.39 (
% 99.67/13.39 ('#B') @ (
% 99.67/13.39 (
% 99.67/13.39 ('#B') @ (
% 99.67/13.39 '#S'))) @
% 99.67/13.39 (
% 99.67/13.39 (
% 99.67/13.39 ('#B') @ (
% 99.67/13.39 (
% 99.67/13.39 ('#B') @ (
% 99.67/13.39 (
% 99.67/13.39 ('#B') @ (
% 99.67/13.39 =>))))) @
% 99.67/13.39 (
% 99.67/13.39 (
% 99.67/13.39 ('#B') @ (
% 99.67/13.39 (
% 99.67/13.39 ('#B') @ (
% 99.67/13.39 (
% 99.67/13.39 ('#C') @ in)))) @
% 99.67/13.39 injFuncSet)))))))) @
% 99.67/13.39 (
% 99.67/13.39 (
% 99.67/13.39 ('#B') @ (
% 99.67/13.39 (
% 99.67/13.39 ('#B') @ (
% 99.67/13.39 (
% 99.67/13.39 ('#C') @ in)))) @
% 99.67/13.39 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.67/13.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1347])).
% 99.67/13.39 thf(zip_derived_cl1361, plain,
% 99.67/13.39 (~ (((symdiffIneg2) =>
% 99.67/13.39 (((secondinupair) =>
% 99.67/13.39 (((setukpairIL) =>
% 99.67/13.39 (((setukpairIR) =>
% 99.67/13.39 (((kpairiskpair) =>
% 99.67/13.39 (((kpairp) =>
% 99.67/13.39 (((singletonsubset) =>
% 99.67/13.39 (((singletoninpowerset) =>
% 99.67/13.39 (((singletoninpowunion) =>
% 99.67/13.39 (((upairset2E) =>
% 99.67/13.39 (((upairsubunion) =>
% 99.67/13.39 (((upairinpowunion) =>
% 99.67/13.39 (((ubforcartprodlem1) =>
% 99.67/13.39 (((ubforcartprodlem2) =>
% 99.67/13.39 (((ubforcartprodlem3) =>
% 99.67/13.39 (((cartprodpairin) =>
% 99.67/13.39 (((cartprodmempair1) =>
% 99.67/13.39 (((cartprodmempair) =>
% 99.67/13.39 (((setunionE2) =>
% 99.67/13.39 (((setunionsingleton1) =>
% 99.67/13.39 (((setunionsingleton2) =>
% 99.67/13.39 (((setunionsingleton) =>
% 99.67/13.39 (((singletonprop) =>
% 99.67/13.39 (((ex1E1) =>
% 99.67/13.39 (((ex1I) =>
% 99.67/13.39 (((ex1I2) =>
% 99.67/13.39 (((singletonsuniq) =>
% 99.67/13.39 (((setukpairinjL1) =>
% 99.67/13.39 (((kfstsingleton) =>
% 99.67/13.39 (((theprop) =>
% 99.67/13.39 ((
% 99.67/13.39 (kfstpairEq) =>
% 99.67/13.39 ((
% 99.67/13.39 (cartprodfstin) =>
% 99.67/13.39 ((
% 99.67/13.39 (setukpairinjL2) =>
% 99.67/13.39 ((
% 99.67/13.39 (setukpairinjL) =>
% 99.67/13.39 ((
% 99.67/13.39 (setukpairinjR11) =>
% 99.67/13.39 ((
% 99.67/13.39 (setukpairinjR12) =>
% 99.67/13.39 ((
% 99.67/13.39 (setukpairinjR1) =>
% 99.67/13.39 ((
% 99.67/13.39 (upairequniteq) =>
% 99.67/13.39 ((
% 99.67/13.39 (setukpairinjR2) =>
% 99.67/13.39 ((
% 99.67/13.39 (setukpairinjR) =>
% 99.67/13.39 ((
% 99.67/13.39 (ksndsingleton) =>
% 99.67/13.39 ((
% 99.67/13.39 (ksndpairEq) =>
% 99.67/13.39 ((
% 99.67/13.39 (kpairsurjEq) =>
% 99.67/13.39 ((
% 99.67/13.39 (cartprodsndin) =>
% 99.67/13.39 ((
% 99.67/13.39 (cartprodpairmemEL) =>
% 99.67/13.39 ((
% 99.67/13.39 (cartprodpairmemER) =>
% 99.67/13.39 ((
% 99.67/13.39 (cartprodmempaircEq) =>
% 99.67/13.39 ((
% 99.67/13.39 (cartprodfstpairEq) =>
% 99.67/13.39 ((
% 99.67/13.39 (cartprodsndpairEq) =>
% 99.67/13.39 ((
% 99.67/13.39 (cartprodpairsurjEq) =>
% 99.67/13.39 ((
% 99.67/13.39 (dpsetconstrI) =>
% 99.67/13.39 ((
% 99.67/13.39 (dpsetconstrSub) =>
% 99.67/13.39 ((
% 99.67/13.39 (setOfPairsIsBReln) =>
% 99.67/13.39 ((
% 99.67/13.39 (dpsetconstrERa) =>
% 99.67/13.39 ((
% 99.67/13.39 (dpsetconstrEL1) =>
% 99.67/13.39 ((
% 99.67/13.39 (dpsetconstrEL2) =>
% 99.67/13.39 ((
% 99.67/13.39 (dpsetconstrER) =>
% 99.67/13.39 ((
% 99.67/13.39 (funcImageSingleton) =>
% 99.67/13.39 ((
% 99.67/13.39 (apProp) =>
% 99.67/13.39 ((
% 99.67/13.39 (app) =>
% 99.67/13.39 ((
% 99.67/13.39 (infuncsetfunc) =>
% 99.67/13.39 ((
% 99.67/13.39 (ap2p) =>
% 99.67/13.39 ((
% 99.67/13.39 (funcinfuncset) =>
% 99.67/13.39 ((
% 99.67/13.39 (lamProp) =>
% 99.67/13.39 ((
% 99.67/13.39 (lamp) =>
% 99.67/13.39 ((
% 99.67/13.39 (lam2p) =>
% 99.67/13.39 ((
% 99.67/13.39 (brelnall1) =>
% 99.67/13.39 ((
% 99.67/13.39 (brelnall2) =>
% 99.67/13.39 ((
% 99.67/13.39 (ex1E2) =>
% 99.67/13.39 ((
% 99.67/13.39 (funcGraphProp1) =>
% 99.67/13.39 ((
% 99.67/13.39 (funcGraphProp3) =>
% 99.67/13.39 ((
% 99.67/13.39 (funcGraphProp2) =>
% 99.67/13.39 ((
% 99.67/13.39 (funcextLem) =>
% 99.67/13.39 ((
% 99.67/13.39 (funcGraphProp4) =>
% 99.67/13.39 ((
% 99.67/13.39 (subbreln) =>
% 99.67/13.39 ((
% 99.67/13.39 (eqbreln) =>
% 99.67/13.39 ((
% 99.67/13.39 (funcext) =>
% 99.67/13.39 ((
% 99.67/13.39 (funcext2) =>
% 99.67/13.39 ((
% 99.67/13.39 (ap2apEq1) =>
% 99.67/13.39 ((
% 99.67/13.39 (ap2apEq2) =>
% 99.67/13.39 ((
% 99.67/13.39 (beta1) =>
% 99.67/13.39 ((
% 99.67/13.39 (eta1) =>
% 99.67/13.39 ((
% 99.67/13.39 (lam2lamEq) =>
% 99.67/13.39 ((
% 99.67/13.39 (beta2) =>
% 99.67/13.39 ((
% 99.67/13.39 (eta2) =>
% 99.67/13.39 ((
% 99.67/13.39 (iffalseProp1) =>
% 99.67/13.39 ((
% 99.67/13.39 (iffalseProp2) =>
% 99.67/13.39 ((
% 99.67/13.39 (iftrueProp1) =>
% 99.67/13.39 ((
% 99.67/13.39 (iftrueProp2) =>
% 99.67/13.39 ((
% 99.67/13.39 (ifSingleton) =>
% 99.67/13.39 ((
% 99.67/13.39 (ifp) =>
% 99.67/13.39 ((
% 99.67/13.39 (theeq) =>
% 99.67/13.39 ((
% 99.67/13.39 (iftrue) =>
% 99.67/13.39 ((
% 99.67/13.39 (iffalse) =>
% 99.67/13.39 ((
% 99.67/13.39 (iftrueorfalse) =>
% 99.67/13.39 ((
% 99.67/13.39 (binintersectT_lem) =>
% 99.67/13.39 ((
% 99.67/13.39 (binunionT_lem) =>
% 99.67/13.39 ((
% 99.67/13.39 (powersetT_lem) =>
% 99.67/13.39 ((
% 99.67/13.39 (setminusT_lem) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementT_lem) =>
% 99.67/13.39 ((
% 99.67/13.39 (setextT) =>
% 99.67/13.39 ((
% 99.67/13.39 (subsetTI) =>
% 99.67/13.39 ((
% 99.67/13.39 (powersetTI1) =>
% 99.67/13.39 ((
% 99.67/13.39 (powersetTE1) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementTI1) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementTE1) =>
% 99.67/13.39 ((
% 99.67/13.39 (binintersectTELcontra) =>
% 99.67/13.39 ((
% 99.67/13.39 (binintersectTERcontra) =>
% 99.67/13.39 ((
% 99.67/13.39 (contrasubsetT) =>
% 99.67/13.39 ((
% 99.67/13.39 (contrasubsetT1) =>
% 99.67/13.39 ((
% 99.67/13.39 (contrasubsetT2) =>
% 99.67/13.39 ((
% 99.67/13.39 (contrasubsetT3) =>
% 99.67/13.39 ((
% 99.67/13.39 (doubleComplementI1) =>
% 99.67/13.39 ((
% 99.67/13.39 (doubleComplementE1) =>
% 99.67/13.39 ((
% 99.67/13.39 (doubleComplementSub1) =>
% 99.67/13.39 ((
% 99.67/13.39 (doubleComplementSub2) =>
% 99.67/13.39 ((
% 99.67/13.39 (doubleComplementEq) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementTnotintersectT) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementImpComplementIntersect) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementSubsetComplementIntersect) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementInPowersetComplementIntersect) =>
% 99.67/13.39 ((
% 99.67/13.39 (contraSubsetComplement) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementTcontraSubset) =>
% 99.67/13.39 ((
% 99.67/13.39 (binunionTILcontra) =>
% 99.67/13.39 ((
% 99.67/13.39 (binunionTIRcontra) =>
% 99.67/13.39 ((
% 99.67/13.39 (inIntersectImpInUnion) =>
% 99.67/13.39 ((
% 99.67/13.39 (inIntersectImpInUnion2) =>
% 99.67/13.39 ((
% 99.67/13.39 (inIntersectImpInIntersectUnions) =>
% 99.67/13.39 ((
% 99.67/13.39 (intersectInPowersetIntersectUnions) =>
% 99.67/13.39 ((
% 99.67/13.39 (inComplementUnionImpNotIn1) =>
% 99.67/13.39 ((
% 99.67/13.39 (inComplementUnionImpInComplement1) =>
% 99.67/13.39 ((
% 99.67/13.39 (binunionTE) =>
% 99.67/13.39 ((
% 99.67/13.39 (binunionTEcontra) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan2a1) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementUnionInPowersetComplement) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan2a2) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan1a) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan1b) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan1) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan2a) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan2b2) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan2b) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan2) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz13rule0) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz13rule1) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz13rule2) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz13rule3) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz13rule4) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz1_1) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz1_2) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz1_3) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz1_4) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz1_5) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1all2) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1SetBreln1) =>
% 99.67/13.39 ((
% 99.67/13.39 (choice2fnsingleton) =>
% 99.67/13.39 ((
% 99.67/13.39 (setOfPairsIsBReln1) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1all1) =>
% 99.67/13.39 ((
% 99.67/13.39 (subbreln1) =>
% 99.67/13.39 ((
% 99.67/13.39 (eqbreln1) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1invprop) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1invI) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1invE) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1compprop) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1compI) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1compE) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1compEex) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1unionprop) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1unionIL) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1unionIR) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1unionI) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1unionE) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1unionEcases) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1unionCommutes) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz2Ex) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz2W) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz2A) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz2B) =>
% 99.67/13.39 ((
% 99.67/13.39 (image1Ex) =>
% 99.67/13.39 ((
% 99.67/13.39 (image1Ex1) =>
% 99.67/13.39 ((
% 99.67/13.39 (image1Equiv) =>
% 99.67/13.39 ((
% 99.67/13.39 (image1E) =>
% 99.67/13.39 ((
% 99.67/13.39 (image1I) =>
% 99.67/13.39 ((
% 99.67/13.39 (injFuncInInjFuncSet) =>
% 99.67/13.39 ((
% 99.67/13.39 (!!) @ (
% 99.67/13.39 (('#B') @ (
% 99.67/13.39 !!) @
% 99.67/13.39 (
% 99.67/13.39 (
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% 99.67/13.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1354])).
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% 99.67/13.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])).
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% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 ((
% 99.67/13.39 (demorgan2b) =>
% 99.67/13.39 ((
% 99.67/13.39 (demorgan2) =>
% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 ((
% 99.67/13.39 (woz13rule2) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz13rule3) =>
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% 99.67/13.39 (woz13rule4) =>
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% 99.67/13.39 (woz1_2) =>
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% 99.67/13.39 (woz1_3) =>
% 99.67/13.39 ((
% 99.67/13.39 (woz1_4) =>
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% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 ((
% 99.67/13.39 (breln1invE) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1compprop) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1compI) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1compE) =>
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% 99.67/13.39 (breln1compEex) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1unionprop) =>
% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 (breln1unionI) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1unionE) =>
% 99.67/13.39 ((
% 99.67/13.39 (breln1unionEcases) =>
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% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 ((
% 99.67/13.39 (woz2B) =>
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% 99.67/13.39 ((
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% 99.67/13.39 ((
% 99.67/13.39 (image1Equiv) =>
% 99.67/13.39 ((
% 99.67/13.39 (image1E) =>
% 99.67/13.39 ((
% 99.67/13.39 (image1I) =>
% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 (
% 99.67/13.39 (
% 99.67/13.39 ('#B') @ (
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% 99.67/13.39 ('#B') @ (
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% 99.67/13.39 (
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% 99.67/13.39 injFuncSet)))))))) @
% 99.67/13.39 (
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% 99.67/13.39 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.67/13.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1369])).
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% 99.67/13.39 (kpairsurjEq) =>
% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 ((
% 99.67/13.39 (cartprodmempaircEq) =>
% 99.67/13.39 ((
% 99.67/13.39 (cartprodfstpairEq) =>
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% 99.67/13.39 (cartprodsndpairEq) =>
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% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 ((
% 99.67/13.39 (contrasubsetT3) =>
% 99.67/13.39 ((
% 99.67/13.39 (doubleComplementI1) =>
% 99.67/13.39 ((
% 99.67/13.39 (doubleComplementE1) =>
% 99.67/13.39 ((
% 99.67/13.39 (doubleComplementSub1) =>
% 99.67/13.39 ((
% 99.67/13.39 (doubleComplementSub2) =>
% 99.67/13.39 ((
% 99.67/13.39 (doubleComplementEq) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementTnotintersectT) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementImpComplementIntersect) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementSubsetComplementIntersect) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementInPowersetComplementIntersect) =>
% 99.67/13.39 ((
% 99.67/13.39 (contraSubsetComplement) =>
% 99.67/13.39 ((
% 99.67/13.39 (complementTcontraSubset) =>
% 99.67/13.39 ((
% 99.67/13.39 (binunionTILcontra) =>
% 99.67/13.39 ((
% 99.67/13.39 (binunionTIRcontra) =>
% 99.67/13.39 ((
% 99.67/13.39 (inIntersectImpInUnion) =>
% 99.67/13.39 ((
% 99.67/13.39 (inIntersectImpInUnion2) =>
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% 99.67/13.39 ((
% 99.67/13.39 (intersectInPowersetIntersectUnions) =>
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% 99.67/13.39 ((
% 99.67/13.39 (inComplementUnionImpInComplement1) =>
% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.67/13.39 (demorgan2) =>
% 99.67/13.39 ((
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% 99.67/13.39 ((
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% 99.74/13.39 ((
% 99.74/13.39 (setOfPairsIsBReln) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrERa) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrEL1) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrEL2) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrER) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcImageSingleton) =>
% 99.74/13.39 ((
% 99.74/13.39 (apProp) =>
% 99.74/13.39 ((
% 99.74/13.39 (app) =>
% 99.74/13.39 ((
% 99.74/13.39 (infuncsetfunc) =>
% 99.74/13.39 ((
% 99.74/13.39 (ap2p) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcinfuncset) =>
% 99.74/13.39 ((
% 99.74/13.39 (lamProp) =>
% 99.74/13.39 ((
% 99.74/13.39 (lamp) =>
% 99.74/13.39 ((
% 99.74/13.39 (lam2p) =>
% 99.74/13.39 ((
% 99.74/13.39 (brelnall1) =>
% 99.74/13.39 ((
% 99.74/13.39 (brelnall2) =>
% 99.74/13.39 ((
% 99.74/13.39 (ex1E2) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp1) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp3) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp2) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcextLem) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp4) =>
% 99.74/13.39 ((
% 99.74/13.39 (subbreln) =>
% 99.74/13.39 ((
% 99.74/13.39 (eqbreln) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcext) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcext2) =>
% 99.74/13.39 ((
% 99.74/13.39 (ap2apEq1) =>
% 99.74/13.39 ((
% 99.74/13.39 (ap2apEq2) =>
% 99.74/13.39 ((
% 99.74/13.39 (beta1) =>
% 99.74/13.39 ((
% 99.74/13.39 (eta1) =>
% 99.74/13.39 ((
% 99.74/13.39 (lam2lamEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (beta2) =>
% 99.74/13.39 ((
% 99.74/13.39 (eta2) =>
% 99.74/13.39 ((
% 99.74/13.39 (iffalseProp1) =>
% 99.74/13.39 ((
% 99.74/13.39 (iffalseProp2) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrueProp1) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrueProp2) =>
% 99.74/13.39 ((
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% 99.74/13.39 ((
% 99.74/13.39 (ifp) =>
% 99.74/13.39 ((
% 99.74/13.39 (theeq) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrue) =>
% 99.74/13.39 ((
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% 99.74/13.39 ((
% 99.74/13.39 (iftrueorfalse) =>
% 99.74/13.39 ((
% 99.74/13.39 (binintersectT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (powersetT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (setminusT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (setextT) =>
% 99.74/13.39 ((
% 99.74/13.39 (subsetTI) =>
% 99.74/13.39 ((
% 99.74/13.39 (powersetTI1) =>
% 99.74/13.39 ((
% 99.74/13.39 (powersetTE1) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTI1) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTE1) =>
% 99.74/13.39 ((
% 99.74/13.39 (binintersectTELcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (binintersectTERcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT1) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT2) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT3) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementI1) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementE1) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementSub1) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementSub2) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTnotintersectT) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementImpComplementIntersect) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementSubsetComplementIntersect) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementInPowersetComplementIntersect) =>
% 99.74/13.39 ((
% 99.74/13.39 (contraSubsetComplement) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTcontraSubset) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionTILcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionTIRcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (inIntersectImpInUnion) =>
% 99.74/13.39 ((
% 99.74/13.39 (inIntersectImpInUnion2) =>
% 99.74/13.39 ((
% 99.74/13.39 (inIntersectImpInIntersectUnions) =>
% 99.74/13.39 ((
% 99.74/13.39 (intersectInPowersetIntersectUnions) =>
% 99.74/13.39 ((
% 99.74/13.39 (inComplementUnionImpNotIn1) =>
% 99.74/13.39 ((
% 99.74/13.39 (inComplementUnionImpInComplement1) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionTE) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionTEcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan2a1) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementUnionInPowersetComplement) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan2a2) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan1a) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan1b) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan1) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan2a) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan2b2) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan2b) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan2) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz13rule0) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz13rule1) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz13rule2) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz13rule3) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz13rule4) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz1_1) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz1_2) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz1_3) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz1_4) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz1_5) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1all2) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1SetBreln1) =>
% 99.74/13.39 ((
% 99.74/13.39 (choice2fnsingleton) =>
% 99.74/13.39 ((
% 99.74/13.39 (setOfPairsIsBReln1) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1all1) =>
% 99.74/13.39 ((
% 99.74/13.39 (subbreln1) =>
% 99.74/13.39 ((
% 99.74/13.39 (eqbreln1) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1invprop) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1invI) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1invE) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1compprop) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1compI) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1compE) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1compEex) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1unionprop) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1unionIL) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1unionIR) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1unionI) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1unionE) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1unionEcases) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1unionCommutes) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz2Ex) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz2W) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz2A) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz2B) =>
% 99.74/13.39 ((
% 99.74/13.39 (image1Ex) =>
% 99.74/13.39 ((
% 99.74/13.39 (image1Ex1) =>
% 99.74/13.39 ((
% 99.74/13.39 (image1Equiv) =>
% 99.74/13.39 ((
% 99.74/13.39 (image1E) =>
% 99.74/13.39 ((
% 99.74/13.39 (image1I) =>
% 99.74/13.39 ((
% 99.74/13.39 (injFuncInInjFuncSet) =>
% 99.74/13.39 ((
% 99.74/13.39 (!!) @ (
% 99.74/13.39 (('#B') @ (
% 99.74/13.39 !!) @
% 99.74/13.39 (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 !!))) @
% 99.74/13.39 (
% 99.74/13.39 (
% 99.74/13.39 ('#S') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 '#S') @
% 99.74/13.39 (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 '#S'))) @
% 99.74/13.39 (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 =>))))) @
% 99.74/13.39 (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#C') @ in)))) @
% 99.74/13.39 injFuncSet)))))))) @
% 99.74/13.39 (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#C') @ in)))) @
% 99.74/13.39 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.74/13.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1396])).
% 99.74/13.39 thf(zip_derived_cl1420, plain,
% 99.74/13.39 (~ (((singletonsubset) =>
% 99.74/13.39 (((singletoninpowerset) =>
% 99.74/13.39 (((singletoninpowunion) =>
% 99.74/13.39 (((upairset2E) =>
% 99.74/13.39 (((upairsubunion) =>
% 99.74/13.39 (((upairinpowunion) =>
% 99.74/13.39 (((ubforcartprodlem1) =>
% 99.74/13.39 (((ubforcartprodlem2) =>
% 99.74/13.39 (((ubforcartprodlem3) =>
% 99.74/13.39 (((cartprodpairin) =>
% 99.74/13.39 (((cartprodmempair1) =>
% 99.74/13.39 (((cartprodmempair) =>
% 99.74/13.39 (((setunionE2) =>
% 99.74/13.39 (((setunionsingleton1) =>
% 99.74/13.39 (((setunionsingleton2) =>
% 99.74/13.39 (((setunionsingleton) =>
% 99.74/13.39 (((singletonprop) =>
% 99.74/13.39 (((ex1E1) =>
% 99.74/13.39 (((ex1I) =>
% 99.74/13.39 (((ex1I2) =>
% 99.74/13.39 (((singletonsuniq) =>
% 99.74/13.39 (((setukpairinjL1) =>
% 99.74/13.39 (((kfstsingleton) =>
% 99.74/13.39 (((theprop) =>
% 99.74/13.39 (((kfstpairEq) =>
% 99.74/13.39 (((cartprodfstin) =>
% 99.74/13.39 (((setukpairinjL2) =>
% 99.74/13.39 (((setukpairinjL) =>
% 99.74/13.39 (((setukpairinjR11) =>
% 99.74/13.39 (((setukpairinjR12) =>
% 99.74/13.39 ((
% 99.74/13.39 (setukpairinjR1) =>
% 99.74/13.39 ((
% 99.74/13.39 (upairequniteq) =>
% 99.74/13.39 ((
% 99.74/13.39 (setukpairinjR2) =>
% 99.74/13.39 ((
% 99.74/13.39 (setukpairinjR) =>
% 99.74/13.39 ((
% 99.74/13.39 (ksndsingleton) =>
% 99.74/13.39 ((
% 99.74/13.39 (ksndpairEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (kpairsurjEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodsndin) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodpairmemEL) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodpairmemER) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodmempaircEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodfstpairEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodsndpairEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodpairsurjEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrI) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrSub) =>
% 99.74/13.39 ((
% 99.74/13.39 (setOfPairsIsBReln) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrERa) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrEL1) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrEL2) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrER) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcImageSingleton) =>
% 99.74/13.39 ((
% 99.74/13.39 (apProp) =>
% 99.74/13.39 ((
% 99.74/13.39 (app) =>
% 99.74/13.39 ((
% 99.74/13.39 (infuncsetfunc) =>
% 99.74/13.39 ((
% 99.74/13.39 (ap2p) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcinfuncset) =>
% 99.74/13.39 ((
% 99.74/13.39 (lamProp) =>
% 99.74/13.39 ((
% 99.74/13.39 (lamp) =>
% 99.74/13.39 ((
% 99.74/13.39 (lam2p) =>
% 99.74/13.39 ((
% 99.74/13.39 (brelnall1) =>
% 99.74/13.39 ((
% 99.74/13.39 (brelnall2) =>
% 99.74/13.39 ((
% 99.74/13.39 (ex1E2) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp1) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp3) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp2) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcextLem) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp4) =>
% 99.74/13.39 ((
% 99.74/13.39 (subbreln) =>
% 99.74/13.39 ((
% 99.74/13.39 (eqbreln) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcext) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcext2) =>
% 99.74/13.39 ((
% 99.74/13.39 (ap2apEq1) =>
% 99.74/13.39 ((
% 99.74/13.39 (ap2apEq2) =>
% 99.74/13.39 ((
% 99.74/13.39 (beta1) =>
% 99.74/13.39 ((
% 99.74/13.39 (eta1) =>
% 99.74/13.39 ((
% 99.74/13.39 (lam2lamEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (beta2) =>
% 99.74/13.39 ((
% 99.74/13.39 (eta2) =>
% 99.74/13.39 ((
% 99.74/13.39 (iffalseProp1) =>
% 99.74/13.39 ((
% 99.74/13.39 (iffalseProp2) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrueProp1) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrueProp2) =>
% 99.74/13.39 ((
% 99.74/13.39 (ifSingleton) =>
% 99.74/13.39 ((
% 99.74/13.39 (ifp) =>
% 99.74/13.39 ((
% 99.74/13.39 (theeq) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrue) =>
% 99.74/13.39 ((
% 99.74/13.39 (iffalse) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrueorfalse) =>
% 99.74/13.39 ((
% 99.74/13.39 (binintersectT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (powersetT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (setminusT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (setextT) =>
% 99.74/13.39 ((
% 99.74/13.39 (subsetTI) =>
% 99.74/13.39 ((
% 99.74/13.39 (powersetTI1) =>
% 99.74/13.39 ((
% 99.74/13.39 (powersetTE1) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTI1) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTE1) =>
% 99.74/13.39 ((
% 99.74/13.39 (binintersectTELcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (binintersectTERcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT1) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT2) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT3) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementI1) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementE1) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementSub1) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementSub2) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTnotintersectT) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementImpComplementIntersect) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementSubsetComplementIntersect) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementInPowersetComplementIntersect) =>
% 99.74/13.39 ((
% 99.74/13.39 (contraSubsetComplement) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTcontraSubset) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionTILcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionTIRcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (inIntersectImpInUnion) =>
% 99.74/13.39 ((
% 99.74/13.39 (inIntersectImpInUnion2) =>
% 99.74/13.39 ((
% 99.74/13.39 (inIntersectImpInIntersectUnions) =>
% 99.74/13.39 ((
% 99.74/13.39 (intersectInPowersetIntersectUnions) =>
% 99.74/13.39 ((
% 99.74/13.39 (inComplementUnionImpNotIn1) =>
% 99.74/13.39 ((
% 99.74/13.39 (inComplementUnionImpInComplement1) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionTE) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionTEcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan2a1) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementUnionInPowersetComplement) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan2a2) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan1a) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan1b) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan1) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan2a) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan2b2) =>
% 99.74/13.39 ((
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% 99.74/13.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1407])).
% 99.74/13.39 thf(zip_derived_cl1433, plain,
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% 99.74/13.39 ((
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% 99.74/13.39 ((
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% 99.74/13.39 ((
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% 99.74/13.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1420])).
% 99.74/13.39 thf(zip_derived_cl1444, plain,
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% 99.74/13.39 (setukpairinjR2) =>
% 99.74/13.39 ((
% 99.74/13.39 (setukpairinjR) =>
% 99.74/13.39 ((
% 99.74/13.39 (ksndsingleton) =>
% 99.74/13.39 ((
% 99.74/13.39 (ksndpairEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (kpairsurjEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodsndin) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodpairmemEL) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodpairmemER) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodmempaircEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodfstpairEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodsndpairEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodpairsurjEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrI) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrSub) =>
% 99.74/13.39 ((
% 99.74/13.39 (setOfPairsIsBReln) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrERa) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrEL1) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrEL2) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrER) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcImageSingleton) =>
% 99.74/13.39 ((
% 99.74/13.39 (apProp) =>
% 99.74/13.39 ((
% 99.74/13.39 (app) =>
% 99.74/13.39 ((
% 99.74/13.39 (infuncsetfunc) =>
% 99.74/13.39 ((
% 99.74/13.39 (ap2p) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcinfuncset) =>
% 99.74/13.39 ((
% 99.74/13.39 (lamProp) =>
% 99.74/13.39 ((
% 99.74/13.39 (lamp) =>
% 99.74/13.39 ((
% 99.74/13.39 (lam2p) =>
% 99.74/13.39 ((
% 99.74/13.39 (brelnall1) =>
% 99.74/13.39 ((
% 99.74/13.39 (brelnall2) =>
% 99.74/13.39 ((
% 99.74/13.39 (ex1E2) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp1) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp3) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp2) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcextLem) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp4) =>
% 99.74/13.39 ((
% 99.74/13.39 (subbreln) =>
% 99.74/13.39 ((
% 99.74/13.39 (eqbreln) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcext) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcext2) =>
% 99.74/13.39 ((
% 99.74/13.39 (ap2apEq1) =>
% 99.74/13.39 ((
% 99.74/13.39 (ap2apEq2) =>
% 99.74/13.39 ((
% 99.74/13.39 (beta1) =>
% 99.74/13.39 ((
% 99.74/13.39 (eta1) =>
% 99.74/13.39 ((
% 99.74/13.39 (lam2lamEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (beta2) =>
% 99.74/13.39 ((
% 99.74/13.39 (eta2) =>
% 99.74/13.39 ((
% 99.74/13.39 (iffalseProp1) =>
% 99.74/13.39 ((
% 99.74/13.39 (iffalseProp2) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrueProp1) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrueProp2) =>
% 99.74/13.39 ((
% 99.74/13.39 (ifSingleton) =>
% 99.74/13.39 ((
% 99.74/13.39 (ifp) =>
% 99.74/13.39 ((
% 99.74/13.39 (theeq) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrue) =>
% 99.74/13.39 ((
% 99.74/13.39 (iffalse) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrueorfalse) =>
% 99.74/13.39 ((
% 99.74/13.39 (binintersectT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (powersetT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (setminusT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (setextT) =>
% 99.74/13.39 ((
% 99.74/13.39 (subsetTI) =>
% 99.74/13.39 ((
% 99.74/13.39 (powersetTI1) =>
% 99.74/13.39 ((
% 99.74/13.39 (powersetTE1) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTI1) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTE1) =>
% 99.74/13.39 ((
% 99.74/13.39 (binintersectTELcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (binintersectTERcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT1) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT2) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT3) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementI1) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementE1) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementSub1) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementSub2) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTnotintersectT) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementImpComplementIntersect) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementSubsetComplementIntersect) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementInPowersetComplementIntersect) =>
% 99.74/13.39 ((
% 99.74/13.39 (contraSubsetComplement) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTcontraSubset) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionTILcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionTIRcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (inIntersectImpInUnion) =>
% 99.74/13.39 ((
% 99.74/13.39 (inIntersectImpInUnion2) =>
% 99.74/13.39 ((
% 99.74/13.39 (inIntersectImpInIntersectUnions) =>
% 99.74/13.39 ((
% 99.74/13.39 (intersectInPowersetIntersectUnions) =>
% 99.74/13.39 ((
% 99.74/13.39 (inComplementUnionImpNotIn1) =>
% 99.74/13.39 ((
% 99.74/13.39 (inComplementUnionImpInComplement1) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionTE) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionTEcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan2a1) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementUnionInPowersetComplement) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan2a2) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan1a) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan1b) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan1) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan2a) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan2b2) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan2b) =>
% 99.74/13.39 ((
% 99.74/13.39 (demorgan2) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz13rule0) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz13rule1) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz13rule2) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz13rule3) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz13rule4) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz1_1) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz1_2) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz1_3) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz1_4) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz1_5) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1all2) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1SetBreln1) =>
% 99.74/13.39 ((
% 99.74/13.39 (choice2fnsingleton) =>
% 99.74/13.39 ((
% 99.74/13.39 (setOfPairsIsBReln1) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1all1) =>
% 99.74/13.39 ((
% 99.74/13.39 (subbreln1) =>
% 99.74/13.39 ((
% 99.74/13.39 (eqbreln1) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1invprop) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1invI) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1invE) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1compprop) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1compI) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1compE) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1compEex) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1unionprop) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1unionIL) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1unionIR) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1unionI) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1unionE) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1unionEcases) =>
% 99.74/13.39 ((
% 99.74/13.39 (breln1unionCommutes) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz2Ex) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz2W) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz2A) =>
% 99.74/13.39 ((
% 99.74/13.39 (woz2B) =>
% 99.74/13.39 ((
% 99.74/13.39 (image1Ex) =>
% 99.74/13.39 ((
% 99.74/13.39 (image1Ex1) =>
% 99.74/13.39 ((
% 99.74/13.39 (image1Equiv) =>
% 99.74/13.39 ((
% 99.74/13.39 (image1E) =>
% 99.74/13.39 ((
% 99.74/13.39 (image1I) =>
% 99.74/13.39 ((
% 99.74/13.39 (injFuncInInjFuncSet) =>
% 99.74/13.39 ((
% 99.74/13.39 (!!) @ (
% 99.74/13.39 (('#B') @ (
% 99.74/13.39 !!) @
% 99.74/13.39 (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 !!))) @
% 99.74/13.39 (
% 99.74/13.39 (
% 99.74/13.39 ('#S') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 '#S') @
% 99.74/13.39 (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 '#S'))) @
% 99.74/13.39 (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 =>))))) @
% 99.74/13.39 (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#C') @ in)))) @
% 99.74/13.39 injFuncSet)))))))) @
% 99.74/13.39 (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#B') @ (
% 99.74/13.39 (
% 99.74/13.39 ('#C') @ in)))) @
% 99.74/13.39 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.74/13.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1433])).
% 99.74/13.39 thf(zip_derived_cl1452, plain,
% 99.74/13.39 (~ (((upairset2E) =>
% 99.74/13.39 (((upairsubunion) =>
% 99.74/13.39 (((upairinpowunion) =>
% 99.74/13.39 (((ubforcartprodlem1) =>
% 99.74/13.39 (((ubforcartprodlem2) =>
% 99.74/13.39 (((ubforcartprodlem3) =>
% 99.74/13.39 (((cartprodpairin) =>
% 99.74/13.39 (((cartprodmempair1) =>
% 99.74/13.39 (((cartprodmempair) =>
% 99.74/13.39 (((setunionE2) =>
% 99.74/13.39 (((setunionsingleton1) =>
% 99.74/13.39 (((setunionsingleton2) =>
% 99.74/13.39 (((setunionsingleton) =>
% 99.74/13.39 (((singletonprop) =>
% 99.74/13.39 (((ex1E1) =>
% 99.74/13.39 (((ex1I) =>
% 99.74/13.39 (((ex1I2) =>
% 99.74/13.39 (((singletonsuniq) =>
% 99.74/13.39 (((setukpairinjL1) =>
% 99.74/13.39 (((kfstsingleton) =>
% 99.74/13.39 (((theprop) =>
% 99.74/13.39 (((kfstpairEq) =>
% 99.74/13.39 (((cartprodfstin) =>
% 99.74/13.39 (((setukpairinjL2) =>
% 99.74/13.39 (((setukpairinjL) =>
% 99.74/13.39 (((setukpairinjR11) =>
% 99.74/13.39 (((setukpairinjR12) =>
% 99.74/13.39 (((setukpairinjR1) =>
% 99.74/13.39 (((upairequniteq) =>
% 99.74/13.39 (((setukpairinjR2) =>
% 99.74/13.39 ((
% 99.74/13.39 (setukpairinjR) =>
% 99.74/13.39 ((
% 99.74/13.39 (ksndsingleton) =>
% 99.74/13.39 ((
% 99.74/13.39 (ksndpairEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (kpairsurjEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodsndin) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodpairmemEL) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodpairmemER) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodmempaircEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodfstpairEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodsndpairEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodpairsurjEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrI) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrSub) =>
% 99.74/13.39 ((
% 99.74/13.39 (setOfPairsIsBReln) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrERa) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrEL1) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrEL2) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrER) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcImageSingleton) =>
% 99.74/13.39 ((
% 99.74/13.39 (apProp) =>
% 99.74/13.39 ((
% 99.74/13.39 (app) =>
% 99.74/13.39 ((
% 99.74/13.39 (infuncsetfunc) =>
% 99.74/13.39 ((
% 99.74/13.39 (ap2p) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcinfuncset) =>
% 99.74/13.39 ((
% 99.74/13.39 (lamProp) =>
% 99.74/13.39 ((
% 99.74/13.39 (lamp) =>
% 99.74/13.39 ((
% 99.74/13.39 (lam2p) =>
% 99.74/13.39 ((
% 99.74/13.39 (brelnall1) =>
% 99.74/13.39 ((
% 99.74/13.39 (brelnall2) =>
% 99.74/13.39 ((
% 99.74/13.39 (ex1E2) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp1) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp3) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp2) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcextLem) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp4) =>
% 99.74/13.39 ((
% 99.74/13.39 (subbreln) =>
% 99.74/13.39 ((
% 99.74/13.39 (eqbreln) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcext) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcext2) =>
% 99.74/13.39 ((
% 99.74/13.39 (ap2apEq1) =>
% 99.74/13.39 ((
% 99.74/13.39 (ap2apEq2) =>
% 99.74/13.39 ((
% 99.74/13.39 (beta1) =>
% 99.74/13.39 ((
% 99.74/13.39 (eta1) =>
% 99.74/13.39 ((
% 99.74/13.39 (lam2lamEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (beta2) =>
% 99.74/13.39 ((
% 99.74/13.39 (eta2) =>
% 99.74/13.39 ((
% 99.74/13.39 (iffalseProp1) =>
% 99.74/13.39 ((
% 99.74/13.39 (iffalseProp2) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrueProp1) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrueProp2) =>
% 99.74/13.39 ((
% 99.74/13.39 (ifSingleton) =>
% 99.74/13.39 ((
% 99.74/13.39 (ifp) =>
% 99.74/13.39 ((
% 99.74/13.39 (theeq) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrue) =>
% 99.74/13.39 ((
% 99.74/13.39 (iffalse) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrueorfalse) =>
% 99.74/13.39 ((
% 99.74/13.39 (binintersectT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (powersetT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (setminusT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (setextT) =>
% 99.74/13.39 ((
% 99.74/13.39 (subsetTI) =>
% 99.74/13.39 ((
% 99.74/13.39 (powersetTI1) =>
% 99.74/13.39 ((
% 99.74/13.39 (powersetTE1) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTI1) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTE1) =>
% 99.74/13.39 ((
% 99.74/13.39 (binintersectTELcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (binintersectTERcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT1) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT2) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT3) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementI1) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementE1) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementSub1) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementSub2) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTnotintersectT) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementImpComplementIntersect) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementSubsetComplementIntersect) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementInPowersetComplementIntersect) =>
% 99.74/13.39 ((
% 99.74/13.39 (contraSubsetComplement) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTcontraSubset) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionTILcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionTIRcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (inIntersectImpInUnion) =>
% 99.74/13.39 ((
% 99.74/13.39 (inIntersectImpInUnion2) =>
% 99.74/13.39 ((
% 99.74/13.39 (inIntersectImpInIntersectUnions) =>
% 99.74/13.39 ((
% 99.74/13.39 (intersectInPowersetIntersectUnions) =>
% 99.74/13.39 ((
% 99.74/13.39 (inComplementUnionImpNotIn1) =>
% 99.74/13.39 ((
% 99.74/13.39 (inComplementUnionImpInComplement1) =>
% 99.74/13.39 ((
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% 99.74/13.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1444])).
% 99.74/13.39 thf(zip_derived_cl1459, plain,
% 99.74/13.39 (~ (((upairsubunion) =>
% 99.74/13.39 (((upairinpowunion) =>
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% 99.74/13.39 (((ubforcartprodlem2) =>
% 99.74/13.39 (((ubforcartprodlem3) =>
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% 99.74/13.39 (((cartprodmempair1) =>
% 99.74/13.39 (((cartprodmempair) =>
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% 99.74/13.39 ((
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% 99.74/13.39 ((
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% 99.74/13.39 ((
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% 99.74/13.39 ((
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% 99.74/13.39 ((
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% 99.74/13.39 ((
% 99.74/13.39 (complementSubsetComplementIntersect) =>
% 99.74/13.39 ((
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% 99.74/13.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1452])).
% 99.74/13.39 thf(zip_derived_cl1466, plain,
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% 99.74/13.39 (((kfstpairEq) =>
% 99.74/13.39 (((cartprodfstin) =>
% 99.74/13.39 (((setukpairinjL2) =>
% 99.74/13.39 (((setukpairinjL) =>
% 99.74/13.39 (((setukpairinjR11) =>
% 99.74/13.39 (((setukpairinjR12) =>
% 99.74/13.39 (((setukpairinjR1) =>
% 99.74/13.39 (((upairequniteq) =>
% 99.74/13.39 (((setukpairinjR2) =>
% 99.74/13.39 (((setukpairinjR) =>
% 99.74/13.39 (((ksndsingleton) =>
% 99.74/13.39 ((
% 99.74/13.39 (ksndpairEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (kpairsurjEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodsndin) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodpairmemEL) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodpairmemER) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodmempaircEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodfstpairEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodsndpairEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (cartprodpairsurjEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrI) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrSub) =>
% 99.74/13.39 ((
% 99.74/13.39 (setOfPairsIsBReln) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrERa) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrEL1) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrEL2) =>
% 99.74/13.39 ((
% 99.74/13.39 (dpsetconstrER) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcImageSingleton) =>
% 99.74/13.39 ((
% 99.74/13.39 (apProp) =>
% 99.74/13.39 ((
% 99.74/13.39 (app) =>
% 99.74/13.39 ((
% 99.74/13.39 (infuncsetfunc) =>
% 99.74/13.39 ((
% 99.74/13.39 (ap2p) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcinfuncset) =>
% 99.74/13.39 ((
% 99.74/13.39 (lamProp) =>
% 99.74/13.39 ((
% 99.74/13.39 (lamp) =>
% 99.74/13.39 ((
% 99.74/13.39 (lam2p) =>
% 99.74/13.39 ((
% 99.74/13.39 (brelnall1) =>
% 99.74/13.39 ((
% 99.74/13.39 (brelnall2) =>
% 99.74/13.39 ((
% 99.74/13.39 (ex1E2) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp1) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp3) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp2) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcextLem) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcGraphProp4) =>
% 99.74/13.39 ((
% 99.74/13.39 (subbreln) =>
% 99.74/13.39 ((
% 99.74/13.39 (eqbreln) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcext) =>
% 99.74/13.39 ((
% 99.74/13.39 (funcext2) =>
% 99.74/13.39 ((
% 99.74/13.39 (ap2apEq1) =>
% 99.74/13.39 ((
% 99.74/13.39 (ap2apEq2) =>
% 99.74/13.39 ((
% 99.74/13.39 (beta1) =>
% 99.74/13.39 ((
% 99.74/13.39 (eta1) =>
% 99.74/13.39 ((
% 99.74/13.39 (lam2lamEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (beta2) =>
% 99.74/13.39 ((
% 99.74/13.39 (eta2) =>
% 99.74/13.39 ((
% 99.74/13.39 (iffalseProp1) =>
% 99.74/13.39 ((
% 99.74/13.39 (iffalseProp2) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrueProp1) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrueProp2) =>
% 99.74/13.39 ((
% 99.74/13.39 (ifSingleton) =>
% 99.74/13.39 ((
% 99.74/13.39 (ifp) =>
% 99.74/13.39 ((
% 99.74/13.39 (theeq) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrue) =>
% 99.74/13.39 ((
% 99.74/13.39 (iffalse) =>
% 99.74/13.39 ((
% 99.74/13.39 (iftrueorfalse) =>
% 99.74/13.39 ((
% 99.74/13.39 (binintersectT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (powersetT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (setminusT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementT_lem) =>
% 99.74/13.39 ((
% 99.74/13.39 (setextT) =>
% 99.74/13.39 ((
% 99.74/13.39 (subsetTI) =>
% 99.74/13.39 ((
% 99.74/13.39 (powersetTI1) =>
% 99.74/13.39 ((
% 99.74/13.39 (powersetTE1) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTI1) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTE1) =>
% 99.74/13.39 ((
% 99.74/13.39 (binintersectTELcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (binintersectTERcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT1) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT2) =>
% 99.74/13.39 ((
% 99.74/13.39 (contrasubsetT3) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementI1) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementE1) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementSub1) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementSub2) =>
% 99.74/13.39 ((
% 99.74/13.39 (doubleComplementEq) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTnotintersectT) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementImpComplementIntersect) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementSubsetComplementIntersect) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementInPowersetComplementIntersect) =>
% 99.74/13.39 ((
% 99.74/13.39 (contraSubsetComplement) =>
% 99.74/13.39 ((
% 99.74/13.39 (complementTcontraSubset) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionTILcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (binunionTIRcontra) =>
% 99.74/13.39 ((
% 99.74/13.39 (inIntersectImpInUnion) =>
% 99.74/13.39 ((
% 99.74/13.39 (inIntersectImpInUnion2) =>
% 99.74/13.39 ((
% 99.74/13.39 (inIntersectImpInIntersectUnions) =>
% 99.74/13.40 ((
% 99.74/13.40 (intersectInPowersetIntersectUnions) =>
% 99.74/13.40 ((
% 99.74/13.40 (inComplementUnionImpNotIn1) =>
% 99.74/13.40 ((
% 99.74/13.40 (inComplementUnionImpInComplement1) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTE) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTEcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementUnionInPowersetComplement) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a2) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1a) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1b) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2b2) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2b) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule0) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule1) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule2) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule3) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule4) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_1) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_2) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_3) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_4) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_5) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1all2) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1SetBreln1) =>
% 99.74/13.40 ((
% 99.74/13.40 (choice2fnsingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (setOfPairsIsBReln1) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1all1) =>
% 99.74/13.40 ((
% 99.74/13.40 (subbreln1) =>
% 99.74/13.40 ((
% 99.74/13.40 (eqbreln1) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1invprop) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1invI) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1invE) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1compprop) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1compI) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1compE) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1compEex) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionprop) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionIL) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionIR) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionI) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionE) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionEcases) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionCommutes) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz2Ex) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz2W) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz2A) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz2B) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1Ex) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1Ex1) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1Equiv) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1E) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1I) =>
% 99.74/13.40 ((
% 99.74/13.40 (injFuncInInjFuncSet) =>
% 99.74/13.40 ((
% 99.74/13.40 (!!) @ (
% 99.74/13.40 (('#B') @ (
% 99.74/13.40 !!) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 !!))) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#S') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 '#S') @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 '#S'))) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 =>))))) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#C') @ in)))) @
% 99.74/13.40 injFuncSet)))))))) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#C') @ in)))) @
% 99.74/13.40 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.74/13.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1459])).
% 99.74/13.40 thf(zip_derived_cl1473, plain,
% 99.74/13.40 (~ (((ubforcartprodlem1) =>
% 99.74/13.40 (((ubforcartprodlem2) =>
% 99.74/13.40 (((ubforcartprodlem3) =>
% 99.74/13.40 (((cartprodpairin) =>
% 99.74/13.40 (((cartprodmempair1) =>
% 99.74/13.40 (((cartprodmempair) =>
% 99.74/13.40 (((setunionE2) =>
% 99.74/13.40 (((setunionsingleton1) =>
% 99.74/13.40 (((setunionsingleton2) =>
% 99.74/13.40 (((setunionsingleton) =>
% 99.74/13.40 (((singletonprop) =>
% 99.74/13.40 (((ex1E1) =>
% 99.74/13.40 (((ex1I) =>
% 99.74/13.40 (((ex1I2) =>
% 99.74/13.40 (((singletonsuniq) =>
% 99.74/13.40 (((setukpairinjL1) =>
% 99.74/13.40 (((kfstsingleton) =>
% 99.74/13.40 (((theprop) =>
% 99.74/13.40 (((kfstpairEq) =>
% 99.74/13.40 (((cartprodfstin) =>
% 99.74/13.40 (((setukpairinjL2) =>
% 99.74/13.40 (((setukpairinjL) =>
% 99.74/13.40 (((setukpairinjR11) =>
% 99.74/13.40 (((setukpairinjR12) =>
% 99.74/13.40 (((setukpairinjR1) =>
% 99.74/13.40 (((upairequniteq) =>
% 99.74/13.40 (((setukpairinjR2) =>
% 99.74/13.40 (((setukpairinjR) =>
% 99.74/13.40 (((ksndsingleton) =>
% 99.74/13.40 (((ksndpairEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (kpairsurjEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodsndin) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodpairmemEL) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodpairmemER) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodmempaircEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodfstpairEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodsndpairEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodpairsurjEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrI) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrSub) =>
% 99.74/13.40 ((
% 99.74/13.40 (setOfPairsIsBReln) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrERa) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrEL1) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrEL2) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrER) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcImageSingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (apProp) =>
% 99.74/13.40 ((
% 99.74/13.40 (app) =>
% 99.74/13.40 ((
% 99.74/13.40 (infuncsetfunc) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2p) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcinfuncset) =>
% 99.74/13.40 ((
% 99.74/13.40 (lamProp) =>
% 99.74/13.40 ((
% 99.74/13.40 (lamp) =>
% 99.74/13.40 ((
% 99.74/13.40 (lam2p) =>
% 99.74/13.40 ((
% 99.74/13.40 (brelnall1) =>
% 99.74/13.40 ((
% 99.74/13.40 (brelnall2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ex1E2) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp3) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcextLem) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp4) =>
% 99.74/13.40 ((
% 99.74/13.40 (subbreln) =>
% 99.74/13.40 ((
% 99.74/13.40 (eqbreln) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcext) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcext2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2apEq1) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2apEq2) =>
% 99.74/13.40 ((
% 99.74/13.40 (beta1) =>
% 99.74/13.40 ((
% 99.74/13.40 (eta1) =>
% 99.74/13.40 ((
% 99.74/13.40 (lam2lamEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (beta2) =>
% 99.74/13.40 ((
% 99.74/13.40 (eta2) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalseProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalseProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ifSingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (ifp) =>
% 99.74/13.40 ((
% 99.74/13.40 (theeq) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrue) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalse) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueorfalse) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (setminusT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (setextT) =>
% 99.74/13.40 ((
% 99.74/13.40 (subsetTI) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetTI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetTE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectTELcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectTERcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT1) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT2) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT3) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementSub1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementSub2) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTnotintersectT) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementImpComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementSubsetComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementInPowersetComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (contraSubsetComplement) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTcontraSubset) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTILcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTIRcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInUnion) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInUnion2) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInIntersectUnions) =>
% 99.74/13.40 ((
% 99.74/13.40 (intersectInPowersetIntersectUnions) =>
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% 99.74/13.40 (((upairequniteq) =>
% 99.74/13.40 (((setukpairinjR2) =>
% 99.74/13.40 (((setukpairinjR) =>
% 99.74/13.40 (((ksndsingleton) =>
% 99.74/13.40 (((ksndpairEq) =>
% 99.74/13.40 (((kpairsurjEq) =>
% 99.74/13.40 (((cartprodsndin) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodpairmemEL) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodpairmemER) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodmempaircEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodfstpairEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodsndpairEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodpairsurjEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrI) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrSub) =>
% 99.74/13.40 ((
% 99.74/13.40 (setOfPairsIsBReln) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrERa) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrEL1) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrEL2) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrER) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcImageSingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (apProp) =>
% 99.74/13.40 ((
% 99.74/13.40 (app) =>
% 99.74/13.40 ((
% 99.74/13.40 (infuncsetfunc) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2p) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcinfuncset) =>
% 99.74/13.40 ((
% 99.74/13.40 (lamProp) =>
% 99.74/13.40 ((
% 99.74/13.40 (lamp) =>
% 99.74/13.40 ((
% 99.74/13.40 (lam2p) =>
% 99.74/13.40 ((
% 99.74/13.40 (brelnall1) =>
% 99.74/13.40 ((
% 99.74/13.40 (brelnall2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ex1E2) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp3) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcextLem) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp4) =>
% 99.74/13.40 ((
% 99.74/13.40 (subbreln) =>
% 99.74/13.40 ((
% 99.74/13.40 (eqbreln) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcext) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcext2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2apEq1) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2apEq2) =>
% 99.74/13.40 ((
% 99.74/13.40 (beta1) =>
% 99.74/13.40 ((
% 99.74/13.40 (eta1) =>
% 99.74/13.40 ((
% 99.74/13.40 (lam2lamEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (beta2) =>
% 99.74/13.40 ((
% 99.74/13.40 (eta2) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalseProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalseProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ifSingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (ifp) =>
% 99.74/13.40 ((
% 99.74/13.40 (theeq) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrue) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalse) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueorfalse) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (setminusT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (setextT) =>
% 99.74/13.40 ((
% 99.74/13.40 (subsetTI) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetTI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetTE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectTELcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectTERcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT1) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT2) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT3) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementSub1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementSub2) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTnotintersectT) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementImpComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementSubsetComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementInPowersetComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (contraSubsetComplement) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTcontraSubset) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTILcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTIRcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInUnion) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInUnion2) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInIntersectUnions) =>
% 99.74/13.40 ((
% 99.74/13.40 (intersectInPowersetIntersectUnions) =>
% 99.74/13.40 ((
% 99.74/13.40 (inComplementUnionImpNotIn1) =>
% 99.74/13.40 ((
% 99.74/13.40 (inComplementUnionImpInComplement1) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTE) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTEcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementUnionInPowersetComplement) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a2) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1a) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1b) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2b2) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2b) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule0) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule1) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule2) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule3) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule4) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_1) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_2) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_3) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_4) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_5) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1all2) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1SetBreln1) =>
% 99.74/13.40 ((
% 99.74/13.40 (choice2fnsingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (setOfPairsIsBReln1) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1all1) =>
% 99.74/13.40 ((
% 99.74/13.40 (subbreln1) =>
% 99.74/13.40 ((
% 99.74/13.40 (eqbreln1) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1invprop) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1invI) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1invE) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1compprop) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1compI) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1compE) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1compEex) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionprop) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionIL) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionIR) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionI) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionE) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionEcases) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionCommutes) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz2Ex) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz2W) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz2A) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz2B) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1Ex) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1Ex1) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1Equiv) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1E) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1I) =>
% 99.74/13.40 ((
% 99.74/13.40 (injFuncInInjFuncSet) =>
% 99.74/13.40 ((
% 99.74/13.40 (!!) @ (
% 99.74/13.40 (('#B') @ (
% 99.74/13.40 !!) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 !!))) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#S') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 '#S') @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 '#S'))) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 =>))))) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#C') @ in)))) @
% 99.74/13.40 injFuncSet)))))))) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#C') @ in)))) @
% 99.74/13.40 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.74/13.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1480])).
% 99.74/13.40 thf(zip_derived_cl1496, plain,
% 99.74/13.40 (~ (((cartprodpairin) =>
% 99.74/13.40 (((cartprodmempair1) =>
% 99.74/13.40 (((cartprodmempair) =>
% 99.74/13.40 (((setunionE2) =>
% 99.74/13.40 (((setunionsingleton1) =>
% 99.74/13.40 (((setunionsingleton2) =>
% 99.74/13.40 (((setunionsingleton) =>
% 99.74/13.40 (((singletonprop) =>
% 99.74/13.40 (((ex1E1) =>
% 99.74/13.40 (((ex1I) =>
% 99.74/13.40 (((ex1I2) =>
% 99.74/13.40 (((singletonsuniq) =>
% 99.74/13.40 (((setukpairinjL1) =>
% 99.74/13.40 (((kfstsingleton) =>
% 99.74/13.40 (((theprop) =>
% 99.74/13.40 (((kfstpairEq) =>
% 99.74/13.40 (((cartprodfstin) =>
% 99.74/13.40 (((setukpairinjL2) =>
% 99.74/13.40 (((setukpairinjL) =>
% 99.74/13.40 (((setukpairinjR11) =>
% 99.74/13.40 (((setukpairinjR12) =>
% 99.74/13.40 (((setukpairinjR1) =>
% 99.74/13.40 (((upairequniteq) =>
% 99.74/13.40 (((setukpairinjR2) =>
% 99.74/13.40 (((setukpairinjR) =>
% 99.74/13.40 (((ksndsingleton) =>
% 99.74/13.40 (((ksndpairEq) =>
% 99.74/13.40 (((kpairsurjEq) =>
% 99.74/13.40 (((cartprodsndin) =>
% 99.74/13.40 (((cartprodpairmemEL) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodpairmemER) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodmempaircEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodfstpairEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodsndpairEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodpairsurjEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrI) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrSub) =>
% 99.74/13.40 ((
% 99.74/13.40 (setOfPairsIsBReln) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrERa) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrEL1) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrEL2) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrER) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcImageSingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (apProp) =>
% 99.74/13.40 ((
% 99.74/13.40 (app) =>
% 99.74/13.40 ((
% 99.74/13.40 (infuncsetfunc) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2p) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcinfuncset) =>
% 99.74/13.40 ((
% 99.74/13.40 (lamProp) =>
% 99.74/13.40 ((
% 99.74/13.40 (lamp) =>
% 99.74/13.40 ((
% 99.74/13.40 (lam2p) =>
% 99.74/13.40 ((
% 99.74/13.40 (brelnall1) =>
% 99.74/13.40 ((
% 99.74/13.40 (brelnall2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ex1E2) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp3) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcextLem) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp4) =>
% 99.74/13.40 ((
% 99.74/13.40 (subbreln) =>
% 99.74/13.40 ((
% 99.74/13.40 (eqbreln) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcext) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcext2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2apEq1) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2apEq2) =>
% 99.74/13.40 ((
% 99.74/13.40 (beta1) =>
% 99.74/13.40 ((
% 99.74/13.40 (eta1) =>
% 99.74/13.40 ((
% 99.74/13.40 (lam2lamEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (beta2) =>
% 99.74/13.40 ((
% 99.74/13.40 (eta2) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalseProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalseProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ifSingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (ifp) =>
% 99.74/13.40 ((
% 99.74/13.40 (theeq) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrue) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalse) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueorfalse) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (setminusT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (setextT) =>
% 99.74/13.40 ((
% 99.74/13.40 (subsetTI) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetTI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetTE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectTELcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectTERcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT1) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT2) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT3) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementSub1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementSub2) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTnotintersectT) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementImpComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementSubsetComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementInPowersetComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (contraSubsetComplement) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTcontraSubset) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTILcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTIRcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInUnion) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInUnion2) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInIntersectUnions) =>
% 99.74/13.40 ((
% 99.74/13.40 (intersectInPowersetIntersectUnions) =>
% 99.74/13.40 ((
% 99.74/13.40 (inComplementUnionImpNotIn1) =>
% 99.74/13.40 ((
% 99.74/13.40 (inComplementUnionImpInComplement1) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTE) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTEcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementUnionInPowersetComplement) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a2) =>
% 99.74/13.40 ((
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% 99.74/13.40 (dpsetconstrERa) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrEL1) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrEL2) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrER) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcImageSingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (apProp) =>
% 99.74/13.40 ((
% 99.74/13.40 (app) =>
% 99.74/13.40 ((
% 99.74/13.40 (infuncsetfunc) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2p) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcinfuncset) =>
% 99.74/13.40 ((
% 99.74/13.40 (lamProp) =>
% 99.74/13.40 ((
% 99.74/13.40 (lamp) =>
% 99.74/13.40 ((
% 99.74/13.40 (lam2p) =>
% 99.74/13.40 ((
% 99.74/13.40 (brelnall1) =>
% 99.74/13.40 ((
% 99.74/13.40 (brelnall2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ex1E2) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp3) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcextLem) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp4) =>
% 99.74/13.40 ((
% 99.74/13.40 (subbreln) =>
% 99.74/13.40 ((
% 99.74/13.40 (eqbreln) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcext) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcext2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2apEq1) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2apEq2) =>
% 99.74/13.40 ((
% 99.74/13.40 (beta1) =>
% 99.74/13.40 ((
% 99.74/13.40 (eta1) =>
% 99.74/13.40 ((
% 99.74/13.40 (lam2lamEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (beta2) =>
% 99.74/13.40 ((
% 99.74/13.40 (eta2) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalseProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalseProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ifSingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (ifp) =>
% 99.74/13.40 ((
% 99.74/13.40 (theeq) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrue) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalse) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueorfalse) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (setminusT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (setextT) =>
% 99.74/13.40 ((
% 99.74/13.40 (subsetTI) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetTI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetTE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectTELcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectTERcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT1) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT2) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT3) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementSub1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementSub2) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTnotintersectT) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementImpComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementSubsetComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementInPowersetComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (contraSubsetComplement) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTcontraSubset) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTILcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTIRcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInUnion) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInUnion2) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInIntersectUnions) =>
% 99.74/13.40 ((
% 99.74/13.40 (intersectInPowersetIntersectUnions) =>
% 99.74/13.40 ((
% 99.74/13.40 (inComplementUnionImpNotIn1) =>
% 99.74/13.40 ((
% 99.74/13.40 (inComplementUnionImpInComplement1) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTE) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTEcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementUnionInPowersetComplement) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a2) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1a) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1b) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2b2) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2b) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule0) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule1) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule2) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule3) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule4) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_1) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_2) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_3) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_4) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_5) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1all2) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1SetBreln1) =>
% 99.74/13.40 ((
% 99.74/13.40 (choice2fnsingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (setOfPairsIsBReln1) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1all1) =>
% 99.74/13.40 ((
% 99.74/13.40 (subbreln1) =>
% 99.74/13.40 ((
% 99.74/13.40 (eqbreln1) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1invprop) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1invI) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1invE) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1compprop) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1compI) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1compE) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1compEex) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionprop) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionIL) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionIR) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionI) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionE) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionEcases) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionCommutes) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz2Ex) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz2W) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz2A) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz2B) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1Ex) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1Ex1) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1Equiv) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1E) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1I) =>
% 99.74/13.40 ((
% 99.74/13.40 (injFuncInInjFuncSet) =>
% 99.74/13.40 ((
% 99.74/13.40 (!!) @ (
% 99.74/13.40 (('#B') @ (
% 99.74/13.40 !!) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 !!))) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#S') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 '#S') @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 '#S'))) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 =>))))) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#C') @ in)))) @
% 99.74/13.40 injFuncSet)))))))) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#C') @ in)))) @
% 99.74/13.40 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.74/13.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1505])).
% 99.74/13.40 thf(zip_derived_cl1525, plain,
% 99.74/13.40 (~ (((setunionE2) =>
% 99.74/13.40 (((setunionsingleton1) =>
% 99.74/13.40 (((setunionsingleton2) =>
% 99.74/13.40 (((setunionsingleton) =>
% 99.74/13.40 (((singletonprop) =>
% 99.74/13.40 (((ex1E1) =>
% 99.74/13.40 (((ex1I) =>
% 99.74/13.40 (((ex1I2) =>
% 99.74/13.40 (((singletonsuniq) =>
% 99.74/13.40 (((setukpairinjL1) =>
% 99.74/13.40 (((kfstsingleton) =>
% 99.74/13.40 (((theprop) =>
% 99.74/13.40 (((kfstpairEq) =>
% 99.74/13.40 (((cartprodfstin) =>
% 99.74/13.40 (((setukpairinjL2) =>
% 99.74/13.40 (((setukpairinjL) =>
% 99.74/13.40 (((setukpairinjR11) =>
% 99.74/13.40 (((setukpairinjR12) =>
% 99.74/13.40 (((setukpairinjR1) =>
% 99.74/13.40 (((upairequniteq) =>
% 99.74/13.40 (((setukpairinjR2) =>
% 99.74/13.40 (((setukpairinjR) =>
% 99.74/13.40 (((ksndsingleton) =>
% 99.74/13.40 (((ksndpairEq) =>
% 99.74/13.40 (((kpairsurjEq) =>
% 99.74/13.40 (((cartprodsndin) =>
% 99.74/13.40 (((cartprodpairmemEL) =>
% 99.74/13.40 (((cartprodpairmemER) =>
% 99.74/13.40 (((cartprodmempaircEq) =>
% 99.74/13.40 (((cartprodfstpairEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodsndpairEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (cartprodpairsurjEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrI) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrSub) =>
% 99.74/13.40 ((
% 99.74/13.40 (setOfPairsIsBReln) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrERa) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrEL1) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrEL2) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrER) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcImageSingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (apProp) =>
% 99.74/13.40 ((
% 99.74/13.40 (app) =>
% 99.74/13.40 ((
% 99.74/13.40 (infuncsetfunc) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2p) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcinfuncset) =>
% 99.74/13.40 ((
% 99.74/13.40 (lamProp) =>
% 99.74/13.40 ((
% 99.74/13.40 (lamp) =>
% 99.74/13.40 ((
% 99.74/13.40 (lam2p) =>
% 99.74/13.40 ((
% 99.74/13.40 (brelnall1) =>
% 99.74/13.40 ((
% 99.74/13.40 (brelnall2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ex1E2) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp3) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcextLem) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp4) =>
% 99.74/13.40 ((
% 99.74/13.40 (subbreln) =>
% 99.74/13.40 ((
% 99.74/13.40 (eqbreln) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcext) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcext2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2apEq1) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2apEq2) =>
% 99.74/13.40 ((
% 99.74/13.40 (beta1) =>
% 99.74/13.40 ((
% 99.74/13.40 (eta1) =>
% 99.74/13.40 ((
% 99.74/13.40 (lam2lamEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (beta2) =>
% 99.74/13.40 ((
% 99.74/13.40 (eta2) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalseProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalseProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ifSingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (ifp) =>
% 99.74/13.40 ((
% 99.74/13.40 (theeq) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrue) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalse) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueorfalse) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (setminusT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (setextT) =>
% 99.74/13.40 ((
% 99.74/13.40 (subsetTI) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetTI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetTE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectTELcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectTERcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT1) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT2) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT3) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementSub1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementSub2) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTnotintersectT) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementImpComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementSubsetComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementInPowersetComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (contraSubsetComplement) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTcontraSubset) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTILcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTIRcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInUnion) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInUnion2) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInIntersectUnions) =>
% 99.74/13.40 ((
% 99.74/13.40 (intersectInPowersetIntersectUnions) =>
% 99.74/13.40 ((
% 99.74/13.40 (inComplementUnionImpNotIn1) =>
% 99.74/13.40 ((
% 99.74/13.40 (inComplementUnionImpInComplement1) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTE) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTEcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementUnionInPowersetComplement) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a2) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1a) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1b) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2b2) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2b) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule0) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule1) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule2) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule3) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule4) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_1) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_2) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_3) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_4) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_5) =>
% 99.74/13.40 ((
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% 99.74/13.40 (ap2apEq2) =>
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% 99.74/13.40 (eta1) =>
% 99.74/13.40 ((
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% 99.74/13.40 ((
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% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2b2) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2b) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2) =>
% 99.74/13.40 ((
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% 99.74/13.40 ((
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% 99.74/13.40 (woz13rule2) =>
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% 99.74/13.40 (woz13rule3) =>
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% 99.74/13.40 (woz1_2) =>
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% 99.74/13.40 (woz1_3) =>
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% 99.74/13.40 (woz1_5) =>
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% 99.74/13.40 ((
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% 99.74/13.40 ((
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% 99.74/13.40 (breln1compEex) =>
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% 99.74/13.40 ((
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% 99.74/13.40 (breln1unionI) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionE) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionEcases) =>
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% 99.74/13.40 (breln1unionCommutes) =>
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% 99.74/13.40 ((
% 99.74/13.40 (woz2W) =>
% 99.74/13.40 ((
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% 99.74/13.40 ((
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% 99.74/13.40 ((
% 99.74/13.40 (image1Ex1) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1Equiv) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1E) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1I) =>
% 99.74/13.40 ((
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% 99.74/13.40 (
% 99.74/13.40 (
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% 99.74/13.40 ((
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% 99.74/13.40 ((
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% 99.74/13.40 ((
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% 99.74/13.40 ((
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% 99.74/13.40 ((
% 99.74/13.40 (complementTcontraSubset) =>
% 99.74/13.40 ((
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% 99.74/13.40 ((
% 99.74/13.40 (intersectInPowersetIntersectUnions) =>
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% 99.74/13.40 ((
% 99.74/13.40 (inComplementUnionImpInComplement1) =>
% 99.74/13.40 ((
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% 99.74/13.40 ((
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% 99.74/13.40 ((
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% 99.74/13.40 ((
% 99.74/13.40 (complementUnionInPowersetComplement) =>
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% 99.74/13.40 (demorgan2a2) =>
% 99.74/13.40 ((
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% 99.74/13.40 ((
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% 99.74/13.40 ((
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% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2b2) =>
% 99.74/13.40 ((
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% 99.74/13.40 (((setukpairinjR11) =>
% 99.74/13.40 (((setukpairinjR12) =>
% 99.74/13.40 (((setukpairinjR1) =>
% 99.74/13.40 (((upairequniteq) =>
% 99.74/13.40 (((setukpairinjR2) =>
% 99.74/13.40 (((setukpairinjR) =>
% 99.74/13.40 (((ksndsingleton) =>
% 99.74/13.40 (((ksndpairEq) =>
% 99.74/13.40 (((kpairsurjEq) =>
% 99.74/13.40 (((cartprodsndin) =>
% 99.74/13.40 (((cartprodpairmemEL) =>
% 99.74/13.40 (((cartprodpairmemER) =>
% 99.74/13.40 (((cartprodmempaircEq) =>
% 99.74/13.40 (((cartprodfstpairEq) =>
% 99.74/13.40 (((cartprodsndpairEq) =>
% 99.74/13.40 (((cartprodpairsurjEq) =>
% 99.74/13.40 (((dpsetconstrI) =>
% 99.74/13.40 (((dpsetconstrSub) =>
% 99.74/13.40 (((setOfPairsIsBReln) =>
% 99.74/13.40 (((dpsetconstrERa) =>
% 99.74/13.40 (((dpsetconstrEL1) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrEL2) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrER) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcImageSingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (apProp) =>
% 99.74/13.40 ((
% 99.74/13.40 (app) =>
% 99.74/13.40 ((
% 99.74/13.40 (infuncsetfunc) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2p) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcinfuncset) =>
% 99.74/13.40 ((
% 99.74/13.40 (lamProp) =>
% 99.74/13.40 ((
% 99.74/13.40 (lamp) =>
% 99.74/13.40 ((
% 99.74/13.40 (lam2p) =>
% 99.74/13.40 ((
% 99.74/13.40 (brelnall1) =>
% 99.74/13.40 ((
% 99.74/13.40 (brelnall2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ex1E2) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp3) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcextLem) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp4) =>
% 99.74/13.40 ((
% 99.74/13.40 (subbreln) =>
% 99.74/13.40 ((
% 99.74/13.40 (eqbreln) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcext) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcext2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2apEq1) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2apEq2) =>
% 99.74/13.40 ((
% 99.74/13.40 (beta1) =>
% 99.74/13.40 ((
% 99.74/13.40 (eta1) =>
% 99.74/13.40 ((
% 99.74/13.40 (lam2lamEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (beta2) =>
% 99.74/13.40 ((
% 99.74/13.40 (eta2) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalseProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalseProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ifSingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (ifp) =>
% 99.74/13.40 ((
% 99.74/13.40 (theeq) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrue) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalse) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueorfalse) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (setminusT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (setextT) =>
% 99.74/13.40 ((
% 99.74/13.40 (subsetTI) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetTI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetTE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectTELcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectTERcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT1) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT2) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT3) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementSub1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementSub2) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTnotintersectT) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementImpComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementSubsetComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementInPowersetComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (contraSubsetComplement) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTcontraSubset) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTILcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTIRcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInUnion) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInUnion2) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInIntersectUnions) =>
% 99.74/13.40 ((
% 99.74/13.40 (intersectInPowersetIntersectUnions) =>
% 99.74/13.40 ((
% 99.74/13.40 (inComplementUnionImpNotIn1) =>
% 99.74/13.40 ((
% 99.74/13.40 (inComplementUnionImpInComplement1) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTE) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTEcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementUnionInPowersetComplement) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a2) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1a) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1b) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2b2) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2b) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule0) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule1) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule2) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule3) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule4) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_1) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_2) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_3) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_4) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_5) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1all2) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1SetBreln1) =>
% 99.74/13.40 ((
% 99.74/13.40 (choice2fnsingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (setOfPairsIsBReln1) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1all1) =>
% 99.74/13.40 ((
% 99.74/13.40 (subbreln1) =>
% 99.74/13.40 ((
% 99.74/13.40 (eqbreln1) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1invprop) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1invI) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1invE) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1compprop) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1compI) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1compE) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1compEex) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionprop) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionIL) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionIR) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionI) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionE) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionEcases) =>
% 99.74/13.40 ((
% 99.74/13.40 (breln1unionCommutes) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz2Ex) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz2W) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz2A) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz2B) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1Ex) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1Ex1) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1Equiv) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1E) =>
% 99.74/13.40 ((
% 99.74/13.40 (image1I) =>
% 99.74/13.40 ((
% 99.74/13.40 (injFuncInInjFuncSet) =>
% 99.74/13.40 ((
% 99.74/13.40 (!!) @ (
% 99.74/13.40 (('#B') @ (
% 99.74/13.40 !!) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 !!))) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#S') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 '#S') @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 '#S'))) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 =>))))) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#C') @ in)))) @
% 99.74/13.40 injFuncSet)))))))) @
% 99.74/13.40 (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#B') @ (
% 99.74/13.40 (
% 99.74/13.40 ('#C') @ in)))) @
% 99.74/13.40 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.74/13.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1582])).
% 99.74/13.40 thf(zip_derived_cl1599, plain,
% 99.74/13.40 (~ (((singletonsuniq) =>
% 99.74/13.40 (((setukpairinjL1) =>
% 99.74/13.40 (((kfstsingleton) =>
% 99.74/13.40 (((theprop) =>
% 99.74/13.40 (((kfstpairEq) =>
% 99.74/13.40 (((cartprodfstin) =>
% 99.74/13.40 (((setukpairinjL2) =>
% 99.74/13.40 (((setukpairinjL) =>
% 99.74/13.40 (((setukpairinjR11) =>
% 99.74/13.40 (((setukpairinjR12) =>
% 99.74/13.40 (((setukpairinjR1) =>
% 99.74/13.40 (((upairequniteq) =>
% 99.74/13.40 (((setukpairinjR2) =>
% 99.74/13.40 (((setukpairinjR) =>
% 99.74/13.40 (((ksndsingleton) =>
% 99.74/13.40 (((ksndpairEq) =>
% 99.74/13.40 (((kpairsurjEq) =>
% 99.74/13.40 (((cartprodsndin) =>
% 99.74/13.40 (((cartprodpairmemEL) =>
% 99.74/13.40 (((cartprodpairmemER) =>
% 99.74/13.40 (((cartprodmempaircEq) =>
% 99.74/13.40 (((cartprodfstpairEq) =>
% 99.74/13.40 (((cartprodsndpairEq) =>
% 99.74/13.40 (((cartprodpairsurjEq) =>
% 99.74/13.40 (((dpsetconstrI) =>
% 99.74/13.40 (((dpsetconstrSub) =>
% 99.74/13.40 (((setOfPairsIsBReln) =>
% 99.74/13.40 (((dpsetconstrERa) =>
% 99.74/13.40 (((dpsetconstrEL1) =>
% 99.74/13.40 (((dpsetconstrEL2) =>
% 99.74/13.40 ((
% 99.74/13.40 (dpsetconstrER) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcImageSingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (apProp) =>
% 99.74/13.40 ((
% 99.74/13.40 (app) =>
% 99.74/13.40 ((
% 99.74/13.40 (infuncsetfunc) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2p) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcinfuncset) =>
% 99.74/13.40 ((
% 99.74/13.40 (lamProp) =>
% 99.74/13.40 ((
% 99.74/13.40 (lamp) =>
% 99.74/13.40 ((
% 99.74/13.40 (lam2p) =>
% 99.74/13.40 ((
% 99.74/13.40 (brelnall1) =>
% 99.74/13.40 ((
% 99.74/13.40 (brelnall2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ex1E2) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp3) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcextLem) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcGraphProp4) =>
% 99.74/13.40 ((
% 99.74/13.40 (subbreln) =>
% 99.74/13.40 ((
% 99.74/13.40 (eqbreln) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcext) =>
% 99.74/13.40 ((
% 99.74/13.40 (funcext2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2apEq1) =>
% 99.74/13.40 ((
% 99.74/13.40 (ap2apEq2) =>
% 99.74/13.40 ((
% 99.74/13.40 (beta1) =>
% 99.74/13.40 ((
% 99.74/13.40 (eta1) =>
% 99.74/13.40 ((
% 99.74/13.40 (lam2lamEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (beta2) =>
% 99.74/13.40 ((
% 99.74/13.40 (eta2) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalseProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalseProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueProp1) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueProp2) =>
% 99.74/13.40 ((
% 99.74/13.40 (ifSingleton) =>
% 99.74/13.40 ((
% 99.74/13.40 (ifp) =>
% 99.74/13.40 ((
% 99.74/13.40 (theeq) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrue) =>
% 99.74/13.40 ((
% 99.74/13.40 (iffalse) =>
% 99.74/13.40 ((
% 99.74/13.40 (iftrueorfalse) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (setminusT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementT_lem) =>
% 99.74/13.40 ((
% 99.74/13.40 (setextT) =>
% 99.74/13.40 ((
% 99.74/13.40 (subsetTI) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetTI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (powersetTE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectTELcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (binintersectTERcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT1) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT2) =>
% 99.74/13.40 ((
% 99.74/13.40 (contrasubsetT3) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementI1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementE1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementSub1) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementSub2) =>
% 99.74/13.40 ((
% 99.74/13.40 (doubleComplementEq) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTnotintersectT) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementImpComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementSubsetComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementInPowersetComplementIntersect) =>
% 99.74/13.40 ((
% 99.74/13.40 (contraSubsetComplement) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementTcontraSubset) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTILcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTIRcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInUnion) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInUnion2) =>
% 99.74/13.40 ((
% 99.74/13.40 (inIntersectImpInIntersectUnions) =>
% 99.74/13.40 ((
% 99.74/13.40 (intersectInPowersetIntersectUnions) =>
% 99.74/13.40 ((
% 99.74/13.40 (inComplementUnionImpNotIn1) =>
% 99.74/13.40 ((
% 99.74/13.40 (inComplementUnionImpInComplement1) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTE) =>
% 99.74/13.40 ((
% 99.74/13.40 (binunionTEcontra) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a1) =>
% 99.74/13.40 ((
% 99.74/13.40 (complementUnionInPowersetComplement) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a2) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1a) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1b) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan1) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2a) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2b2) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2b) =>
% 99.74/13.40 ((
% 99.74/13.40 (demorgan2) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule0) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule1) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule2) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule3) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz13rule4) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_1) =>
% 99.74/13.40 ((
% 99.74/13.40 (woz1_2) =>
% 99.74/13.40 ((
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% 99.86/13.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1678])).
% 99.86/13.41 thf(zip_derived_cl1711, plain,
% 99.86/13.41 (~ (((setukpairinjR12) =>
% 99.86/13.41 (((setukpairinjR1) =>
% 99.86/13.41 (((upairequniteq) =>
% 99.86/13.41 (((setukpairinjR2) =>
% 99.86/13.41 (((setukpairinjR) =>
% 99.86/13.41 (((ksndsingleton) =>
% 99.86/13.41 (((ksndpairEq) =>
% 99.86/13.41 (((kpairsurjEq) =>
% 99.86/13.41 (((cartprodsndin) =>
% 99.86/13.41 (((cartprodpairmemEL) =>
% 99.86/13.41 (((cartprodpairmemER) =>
% 99.86/13.41 (((cartprodmempaircEq) =>
% 99.86/13.41 (((cartprodfstpairEq) =>
% 99.86/13.41 (((cartprodsndpairEq) =>
% 99.86/13.41 (((cartprodpairsurjEq) =>
% 99.86/13.41 (((dpsetconstrI) =>
% 99.86/13.41 (((dpsetconstrSub) =>
% 99.86/13.41 (((setOfPairsIsBReln) =>
% 99.86/13.41 (((dpsetconstrERa) =>
% 99.86/13.41 (((dpsetconstrEL1) =>
% 99.86/13.41 (((dpsetconstrEL2) =>
% 99.86/13.41 (((dpsetconstrER) =>
% 99.86/13.41 (((funcImageSingleton) =>
% 99.86/13.41 (((apProp) =>
% 99.86/13.41 (((app) =>
% 99.86/13.41 (((infuncsetfunc) =>
% 99.86/13.41 (((ap2p) =>
% 99.86/13.41 (((funcinfuncset) =>
% 99.86/13.41 (((lamProp) =>
% 99.86/13.41 (((lamp) =>
% 99.86/13.41 ((
% 99.86/13.41 (lam2p) =>
% 99.86/13.41 ((
% 99.86/13.41 (brelnall1) =>
% 99.86/13.41 ((
% 99.86/13.41 (brelnall2) =>
% 99.86/13.41 ((
% 99.86/13.41 (ex1E2) =>
% 99.86/13.41 ((
% 99.86/13.41 (funcGraphProp1) =>
% 99.86/13.41 ((
% 99.86/13.41 (funcGraphProp3) =>
% 99.86/13.41 ((
% 99.86/13.41 (funcGraphProp2) =>
% 99.86/13.41 ((
% 99.86/13.41 (funcextLem) =>
% 99.86/13.41 ((
% 99.86/13.41 (funcGraphProp4) =>
% 99.86/13.41 ((
% 99.86/13.41 (subbreln) =>
% 99.86/13.41 ((
% 99.86/13.41 (eqbreln) =>
% 99.86/13.41 ((
% 99.86/13.41 (funcext) =>
% 99.86/13.41 ((
% 99.86/13.41 (funcext2) =>
% 99.86/13.41 ((
% 99.86/13.41 (ap2apEq1) =>
% 99.86/13.41 ((
% 99.86/13.41 (ap2apEq2) =>
% 99.86/13.41 ((
% 99.86/13.41 (beta1) =>
% 99.86/13.41 ((
% 99.86/13.41 (eta1) =>
% 99.86/13.41 ((
% 99.86/13.41 (lam2lamEq) =>
% 99.86/13.41 ((
% 99.86/13.41 (beta2) =>
% 99.86/13.41 ((
% 99.86/13.41 (eta2) =>
% 99.86/13.41 ((
% 99.86/13.41 (iffalseProp1) =>
% 99.86/13.41 ((
% 99.86/13.41 (iffalseProp2) =>
% 99.86/13.41 ((
% 99.86/13.41 (iftrueProp1) =>
% 99.86/13.41 ((
% 99.86/13.41 (iftrueProp2) =>
% 99.86/13.41 ((
% 99.86/13.41 (ifSingleton) =>
% 99.86/13.41 ((
% 99.86/13.41 (ifp) =>
% 99.86/13.41 ((
% 99.86/13.41 (theeq) =>
% 99.86/13.41 ((
% 99.86/13.41 (iftrue) =>
% 99.86/13.41 ((
% 99.86/13.41 (iffalse) =>
% 99.86/13.41 ((
% 99.86/13.41 (iftrueorfalse) =>
% 99.86/13.41 ((
% 99.86/13.41 (binintersectT_lem) =>
% 99.86/13.41 ((
% 99.86/13.41 (binunionT_lem) =>
% 99.86/13.41 ((
% 99.86/13.41 (powersetT_lem) =>
% 99.86/13.41 ((
% 99.86/13.41 (setminusT_lem) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementT_lem) =>
% 99.86/13.41 ((
% 99.86/13.41 (setextT) =>
% 99.86/13.41 ((
% 99.86/13.41 (subsetTI) =>
% 99.86/13.41 ((
% 99.86/13.41 (powersetTI1) =>
% 99.86/13.41 ((
% 99.86/13.41 (powersetTE1) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementTI1) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementTE1) =>
% 99.86/13.41 ((
% 99.86/13.41 (binintersectTELcontra) =>
% 99.86/13.41 ((
% 99.86/13.41 (binintersectTERcontra) =>
% 99.86/13.41 ((
% 99.86/13.41 (contrasubsetT) =>
% 99.86/13.41 ((
% 99.86/13.41 (contrasubsetT1) =>
% 99.86/13.41 ((
% 99.86/13.41 (contrasubsetT2) =>
% 99.86/13.41 ((
% 99.86/13.41 (contrasubsetT3) =>
% 99.86/13.41 ((
% 99.86/13.41 (doubleComplementI1) =>
% 99.86/13.41 ((
% 99.86/13.41 (doubleComplementE1) =>
% 99.86/13.41 ((
% 99.86/13.41 (doubleComplementSub1) =>
% 99.86/13.41 ((
% 99.86/13.41 (doubleComplementSub2) =>
% 99.86/13.41 ((
% 99.86/13.41 (doubleComplementEq) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementTnotintersectT) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementImpComplementIntersect) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementSubsetComplementIntersect) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementInPowersetComplementIntersect) =>
% 99.86/13.41 ((
% 99.86/13.41 (contraSubsetComplement) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementTcontraSubset) =>
% 99.86/13.41 ((
% 99.86/13.41 (binunionTILcontra) =>
% 99.86/13.41 ((
% 99.86/13.41 (binunionTIRcontra) =>
% 99.86/13.41 ((
% 99.86/13.41 (inIntersectImpInUnion) =>
% 99.86/13.41 ((
% 99.86/13.41 (inIntersectImpInUnion2) =>
% 99.86/13.41 ((
% 99.86/13.41 (inIntersectImpInIntersectUnions) =>
% 99.86/13.41 ((
% 99.86/13.41 (intersectInPowersetIntersectUnions) =>
% 99.86/13.41 ((
% 99.86/13.41 (inComplementUnionImpNotIn1) =>
% 99.86/13.41 ((
% 99.86/13.41 (inComplementUnionImpInComplement1) =>
% 99.86/13.41 ((
% 99.86/13.41 (binunionTE) =>
% 99.86/13.41 ((
% 99.86/13.41 (binunionTEcontra) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan2a1) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementUnionInPowersetComplement) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan2a2) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan1a) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan1b) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan1) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan2a) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan2b2) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan2b) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan2) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz13rule0) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz13rule1) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz13rule2) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz13rule3) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz13rule4) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz1_1) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz1_2) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz1_3) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz1_4) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz1_5) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1all2) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1SetBreln1) =>
% 99.86/13.41 ((
% 99.86/13.41 (choice2fnsingleton) =>
% 99.86/13.41 ((
% 99.86/13.41 (setOfPairsIsBReln1) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1all1) =>
% 99.86/13.41 ((
% 99.86/13.41 (subbreln1) =>
% 99.86/13.41 ((
% 99.86/13.41 (eqbreln1) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1invprop) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1invI) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1invE) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1compprop) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1compI) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1compE) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1compEex) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1unionprop) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1unionIL) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1unionIR) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1unionI) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1unionE) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1unionEcases) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1unionCommutes) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz2Ex) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz2W) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz2A) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz2B) =>
% 99.86/13.41 ((
% 99.86/13.41 (image1Ex) =>
% 99.86/13.41 ((
% 99.86/13.41 (image1Ex1) =>
% 99.86/13.41 ((
% 99.86/13.41 (image1Equiv) =>
% 99.86/13.41 ((
% 99.86/13.41 (image1E) =>
% 99.86/13.41 ((
% 99.86/13.41 (image1I) =>
% 99.86/13.41 ((
% 99.86/13.41 (injFuncInInjFuncSet) =>
% 99.86/13.41 ((
% 99.86/13.41 (!!) @ (
% 99.86/13.41 (('#B') @ (
% 99.86/13.41 !!) @
% 99.86/13.41 (
% 99.86/13.41 (
% 99.86/13.41 ('#B') @ (
% 99.86/13.41 (
% 99.86/13.41 ('#B') @ (
% 99.86/13.41 !!))) @
% 99.86/13.41 (
% 99.86/13.41 (
% 99.86/13.41 ('#S') @ (
% 99.86/13.41 (
% 99.86/13.41 ('#B') @ (
% 99.86/13.41 '#S') @
% 99.86/13.41 (
% 99.86/13.41 (
% 99.86/13.41 ('#B') @ (
% 99.86/13.41 (
% 99.86/13.41 ('#B') @ (
% 99.86/13.41 '#S'))) @
% 99.86/13.41 (
% 99.86/13.41 (
% 99.86/13.41 ('#B') @ (
% 99.86/13.41 (
% 99.86/13.41 ('#B') @ (
% 99.86/13.41 (
% 99.86/13.41 ('#B') @ (
% 99.86/13.41 =>))))) @
% 99.86/13.41 (
% 99.86/13.41 (
% 99.86/13.41 ('#B') @ (
% 99.86/13.41 (
% 99.86/13.41 ('#B') @ (
% 99.86/13.41 (
% 99.86/13.41 ('#C') @ in)))) @
% 99.86/13.41 injFuncSet)))))))) @
% 99.86/13.41 (
% 99.86/13.41 (
% 99.86/13.41 ('#B') @ (
% 99.86/13.41 (
% 99.86/13.41 ('#B') @ (
% 99.86/13.41 (
% 99.86/13.41 ('#C') @ in)))) @
% 99.86/13.41 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.86/13.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1695])).
% 99.86/13.41 thf(zip_derived_cl1725, plain,
% 99.86/13.41 (~ (((setukpairinjR1) =>
% 99.86/13.41 (((upairequniteq) =>
% 99.86/13.41 (((setukpairinjR2) =>
% 99.86/13.41 (((setukpairinjR) =>
% 99.86/13.41 (((ksndsingleton) =>
% 99.86/13.41 (((ksndpairEq) =>
% 99.86/13.41 (((kpairsurjEq) =>
% 99.86/13.41 (((cartprodsndin) =>
% 99.86/13.41 (((cartprodpairmemEL) =>
% 99.86/13.41 (((cartprodpairmemER) =>
% 99.86/13.41 (((cartprodmempaircEq) =>
% 99.86/13.41 (((cartprodfstpairEq) =>
% 99.86/13.41 (((cartprodsndpairEq) =>
% 99.86/13.41 (((cartprodpairsurjEq) =>
% 99.86/13.41 (((dpsetconstrI) =>
% 99.86/13.41 (((dpsetconstrSub) =>
% 99.86/13.41 (((setOfPairsIsBReln) =>
% 99.86/13.41 (((dpsetconstrERa) =>
% 99.86/13.41 (((dpsetconstrEL1) =>
% 99.86/13.41 (((dpsetconstrEL2) =>
% 99.86/13.41 (((dpsetconstrER) =>
% 99.86/13.41 (((funcImageSingleton) =>
% 99.86/13.41 (((apProp) =>
% 99.86/13.41 (((app) =>
% 99.86/13.41 (((infuncsetfunc) =>
% 99.86/13.41 (((ap2p) =>
% 99.86/13.41 (((funcinfuncset) =>
% 99.86/13.41 (((lamProp) =>
% 99.86/13.41 (((lamp) =>
% 99.86/13.41 (((lam2p) =>
% 99.86/13.41 ((
% 99.86/13.41 (brelnall1) =>
% 99.86/13.41 ((
% 99.86/13.41 (brelnall2) =>
% 99.86/13.41 ((
% 99.86/13.41 (ex1E2) =>
% 99.86/13.41 ((
% 99.86/13.41 (funcGraphProp1) =>
% 99.86/13.41 ((
% 99.86/13.41 (funcGraphProp3) =>
% 99.86/13.41 ((
% 99.86/13.41 (funcGraphProp2) =>
% 99.86/13.41 ((
% 99.86/13.41 (funcextLem) =>
% 99.86/13.41 ((
% 99.86/13.41 (funcGraphProp4) =>
% 99.86/13.41 ((
% 99.86/13.41 (subbreln) =>
% 99.86/13.41 ((
% 99.86/13.41 (eqbreln) =>
% 99.86/13.41 ((
% 99.86/13.41 (funcext) =>
% 99.86/13.41 ((
% 99.86/13.41 (funcext2) =>
% 99.86/13.41 ((
% 99.86/13.41 (ap2apEq1) =>
% 99.86/13.41 ((
% 99.86/13.41 (ap2apEq2) =>
% 99.86/13.41 ((
% 99.86/13.41 (beta1) =>
% 99.86/13.41 ((
% 99.86/13.41 (eta1) =>
% 99.86/13.41 ((
% 99.86/13.41 (lam2lamEq) =>
% 99.86/13.41 ((
% 99.86/13.41 (beta2) =>
% 99.86/13.41 ((
% 99.86/13.41 (eta2) =>
% 99.86/13.41 ((
% 99.86/13.41 (iffalseProp1) =>
% 99.86/13.41 ((
% 99.86/13.41 (iffalseProp2) =>
% 99.86/13.41 ((
% 99.86/13.41 (iftrueProp1) =>
% 99.86/13.41 ((
% 99.86/13.41 (iftrueProp2) =>
% 99.86/13.41 ((
% 99.86/13.41 (ifSingleton) =>
% 99.86/13.41 ((
% 99.86/13.41 (ifp) =>
% 99.86/13.41 ((
% 99.86/13.41 (theeq) =>
% 99.86/13.41 ((
% 99.86/13.41 (iftrue) =>
% 99.86/13.41 ((
% 99.86/13.41 (iffalse) =>
% 99.86/13.41 ((
% 99.86/13.41 (iftrueorfalse) =>
% 99.86/13.41 ((
% 99.86/13.41 (binintersectT_lem) =>
% 99.86/13.41 ((
% 99.86/13.41 (binunionT_lem) =>
% 99.86/13.41 ((
% 99.86/13.41 (powersetT_lem) =>
% 99.86/13.41 ((
% 99.86/13.41 (setminusT_lem) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementT_lem) =>
% 99.86/13.41 ((
% 99.86/13.41 (setextT) =>
% 99.86/13.41 ((
% 99.86/13.41 (subsetTI) =>
% 99.86/13.41 ((
% 99.86/13.41 (powersetTI1) =>
% 99.86/13.41 ((
% 99.86/13.41 (powersetTE1) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementTI1) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementTE1) =>
% 99.86/13.41 ((
% 99.86/13.41 (binintersectTELcontra) =>
% 99.86/13.41 ((
% 99.86/13.41 (binintersectTERcontra) =>
% 99.86/13.41 ((
% 99.86/13.41 (contrasubsetT) =>
% 99.86/13.41 ((
% 99.86/13.41 (contrasubsetT1) =>
% 99.86/13.41 ((
% 99.86/13.41 (contrasubsetT2) =>
% 99.86/13.41 ((
% 99.86/13.41 (contrasubsetT3) =>
% 99.86/13.41 ((
% 99.86/13.41 (doubleComplementI1) =>
% 99.86/13.41 ((
% 99.86/13.41 (doubleComplementE1) =>
% 99.86/13.41 ((
% 99.86/13.41 (doubleComplementSub1) =>
% 99.86/13.41 ((
% 99.86/13.41 (doubleComplementSub2) =>
% 99.86/13.41 ((
% 99.86/13.41 (doubleComplementEq) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementTnotintersectT) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementImpComplementIntersect) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementSubsetComplementIntersect) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementInPowersetComplementIntersect) =>
% 99.86/13.41 ((
% 99.86/13.41 (contraSubsetComplement) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementTcontraSubset) =>
% 99.86/13.41 ((
% 99.86/13.41 (binunionTILcontra) =>
% 99.86/13.41 ((
% 99.86/13.41 (binunionTIRcontra) =>
% 99.86/13.41 ((
% 99.86/13.41 (inIntersectImpInUnion) =>
% 99.86/13.41 ((
% 99.86/13.41 (inIntersectImpInUnion2) =>
% 99.86/13.41 ((
% 99.86/13.41 (inIntersectImpInIntersectUnions) =>
% 99.86/13.41 ((
% 99.86/13.41 (intersectInPowersetIntersectUnions) =>
% 99.86/13.41 ((
% 99.86/13.41 (inComplementUnionImpNotIn1) =>
% 99.86/13.41 ((
% 99.86/13.41 (inComplementUnionImpInComplement1) =>
% 99.86/13.41 ((
% 99.86/13.41 (binunionTE) =>
% 99.86/13.41 ((
% 99.86/13.41 (binunionTEcontra) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan2a1) =>
% 99.86/13.41 ((
% 99.86/13.41 (complementUnionInPowersetComplement) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan2a2) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan1a) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan1b) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan1) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan2a) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan2b2) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan2b) =>
% 99.86/13.41 ((
% 99.86/13.41 (demorgan2) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz13rule0) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz13rule1) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz13rule2) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz13rule3) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz13rule4) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz1_1) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz1_2) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz1_3) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz1_4) =>
% 99.86/13.41 ((
% 99.86/13.41 (woz1_5) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1all2) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1SetBreln1) =>
% 99.86/13.41 ((
% 99.86/13.41 (choice2fnsingleton) =>
% 99.86/13.41 ((
% 99.86/13.41 (setOfPairsIsBReln1) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1all1) =>
% 99.86/13.41 ((
% 99.86/13.41 (subbreln1) =>
% 99.86/13.41 ((
% 99.86/13.41 (eqbreln1) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1invprop) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1invI) =>
% 99.86/13.41 ((
% 99.86/13.41 (breln1invE) =>
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% 99.93/13.42 thf(zip_derived_cl1787, plain,
% 99.93/13.42 (~ (((kpairsurjEq) =>
% 99.93/13.42 (((cartprodsndin) =>
% 99.93/13.42 (((cartprodpairmemEL) =>
% 99.93/13.42 (((cartprodpairmemER) =>
% 99.93/13.42 (((cartprodmempaircEq) =>
% 99.93/13.42 (((cartprodfstpairEq) =>
% 99.93/13.42 (((cartprodsndpairEq) =>
% 99.93/13.42 (((cartprodpairsurjEq) =>
% 99.93/13.42 (((dpsetconstrI) =>
% 99.93/13.42 (((dpsetconstrSub) =>
% 99.93/13.42 (((setOfPairsIsBReln) =>
% 99.93/13.42 (((dpsetconstrERa) =>
% 99.93/13.42 (((dpsetconstrEL1) =>
% 99.93/13.42 (((dpsetconstrEL2) =>
% 99.93/13.42 (((dpsetconstrER) =>
% 99.93/13.42 (((funcImageSingleton) =>
% 99.93/13.42 (((apProp) =>
% 99.93/13.42 (((app) =>
% 99.93/13.42 (((infuncsetfunc) =>
% 99.93/13.42 (((ap2p) =>
% 99.93/13.42 (((funcinfuncset) =>
% 99.93/13.42 (((lamProp) =>
% 99.93/13.42 (((lamp) =>
% 99.93/13.42 (((lam2p) =>
% 99.93/13.42 (((brelnall1) =>
% 99.93/13.42 (((brelnall2) =>
% 99.93/13.42 (((ex1E2) =>
% 99.93/13.42 (((funcGraphProp1) =>
% 99.93/13.42 (((funcGraphProp3) =>
% 99.93/13.42 (((funcGraphProp2) =>
% 99.93/13.42 ((
% 99.93/13.42 (funcextLem) =>
% 99.93/13.42 ((
% 99.93/13.42 (funcGraphProp4) =>
% 99.93/13.42 ((
% 99.93/13.42 (subbreln) =>
% 99.93/13.42 ((
% 99.93/13.42 (eqbreln) =>
% 99.93/13.42 ((
% 99.93/13.42 (funcext) =>
% 99.93/13.42 ((
% 99.93/13.42 (funcext2) =>
% 99.93/13.42 ((
% 99.93/13.42 (ap2apEq1) =>
% 99.93/13.42 ((
% 99.93/13.42 (ap2apEq2) =>
% 99.93/13.42 ((
% 99.93/13.42 (beta1) =>
% 99.93/13.42 ((
% 99.93/13.42 (eta1) =>
% 99.93/13.42 ((
% 99.93/13.42 (lam2lamEq) =>
% 99.93/13.42 ((
% 99.93/13.42 (beta2) =>
% 99.93/13.42 ((
% 99.93/13.42 (eta2) =>
% 99.93/13.42 ((
% 99.93/13.42 (iffalseProp1) =>
% 99.93/13.42 ((
% 99.93/13.42 (iffalseProp2) =>
% 99.93/13.42 ((
% 99.93/13.42 (iftrueProp1) =>
% 99.93/13.42 ((
% 99.93/13.42 (iftrueProp2) =>
% 99.93/13.42 ((
% 99.93/13.42 (ifSingleton) =>
% 99.93/13.42 ((
% 99.93/13.42 (ifp) =>
% 99.93/13.42 ((
% 99.93/13.42 (theeq) =>
% 99.93/13.42 ((
% 99.93/13.42 (iftrue) =>
% 99.93/13.42 ((
% 99.93/13.42 (iffalse) =>
% 99.93/13.42 ((
% 99.93/13.42 (iftrueorfalse) =>
% 99.93/13.42 ((
% 99.93/13.42 (binintersectT_lem) =>
% 99.93/13.42 ((
% 99.93/13.42 (binunionT_lem) =>
% 99.93/13.42 ((
% 99.93/13.42 (powersetT_lem) =>
% 99.93/13.42 ((
% 99.93/13.42 (setminusT_lem) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementT_lem) =>
% 99.93/13.42 ((
% 99.93/13.42 (setextT) =>
% 99.93/13.42 ((
% 99.93/13.42 (subsetTI) =>
% 99.93/13.42 ((
% 99.93/13.42 (powersetTI1) =>
% 99.93/13.42 ((
% 99.93/13.42 (powersetTE1) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementTI1) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementTE1) =>
% 99.93/13.42 ((
% 99.93/13.42 (binintersectTELcontra) =>
% 99.93/13.42 ((
% 99.93/13.42 (binintersectTERcontra) =>
% 99.93/13.42 ((
% 99.93/13.42 (contrasubsetT) =>
% 99.93/13.42 ((
% 99.93/13.42 (contrasubsetT1) =>
% 99.93/13.42 ((
% 99.93/13.42 (contrasubsetT2) =>
% 99.93/13.42 ((
% 99.93/13.42 (contrasubsetT3) =>
% 99.93/13.42 ((
% 99.93/13.42 (doubleComplementI1) =>
% 99.93/13.42 ((
% 99.93/13.42 (doubleComplementE1) =>
% 99.93/13.42 ((
% 99.93/13.42 (doubleComplementSub1) =>
% 99.93/13.42 ((
% 99.93/13.42 (doubleComplementSub2) =>
% 99.93/13.42 ((
% 99.93/13.42 (doubleComplementEq) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementTnotintersectT) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementImpComplementIntersect) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementSubsetComplementIntersect) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementInPowersetComplementIntersect) =>
% 99.93/13.42 ((
% 99.93/13.42 (contraSubsetComplement) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementTcontraSubset) =>
% 99.93/13.42 ((
% 99.93/13.42 (binunionTILcontra) =>
% 99.93/13.42 ((
% 99.93/13.42 (binunionTIRcontra) =>
% 99.93/13.42 ((
% 99.93/13.42 (inIntersectImpInUnion) =>
% 99.93/13.42 ((
% 99.93/13.42 (inIntersectImpInUnion2) =>
% 99.93/13.42 ((
% 99.93/13.42 (inIntersectImpInIntersectUnions) =>
% 99.93/13.42 ((
% 99.93/13.42 (intersectInPowersetIntersectUnions) =>
% 99.93/13.42 ((
% 99.93/13.42 (inComplementUnionImpNotIn1) =>
% 99.93/13.42 ((
% 99.93/13.42 (inComplementUnionImpInComplement1) =>
% 99.93/13.42 ((
% 99.93/13.42 (binunionTE) =>
% 99.93/13.42 ((
% 99.93/13.42 (binunionTEcontra) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan2a1) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementUnionInPowersetComplement) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan2a2) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan1a) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan1b) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan1) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan2a) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan2b2) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan2b) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan2) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz13rule0) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz13rule1) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz13rule2) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz13rule3) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz13rule4) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz1_1) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz1_2) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz1_3) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz1_4) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz1_5) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1all2) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1SetBreln1) =>
% 99.93/13.42 ((
% 99.93/13.42 (choice2fnsingleton) =>
% 99.93/13.42 ((
% 99.93/13.42 (setOfPairsIsBReln1) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1all1) =>
% 99.93/13.42 ((
% 99.93/13.42 (subbreln1) =>
% 99.93/13.42 ((
% 99.93/13.42 (eqbreln1) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1invprop) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1invI) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1invE) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1compprop) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1compI) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1compE) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1compEex) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1unionprop) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1unionIL) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1unionIR) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1unionI) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1unionE) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1unionEcases) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1unionCommutes) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz2Ex) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz2W) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz2A) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz2B) =>
% 99.93/13.42 ((
% 99.93/13.42 (image1Ex) =>
% 99.93/13.42 ((
% 99.93/13.42 (image1Ex1) =>
% 99.93/13.42 ((
% 99.93/13.42 (image1Equiv) =>
% 99.93/13.42 ((
% 99.93/13.42 (image1E) =>
% 99.93/13.42 ((
% 99.93/13.42 (image1I) =>
% 99.93/13.42 ((
% 99.93/13.42 (injFuncInInjFuncSet) =>
% 99.93/13.42 ((
% 99.93/13.42 (!!) @ (
% 99.93/13.42 (('#B') @ (
% 99.93/13.42 !!) @
% 99.93/13.42 (
% 99.93/13.42 (
% 99.93/13.42 ('#B') @ (
% 99.93/13.42 (
% 99.93/13.42 ('#B') @ (
% 99.93/13.42 !!))) @
% 99.93/13.42 (
% 99.93/13.42 (
% 99.93/13.42 ('#S') @ (
% 99.93/13.42 (
% 99.93/13.42 ('#B') @ (
% 99.93/13.42 '#S') @
% 99.93/13.42 (
% 99.93/13.42 (
% 99.93/13.42 ('#B') @ (
% 99.93/13.42 (
% 99.93/13.42 ('#B') @ (
% 99.93/13.42 '#S'))) @
% 99.93/13.42 (
% 99.93/13.42 (
% 99.93/13.42 ('#B') @ (
% 99.93/13.42 (
% 99.93/13.42 ('#B') @ (
% 99.93/13.42 (
% 99.93/13.42 ('#B') @ (
% 99.93/13.42 =>))))) @
% 99.93/13.42 (
% 99.93/13.42 (
% 99.93/13.42 ('#B') @ (
% 99.93/13.42 (
% 99.93/13.42 ('#B') @ (
% 99.93/13.42 (
% 99.93/13.42 ('#C') @ in)))) @
% 99.93/13.42 injFuncSet)))))))) @
% 99.93/13.42 (
% 99.93/13.42 (
% 99.93/13.42 ('#B') @ (
% 99.93/13.42 (
% 99.93/13.42 ('#B') @ (
% 99.93/13.42 (
% 99.93/13.42 ('#C') @ in)))) @
% 99.93/13.42 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.93/13.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1779])).
% 99.93/13.42 thf(zip_derived_cl1796, plain,
% 99.93/13.42 (~ (((cartprodsndin) =>
% 99.93/13.42 (((cartprodpairmemEL) =>
% 99.93/13.42 (((cartprodpairmemER) =>
% 99.93/13.42 (((cartprodmempaircEq) =>
% 99.93/13.42 (((cartprodfstpairEq) =>
% 99.93/13.42 (((cartprodsndpairEq) =>
% 99.93/13.42 (((cartprodpairsurjEq) =>
% 99.93/13.42 (((dpsetconstrI) =>
% 99.93/13.42 (((dpsetconstrSub) =>
% 99.93/13.42 (((setOfPairsIsBReln) =>
% 99.93/13.42 (((dpsetconstrERa) =>
% 99.93/13.42 (((dpsetconstrEL1) =>
% 99.93/13.42 (((dpsetconstrEL2) =>
% 99.93/13.42 (((dpsetconstrER) =>
% 99.93/13.42 (((funcImageSingleton) =>
% 99.93/13.42 (((apProp) =>
% 99.93/13.42 (((app) =>
% 99.93/13.42 (((infuncsetfunc) =>
% 99.93/13.42 (((ap2p) =>
% 99.93/13.42 (((funcinfuncset) =>
% 99.93/13.42 (((lamProp) =>
% 99.93/13.42 (((lamp) =>
% 99.93/13.42 (((lam2p) =>
% 99.93/13.42 (((brelnall1) =>
% 99.93/13.42 (((brelnall2) =>
% 99.93/13.42 (((ex1E2) =>
% 99.93/13.42 (((funcGraphProp1) =>
% 99.93/13.42 (((funcGraphProp3) =>
% 99.93/13.42 (((funcGraphProp2) =>
% 99.93/13.42 (((funcextLem) =>
% 99.93/13.42 ((
% 99.93/13.42 (funcGraphProp4) =>
% 99.93/13.42 ((
% 99.93/13.42 (subbreln) =>
% 99.93/13.42 ((
% 99.93/13.42 (eqbreln) =>
% 99.93/13.42 ((
% 99.93/13.42 (funcext) =>
% 99.93/13.42 ((
% 99.93/13.42 (funcext2) =>
% 99.93/13.42 ((
% 99.93/13.42 (ap2apEq1) =>
% 99.93/13.42 ((
% 99.93/13.42 (ap2apEq2) =>
% 99.93/13.42 ((
% 99.93/13.42 (beta1) =>
% 99.93/13.42 ((
% 99.93/13.42 (eta1) =>
% 99.93/13.42 ((
% 99.93/13.42 (lam2lamEq) =>
% 99.93/13.42 ((
% 99.93/13.42 (beta2) =>
% 99.93/13.42 ((
% 99.93/13.42 (eta2) =>
% 99.93/13.42 ((
% 99.93/13.42 (iffalseProp1) =>
% 99.93/13.42 ((
% 99.93/13.42 (iffalseProp2) =>
% 99.93/13.42 ((
% 99.93/13.42 (iftrueProp1) =>
% 99.93/13.42 ((
% 99.93/13.42 (iftrueProp2) =>
% 99.93/13.42 ((
% 99.93/13.42 (ifSingleton) =>
% 99.93/13.42 ((
% 99.93/13.42 (ifp) =>
% 99.93/13.42 ((
% 99.93/13.42 (theeq) =>
% 99.93/13.42 ((
% 99.93/13.42 (iftrue) =>
% 99.93/13.42 ((
% 99.93/13.42 (iffalse) =>
% 99.93/13.42 ((
% 99.93/13.42 (iftrueorfalse) =>
% 99.93/13.42 ((
% 99.93/13.42 (binintersectT_lem) =>
% 99.93/13.42 ((
% 99.93/13.42 (binunionT_lem) =>
% 99.93/13.42 ((
% 99.93/13.42 (powersetT_lem) =>
% 99.93/13.42 ((
% 99.93/13.42 (setminusT_lem) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementT_lem) =>
% 99.93/13.42 ((
% 99.93/13.42 (setextT) =>
% 99.93/13.42 ((
% 99.93/13.42 (subsetTI) =>
% 99.93/13.42 ((
% 99.93/13.42 (powersetTI1) =>
% 99.93/13.42 ((
% 99.93/13.42 (powersetTE1) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementTI1) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementTE1) =>
% 99.93/13.42 ((
% 99.93/13.42 (binintersectTELcontra) =>
% 99.93/13.42 ((
% 99.93/13.42 (binintersectTERcontra) =>
% 99.93/13.42 ((
% 99.93/13.42 (contrasubsetT) =>
% 99.93/13.42 ((
% 99.93/13.42 (contrasubsetT1) =>
% 99.93/13.42 ((
% 99.93/13.42 (contrasubsetT2) =>
% 99.93/13.42 ((
% 99.93/13.42 (contrasubsetT3) =>
% 99.93/13.42 ((
% 99.93/13.42 (doubleComplementI1) =>
% 99.93/13.42 ((
% 99.93/13.42 (doubleComplementE1) =>
% 99.93/13.42 ((
% 99.93/13.42 (doubleComplementSub1) =>
% 99.93/13.42 ((
% 99.93/13.42 (doubleComplementSub2) =>
% 99.93/13.42 ((
% 99.93/13.42 (doubleComplementEq) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementTnotintersectT) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementImpComplementIntersect) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementSubsetComplementIntersect) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementInPowersetComplementIntersect) =>
% 99.93/13.42 ((
% 99.93/13.42 (contraSubsetComplement) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementTcontraSubset) =>
% 99.93/13.42 ((
% 99.93/13.42 (binunionTILcontra) =>
% 99.93/13.42 ((
% 99.93/13.42 (binunionTIRcontra) =>
% 99.93/13.42 ((
% 99.93/13.42 (inIntersectImpInUnion) =>
% 99.93/13.42 ((
% 99.93/13.42 (inIntersectImpInUnion2) =>
% 99.93/13.42 ((
% 99.93/13.42 (inIntersectImpInIntersectUnions) =>
% 99.93/13.42 ((
% 99.93/13.42 (intersectInPowersetIntersectUnions) =>
% 99.93/13.42 ((
% 99.93/13.42 (inComplementUnionImpNotIn1) =>
% 99.93/13.42 ((
% 99.93/13.42 (inComplementUnionImpInComplement1) =>
% 99.93/13.42 ((
% 99.93/13.42 (binunionTE) =>
% 99.93/13.42 ((
% 99.93/13.42 (binunionTEcontra) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan2a1) =>
% 99.93/13.42 ((
% 99.93/13.42 (complementUnionInPowersetComplement) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan2a2) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan1a) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan1b) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan1) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan2a) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan2b2) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan2b) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan2) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz13rule0) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz13rule1) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz13rule2) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz13rule3) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz13rule4) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz1_1) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz1_2) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz1_3) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz1_4) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz1_5) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1all2) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1SetBreln1) =>
% 99.93/13.42 ((
% 99.93/13.42 (choice2fnsingleton) =>
% 99.93/13.42 ((
% 99.93/13.42 (setOfPairsIsBReln1) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1all1) =>
% 99.93/13.42 ((
% 99.93/13.42 (subbreln1) =>
% 99.93/13.42 ((
% 99.93/13.42 (eqbreln1) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1invprop) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1invI) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1invE) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1compprop) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1compI) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1compE) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1compEex) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1unionprop) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1unionIL) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1unionIR) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1unionI) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1unionE) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1unionEcases) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1unionCommutes) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz2Ex) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz2W) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz2A) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz2B) =>
% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
% 99.93/13.42 (breln1unionEcases) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1unionCommutes) =>
% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 (
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% 99.93/13.42 (
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% 99.93/13.42 injFuncSet)))))))) @
% 99.93/13.42 (
% 99.93/13.42 (
% 99.93/13.42 ('#B') @ (
% 99.93/13.42 (
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% 99.93/13.42 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.93/13.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1807])).
% 99.93/13.42 thf(zip_derived_cl1825, plain,
% 99.93/13.42 (~ (((cartprodmempaircEq) =>
% 99.93/13.42 (((cartprodfstpairEq) =>
% 99.93/13.42 (((cartprodsndpairEq) =>
% 99.93/13.42 (((cartprodpairsurjEq) =>
% 99.93/13.42 (((dpsetconstrI) =>
% 99.93/13.42 (((dpsetconstrSub) =>
% 99.93/13.42 (((setOfPairsIsBReln) =>
% 99.93/13.42 (((dpsetconstrERa) =>
% 99.93/13.42 (((dpsetconstrEL1) =>
% 99.93/13.42 (((dpsetconstrEL2) =>
% 99.93/13.42 (((dpsetconstrER) =>
% 99.93/13.42 (((funcImageSingleton) =>
% 99.93/13.42 (((apProp) =>
% 99.93/13.42 (((app) =>
% 99.93/13.42 (((infuncsetfunc) =>
% 99.93/13.42 (((ap2p) =>
% 99.93/13.42 (((funcinfuncset) =>
% 99.93/13.42 (((lamProp) =>
% 99.93/13.42 (((lamp) =>
% 99.93/13.42 (((lam2p) =>
% 99.93/13.42 (((brelnall1) =>
% 99.93/13.42 (((brelnall2) =>
% 99.93/13.42 (((ex1E2) =>
% 99.93/13.42 (((funcGraphProp1) =>
% 99.93/13.42 (((funcGraphProp3) =>
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% 99.93/13.42 ((
% 99.93/13.42 (funcext2) =>
% 99.93/13.42 ((
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% 99.93/13.42 ((
% 99.93/13.42 (ap2apEq2) =>
% 99.93/13.42 ((
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% 99.93/13.42 ((
% 99.93/13.42 (eta1) =>
% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
% 99.93/13.42 (iffalseProp2) =>
% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
% 99.93/13.42 (contrasubsetT3) =>
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
% 99.93/13.42 (complementInPowersetComplementIntersect) =>
% 99.93/13.42 ((
% 99.93/13.42 (contraSubsetComplement) =>
% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
% 99.93/13.42 (binunionTIRcontra) =>
% 99.93/13.42 ((
% 99.93/13.42 (inIntersectImpInUnion) =>
% 99.93/13.42 ((
% 99.93/13.42 (inIntersectImpInUnion2) =>
% 99.93/13.42 ((
% 99.93/13.42 (inIntersectImpInIntersectUnions) =>
% 99.93/13.42 ((
% 99.93/13.42 (intersectInPowersetIntersectUnions) =>
% 99.93/13.42 ((
% 99.93/13.42 (inComplementUnionImpNotIn1) =>
% 99.93/13.42 ((
% 99.93/13.42 (inComplementUnionImpInComplement1) =>
% 99.93/13.42 ((
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% 99.93/13.42 ((
% 99.93/13.42 (binunionTEcontra) =>
% 99.93/13.42 ((
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% 99.93/13.42 ((
% 99.93/13.42 (complementUnionInPowersetComplement) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan2a2) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan1a) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan1b) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan1) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan2a) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan2b2) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan2b) =>
% 99.93/13.42 ((
% 99.93/13.42 (demorgan2) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz13rule0) =>
% 99.93/13.42 ((
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% 99.93/13.42 ((
% 99.93/13.42 (woz13rule2) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz13rule3) =>
% 99.93/13.42 ((
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% 99.93/13.42 ((
% 99.93/13.42 (woz1_2) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz1_3) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz1_4) =>
% 99.93/13.42 ((
% 99.93/13.42 (woz1_5) =>
% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
% 99.93/13.42 (breln1invI) =>
% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
% 99.93/13.42 (breln1compEex) =>
% 99.93/13.42 ((
% 99.93/13.42 (breln1unionprop) =>
% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
% 99.93/13.42 (image1Equiv) =>
% 99.93/13.42 ((
% 99.93/13.42 (image1E) =>
% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 ((
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% 99.93/13.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1816])).
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% 99.93/13.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1825])).
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% 99.93/13.42 (~ (((cartprodsndpairEq) =>
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% 99.93/13.45 (((binunionTIRcontra) =>
% 99.93/13.45 (((inIntersectImpInUnion) =>
% 99.93/13.45 (((inIntersectImpInUnion2) =>
% 99.93/13.45 (((inIntersectImpInIntersectUnions) =>
% 99.93/13.45 (((intersectInPowersetIntersectUnions) =>
% 99.93/13.45 (((inComplementUnionImpNotIn1) =>
% 99.93/13.45 (((inComplementUnionImpInComplement1) =>
% 99.93/13.45 (((binunionTE) =>
% 99.93/13.45 (((binunionTEcontra) =>
% 99.93/13.45 (((demorgan2a1) =>
% 99.93/13.45 (((complementUnionInPowersetComplement) =>
% 99.93/13.45 (((demorgan2a2) =>
% 99.93/13.45 (((demorgan1a) =>
% 99.93/13.45 (((demorgan1b) =>
% 99.93/13.45 (((demorgan1) =>
% 99.93/13.45 (((demorgan2a) =>
% 99.93/13.45 (((demorgan2b2) =>
% 99.93/13.45 (((demorgan2b) =>
% 99.93/13.45 (((demorgan2) =>
% 99.93/13.45 (((woz13rule0) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz13rule1) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz13rule2) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz13rule3) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz13rule4) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_1) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_2) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_3) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_4) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_5) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1all2) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1SetBreln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (choice2fnsingleton) =>
% 99.93/13.45 ((
% 99.93/13.45 (setOfPairsIsBReln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1all1) =>
% 99.93/13.45 ((
% 99.93/13.45 (subbreln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (eqbreln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invprop) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invI) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invE) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1compprop) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1compI) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1compE) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1compEex) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionprop) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionIL) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionIR) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionI) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionE) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionEcases) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionCommutes) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz2Ex) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz2W) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz2A) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz2B) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1Ex) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1Ex1) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1Equiv) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1E) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1I) =>
% 99.93/13.45 ((
% 99.93/13.45 (injFuncInInjFuncSet) =>
% 99.93/13.45 ((
% 99.93/13.45 (!!) @ (
% 99.93/13.45 (('#B') @ (
% 99.93/13.45 !!) @
% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 !!))) @
% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#S') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 '#S') @
% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 '#S'))) @
% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 =>))))) @
% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
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% 99.93/13.45 injFuncSet)))))))) @
% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#C') @ in)))) @
% 99.93/13.45 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.93/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2648])).
% 99.93/13.45 thf(zip_derived_cl2680, plain,
% 99.93/13.45 (~ (((doubleComplementSub2) =>
% 99.93/13.45 (((doubleComplementEq) =>
% 99.93/13.45 (((complementTnotintersectT) =>
% 99.93/13.45 (((complementImpComplementIntersect) =>
% 99.93/13.45 (((complementSubsetComplementIntersect) =>
% 99.93/13.45 (((complementInPowersetComplementIntersect) =>
% 99.93/13.45 (((contraSubsetComplement) =>
% 99.93/13.45 (((complementTcontraSubset) =>
% 99.93/13.45 (((binunionTILcontra) =>
% 99.93/13.45 (((binunionTIRcontra) =>
% 99.93/13.45 (((inIntersectImpInUnion) =>
% 99.93/13.45 (((inIntersectImpInUnion2) =>
% 99.93/13.45 (((inIntersectImpInIntersectUnions) =>
% 99.93/13.45 (((intersectInPowersetIntersectUnions) =>
% 99.93/13.45 (((inComplementUnionImpNotIn1) =>
% 99.93/13.45 (((inComplementUnionImpInComplement1) =>
% 99.93/13.45 (((binunionTE) =>
% 99.93/13.45 (((binunionTEcontra) =>
% 99.93/13.45 (((demorgan2a1) =>
% 99.93/13.45 (((complementUnionInPowersetComplement) =>
% 99.93/13.45 (((demorgan2a2) =>
% 99.93/13.45 (((demorgan1a) =>
% 99.93/13.45 (((demorgan1b) =>
% 99.93/13.45 (((demorgan1) =>
% 99.93/13.45 (((demorgan2a) =>
% 99.93/13.45 (((demorgan2b2) =>
% 99.93/13.45 (((demorgan2b) =>
% 99.93/13.45 (((demorgan2) =>
% 99.93/13.45 (((woz13rule0) =>
% 99.93/13.45 (((woz13rule1) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz13rule2) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz13rule3) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz13rule4) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_1) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_2) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_3) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_4) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_5) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1all2) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1SetBreln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (choice2fnsingleton) =>
% 99.93/13.45 ((
% 99.93/13.45 (setOfPairsIsBReln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1all1) =>
% 99.93/13.45 ((
% 99.93/13.45 (subbreln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (eqbreln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invprop) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invI) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invE) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1compprop) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1compI) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1compE) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1compEex) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionprop) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionIL) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionIR) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionI) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionE) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionEcases) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionCommutes) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz2Ex) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz2W) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz2A) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz2B) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1Ex) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1Ex1) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1Equiv) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1E) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1I) =>
% 99.93/13.45 ((
% 99.93/13.45 (injFuncInInjFuncSet) =>
% 99.93/13.45 ((
% 99.93/13.45 (!!) @ (
% 99.93/13.45 (('#B') @ (
% 99.93/13.45 !!) @
% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 !!))) @
% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#S') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 '#S') @
% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 '#S'))) @
% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 =>))))) @
% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#C') @ in)))) @
% 99.93/13.45 injFuncSet)))))))) @
% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#C') @ in)))) @
% 99.93/13.45 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.93/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2665])).
% 99.93/13.45 thf(zip_derived_cl2692, plain,
% 99.93/13.45 (~ (((doubleComplementEq) =>
% 99.93/13.45 (((complementTnotintersectT) =>
% 99.93/13.45 (((complementImpComplementIntersect) =>
% 99.93/13.45 (((complementSubsetComplementIntersect) =>
% 99.93/13.45 (((complementInPowersetComplementIntersect) =>
% 99.93/13.45 (((contraSubsetComplement) =>
% 99.93/13.45 (((complementTcontraSubset) =>
% 99.93/13.45 (((binunionTILcontra) =>
% 99.93/13.45 (((binunionTIRcontra) =>
% 99.93/13.45 (((inIntersectImpInUnion) =>
% 99.93/13.45 (((inIntersectImpInUnion2) =>
% 99.93/13.45 (((inIntersectImpInIntersectUnions) =>
% 99.93/13.45 (((intersectInPowersetIntersectUnions) =>
% 99.93/13.45 (((inComplementUnionImpNotIn1) =>
% 99.93/13.45 (((inComplementUnionImpInComplement1) =>
% 99.93/13.45 (((binunionTE) =>
% 99.93/13.45 (((binunionTEcontra) =>
% 99.93/13.45 (((demorgan2a1) =>
% 99.93/13.45 (((complementUnionInPowersetComplement) =>
% 99.93/13.45 (((demorgan2a2) =>
% 99.93/13.45 (((demorgan1a) =>
% 99.93/13.45 (((demorgan1b) =>
% 99.93/13.45 (((demorgan1) =>
% 99.93/13.45 (((demorgan2a) =>
% 99.93/13.45 (((demorgan2b2) =>
% 99.93/13.45 (((demorgan2b) =>
% 99.93/13.45 (((demorgan2) =>
% 99.93/13.45 (((woz13rule0) =>
% 99.93/13.45 (((woz13rule1) =>
% 99.93/13.45 (((woz13rule2) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz13rule3) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz13rule4) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_1) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_2) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_3) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_4) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_5) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1all2) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1SetBreln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (choice2fnsingleton) =>
% 99.93/13.45 ((
% 99.93/13.45 (setOfPairsIsBReln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1all1) =>
% 99.93/13.45 ((
% 99.93/13.45 (subbreln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (eqbreln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invprop) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invI) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invE) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1compprop) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1compI) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1compE) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1compEex) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionprop) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionIL) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionIR) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionI) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionE) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionEcases) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionCommutes) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz2Ex) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz2W) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz2A) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz2B) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1Ex) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1Ex1) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1Equiv) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1E) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1I) =>
% 99.93/13.45 ((
% 99.93/13.45 (injFuncInInjFuncSet) =>
% 99.93/13.45 ((
% 99.93/13.45 (!!) @ (
% 99.93/13.45 (('#B') @ (
% 99.93/13.45 !!) @
% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
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% 99.93/13.45 (
% 99.93/13.45 (
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% 99.93/13.45 (
% 99.93/13.45 (
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% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
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% 99.93/13.45 (
% 99.93/13.45 (
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% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
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% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
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% 99.93/13.45 injFuncSet)))))))) @
% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#C') @ in)))) @
% 99.93/13.45 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.93/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2680])).
% 99.93/13.45 thf(zip_derived_cl2704, plain,
% 99.93/13.45 (~ (((complementTnotintersectT) =>
% 99.93/13.45 (((complementImpComplementIntersect) =>
% 99.93/13.45 (((complementSubsetComplementIntersect) =>
% 99.93/13.45 (((complementInPowersetComplementIntersect) =>
% 99.93/13.45 (((contraSubsetComplement) =>
% 99.93/13.45 (((complementTcontraSubset) =>
% 99.93/13.45 (((binunionTILcontra) =>
% 99.93/13.45 (((binunionTIRcontra) =>
% 99.93/13.45 (((inIntersectImpInUnion) =>
% 99.93/13.45 (((inIntersectImpInUnion2) =>
% 99.93/13.45 (((inIntersectImpInIntersectUnions) =>
% 99.93/13.45 (((intersectInPowersetIntersectUnions) =>
% 99.93/13.45 (((inComplementUnionImpNotIn1) =>
% 99.93/13.45 (((inComplementUnionImpInComplement1) =>
% 99.93/13.45 (((binunionTE) =>
% 99.93/13.45 (((binunionTEcontra) =>
% 99.93/13.45 (((demorgan2a1) =>
% 99.93/13.45 (((complementUnionInPowersetComplement) =>
% 99.93/13.45 (((demorgan2a2) =>
% 99.93/13.45 (((demorgan1a) =>
% 99.93/13.45 (((demorgan1b) =>
% 99.93/13.45 (((demorgan1) =>
% 99.93/13.45 (((demorgan2a) =>
% 99.93/13.45 (((demorgan2b2) =>
% 99.93/13.45 (((demorgan2b) =>
% 99.93/13.45 (((demorgan2) =>
% 99.93/13.45 (((woz13rule0) =>
% 99.93/13.45 (((woz13rule1) =>
% 99.93/13.45 (((woz13rule2) =>
% 99.93/13.45 (((woz13rule3) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz13rule4) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_1) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_2) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_3) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_4) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz1_5) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1all2) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1SetBreln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (choice2fnsingleton) =>
% 99.93/13.45 ((
% 99.93/13.45 (setOfPairsIsBReln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1all1) =>
% 99.93/13.45 ((
% 99.93/13.45 (subbreln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (eqbreln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invprop) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invI) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invE) =>
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% 99.93/13.45 ((
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% 99.93/13.45 ((
% 99.93/13.45 (breln1compE) =>
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
% 99.93/13.45 (image1Equiv) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1E) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1I) =>
% 99.93/13.45 ((
% 99.93/13.45 (injFuncInInjFuncSet) =>
% 99.93/13.45 ((
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% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
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% 99.93/13.45 (
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% 99.93/13.45 injFuncSet)))))))) @
% 99.93/13.45 (
% 99.93/13.45 (
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% 99.93/13.45 (
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% 99.93/13.45 (
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% 99.93/13.45 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.93/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2803])).
% 99.93/13.45 thf(zip_derived_cl2823, plain,
% 99.93/13.45 (~ (((inComplementUnionImpNotIn1) =>
% 99.93/13.45 (((inComplementUnionImpInComplement1) =>
% 99.93/13.45 (((binunionTE) =>
% 99.93/13.45 (((binunionTEcontra) =>
% 99.93/13.45 (((demorgan2a1) =>
% 99.93/13.45 (((complementUnionInPowersetComplement) =>
% 99.93/13.45 (((demorgan2a2) =>
% 99.93/13.45 (((demorgan1a) =>
% 99.93/13.45 (((demorgan1b) =>
% 99.93/13.45 (((demorgan1) =>
% 99.93/13.45 (((demorgan2a) =>
% 99.93/13.45 (((demorgan2b2) =>
% 99.93/13.45 (((demorgan2b) =>
% 99.93/13.45 (((demorgan2) =>
% 99.93/13.45 (((woz13rule0) =>
% 99.93/13.45 (((woz13rule1) =>
% 99.93/13.45 (((woz13rule2) =>
% 99.93/13.45 (((woz13rule3) =>
% 99.93/13.45 (((woz13rule4) =>
% 99.93/13.45 (((woz1_1) =>
% 99.93/13.45 (((woz1_2) =>
% 99.93/13.45 (((woz1_3) =>
% 99.93/13.45 (((woz1_4) =>
% 99.93/13.45 (((woz1_5) =>
% 99.93/13.45 (((breln1all2) =>
% 99.93/13.45 (((breln1SetBreln1) =>
% 99.93/13.45 (((choice2fnsingleton) =>
% 99.93/13.45 (((setOfPairsIsBReln1) =>
% 99.93/13.45 (((breln1all1) =>
% 99.93/13.45 (((subbreln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (eqbreln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invprop) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invI) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invE) =>
% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
% 99.93/13.45 (breln1compE) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1compEex) =>
% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
% 99.93/13.45 (breln1unionI) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionE) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionEcases) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionCommutes) =>
% 99.93/13.45 ((
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% 99.93/13.45 ((
% 99.93/13.45 (woz2W) =>
% 99.93/13.45 ((
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% 99.93/13.45 ((
% 99.93/13.45 (woz2B) =>
% 99.93/13.45 ((
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% 99.93/13.45 ((
% 99.93/13.45 (image1Ex1) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1Equiv) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1E) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1I) =>
% 99.93/13.45 ((
% 99.93/13.45 (injFuncInInjFuncSet) =>
% 99.93/13.45 ((
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% 99.93/13.45 (('#B') @ (
% 99.93/13.45 !!) @
% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
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% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#S') @ (
% 99.93/13.45 (
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% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
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% 99.93/13.45 (
% 99.93/13.45 (
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% 99.93/13.45 (
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% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 =>))))) @
% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
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% 99.93/13.45 injFuncSet)))))))) @
% 99.93/13.45 (
% 99.93/13.45 (
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% 99.93/13.45 (
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% 99.93/13.45 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.93/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2813])).
% 99.93/13.45 thf(zip_derived_cl2834, plain,
% 99.93/13.45 (~ (((inComplementUnionImpInComplement1) =>
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% 99.93/13.45 (((binunionTEcontra) =>
% 99.93/13.45 (((demorgan2a1) =>
% 99.93/13.45 (((complementUnionInPowersetComplement) =>
% 99.93/13.45 (((demorgan2a2) =>
% 99.93/13.45 (((demorgan1a) =>
% 99.93/13.45 (((demorgan1b) =>
% 99.93/13.45 (((demorgan1) =>
% 99.93/13.45 (((demorgan2a) =>
% 99.93/13.45 (((demorgan2b2) =>
% 99.93/13.45 (((demorgan2b) =>
% 99.93/13.45 (((demorgan2) =>
% 99.93/13.45 (((woz13rule0) =>
% 99.93/13.45 (((woz13rule1) =>
% 99.93/13.45 (((woz13rule2) =>
% 99.93/13.45 (((woz13rule3) =>
% 99.93/13.45 (((woz13rule4) =>
% 99.93/13.45 (((woz1_1) =>
% 99.93/13.45 (((woz1_2) =>
% 99.93/13.45 (((woz1_3) =>
% 99.93/13.45 (((woz1_4) =>
% 99.93/13.45 (((woz1_5) =>
% 99.93/13.45 (((breln1all2) =>
% 99.93/13.45 (((breln1SetBreln1) =>
% 99.93/13.45 (((choice2fnsingleton) =>
% 99.93/13.45 (((setOfPairsIsBReln1) =>
% 99.93/13.45 (((breln1all1) =>
% 99.93/13.45 (((subbreln1) =>
% 99.93/13.45 (((eqbreln1) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invprop) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invI) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1invE) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1compprop) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1compI) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1compE) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1compEex) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionprop) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionIL) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionIR) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionI) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionE) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionEcases) =>
% 99.93/13.45 ((
% 99.93/13.45 (breln1unionCommutes) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz2Ex) =>
% 99.93/13.45 ((
% 99.93/13.45 (woz2W) =>
% 99.93/13.45 ((
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% 99.93/13.45 ((
% 99.93/13.45 (woz2B) =>
% 99.93/13.45 ((
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% 99.93/13.45 ((
% 99.93/13.45 (image1Ex1) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1Equiv) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1E) =>
% 99.93/13.45 ((
% 99.93/13.45 (image1I) =>
% 99.93/13.45 ((
% 99.93/13.45 (injFuncInInjFuncSet) =>
% 99.93/13.45 ((
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% 99.93/13.45 injFuncSet)))))))) @
% 99.93/13.45 (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
% 99.93/13.45 ('#B') @ (
% 99.93/13.45 (
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% 99.93/13.45 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.93/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2823])).
% 99.93/13.45 thf(zip_derived_cl2845, plain,
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% 99.93/13.45 (((demorgan1b) =>
% 99.93/13.45 (((demorgan1) =>
% 99.93/13.45 (((demorgan2a) =>
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% 99.93/13.45 (((woz1_3) =>
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 ((
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% 99.93/13.45 (
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% 99.93/13.45 injFuncSet)))))))) @
% 99.93/13.45 (
% 99.93/13.45 (
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% 99.93/13.45 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.93/13.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2834])).
% 99.93/13.45 thf(zip_derived_cl2857, plain,
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% 99.93/13.45 (((demorgan2a) =>
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% 99.93/13.45 (((woz1_3) =>
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% 99.93/13.45 ((
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% 99.93/13.46 (dsetconstr @ (funcSet @ '#sk47' @ '#sk48') @
% 99.93/13.46 (injective @ '#sk47' @ '#sk48')))),
% 99.93/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3617])).
% 99.93/13.46 thf(zip_derived_cl3627, plain,
% 99.93/13.46 (~ (in @
% 99.93/13.46 ('#sk12' @ (funcSet @ '#sk47' @ '#sk48') @
% 99.93/13.46 (dsetconstr @ (funcSet @ '#sk47' @ '#sk48') @
% 99.93/13.46 (injective @ '#sk47' @ '#sk48'))) @
% 99.93/13.46 (funcSet @ '#sk47' @ '#sk48'))),
% 99.93/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3617])).
% 99.93/13.46 thf(zip_derived_cl88, plain, ( (dsetconstrEL)),
% 99.93/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 99.93/13.46 thf(dsetconstrEL, axiom, (dsetconstrEL) =>
% 99.93/13.46 ((((!!) @ (^[Y0 : $i]:
% 99.93/13.46 (((!!) @ (^[Y1 : $i > $o]:
% 99.93/13.46 (((!!) @ (^[Y2 : $i]:
% 99.93/13.46 (((in @ Y2 @
% 99.93/13.46 (dsetconstr @ Y0 @
% 99.93/13.46 (^[Y3 : $i]: (Y1 @ Y3)))) =>
% 99.93/13.46 (in @ Y2 @ Y0))))))))))))
% 99.93/13.46 = ($true))).
% 99.93/13.46 thf('5', plain,
% 99.93/13.46 (( dsetconstrEL ) <=>
% 99.93/13.46 ( ![X5:$i,X7:( $i > $o ),X9:$i]:
% 99.93/13.46 ( ( in @ X9 @ ( dsetconstr @ X5 @ ( ^[V_1:$i]: ( X7 @ V_1 ) ) ) ) =>
% 99.93/13.46 ( in @ X9 @ X5 ) ) )),
% 99.93/13.46 inference('rw.lit', [status(esa)], [dsetconstrEL])).
% 99.93/13.46 thf(zip_derived_cl103, plain,
% 99.93/13.46 ( (((!!) @ (^[Y0 : $i]:
% 99.93/13.46 (((!!) @ (^[Y1 : $i > $o]:
% 99.93/13.46 (((!!) @ (^[Y2 : $i]:
% 99.93/13.46 (((in @ Y2 @
% 99.93/13.46 (dsetconstr @ Y0 @
% 99.93/13.46 (^[Y3 : $i]: (Y1 @ Y3)))) =>
% 99.93/13.46 (in @ Y2 @ Y0))))))))))))),
% 99.93/13.46 inference('rw_clause', [status(thm)], [zip_derived_cl88, '5'])).
% 99.93/13.46 thf(zip_derived_cl119, plain,
% 99.93/13.46 ( (((!!) @ ((('#B') @ (!!) @
% 99.93/13.46 ((('#B') @ ((('#B') @ (!!))) @
% 99.93/13.46 ((('#S') @ ((('#B') @ ('#C') @
% 99.93/13.46 ((('#B') @ ((('#B') @ ('#S'))) @
% 99.93/13.46 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 99.93/13.46 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @
% 99.93/13.46 dsetconstr)))))))) @
% 99.93/13.46 ((('#C') @ in))))))))))),
% 99.93/13.46 inference('comb-normalize', [status(thm)], [zip_derived_cl103])).
% 99.93/13.46 thf(zip_derived_cl120, plain,
% 99.93/13.46 (![X2 : $i]:
% 99.93/13.46 (((!!) @ ((('#B') @ (!!) @
% 99.93/13.46 ((('#C') @ ((('#B') @ ('#S') @
% 99.93/13.46 ((('#B') @ ((('#B') @ (=>))) @
% 99.93/13.46 ((('#B') @ ((('#C') @ in)) @
% 99.93/13.46 (dsetconstr @ X2))))))) @
% 99.93/13.46 ((('#C') @ in @ X2))))))))),
% 99.93/13.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl119])).
% 99.93/13.46 thf(zip_derived_cl137, plain,
% 99.93/13.46 (![X2 : $i, X4 : $i > $o]:
% 99.93/13.46 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 99.93/13.46 ((('#C') @ in @ (dsetconstr @ X2 @ X4))))) @
% 99.93/13.46 ((('#C') @ in @ X2))))))),
% 99.93/13.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl120])).
% 99.93/13.46 thf(zip_derived_cl152, plain,
% 99.93/13.46 (![X2 : $i, X4 : $i > $o, X6 : $i]:
% 99.93/13.46 (((in @ X6 @ (dsetconstr @ X2 @ X4)) => (in @ X6 @ X2)))),
% 99.93/13.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl137])).
% 99.93/13.46 thf(zip_derived_cl167, plain,
% 99.93/13.46 (![X2 : $i, X4 : $i > $o, X6 : $i]:
% 99.93/13.46 (~ (in @ X6 @ (dsetconstr @ X2 @ X4)) | (in @ X6 @ X2))),
% 99.93/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl152])).
% 99.93/13.46 thf(zip_derived_cl9872, plain, ($false),
% 99.93/13.46 inference('eprover', [status(thm)],
% 99.93/13.46 [zip_derived_cl3626, zip_derived_cl3627, zip_derived_cl167])).
% 99.93/13.46
% 99.93/13.46 % SZS output end Refutation
% 99.93/13.46
% 99.93/13.46
% 99.93/13.46 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 99.93/13.46 % Terminating...
% 100.55/13.57 % Runner terminated.
% 100.55/13.58 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------