%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU801^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.fFMthCEJ0y true
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:56:28 PM UTC 2025
% Result : Theorem 98.61s 16.50s
% Output : Refutation 100.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.28 % Problem : SEU801^1 : TPTP v9.2.0. Released v3.7.0.
% 0.04/0.30 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.fFMthCEJ0y true
% 0.10/0.49 % Computer : n022.cluster.edu
% 0.10/0.49 % Model : x86_64 x86_64
% 0.10/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.49 % Memory : 8042.1875MB
% 0.10/0.49 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.49 % CPULimit : 300
% 0.10/0.49 % WCLimit : 300
% 0.10/0.49 % DateTime : Wed Oct 1 16:14:53 EDT 2025
% 0.10/0.49 % CPUTime :
% 0.10/0.49 % Running portfolio for 300 s
% 0.10/0.49 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.49 % Number of cores: 8
% 0.10/0.50 % Python version: Python 3.6.8
% 0.10/0.50 % Running in HO mode
% 0.26/0.76 % Total configuration time : 828
% 0.26/0.76 % Estimated wc time : 1656
% 0.26/0.76 % Estimated cpu time (8 cpus) : 207.0
% 0.26/0.88 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.26/0.88 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.26/0.89 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.26/0.91 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.26/0.91 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.26/0.92 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.26/0.92 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.26/0.96 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 98.61/16.50 % Solved by lams/40_b.comb.sh.
% 98.61/16.50 % done 0 iterations in 15.019s
% 98.61/16.50 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 98.61/16.50 % SZS output start Refutation
% 98.61/16.50 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 98.61/16.50 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 98.61/16.50 thf(notdexE_type, type, notdexE: $o).
% 98.61/16.50 thf(setunionAx_type, type, setunionAx: $o).
% 98.61/16.50 thf(setminusELneg_type, type, setminusELneg: $o).
% 98.61/16.50 thf(breln1unionEcases_type, type, breln1unionEcases: $o).
% 98.61/16.50 thf(powersetE_type, type, powersetE: $o).
% 98.61/16.50 thf(woz1_1_type, type, woz1_1: $o).
% 98.61/16.50 thf(omegaSAx_type, type, omegaSAx: $o).
% 98.61/16.50 thf(breln1unionI_type, type, breln1unionI: $o).
% 98.61/16.50 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 98.61/16.50 $o).
% 98.61/16.50 thf(exuI1_type, type, exuI1: $o).
% 98.61/16.50 thf(exuI2_type, type, exuI2: $o).
% 98.61/16.50 thf(notequalI2_type, type, notequalI2: $o).
% 98.61/16.50 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 98.61/16.50 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 98.61/16.50 thf(upairsubunion_type, type, upairsubunion: $o).
% 98.61/16.50 thf(binunionTE_type, type, binunionTE: $o).
% 98.61/16.50 thf(binunionTEcontra_type, type, binunionTEcontra: $o).
% 98.61/16.50 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 98.61/16.50 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 98.61/16.50 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 98.61/16.50 thf(setminusILneg_type, type, setminusILneg: $o).
% 98.61/16.50 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 98.61/16.50 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 98.61/16.50 thf(funcextLem_type, type, funcextLem: $o).
% 98.61/16.50 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 98.61/16.50 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 98.61/16.50 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 98.61/16.50 thf(eta1_type, type, eta1: $o).
% 98.61/16.50 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 98.61/16.50 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 98.61/16.50 thf(apProp_type, type, apProp: $o).
% 98.61/16.50 thf(setextT_type, type, setextT: $o).
% 98.61/16.50 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions:
% 98.61/16.50 $o).
% 98.61/16.50 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 98.61/16.50 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 98.61/16.50 thf(breln1invprop_type, type, breln1invprop: $o).
% 98.61/16.50 thf(lamProp_type, type, lamProp: $o).
% 98.61/16.50 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 98.61/16.50 thf(ex1E1_type, type, ex1E1: $o).
% 98.61/16.50 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 98.61/16.50 thf(setukpairIR_type, type, setukpairIR: $o).
% 98.61/16.50 thf(brelnall1_type, type, brelnall1: $o).
% 98.61/16.50 thf(binunionE_type, type, binunionE: $o).
% 98.61/16.50 thf(setext_type, type, setext: $o).
% 98.61/16.50 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 98.61/16.50 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 98.61/16.50 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 98.61/16.50 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 98.61/16.50 thf(iftrue_type, type, iftrue: $o).
% 98.61/16.50 thf(woz13rule4_type, type, woz13rule4: $o).
% 98.61/16.50 thf(descr__Cong_type, type, descr__Cong: $o).
% 98.61/16.50 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 98.61/16.50 thf(theprop_type, type, theprop: $o).
% 98.61/16.50 thf(image1I_type, type, image1I: $o).
% 98.61/16.50 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 98.61/16.50 thf(in_type, type, in: $i > $i > $o).
% 98.61/16.50 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 98.61/16.50 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 98.61/16.50 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 98.61/16.50 thf(demorgan1_type, type, demorgan1: $o).
% 98.61/16.50 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 98.61/16.50 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 98.61/16.50 $o).
% 98.61/16.50 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 98.61/16.50 thf(breln1SetBreln1_type, type, breln1SetBreln1: $o).
% 98.61/16.50 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 98.61/16.50 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 98.61/16.50 thf(ex1I2_type, type, ex1I2: $o).
% 98.61/16.50 thf(symdiffI2_type, type, symdiffI2: $o).
% 98.61/16.50 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 98.61/16.50 thf(ifSingleton_type, type, ifSingleton: $o).
% 98.61/16.50 thf(upairset2IR_type, type, upairset2IR: $o).
% 98.61/16.50 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 98.61/16.50 thf(complementTI1_type, type, complementTI1: $o).
% 98.61/16.50 thf(subsetE_type, type, subsetE: $o).
% 98.61/16.50 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 98.61/16.50 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 98.61/16.50 thf(complementUnionInPowersetComplement_type, type, complementUnionInPowersetComplement:
% 98.61/16.50 $o).
% 98.61/16.50 thf(iffalse_type, type, iffalse: $o).
% 98.61/16.50 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 98.61/16.50 thf(setbeta_type, type, setbeta: $o).
% 98.61/16.50 thf(eqinunit_type, type, eqinunit: $o).
% 98.61/16.50 thf(upairsetIL_type, type, upairsetIL: $o).
% 98.61/16.50 thf(powersetI1_type, type, powersetI1: $o).
% 98.61/16.50 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 98.61/16.50 thf(lamp_type, type, lamp: $o).
% 98.61/16.50 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 98.61/16.50 thf(breln1invI_type, type, breln1invI: $o).
% 98.61/16.50 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 98.61/16.50 thf(breln1unionE_type, type, breln1unionE: $o).
% 98.61/16.50 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 98.61/16.50 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 98.61/16.50 thf('#sk12_type', type, '#sk12': $i > $i > $i).
% 98.61/16.50 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 98.61/16.50 thf(powersetAx_type, type, powersetAx: $o).
% 98.61/16.50 thf(woz2Ex_type, type, woz2Ex: $o).
% 98.61/16.50 thf(eta2_type, type, eta2: $o).
% 98.61/16.50 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 98.61/16.50 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 98.61/16.50 thf(image1Ex_type, type, image1Ex: $o).
% 98.61/16.50 thf(powersetI_type, type, powersetI: $o).
% 98.61/16.50 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 98.61/16.50 thf(powersetTE1_type, type, powersetTE1: $o).
% 98.61/16.50 thf(upairsetIR_type, type, upairsetIR: $o).
% 98.61/16.50 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 98.61/16.50 thf(lam2p_type, type, lam2p: $o).
% 98.61/16.50 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 98.61/16.50 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 98.61/16.50 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 98.61/16.50 thf(setOfPairsIsBReln1_type, type, setOfPairsIsBReln1: $o).
% 98.61/16.50 thf(inCongP_type, type, inCongP: $o).
% 98.61/16.50 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 98.61/16.50 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 98.61/16.50 thf(exuE3e_type, type, exuE3e: $o).
% 98.61/16.50 thf(emptysetE_type, type, emptysetE: $o).
% 98.61/16.50 thf(woz13rule2_type, type, woz13rule2: $o).
% 98.61/16.50 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 98.61/16.50 thf(image1E_type, type, image1E: $o).
% 98.61/16.50 thf(setunionI_type, type, setunionI: $o).
% 98.61/16.50 thf(breln1unionIR_type, type, breln1unionIR: $o).
% 98.61/16.50 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 98.61/16.50 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 98.61/16.50 thf(injFuncSetFuncInj_type, type, injFuncSetFuncInj: $o).
% 98.61/16.50 thf(prop2setI_type, type, prop2setI: $o).
% 98.61/16.50 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 98.61/16.50 thf(setminusER_type, type, setminusER: $o).
% 98.61/16.50 thf(exuE2_type, type, exuE2: $o).
% 98.61/16.50 thf(woz1_2_type, type, woz1_2: $o).
% 98.61/16.50 thf(emptyset_type, type, emptyset: $i).
% 98.61/16.50 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 98.61/16.50 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 98.61/16.50 thf(powersetsubset_type, type, powersetsubset: $o).
% 98.61/16.50 thf(upairequniteq_type, type, upairequniteq: $o).
% 98.61/16.50 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 98.61/16.50 thf(injFuncInInjFuncSet_type, type, injFuncInInjFuncSet: $o).
% 98.61/16.50 thf(subPowSU_type, type, subPowSU: $o).
% 98.61/16.50 thf(breln1compprop_type, type, breln1compprop: $o).
% 98.61/16.50 thf(woz2B_type, type, woz2B: $o).
% 98.61/16.50 thf(notequalI1_type, type, notequalI1: $o).
% 98.61/16.50 thf(demorgan2b_type, type, demorgan2b: $o).
% 98.61/16.50 thf(notinemptyset_type, type, notinemptyset: $o).
% 98.61/16.50 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 98.61/16.50 thf(breln1unionIL_type, type, breln1unionIL: $o).
% 98.61/16.50 thf(subsetTrans_type, type, subsetTrans: $o).
% 98.61/16.50 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 98.61/16.50 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 98.61/16.50 thf(kpairp_type, type, kpairp: $o).
% 98.61/16.50 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 98.61/16.50 thf(setminusI_type, type, setminusI: $o).
% 98.61/16.50 thf(binunionIL_type, type, binunionIL: $o).
% 98.61/16.50 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 98.61/16.50 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 98.61/16.50 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 98.61/16.50 thf(powersetTI1_type, type, powersetTI1: $o).
% 98.61/16.50 thf(subsetE2_type, type, subsetE2: $o).
% 98.61/16.50 thf(image1Ex1_type, type, image1Ex1: $o).
% 98.61/16.50 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 98.61/16.50 thf('#sk47_type', type, '#sk47': $i).
% 98.61/16.50 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 98.61/16.50 thf(setextsub_type, type, setextsub: $o).
% 98.61/16.50 thf(binunionLsub_type, type, binunionLsub: $o).
% 98.61/16.50 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 98.61/16.50 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 98.61/16.50 thf(breln1compE_type, type, breln1compE: $o).
% 98.61/16.50 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 98.61/16.50 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 98.61/16.50 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 98.61/16.50 thf(setunionE_type, type, setunionE: $o).
% 98.61/16.50 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 98.61/16.50 thf(complementT_lem_type, type, complementT_lem: $o).
% 98.61/16.50 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 98.61/16.50 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 98.61/16.50 thf(binunionIR_type, type, binunionIR: $o).
% 98.61/16.50 thf(injFuncSetFuncIn_type, type, injFuncSetFuncIn: $o).
% 98.61/16.50 thf(setadjoinE_type, type, setadjoinE: $o).
% 98.61/16.50 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 98.61/16.50 thf(eqbreln1_type, type, eqbreln1: $o).
% 98.61/16.50 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 98.61/16.50 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 98.61/16.50 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 98.61/16.50 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 98.61/16.50 thf(exuE1_type, type, exuE1: $o).
% 98.61/16.50 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 98.61/16.50 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 98.61/16.50 thf(setminusLsub_type, type, setminusLsub: $o).
% 98.61/16.50 thf(notinsingleton_type, type, notinsingleton: $o).
% 98.61/16.50 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions:
% 98.61/16.50 $o).
% 98.61/16.50 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 98.61/16.50 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 98.61/16.50 thf(exuEu_type, type, exuEu: $o).
% 98.61/16.50 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 98.61/16.50 thf(upairsetE_type, type, upairsetE: $o).
% 98.61/16.50 thf(omega0Ax_type, type, omega0Ax: $o).
% 98.61/16.50 thf(breln1invE_type, type, breln1invE: $o).
% 98.61/16.50 thf(breln1unionCommutes_type, type, breln1unionCommutes: $o).
% 98.61/16.50 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 98.61/16.50 thf(app_type, type, app: $o).
% 98.61/16.50 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 98.61/16.50 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 98.61/16.50 thf(notsubsetI_type, type, notsubsetI: $o).
% 98.61/16.50 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 98.61/16.50 thf(woz2W_type, type, woz2W: $o).
% 98.61/16.50 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 98.61/16.50 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 98.61/16.50 thf(setextAx_type, type, setextAx: $o).
% 98.61/16.50 thf(breln1all1_type, type, breln1all1: $o).
% 98.61/16.50 thf(choice2fnsingleton_type, type, choice2fnsingleton: $o).
% 98.61/16.50 thf(breln1compI_type, type, breln1compI: $o).
% 98.61/16.50 thf(demorgan2a1_type, type, demorgan2a1: $o).
% 98.61/16.50 thf(powersetE1_type, type, powersetE1: $o).
% 98.61/16.50 thf(bs114d_type, type, bs114d: $o).
% 98.61/16.50 thf(complementTE1_type, type, complementTE1: $o).
% 98.61/16.50 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 98.61/16.50 thf(breln1all2_type, type, breln1all2: $o).
% 98.61/16.50 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 98.61/16.50 thf(surjective_type, type, surjective: $i > $i > $i > $o).
% 98.61/16.50 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 98.61/16.50 thf(demorgan2b2_type, type, demorgan2b2: $o).
% 98.61/16.50 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 98.61/16.50 thf(subsetI1_type, type, subsetI1: $o).
% 98.61/16.50 thf(symdiffE_type, type, symdiffE: $o).
% 98.61/16.50 thf(woz13rule1_type, type, woz13rule1: $o).
% 98.61/16.50 thf(breln1unionprop_type, type, breln1unionprop: $o).
% 98.61/16.50 thf(descrp_type, type, descrp: $o).
% 98.61/16.50 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 98.61/16.50 thf(foundationAx_type, type, foundationAx: $o).
% 98.61/16.50 thf(brelnall2_type, type, brelnall2: $o).
% 98.61/16.50 thf(emptysetAx_type, type, emptysetAx: $o).
% 98.61/16.50 thf(emptyI_type, type, emptyI: $o).
% 98.61/16.50 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 98.61/16.50 thf(binintersectEL_type, type, binintersectEL: $o).
% 98.61/16.50 thf(emptyE1_type, type, emptyE1: $o).
% 98.61/16.50 thf(demorgan2a_type, type, demorgan2a: $o).
% 98.61/16.50 thf(woz1_3_type, type, woz1_3: $o).
% 98.61/16.50 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 98.61/16.50 thf(vacuousDall_type, type, vacuousDall: $o).
% 98.61/16.50 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 98.61/16.50 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 98.61/16.50 thf(demorgan1a_type, type, demorgan1a: $o).
% 98.61/16.50 thf(ifp_type, type, ifp: $o).
% 98.61/16.50 thf(funcSet_type, type, funcSet: $i > $i > $i).
% 98.61/16.50 thf(binintersectI_type, type, binintersectI: $o).
% 98.61/16.50 thf(beta1_type, type, beta1: $o).
% 98.61/16.50 thf(funcext2_type, type, funcext2: $o).
% 98.61/16.50 thf(subbreln_type, type, subbreln: $o).
% 98.61/16.50 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 98.61/16.50 thf('#sk49_type', type, '#sk49': $i).
% 98.61/16.50 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 98.61/16.50 thf(subbreln1_type, type, subbreln1: $o).
% 98.61/16.50 thf(demorgan2a2_type, type, demorgan2a2: $o).
% 98.61/16.50 thf(image1Equiv_type, type, image1Equiv: $o).
% 98.61/16.50 thf(subsetTI_type, type, subsetTI: $o).
% 98.61/16.50 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 98.61/16.50 thf(ap2p_type, type, ap2p: $o).
% 98.61/16.50 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 98.61/16.50 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 98.61/16.50 thf(symdiffI1_type, type, symdiffI1: $o).
% 98.61/16.50 thf(woz1_4_type, type, woz1_4: $o).
% 98.61/16.50 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 98.61/16.50 thf(subsetI2_type, type, subsetI2: $o).
% 98.61/16.50 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 98.61/16.50 thf(theeq_type, type, theeq: $o).
% 98.61/16.50 thf(setminusERneg_type, type, setminusERneg: $o).
% 98.61/16.50 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 98.61/16.50 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 98.61/16.50 thf(omega__Cong_type, type, omega__Cong: $o).
% 98.61/16.50 thf(demorgan1b_type, type, demorgan1b: $o).
% 98.61/16.50 thf(subsetRefl_type, type, subsetRefl: $o).
% 98.61/16.50 thf(uniqinunit_type, type, uniqinunit: $o).
% 98.61/16.50 thf(eqbreln_type, type, eqbreln: $o).
% 98.61/16.50 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o).
% 98.61/16.50 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 98.61/16.50 thf(breln1compEex_type, type, breln1compEex: $o).
% 98.61/16.50 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 98.61/16.50 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 98.61/16.50 thf(prop2setE_type, type, prop2setE: $o).
% 98.61/16.50 thf(binunionEcases_type, type, binunionEcases: $o).
% 98.61/16.50 thf(omega_type, type, omega: $i).
% 98.61/16.50 thf(nonemptyI_type, type, nonemptyI: $o).
% 98.61/16.50 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 98.61/16.50 thf(woz2A_type, type, woz2A: $o).
% 98.61/16.50 thf(exuE3u_type, type, exuE3u: $o).
% 98.61/16.50 thf(setminusEL_type, type, setminusEL: $o).
% 98.61/16.50 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 98.61/16.50 thf(woz1_5_type, type, woz1_5: $o).
% 98.61/16.50 thf(demorgan2_type, type, demorgan2: $o).
% 98.61/16.50 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 98.61/16.50 thf(sepSubset_type, type, sepSubset: $o).
% 98.61/16.50 thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1:
% 98.61/16.50 $o).
% 98.61/16.50 thf(funcext_type, type, funcext: $o).
% 98.61/16.50 thf(surjFuncSet_type, type, surjFuncSet: $i > $i > $i).
% 98.61/16.50 thf(upairset2E_type, type, upairset2E: $o).
% 98.61/16.50 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 98.61/16.50 thf(exuI3_type, type, exuI3: $o).
% 98.61/16.50 thf(notdallE_type, type, notdallE: $o).
% 98.61/16.50 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 98.61/16.50 thf(binintersectER_type, type, binintersectER: $o).
% 98.61/16.50 thf(woz13rule0_type, type, woz13rule0: $o).
% 98.61/16.50 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 98.61/16.50 thf(beta2_type, type, beta2: $o).
% 98.61/16.50 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 98.61/16.50 thf(exu__Cong_type, type, exu__Cong: $o).
% 98.61/16.50 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 98.61/16.50 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 98.61/16.50 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 98.61/16.50 thf(ex1I_type, type, ex1I: $o).
% 98.61/16.50 thf(secondinupair_type, type, secondinupair: $o).
% 98.61/16.50 thf(singletonprop_type, type, singletonprop: $o).
% 98.61/16.50 thf(singletonsubset_type, type, singletonsubset: $o).
% 98.61/16.50 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 98.61/16.50 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 98.61/16.50 thf(ex1E2_type, type, ex1E2: $o).
% 98.61/16.50 thf(replAx_type, type, replAx: $o).
% 98.61/16.50 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 98.61/16.50 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 98.61/16.50 thf(setukpairIL_type, type, setukpairIL: $o).
% 98.61/16.50 thf(setunionE2_type, type, setunionE2: $o).
% 98.61/16.50 thf(inPowerset_type, type, inPowerset: $o).
% 98.61/16.50 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 98.61/16.50 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 98.61/16.50 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 98.61/16.50 thf(woz13rule3_type, type, woz13rule3: $o).
% 98.61/16.50 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 98.61/16.50 $o).
% 98.61/16.50 thf(in__Cong_type, type, in__Cong: $o).
% 98.61/16.50 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 98.61/16.50 thf(binunionRsub_type, type, binunionRsub: $o).
% 98.61/16.50 thf(subset2powerset_type, type, subset2powerset: $o).
% 98.61/16.50 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 98.61/16.50 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 98.61/16.50 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 98.61/16.50 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 98.61/16.50 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 98.61/16.50 thf(surjFuncSetFuncIn, conjecture,
% 98.61/16.50 (( setextAx ) =>
% 98.61/16.50 ( ( emptysetAx ) =>
% 98.61/16.50 ( ( setadjoinAx ) =>
% 98.61/16.50 ( ( powersetAx ) =>
% 98.61/16.50 ( ( setunionAx ) =>
% 98.61/16.50 ( ( omega0Ax ) =>
% 98.61/16.50 ( ( omegaSAx ) =>
% 98.61/16.50 ( ( omegaIndAx ) =>
% 98.61/16.50 ( ( replAx ) =>
% 98.61/16.50 ( ( foundationAx ) =>
% 98.61/16.50 ( ( wellorderingAx ) =>
% 98.61/16.50 ( ( descrp ) =>
% 98.61/16.50 ( ( dsetconstrI ) =>
% 98.61/16.50 ( ( dsetconstrEL ) =>
% 98.61/16.50 ( ( dsetconstrER ) =>
% 98.61/16.50 ( ( exuE1 ) =>
% 98.61/16.50 ( ( prop2setE ) =>
% 98.61/16.50 ( ( emptysetE ) =>
% 98.61/16.50 ( ( emptysetimpfalse ) =>
% 98.61/16.50 ( ( notinemptyset ) =>
% 98.61/16.50 ( ( exuE3e ) =>
% 98.61/16.50 ( ( setext ) =>
% 98.61/16.50 ( ( emptyI ) =>
% 98.61/16.50 ( ( noeltsimpempty ) =>
% 98.61/16.50 ( ( setbeta ) =>
% 98.61/16.50 ( ( nonemptyE1 ) =>
% 98.61/16.50 ( ( nonemptyI ) =>
% 98.61/16.50 ( ( nonemptyI1 ) =>
% 98.61/16.50 ( ( setadjoinIL ) =>
% 98.61/16.50 ( ( emptyinunitempty ) =>
% 98.61/16.50 ( ( setadjoinIR ) =>
% 98.61/16.50 ( ( setadjoinE ) =>
% 98.61/16.50 ( (
% 98.61/16.50 setadjoinOr ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setoftrueEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powersetI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 emptyinPowerset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 emptyInPowerset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powersetE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setunionI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setunionE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subPowSU ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 exuE2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 nonemptyImpWitness ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 uniqinunit ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 notinsingleton ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 eqinunit ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 singletonsswitch ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 upairsetE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 upairsetIL ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 upairsetIR ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 emptyE1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 vacuousDall ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 quantDeMorgan1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 quantDeMorgan2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 quantDeMorgan3 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 quantDeMorgan4 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 prop2setI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 prop2set2propI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 notdexE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 notdallE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 exuI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 exuI3 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 exuI2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 inCongP ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 in__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 exuE3u ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 exu__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 emptyset__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setadjoin__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powerset__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setunion__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 omega__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 exuEu ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 descr__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 dsetconstr__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subsetI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 eqimpsubset2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 eqimpsubset1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subsetI2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 emptysetsubset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subsetE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subsetE2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 notsubsetI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 notequalI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 notequalI2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subsetRefl ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subsetTrans ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setadjoinSub ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setadjoinSub2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subset2powerset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setextsub ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subsetemptysetimpeq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powersetI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powersetE1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 inPowerset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powersetsubset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 sepInPowerset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 sepSubset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionIL ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 upairset2IR ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionIR ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionEcases ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionLsub ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionRsub ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectSubset5 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectEL ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectLsub ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectSubset2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectSubset3 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectER ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 disjointsetsI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectRsub ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectSubset4 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectSubset1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 bs114d ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusEL ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusER ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusSubset2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusERneg ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusELneg ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusILneg ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusIRneg ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusLsub ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusSubset1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 symdiffE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 symdiffI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 symdiffI2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 symdiffIneg1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 symdiffIneg2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 secondinupair ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairIL ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairIR ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 kpairiskpair ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 kpairp ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 singletonsubset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 singletoninpowerset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 singletoninpowunion ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 upairset2E ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 upairsubunion ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 upairinpowunion ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ubforcartprodlem1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ubforcartprodlem2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ubforcartprodlem3 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodpairin ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodmempair1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodmempair ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setunionE2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setunionsingleton1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setunionsingleton2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setunionsingleton ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 singletonprop ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ex1E1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ex1I ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ex1I2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 singletonsuniq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairinjL1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 kfstsingleton ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 theprop ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 kfstpairEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodfstin ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairinjL2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairinjL ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairinjR11 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairinjR12 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairinjR1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 upairequniteq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairinjR2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairinjR ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ksndsingleton ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ksndpairEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 kpairsurjEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodsndin ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodpairmemEL ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodpairmemER ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodmempaircEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodfstpairEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodsndpairEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodpairsurjEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 dpsetconstrI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 dpsetconstrSub ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setOfPairsIsBReln ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 dpsetconstrERa ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 dpsetconstrEL1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 dpsetconstrEL2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 dpsetconstrER ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcImageSingleton ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 apProp ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 app ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 infuncsetfunc ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ap2p ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcinfuncset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 lamProp ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 lamp ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 lam2p ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 brelnall1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 brelnall2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ex1E2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcGraphProp1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcGraphProp3 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcGraphProp2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcextLem ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcGraphProp4 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subbreln ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 eqbreln ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcext ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcext2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ap2apEq1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ap2apEq2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 beta1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 eta1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 lam2lamEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 beta2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 eta2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 iffalseProp1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 iffalseProp2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 iftrueProp1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 iftrueProp2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ifSingleton ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ifp ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 theeq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 iftrue ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 iffalse ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 iftrueorfalse ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectT_lem ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionT_lem ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powersetT_lem ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusT_lem ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementT_lem ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setextT ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subsetTI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powersetTI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powersetTE1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementTI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementTE1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectTELcontra ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectTERcontra ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 contrasubsetT ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 contrasubsetT1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 contrasubsetT2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 contrasubsetT3 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 doubleComplementI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 doubleComplementE1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 doubleComplementSub1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 doubleComplementSub2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 doubleComplementEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementTnotintersectT ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementImpComplementIntersect ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementSubsetComplementIntersect ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementInPowersetComplementIntersect ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 contraSubsetComplement ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementTcontraSubset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionTILcontra ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionTIRcontra ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 inIntersectImpInUnion ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 inIntersectImpInUnion2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 inIntersectImpInIntersectUnions ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 intersectInPowersetIntersectUnions ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 inComplementUnionImpNotIn1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 inComplementUnionImpInComplement1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionTE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionTEcontra ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan2a1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementUnionInPowersetComplement ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan2a2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan1a ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan1b ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan2a ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan2b2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan2b ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz13rule0 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz13rule1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz13rule2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz13rule3 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz13rule4 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz1_1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz1_2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz1_3 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz1_4 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz1_5 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1all2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1SetBreln1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 choice2fnsingleton ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setOfPairsIsBReln1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1all1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subbreln1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 eqbreln1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1invprop ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1invI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1invE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1compprop ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1compI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1compE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1compEex ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1unionprop ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1unionIL ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1unionIR ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1unionI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1unionE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1unionEcases ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1unionCommutes ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz2Ex ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz2W ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz2A ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz2B ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 image1Ex ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 image1Ex1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 image1Equiv ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 image1E ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 image1I ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 injFuncInInjFuncSet ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 injFuncSetFuncIn ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 injFuncSetFuncInj ) =>
% 98.61/16.50 (
% 98.61/16.50 ![
% 98.61/16.50 A:$i,B:$i,
% 98.61/16.50 Xf:$i]:
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 in @
% 98.61/16.50 Xf @
% 98.61/16.50 (
% 98.61/16.50 surjFuncSet
% 98.61/16.50 @
% 98.61/16.50 A @ B ) ) =>
% 98.61/16.50 (
% 98.61/16.50 in @
% 98.61/16.50 Xf @
% 98.61/16.50 (
% 98.61/16.50 funcSet @
% 98.61/16.50 A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 98.61/16.50 thf(zf_stmt_0, negated_conjecture,
% 98.61/16.50 (~( ( setextAx ) =>
% 98.61/16.50 ( ( emptysetAx ) =>
% 98.61/16.50 ( ( setadjoinAx ) =>
% 98.61/16.50 ( ( powersetAx ) =>
% 98.61/16.50 ( ( setunionAx ) =>
% 98.61/16.50 ( ( omega0Ax ) =>
% 98.61/16.50 ( ( omegaSAx ) =>
% 98.61/16.50 ( ( omegaIndAx ) =>
% 98.61/16.50 ( ( replAx ) =>
% 98.61/16.50 ( ( foundationAx ) =>
% 98.61/16.50 ( ( wellorderingAx ) =>
% 98.61/16.50 ( ( descrp ) =>
% 98.61/16.50 ( ( dsetconstrI ) =>
% 98.61/16.50 ( ( dsetconstrEL ) =>
% 98.61/16.50 ( ( dsetconstrER ) =>
% 98.61/16.50 ( ( exuE1 ) =>
% 98.61/16.50 ( ( prop2setE ) =>
% 98.61/16.50 ( ( emptysetE ) =>
% 98.61/16.50 ( ( emptysetimpfalse ) =>
% 98.61/16.50 ( ( notinemptyset ) =>
% 98.61/16.50 ( ( exuE3e ) =>
% 98.61/16.50 ( ( setext ) =>
% 98.61/16.50 ( ( emptyI ) =>
% 98.61/16.50 ( ( noeltsimpempty ) =>
% 98.61/16.50 ( ( setbeta ) =>
% 98.61/16.50 ( ( nonemptyE1 ) =>
% 98.61/16.50 ( ( nonemptyI ) =>
% 98.61/16.50 ( ( nonemptyI1 ) =>
% 98.61/16.50 ( ( setadjoinIL ) =>
% 98.61/16.50 ( ( emptyinunitempty ) =>
% 98.61/16.50 ( ( setadjoinIR ) =>
% 98.61/16.50 ( (
% 98.61/16.50 setadjoinE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setadjoinOr ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setoftrueEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powersetI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 emptyinPowerset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 emptyInPowerset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powersetE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setunionI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setunionE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subPowSU ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 exuE2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 nonemptyImpWitness ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 uniqinunit ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 notinsingleton ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 eqinunit ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 singletonsswitch ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 upairsetE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 upairsetIL ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 upairsetIR ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 emptyE1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 vacuousDall ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 quantDeMorgan1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 quantDeMorgan2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 quantDeMorgan3 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 quantDeMorgan4 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 prop2setI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 prop2set2propI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 notdexE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 notdallE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 exuI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 exuI3 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 exuI2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 inCongP ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 in__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 exuE3u ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 exu__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 emptyset__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setadjoin__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powerset__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setunion__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 omega__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 exuEu ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 descr__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 dsetconstr__Cong ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subsetI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 eqimpsubset2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 eqimpsubset1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subsetI2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 emptysetsubset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subsetE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subsetE2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 notsubsetI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 notequalI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 notequalI2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subsetRefl ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subsetTrans ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setadjoinSub ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setadjoinSub2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subset2powerset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setextsub ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subsetemptysetimpeq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powersetI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powersetE1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 inPowerset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powersetsubset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 sepInPowerset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 sepSubset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionIL ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 upairset2IR ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionIR ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionEcases ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionLsub ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionRsub ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectSubset5 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectEL ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectLsub ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectSubset2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectSubset3 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectER ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 disjointsetsI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectRsub ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectSubset4 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectSubset1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 bs114d ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusEL ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusER ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusSubset2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusERneg ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusELneg ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusILneg ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusIRneg ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusLsub ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusSubset1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 symdiffE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 symdiffI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 symdiffI2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 symdiffIneg1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 symdiffIneg2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 secondinupair ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairIL ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairIR ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 kpairiskpair ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 kpairp ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 singletonsubset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 singletoninpowerset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 singletoninpowunion ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 upairset2E ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 upairsubunion ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 upairinpowunion ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ubforcartprodlem1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ubforcartprodlem2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ubforcartprodlem3 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodpairin ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodmempair1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodmempair ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setunionE2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setunionsingleton1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setunionsingleton2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setunionsingleton ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 singletonprop ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ex1E1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ex1I ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ex1I2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 singletonsuniq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairinjL1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 kfstsingleton ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 theprop ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 kfstpairEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodfstin ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairinjL2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairinjL ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairinjR11 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairinjR12 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairinjR1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 upairequniteq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairinjR2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setukpairinjR ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ksndsingleton ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ksndpairEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 kpairsurjEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodsndin ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodpairmemEL ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodpairmemER ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodmempaircEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodfstpairEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodsndpairEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 cartprodpairsurjEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 dpsetconstrI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 dpsetconstrSub ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setOfPairsIsBReln ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 dpsetconstrERa ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 dpsetconstrEL1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 dpsetconstrEL2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 dpsetconstrER ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcImageSingleton ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 apProp ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 app ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 infuncsetfunc ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ap2p ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcinfuncset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 lamProp ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 lamp ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 lam2p ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 brelnall1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 brelnall2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ex1E2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcGraphProp1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcGraphProp3 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcGraphProp2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcextLem ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcGraphProp4 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subbreln ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 eqbreln ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcext ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 funcext2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ap2apEq1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ap2apEq2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 beta1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 eta1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 lam2lamEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 beta2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 eta2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 iffalseProp1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 iffalseProp2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 iftrueProp1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 iftrueProp2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ifSingleton ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 ifp ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 theeq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 iftrue ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 iffalse ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 iftrueorfalse ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectT_lem ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionT_lem ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powersetT_lem ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setminusT_lem ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementT_lem ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setextT ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subsetTI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powersetTI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 powersetTE1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementTI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementTE1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectTELcontra ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binintersectTERcontra ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 contrasubsetT ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 contrasubsetT1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 contrasubsetT2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 contrasubsetT3 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 doubleComplementI1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 doubleComplementE1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 doubleComplementSub1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 doubleComplementSub2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 doubleComplementEq ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementTnotintersectT ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementImpComplementIntersect ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementSubsetComplementIntersect ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementInPowersetComplementIntersect ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 contraSubsetComplement ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementTcontraSubset ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionTILcontra ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionTIRcontra ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 inIntersectImpInUnion ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 inIntersectImpInUnion2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 inIntersectImpInIntersectUnions ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 intersectInPowersetIntersectUnions ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 inComplementUnionImpNotIn1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 inComplementUnionImpInComplement1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionTE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 binunionTEcontra ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan2a1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 complementUnionInPowersetComplement ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan2a2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan1a ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan1b ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan2a ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan2b2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan2b ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 demorgan2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz13rule0 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz13rule1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz13rule2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz13rule3 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz13rule4 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz1_1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz1_2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz1_3 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz1_4 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz1_5 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1all2 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1SetBreln1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 choice2fnsingleton ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 setOfPairsIsBReln1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1all1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 subbreln1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 eqbreln1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1invprop ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1invI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1invE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1compprop ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1compI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1compE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1compEex ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1unionprop ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1unionIL ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1unionIR ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1unionI ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1unionE ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1unionEcases ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 breln1unionCommutes ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz2Ex ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz2W ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz2A ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 woz2B ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 image1Ex ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 image1Ex1 ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 image1Equiv ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 image1E ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 image1I ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 injFuncInInjFuncSet ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 injFuncSetFuncIn ) =>
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 injFuncSetFuncInj ) =>
% 98.61/16.50 (
% 98.61/16.50 ![
% 98.61/16.50 A:$i,
% 98.61/16.50 B:$i,
% 98.61/16.50 Xf:$i]:
% 98.61/16.50 (
% 98.61/16.50 (
% 98.61/16.50 in @
% 98.61/16.50 Xf @
% 98.61/16.50 (
% 98.61/16.50 surjFuncSet
% 98.61/16.50 @
% 98.61/16.50 A @ B ) ) =>
% 98.61/16.50 (
% 98.61/16.50 in @
% 98.61/16.50 Xf @
% 98.61/16.50 (
% 98.61/16.50 funcSet @
% 98.61/16.50 A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 98.61/16.50 inference('cnf.neg', [status(esa)], [surjFuncSetFuncIn])).
% 98.61/16.50 thf(zip_derived_cl0, plain,
% 98.61/16.50 (~ (((setextAx) =>
% 98.61/16.50 (((emptysetAx) =>
% 98.61/16.50 (((setadjoinAx) =>
% 98.61/16.50 (((powersetAx) =>
% 98.61/16.50 (((setunionAx) =>
% 98.61/16.50 (((omega0Ax) =>
% 98.61/16.50 (((omegaSAx) =>
% 98.61/16.50 (((omegaIndAx) =>
% 98.61/16.50 (((replAx) =>
% 98.61/16.50 (((foundationAx) =>
% 98.61/16.50 (((wellorderingAx) =>
% 98.61/16.50 (((descrp) =>
% 98.61/16.50 (((dsetconstrI) =>
% 98.61/16.50 (((dsetconstrEL) =>
% 98.61/16.50 (((dsetconstrER) =>
% 98.61/16.50 (((exuE1) =>
% 98.61/16.50 (((prop2setE) =>
% 98.61/16.50 (((emptysetE) =>
% 98.61/16.50 (((emptysetimpfalse) =>
% 98.61/16.50 (((notinemptyset) =>
% 98.61/16.50 (((exuE3e) =>
% 98.61/16.50 (((setext) =>
% 98.61/16.50 (((emptyI) =>
% 98.61/16.50 (((noeltsimpempty) =>
% 98.61/16.50 (((setbeta) =>
% 98.61/16.50 (((nonemptyE1) =>
% 98.61/16.50 (((nonemptyI) =>
% 98.61/16.50 (((nonemptyI1) =>
% 98.61/16.50 (((setadjoinIL) =>
% 98.61/16.50 (((emptyinunitempty) =>
% 98.61/16.50 ((
% 98.61/16.50 (setadjoinIR) =>
% 98.61/16.50 ((
% 98.61/16.50 (setadjoinE) =>
% 98.61/16.50 ((
% 98.61/16.50 (setadjoinOr) =>
% 98.61/16.50 ((
% 98.61/16.50 (setoftrueEq) =>
% 98.61/16.50 ((
% 98.61/16.50 (powersetI) =>
% 98.61/16.50 ((
% 98.61/16.50 (emptyinPowerset) =>
% 98.61/16.50 ((
% 98.61/16.50 (emptyInPowerset) =>
% 98.61/16.50 ((
% 98.61/16.50 (powersetE) =>
% 98.61/16.50 ((
% 98.61/16.50 (setunionI) =>
% 98.61/16.50 ((
% 98.61/16.50 (setunionE) =>
% 98.61/16.50 ((
% 98.61/16.50 (subPowSU) =>
% 98.61/16.50 ((
% 98.61/16.50 (exuE2) =>
% 98.61/16.50 ((
% 98.61/16.50 (nonemptyImpWitness) =>
% 98.61/16.50 ((
% 98.61/16.50 (uniqinunit) =>
% 98.61/16.50 ((
% 98.61/16.50 (notinsingleton) =>
% 98.61/16.50 ((
% 98.61/16.50 (eqinunit) =>
% 98.61/16.50 ((
% 98.61/16.50 (singletonsswitch) =>
% 98.61/16.50 ((
% 98.61/16.50 (upairsetE) =>
% 98.61/16.50 ((
% 98.61/16.50 (upairsetIL) =>
% 98.61/16.50 ((
% 98.61/16.50 (upairsetIR) =>
% 98.61/16.50 ((
% 98.61/16.50 (emptyE1) =>
% 98.61/16.50 ((
% 98.61/16.50 (vacuousDall) =>
% 98.61/16.50 ((
% 98.61/16.50 (quantDeMorgan1) =>
% 98.61/16.50 ((
% 98.61/16.50 (quantDeMorgan2) =>
% 98.61/16.50 ((
% 98.61/16.50 (quantDeMorgan3) =>
% 98.61/16.50 ((
% 98.61/16.50 (quantDeMorgan4) =>
% 98.61/16.50 ((
% 98.61/16.50 (prop2setI) =>
% 98.61/16.50 ((
% 98.61/16.50 (prop2set2propI) =>
% 98.61/16.50 ((
% 98.61/16.50 (notdexE) =>
% 98.61/16.50 ((
% 98.61/16.50 (notdallE) =>
% 98.61/16.50 ((
% 98.61/16.50 (exuI1) =>
% 98.61/16.50 ((
% 98.61/16.50 (exuI3) =>
% 98.61/16.50 ((
% 98.61/16.50 (exuI2) =>
% 98.61/16.50 ((
% 98.61/16.50 (inCongP) =>
% 98.61/16.50 ((
% 98.61/16.50 (in__Cong) =>
% 98.61/16.50 ((
% 98.61/16.50 (exuE3u) =>
% 98.61/16.50 ((
% 98.61/16.50 (exu__Cong) =>
% 98.61/16.50 ((
% 98.61/16.50 (emptyset__Cong) =>
% 98.61/16.50 ((
% 98.61/16.50 (setadjoin__Cong) =>
% 98.61/16.50 ((
% 98.61/16.50 (powerset__Cong) =>
% 98.61/16.50 ((
% 98.61/16.50 (setunion__Cong) =>
% 98.61/16.50 ((
% 98.61/16.50 (omega__Cong) =>
% 98.61/16.50 ((
% 98.61/16.50 (exuEu) =>
% 98.61/16.50 ((
% 98.61/16.50 (descr__Cong) =>
% 98.61/16.50 ((
% 98.61/16.50 (dsetconstr__Cong) =>
% 98.61/16.50 ((
% 98.61/16.50 (subsetI1) =>
% 98.61/16.50 ((
% 98.61/16.50 (eqimpsubset2) =>
% 98.61/16.50 ((
% 98.61/16.50 (eqimpsubset1) =>
% 98.61/16.50 ((
% 98.61/16.50 (subsetI2) =>
% 98.61/16.50 ((
% 98.61/16.50 (emptysetsubset) =>
% 98.61/16.50 ((
% 98.61/16.50 (subsetE) =>
% 98.61/16.50 ((
% 98.61/16.50 (subsetE2) =>
% 98.61/16.50 ((
% 98.61/16.50 (notsubsetI) =>
% 98.61/16.50 ((
% 98.61/16.50 (notequalI1) =>
% 98.61/16.50 ((
% 98.61/16.50 (notequalI2) =>
% 98.61/16.50 ((
% 98.61/16.50 (subsetRefl) =>
% 98.61/16.50 ((
% 98.61/16.50 (subsetTrans) =>
% 98.61/16.50 ((
% 98.61/16.50 (setadjoinSub) =>
% 98.61/16.50 ((
% 98.61/16.50 (setadjoinSub2) =>
% 98.61/16.50 ((
% 98.61/16.50 (subset2powerset) =>
% 98.61/16.50 ((
% 98.61/16.50 (setextsub) =>
% 98.61/16.50 ((
% 98.61/16.50 (subsetemptysetimpeq) =>
% 98.61/16.50 ((
% 98.61/16.50 (powersetI1) =>
% 98.61/16.50 ((
% 98.61/16.50 (powersetE1) =>
% 98.61/16.50 ((
% 98.61/16.50 (inPowerset) =>
% 98.61/16.50 ((
% 98.61/16.50 (powersetsubset) =>
% 98.61/16.50 ((
% 98.61/16.50 (sepInPowerset) =>
% 98.61/16.50 ((
% 98.61/16.50 (sepSubset) =>
% 98.61/16.50 ((
% 98.61/16.50 (binunionIL) =>
% 98.61/16.50 ((
% 98.61/16.50 (upairset2IR) =>
% 98.61/16.50 ((
% 98.61/16.50 (binunionIR) =>
% 98.61/16.50 ((
% 98.61/16.50 (binunionEcases) =>
% 98.61/16.50 ((
% 98.61/16.50 (binunionE) =>
% 98.61/16.50 ((
% 98.61/16.50 (binunionLsub) =>
% 98.61/16.50 ((
% 98.61/16.50 (binunionRsub) =>
% 98.61/16.50 ((
% 98.61/16.50 (binintersectI) =>
% 98.61/16.50 ((
% 98.61/16.50 (binintersectSubset5) =>
% 98.61/16.50 ((
% 98.61/16.50 (binintersectEL) =>
% 98.61/16.50 ((
% 98.61/16.50 (binintersectLsub) =>
% 98.61/16.50 ((
% 98.61/16.50 (binintersectSubset2) =>
% 98.61/16.50 ((
% 98.61/16.50 (binintersectSubset3) =>
% 98.61/16.50 ((
% 98.61/16.50 (binintersectER) =>
% 98.61/16.50 ((
% 98.61/16.50 (disjointsetsI1) =>
% 98.61/16.50 ((
% 98.61/16.50 (binintersectRsub) =>
% 98.61/16.50 ((
% 98.61/16.50 (binintersectSubset4) =>
% 98.61/16.50 ((
% 98.61/16.50 (binintersectSubset1) =>
% 98.61/16.50 ((
% 98.61/16.50 (bs114d) =>
% 98.61/16.50 ((
% 98.61/16.50 (setminusI) =>
% 98.61/16.50 ((
% 98.61/16.50 (setminusEL) =>
% 98.61/16.50 ((
% 98.61/16.50 (setminusER) =>
% 98.61/16.50 ((
% 98.61/16.50 (setminusSubset2) =>
% 98.61/16.50 ((
% 98.61/16.50 (setminusERneg) =>
% 98.61/16.50 ((
% 98.61/16.50 (setminusELneg) =>
% 98.61/16.50 ((
% 98.61/16.50 (setminusILneg) =>
% 98.61/16.50 ((
% 98.61/16.50 (setminusIRneg) =>
% 98.61/16.50 ((
% 98.61/16.50 (setminusLsub) =>
% 98.61/16.50 ((
% 98.61/16.50 (setminusSubset1) =>
% 98.61/16.50 ((
% 98.61/16.50 (symdiffE) =>
% 98.61/16.50 ((
% 98.61/16.50 (symdiffI1) =>
% 98.61/16.50 ((
% 98.61/16.50 (symdiffI2) =>
% 98.61/16.50 ((
% 98.61/16.50 (symdiffIneg1) =>
% 98.61/16.50 ((
% 98.61/16.50 (symdiffIneg2) =>
% 98.61/16.50 ((
% 98.61/16.50 (secondinupair) =>
% 98.61/16.50 ((
% 98.61/16.50 (setukpairIL) =>
% 98.61/16.50 ((
% 98.61/16.50 (setukpairIR) =>
% 98.61/16.50 ((
% 98.61/16.50 (kpairiskpair) =>
% 98.61/16.50 ((
% 98.61/16.50 (kpairp) =>
% 98.61/16.50 ((
% 98.61/16.50 (singletonsubset) =>
% 98.61/16.50 ((
% 98.61/16.50 (singletoninpowerset) =>
% 98.61/16.50 ((
% 98.61/16.50 (singletoninpowunion) =>
% 98.61/16.50 ((
% 98.61/16.50 (upairset2E) =>
% 98.61/16.50 ((
% 98.61/16.50 (upairsubunion) =>
% 98.61/16.50 ((
% 98.61/16.50 (upairinpowunion) =>
% 98.61/16.50 ((
% 98.61/16.50 (ubforcartprodlem1) =>
% 98.61/16.50 ((
% 98.61/16.50 (ubforcartprodlem2) =>
% 98.61/16.50 ((
% 98.61/16.50 (ubforcartprodlem3) =>
% 98.61/16.50 ((
% 98.61/16.50 (cartprodpairin) =>
% 98.61/16.50 ((
% 98.61/16.50 (cartprodmempair1) =>
% 98.61/16.50 ((
% 98.61/16.50 (cartprodmempair) =>
% 98.61/16.50 ((
% 98.61/16.50 (setunionE2) =>
% 98.61/16.50 ((
% 98.61/16.50 (setunionsingleton1) =>
% 98.61/16.50 ((
% 98.61/16.50 (setunionsingleton2) =>
% 98.61/16.50 ((
% 98.61/16.50 (setunionsingleton) =>
% 98.61/16.50 ((
% 98.61/16.50 (singletonprop) =>
% 98.61/16.50 ((
% 98.61/16.50 (ex1E1) =>
% 98.61/16.50 ((
% 98.61/16.50 (ex1I) =>
% 98.61/16.50 ((
% 98.61/16.50 (ex1I2) =>
% 98.61/16.50 ((
% 98.61/16.50 (singletonsuniq) =>
% 98.61/16.50 ((
% 98.61/16.50 (setukpairinjL1) =>
% 98.61/16.50 ((
% 98.61/16.50 (kfstsingleton) =>
% 98.61/16.50 ((
% 98.61/16.50 (theprop) =>
% 98.61/16.50 ((
% 98.61/16.50 (kfstpairEq) =>
% 98.61/16.50 ((
% 98.61/16.50 (cartprodfstin) =>
% 98.61/16.50 ((
% 98.61/16.50 (setukpairinjL2) =>
% 98.61/16.50 ((
% 98.61/16.50 (setukpairinjL) =>
% 98.61/16.50 ((
% 98.61/16.50 (setukpairinjR11) =>
% 98.61/16.50 ((
% 98.61/16.50 (setukpairinjR12) =>
% 98.61/16.50 ((
% 98.61/16.50 (setukpairinjR1) =>
% 98.61/16.50 ((
% 98.61/16.50 (upairequniteq) =>
% 98.61/16.50 ((
% 98.61/16.50 (setukpairinjR2) =>
% 98.61/16.50 ((
% 98.61/16.50 (setukpairinjR) =>
% 98.61/16.50 ((
% 98.61/16.50 (ksndsingleton) =>
% 98.61/16.50 ((
% 98.61/16.50 (ksndpairEq) =>
% 98.61/16.50 ((
% 98.61/16.50 (kpairsurjEq) =>
% 98.61/16.50 ((
% 98.61/16.50 (cartprodsndin) =>
% 98.61/16.50 ((
% 98.61/16.50 (cartprodpairmemEL) =>
% 98.61/16.50 ((
% 98.61/16.50 (cartprodpairmemER) =>
% 98.61/16.50 ((
% 98.61/16.50 (cartprodmempaircEq) =>
% 98.61/16.50 ((
% 98.61/16.50 (cartprodfstpairEq) =>
% 98.61/16.50 ((
% 98.61/16.50 (cartprodsndpairEq) =>
% 98.61/16.50 ((
% 98.61/16.50 (cartprodpairsurjEq) =>
% 98.61/16.50 ((
% 98.61/16.50 (dpsetconstrI) =>
% 98.61/16.50 ((
% 98.61/16.50 (dpsetconstrSub) =>
% 98.61/16.50 ((
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% 98.61/16.51 ((
% 98.61/16.51 (cartprodmempair) =>
% 98.61/16.51 ((
% 98.61/16.51 (setunionE2) =>
% 98.61/16.51 ((
% 98.61/16.51 (setunionsingleton1) =>
% 98.61/16.51 ((
% 98.61/16.51 (setunionsingleton2) =>
% 98.61/16.51 ((
% 98.61/16.51 (setunionsingleton) =>
% 98.61/16.51 ((
% 98.61/16.51 (singletonprop) =>
% 98.61/16.51 ((
% 98.61/16.51 (ex1E1) =>
% 98.61/16.51 ((
% 98.61/16.51 (ex1I) =>
% 98.61/16.51 ((
% 98.61/16.51 (ex1I2) =>
% 98.61/16.51 ((
% 98.61/16.51 (singletonsuniq) =>
% 98.61/16.51 ((
% 98.61/16.51 (setukpairinjL1) =>
% 98.61/16.51 ((
% 98.61/16.51 (kfstsingleton) =>
% 98.61/16.51 ((
% 98.61/16.51 (theprop) =>
% 98.61/16.51 ((
% 98.61/16.51 (kfstpairEq) =>
% 98.61/16.51 ((
% 98.61/16.51 (cartprodfstin) =>
% 98.61/16.51 ((
% 98.61/16.51 (setukpairinjL2) =>
% 98.61/16.51 ((
% 98.61/16.51 (setukpairinjL) =>
% 98.61/16.51 ((
% 98.61/16.51 (setukpairinjR11) =>
% 98.61/16.51 ((
% 98.61/16.51 (setukpairinjR12) =>
% 98.61/16.51 ((
% 98.61/16.51 (setukpairinjR1) =>
% 98.61/16.51 ((
% 98.61/16.51 (upairequniteq) =>
% 98.61/16.51 ((
% 98.61/16.51 (setukpairinjR2) =>
% 98.61/16.51 ((
% 98.61/16.51 (setukpairinjR) =>
% 98.61/16.51 ((
% 98.61/16.51 (ksndsingleton) =>
% 98.61/16.51 ((
% 98.61/16.51 (ksndpairEq) =>
% 98.61/16.51 ((
% 98.61/16.51 (kpairsurjEq) =>
% 98.61/16.51 ((
% 98.61/16.51 (cartprodsndin) =>
% 98.61/16.51 ((
% 98.61/16.51 (cartprodpairmemEL) =>
% 98.61/16.51 ((
% 98.61/16.51 (cartprodpairmemER) =>
% 98.61/16.51 ((
% 98.61/16.51 (cartprodmempaircEq) =>
% 98.61/16.51 ((
% 98.61/16.51 (cartprodfstpairEq) =>
% 98.61/16.51 ((
% 98.61/16.51 (cartprodsndpairEq) =>
% 98.61/16.51 ((
% 98.61/16.51 (cartprodpairsurjEq) =>
% 98.61/16.51 ((
% 98.61/16.51 (dpsetconstrI) =>
% 98.61/16.51 ((
% 98.61/16.51 (dpsetconstrSub) =>
% 98.61/16.51 ((
% 98.61/16.51 (setOfPairsIsBReln) =>
% 98.61/16.51 ((
% 98.61/16.51 (dpsetconstrERa) =>
% 98.61/16.51 ((
% 98.61/16.51 (dpsetconstrEL1) =>
% 98.61/16.51 ((
% 98.61/16.51 (dpsetconstrEL2) =>
% 98.61/16.51 ((
% 98.61/16.51 (dpsetconstrER) =>
% 98.61/16.51 ((
% 98.61/16.51 (funcImageSingleton) =>
% 98.61/16.51 ((
% 98.61/16.51 (apProp) =>
% 98.61/16.51 ((
% 98.61/16.51 (app) =>
% 98.61/16.51 ((
% 98.61/16.51 (infuncsetfunc) =>
% 98.61/16.51 ((
% 98.61/16.51 (ap2p) =>
% 98.61/16.51 ((
% 98.61/16.51 (funcinfuncset) =>
% 98.61/16.51 ((
% 98.61/16.51 (lamProp) =>
% 98.61/16.51 ((
% 98.61/16.51 (lamp) =>
% 98.61/16.51 ((
% 98.61/16.51 (lam2p) =>
% 98.61/16.51 ((
% 98.61/16.51 (brelnall1) =>
% 98.61/16.51 ((
% 98.61/16.51 (brelnall2) =>
% 98.61/16.51 ((
% 98.61/16.51 (ex1E2) =>
% 98.61/16.51 ((
% 98.61/16.51 (funcGraphProp1) =>
% 98.61/16.51 ((
% 98.61/16.51 (funcGraphProp3) =>
% 98.61/16.51 ((
% 98.61/16.51 (funcGraphProp2) =>
% 98.61/16.51 ((
% 98.61/16.51 (funcextLem) =>
% 98.61/16.51 ((
% 98.61/16.51 (funcGraphProp4) =>
% 98.61/16.51 ((
% 98.61/16.51 (subbreln) =>
% 98.61/16.51 ((
% 98.61/16.51 (eqbreln) =>
% 98.61/16.51 ((
% 98.61/16.51 (funcext) =>
% 98.61/16.51 ((
% 98.61/16.51 (funcext2) =>
% 98.61/16.51 ((
% 98.61/16.51 (ap2apEq1) =>
% 98.61/16.51 ((
% 98.61/16.51 (ap2apEq2) =>
% 98.61/16.51 ((
% 98.61/16.51 (beta1) =>
% 98.61/16.51 ((
% 98.61/16.51 (eta1) =>
% 98.61/16.51 ((
% 98.61/16.51 (lam2lamEq) =>
% 98.61/16.51 ((
% 98.61/16.51 (beta2) =>
% 98.61/16.51 ((
% 98.61/16.51 (eta2) =>
% 98.61/16.51 ((
% 98.61/16.51 (iffalseProp1) =>
% 98.61/16.51 ((
% 98.61/16.51 (iffalseProp2) =>
% 98.61/16.51 ((
% 98.61/16.51 (iftrueProp1) =>
% 98.61/16.51 ((
% 98.61/16.51 (iftrueProp2) =>
% 98.61/16.51 ((
% 98.61/16.51 (ifSingleton) =>
% 98.61/16.51 ((
% 98.61/16.51 (ifp) =>
% 98.61/16.51 ((
% 98.61/16.51 (theeq) =>
% 98.61/16.51 ((
% 98.61/16.51 (iftrue) =>
% 98.61/16.51 ((
% 98.61/16.51 (iffalse) =>
% 98.61/16.51 ((
% 98.61/16.51 (iftrueorfalse) =>
% 98.61/16.51 ((
% 98.61/16.51 (binintersectT_lem) =>
% 98.61/16.51 ((
% 98.61/16.51 (binunionT_lem) =>
% 98.61/16.51 ((
% 98.61/16.51 (powersetT_lem) =>
% 98.61/16.51 ((
% 98.61/16.51 (setminusT_lem) =>
% 98.61/16.51 ((
% 98.61/16.51 (complementT_lem) =>
% 98.61/16.51 ((
% 98.61/16.51 (setextT) =>
% 98.61/16.51 ((
% 98.61/16.51 (subsetTI) =>
% 98.61/16.51 ((
% 98.61/16.51 (powersetTI1) =>
% 98.61/16.51 ((
% 98.61/16.51 (powersetTE1) =>
% 98.61/16.51 ((
% 98.61/16.51 (complementTI1) =>
% 98.61/16.51 ((
% 98.61/16.51 (complementTE1) =>
% 98.61/16.51 ((
% 98.61/16.51 (binintersectTELcontra) =>
% 98.61/16.51 ((
% 98.61/16.51 (binintersectTERcontra) =>
% 98.61/16.51 ((
% 98.61/16.51 (contrasubsetT) =>
% 98.61/16.51 ((
% 98.61/16.51 (contrasubsetT1) =>
% 98.61/16.51 ((
% 98.61/16.51 (contrasubsetT2) =>
% 98.61/16.51 ((
% 98.61/16.51 (contrasubsetT3) =>
% 98.61/16.51 ((
% 98.61/16.51 (doubleComplementI1) =>
% 98.61/16.51 ((
% 98.61/16.51 (doubleComplementE1) =>
% 98.61/16.51 ((
% 98.61/16.51 (doubleComplementSub1) =>
% 98.61/16.51 ((
% 98.61/16.51 (doubleComplementSub2) =>
% 98.61/16.51 ((
% 98.61/16.51 (doubleComplementEq) =>
% 98.61/16.51 ((
% 98.61/16.51 (complementTnotintersectT) =>
% 98.61/16.51 ((
% 98.61/16.51 (complementImpComplementIntersect) =>
% 98.61/16.51 ((
% 98.61/16.51 (complementSubsetComplementIntersect) =>
% 98.61/16.51 ((
% 98.61/16.51 (complementInPowersetComplementIntersect) =>
% 98.61/16.51 ((
% 98.61/16.51 (contraSubsetComplement) =>
% 98.61/16.51 ((
% 98.61/16.51 (complementTcontraSubset) =>
% 98.61/16.51 ((
% 98.61/16.51 (binunionTILcontra) =>
% 98.61/16.51 ((
% 98.61/16.51 (binunionTIRcontra) =>
% 98.61/16.51 ((
% 98.61/16.51 (inIntersectImpInUnion) =>
% 98.61/16.51 ((
% 98.61/16.51 (inIntersectImpInUnion2) =>
% 98.61/16.51 ((
% 98.61/16.51 (inIntersectImpInIntersectUnions) =>
% 98.61/16.51 ((
% 98.61/16.51 (intersectInPowersetIntersectUnions) =>
% 98.61/16.51 ((
% 98.61/16.51 (inComplementUnionImpNotIn1) =>
% 98.61/16.51 ((
% 98.61/16.51 (inComplementUnionImpInComplement1) =>
% 98.61/16.51 ((
% 98.61/16.51 (binunionTE) =>
% 98.61/16.51 ((
% 98.61/16.51 (binunionTEcontra) =>
% 98.61/16.51 ((
% 98.61/16.51 (demorgan2a1) =>
% 98.61/16.51 ((
% 98.61/16.51 (complementUnionInPowersetComplement) =>
% 98.61/16.51 ((
% 98.61/16.51 (demorgan2a2) =>
% 98.61/16.51 ((
% 98.61/16.51 (demorgan1a) =>
% 98.61/16.51 ((
% 98.61/16.51 (demorgan1b) =>
% 98.61/16.51 ((
% 98.61/16.51 (demorgan1) =>
% 98.61/16.51 ((
% 98.61/16.51 (demorgan2a) =>
% 98.61/16.51 ((
% 98.61/16.51 (demorgan2b2) =>
% 98.61/16.51 ((
% 98.61/16.51 (demorgan2b) =>
% 98.61/16.51 ((
% 98.61/16.51 (demorgan2) =>
% 98.61/16.51 ((
% 98.61/16.51 (woz13rule0) =>
% 98.61/16.51 ((
% 98.61/16.51 (woz13rule1) =>
% 98.61/16.51 ((
% 98.61/16.51 (woz13rule2) =>
% 98.61/16.51 ((
% 98.61/16.51 (woz13rule3) =>
% 98.61/16.51 ((
% 98.61/16.51 (woz13rule4) =>
% 98.61/16.51 ((
% 98.61/16.51 (woz1_1) =>
% 98.61/16.51 ((
% 98.61/16.51 (woz1_2) =>
% 98.61/16.51 ((
% 98.61/16.51 (woz1_3) =>
% 98.61/16.51 ((
% 98.61/16.51 (woz1_4) =>
% 98.61/16.51 ((
% 98.61/16.51 (woz1_5) =>
% 98.61/16.51 ((
% 98.61/16.51 (breln1all2) =>
% 98.61/16.51 ((
% 98.61/16.51 (breln1SetBreln1) =>
% 98.61/16.51 ((
% 98.61/16.51 (choice2fnsingleton) =>
% 98.61/16.51 ((
% 98.61/16.51 (setOfPairsIsBReln1) =>
% 98.61/16.51 ((
% 98.61/16.51 (breln1all1) =>
% 98.61/16.51 ((
% 98.61/16.51 (subbreln1) =>
% 98.61/16.51 ((
% 98.61/16.51 (eqbreln1) =>
% 98.61/16.51 ((
% 98.61/16.51 (breln1invprop) =>
% 98.61/16.51 ((
% 98.61/16.51 (breln1invI) =>
% 98.61/16.51 ((
% 98.61/16.51 (breln1invE) =>
% 98.61/16.51 ((
% 98.61/16.51 (breln1compprop) =>
% 98.61/16.51 ((
% 98.61/16.51 (breln1compI) =>
% 98.61/16.51 ((
% 98.61/16.51 (breln1compE) =>
% 98.61/16.51 ((
% 98.61/16.51 (breln1compEex) =>
% 98.61/16.51 ((
% 98.61/16.51 (breln1unionprop) =>
% 98.61/16.51 ((
% 98.61/16.51 (breln1unionIL) =>
% 98.61/16.51 ((
% 98.61/16.51 (breln1unionIR) =>
% 98.61/16.51 ((
% 98.61/16.51 (breln1unionI) =>
% 98.61/16.51 ((
% 98.61/16.51 (breln1unionE) =>
% 98.61/16.51 ((
% 98.61/16.51 (breln1unionEcases) =>
% 98.61/16.51 ((
% 98.61/16.51 (breln1unionCommutes) =>
% 98.61/16.51 ((
% 98.61/16.51 (woz2Ex) =>
% 98.61/16.51 ((
% 98.61/16.51 (woz2W) =>
% 98.61/16.51 ((
% 98.61/16.51 (woz2A) =>
% 98.61/16.51 ((
% 98.61/16.51 (woz2B) =>
% 98.61/16.51 ((
% 98.61/16.51 (image1Ex) =>
% 98.61/16.51 ((
% 98.61/16.51 (image1Ex1) =>
% 98.61/16.51 ((
% 98.61/16.51 (image1Equiv) =>
% 98.61/16.51 ((
% 98.61/16.51 (image1E) =>
% 98.61/16.51 ((
% 98.61/16.51 (image1I) =>
% 98.61/16.51 ((
% 98.61/16.51 (injFuncInInjFuncSet) =>
% 98.61/16.51 ((
% 98.61/16.51 (injFuncSetFuncIn) =>
% 98.61/16.51 ((
% 98.61/16.51 (injFuncSetFuncInj) =>
% 98.61/16.51 ((
% 98.61/16.51 (!!) @ (
% 98.61/16.51 (('#B') @ (
% 98.61/16.51 !!) @
% 98.61/16.51 (
% 98.61/16.51 (
% 98.61/16.51 ('#B') @ (
% 98.61/16.51 (
% 98.61/16.51 ('#B') @ (
% 98.61/16.51 !!))) @
% 98.61/16.51 (
% 98.61/16.51 (
% 98.61/16.51 ('#S') @ (
% 98.61/16.51 (
% 98.61/16.51 ('#B') @ (
% 98.61/16.51 '#S') @
% 98.61/16.51 (
% 98.61/16.51 (
% 98.61/16.51 ('#B') @ (
% 98.61/16.51 (
% 98.61/16.51 ('#B') @ (
% 98.61/16.51 '#S'))) @
% 98.61/16.51 (
% 98.61/16.51 (
% 98.61/16.51 ('#B') @ (
% 98.61/16.51 (
% 98.61/16.51 ('#B') @ (
% 98.61/16.51 (
% 98.61/16.51 ('#B') @ (
% 98.61/16.51 =>))))) @
% 98.61/16.51 (
% 98.61/16.51 (
% 98.61/16.51 ('#B') @ (
% 98.61/16.51 (
% 98.61/16.51 ('#B') @ (
% 98.61/16.51 (
% 98.61/16.51 ('#C') @ in)))) @
% 98.61/16.51 surjFuncSet)))))))) @
% 98.61/16.51 (
% 98.61/16.51 (
% 98.61/16.51 ('#B') @ (
% 98.61/16.51 (
% 98.61/16.51 ('#B') @ (
% 98.61/16.51 (
% 98.61/16.51 ('#C') @ in)))) @
% 98.61/16.51 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.61/16.51 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 98.61/16.51 thf(omega0Ax, axiom,(( omega0Ax ) = ((in @ emptyset @ omega)))).
% 98.61/16.51 thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 98.61/16.51 define([status(thm)])).
% 98.61/16.51 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 98.61/16.51 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))).
% 98.61/16.51 thf('1', plain,
% 98.61/16.51 (( emptyinunitempty ) =
% 98.61/16.51 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 98.61/16.51 define([status(thm)])).
% 98.61/16.51 thf(emptyset__Cong, axiom,(( emptyset__Cong ) =
% 98.61/16.51 ((((emptyset) = (emptyset)))))).
% 98.61/16.51 thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 98.61/16.51 define([status(thm)])).
% 98.61/16.51 thf(omega__Cong, axiom,(( omega__Cong ) = ((((omega) = (omega)))))).
% 98.61/16.51 thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 98.61/16.51 define([status(thm)])).
% 98.61/16.51 thf(zip_derived_cl2, plain,
% 98.61/16.51 (~ (((setextAx) =>
% 98.61/16.51 (((emptysetAx) =>
% 98.61/16.51 (((setadjoinAx) =>
% 98.61/16.51 (((powersetAx) =>
% 98.61/16.51 (((setunionAx) =>
% 98.61/16.51 (((in @ emptyset @ omega) =>
% 98.61/16.51 (((omegaSAx) =>
% 98.61/16.51 (((omegaIndAx) =>
% 98.61/16.51 (((replAx) =>
% 98.61/16.51 (((foundationAx) =>
% 98.61/16.51 (((wellorderingAx) =>
% 98.61/16.51 (((descrp) =>
% 98.61/16.51 (((dsetconstrI) =>
% 98.61/16.51 (((dsetconstrEL) =>
% 98.61/16.51 (((dsetconstrER) =>
% 98.61/16.51 (((exuE1) =>
% 98.61/16.51 (((prop2setE) =>
% 98.61/16.51 (((emptysetE) =>
% 98.61/16.51 (((emptysetimpfalse) =>
% 98.61/16.51 (((notinemptyset) =>
% 98.61/16.51 (((exuE3e) =>
% 98.61/16.51 (((setext) =>
% 98.61/16.51 (((emptyI) =>
% 98.61/16.51 (((noeltsimpempty) =>
% 98.61/16.51 (((setbeta) =>
% 98.61/16.51 (((nonemptyE1) =>
% 98.61/16.51 (((nonemptyI) =>
% 98.61/16.51 (((nonemptyI1) =>
% 98.61/16.51 (((setadjoinIL) =>
% 98.61/16.51 (((in @
% 98.61/16.51 emptyset @
% 98.61/16.51 (setadjoin @
% 98.61/16.51 emptyset @
% 98.61/16.51 emptyset)) =>
% 98.61/16.51 ((
% 98.61/16.51 (setadjoinIR) =>
% 98.61/16.51 ((
% 98.61/16.51 (setadjoinE) =>
% 98.61/16.51 ((
% 98.61/16.51 (setadjoinOr) =>
% 98.61/16.51 ((
% 98.61/16.51 (setoftrueEq) =>
% 98.61/16.51 ((
% 98.61/16.51 (powersetI) =>
% 98.61/16.51 ((
% 98.61/16.51 (emptyinPowerset) =>
% 98.61/16.51 ((
% 98.61/16.51 (emptyInPowerset) =>
% 98.61/16.51 ((
% 98.61/16.51 (powersetE) =>
% 98.61/16.51 ((
% 98.61/16.51 (setunionI) =>
% 98.61/16.51 ((
% 98.61/16.51 (setunionE) =>
% 98.61/16.51 ((
% 98.61/16.51 (subPowSU) =>
% 98.61/16.51 ((
% 98.61/16.51 (exuE2) =>
% 98.61/16.51 ((
% 98.61/16.51 (nonemptyImpWitness) =>
% 98.61/16.51 ((
% 98.61/16.51 (uniqinunit) =>
% 98.61/16.51 ((
% 98.61/16.51 (notinsingleton) =>
% 98.61/16.51 ((
% 98.61/16.51 (eqinunit) =>
% 98.61/16.51 ((
% 98.61/16.51 (singletonsswitch) =>
% 98.61/16.51 ((
% 98.61/16.51 (upairsetE) =>
% 98.61/16.51 ((
% 98.61/16.51 (upairsetIL) =>
% 98.61/16.51 ((
% 98.61/16.51 (upairsetIR) =>
% 98.61/16.51 ((
% 98.61/16.51 (emptyE1) =>
% 98.61/16.51 ((
% 98.61/16.51 (vacuousDall) =>
% 98.61/16.51 ((
% 98.61/16.51 (quantDeMorgan1) =>
% 98.61/16.51 ((
% 98.61/16.51 (quantDeMorgan2) =>
% 98.61/16.51 ((
% 98.61/16.51 (quantDeMorgan3) =>
% 98.61/16.51 ((
% 98.61/16.51 (quantDeMorgan4) =>
% 98.61/16.51 ((
% 98.61/16.51 (prop2setI) =>
% 98.61/16.51 ((
% 98.61/16.51 (prop2set2propI) =>
% 98.61/16.51 ((
% 98.61/16.51 (notdexE) =>
% 98.61/16.51 ((
% 98.61/16.51 (notdallE) =>
% 98.61/16.51 ((
% 98.61/16.51 (exuI1) =>
% 98.61/16.51 ((
% 98.61/16.51 (exuI3) =>
% 98.61/16.51 ((
% 98.61/16.51 (exuI2) =>
% 98.61/16.51 ((
% 98.61/16.51 (inCongP) =>
% 98.61/16.51 ((
% 98.61/16.51 (in__Cong) =>
% 98.61/16.51 ((
% 98.61/16.51 (exuE3u) =>
% 98.61/16.51 ((
% 98.61/16.51 (exu__Cong) =>
% 98.61/16.51 ((
% 98.61/16.51 ((
% 98.61/16.51 (emptyset) =
% 98.61/16.51 (emptyset))) =>
% 98.61/16.51 ((
% 98.61/16.51 (setadjoin__Cong) =>
% 98.61/16.51 ((
% 98.61/16.51 (powerset__Cong) =>
% 98.61/16.51 ((
% 98.61/16.51 (setunion__Cong) =>
% 98.61/16.51 ((
% 98.61/16.51 ((
% 98.61/16.51 (omega) =
% 98.61/16.51 (omega))) =>
% 98.61/16.51 ((
% 98.61/16.51 (exuEu) =>
% 98.61/16.51 ((
% 98.61/16.51 (descr__Cong) =>
% 98.61/16.51 ((
% 98.61/16.51 (dsetconstr__Cong) =>
% 98.61/16.51 ((
% 98.61/16.51 (subsetI1) =>
% 98.61/16.51 ((
% 98.61/16.51 (eqimpsubset2) =>
% 98.61/16.51 ((
% 98.61/16.51 (eqimpsubset1) =>
% 98.61/16.51 ((
% 98.61/16.51 (subsetI2) =>
% 98.61/16.51 ((
% 98.61/16.51 (emptysetsubset) =>
% 98.61/16.51 ((
% 98.61/16.51 (subsetE) =>
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% 98.61/16.51 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl2])).
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% 98.61/16.52 ('#B') @ (
% 98.61/16.52 (
% 98.61/16.52 ('#C') @ in)))) @
% 98.61/16.52 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.61/16.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])).
% 98.61/16.52 thf(zip_derived_cl40, plain,
% 98.61/16.52 (~ (((omegaIndAx) =>
% 98.61/16.52 (((replAx) =>
% 98.61/16.52 (((foundationAx) =>
% 98.61/16.52 (((wellorderingAx) =>
% 98.61/16.52 (((descrp) =>
% 98.61/16.52 (((dsetconstrI) =>
% 98.61/16.52 (((dsetconstrEL) =>
% 98.61/16.52 (((dsetconstrER) =>
% 98.61/16.52 (((exuE1) =>
% 98.61/16.52 (((prop2setE) =>
% 98.61/16.52 (((emptysetE) =>
% 98.61/16.52 (((emptysetimpfalse) =>
% 98.61/16.52 (((notinemptyset) =>
% 98.61/16.52 (((exuE3e) =>
% 98.61/16.52 (((setext) =>
% 98.61/16.52 (((emptyI) =>
% 98.61/16.52 (((noeltsimpempty) =>
% 98.61/16.52 (((setbeta) =>
% 98.61/16.52 (((nonemptyE1) =>
% 98.61/16.52 (((nonemptyI) =>
% 98.61/16.52 (((nonemptyI1) =>
% 98.61/16.52 (((setadjoinIL) =>
% 98.61/16.52 (((in @ emptyset @
% 98.61/16.52 (setadjoin @ emptyset @
% 98.61/16.52 emptyset)) =>
% 98.61/16.52 (((setadjoinIR) =>
% 98.61/16.52 (((setadjoinE) =>
% 98.61/16.52 (((setadjoinOr) =>
% 98.61/16.52 (((setoftrueEq) =>
% 98.61/16.52 (((powersetI) =>
% 98.61/16.52 (((emptyinPowerset) =>
% 98.61/16.52 (((emptyInPowerset) =>
% 98.61/16.52 ((
% 98.61/16.52 (powersetE) =>
% 98.61/16.52 ((
% 98.61/16.52 (setunionI) =>
% 98.61/16.52 ((
% 98.61/16.52 (setunionE) =>
% 98.61/16.52 ((
% 98.61/16.52 (subPowSU) =>
% 98.61/16.52 ((
% 98.61/16.52 (exuE2) =>
% 98.61/16.52 ((
% 98.61/16.52 (nonemptyImpWitness) =>
% 98.61/16.52 ((
% 98.61/16.52 (uniqinunit) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (eqinunit) =>
% 98.61/16.52 ((
% 98.61/16.52 (singletonsswitch) =>
% 98.61/16.52 ((
% 98.61/16.52 (upairsetE) =>
% 98.61/16.52 ((
% 98.61/16.52 (upairsetIL) =>
% 98.61/16.52 ((
% 98.61/16.52 (upairsetIR) =>
% 98.61/16.52 ((
% 98.61/16.52 (emptyE1) =>
% 98.61/16.52 ((
% 98.61/16.52 (vacuousDall) =>
% 98.61/16.52 ((
% 98.61/16.52 (quantDeMorgan1) =>
% 98.61/16.52 ((
% 98.61/16.52 (quantDeMorgan2) =>
% 98.61/16.52 ((
% 98.61/16.52 (quantDeMorgan3) =>
% 98.61/16.52 ((
% 98.61/16.52 (quantDeMorgan4) =>
% 98.61/16.52 ((
% 98.61/16.52 (prop2setI) =>
% 98.61/16.52 ((
% 98.61/16.52 (prop2set2propI) =>
% 98.61/16.52 ((
% 98.61/16.52 (notdexE) =>
% 98.61/16.52 ((
% 98.61/16.52 (notdallE) =>
% 98.61/16.52 ((
% 98.61/16.52 (exuI1) =>
% 98.61/16.52 ((
% 98.61/16.52 (exuI3) =>
% 98.61/16.52 ((
% 98.61/16.52 (exuI2) =>
% 98.61/16.52 ((
% 98.61/16.52 (inCongP) =>
% 98.61/16.52 ((
% 98.61/16.52 (in__Cong) =>
% 98.61/16.52 ((
% 98.61/16.52 (exuE3u) =>
% 98.61/16.52 ((
% 98.61/16.52 (exu__Cong) =>
% 98.61/16.52 ((
% 98.61/16.52 (setadjoin__Cong) =>
% 98.61/16.52 ((
% 98.61/16.52 (powerset__Cong) =>
% 98.61/16.52 ((
% 98.61/16.52 (setunion__Cong) =>
% 98.61/16.52 ((
% 98.61/16.52 (exuEu) =>
% 98.61/16.52 ((
% 98.61/16.52 (descr__Cong) =>
% 98.61/16.52 ((
% 98.61/16.52 (dsetconstr__Cong) =>
% 98.61/16.52 ((
% 98.61/16.52 (subsetI1) =>
% 98.61/16.52 ((
% 98.61/16.52 (eqimpsubset2) =>
% 98.61/16.52 ((
% 98.61/16.52 (eqimpsubset1) =>
% 98.61/16.52 ((
% 98.61/16.52 (subsetI2) =>
% 98.61/16.52 ((
% 98.61/16.52 (emptysetsubset) =>
% 98.61/16.52 ((
% 98.61/16.52 (subsetE) =>
% 98.61/16.52 ((
% 98.61/16.52 (subsetE2) =>
% 98.61/16.52 ((
% 98.61/16.52 (notsubsetI) =>
% 98.61/16.52 ((
% 98.61/16.52 (notequalI1) =>
% 98.61/16.52 ((
% 98.61/16.52 (notequalI2) =>
% 98.61/16.52 ((
% 98.61/16.52 (subsetRefl) =>
% 98.61/16.52 ((
% 98.61/16.52 (subsetTrans) =>
% 98.61/16.52 ((
% 98.61/16.52 (setadjoinSub) =>
% 98.61/16.52 ((
% 98.61/16.52 (setadjoinSub2) =>
% 98.61/16.52 ((
% 98.61/16.52 (subset2powerset) =>
% 98.61/16.52 ((
% 98.61/16.52 (setextsub) =>
% 98.61/16.52 ((
% 98.61/16.52 (subsetemptysetimpeq) =>
% 98.61/16.52 ((
% 98.61/16.52 (powersetI1) =>
% 98.61/16.52 ((
% 98.61/16.52 (powersetE1) =>
% 98.61/16.52 ((
% 98.61/16.52 (inPowerset) =>
% 98.61/16.52 ((
% 98.61/16.52 (powersetsubset) =>
% 98.61/16.52 ((
% 98.61/16.52 (sepInPowerset) =>
% 98.61/16.52 ((
% 98.61/16.52 (sepSubset) =>
% 98.61/16.52 ((
% 98.61/16.52 (binunionIL) =>
% 98.61/16.52 ((
% 98.61/16.52 (upairset2IR) =>
% 98.61/16.52 ((
% 98.61/16.52 (binunionIR) =>
% 98.61/16.52 ((
% 98.61/16.52 (binunionEcases) =>
% 98.61/16.52 ((
% 98.61/16.52 (binunionE) =>
% 98.61/16.52 ((
% 98.61/16.52 (binunionLsub) =>
% 98.61/16.52 ((
% 98.61/16.52 (binunionRsub) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectI) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectSubset5) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectEL) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectLsub) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectSubset2) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectSubset3) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectER) =>
% 98.61/16.52 ((
% 98.61/16.52 (disjointsetsI1) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectRsub) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectSubset4) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectSubset1) =>
% 98.61/16.52 ((
% 98.61/16.52 (bs114d) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusI) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusEL) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusER) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusSubset2) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusERneg) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusELneg) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusILneg) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusIRneg) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusLsub) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusSubset1) =>
% 98.61/16.52 ((
% 98.61/16.52 (symdiffE) =>
% 98.61/16.52 ((
% 98.61/16.52 (symdiffI1) =>
% 98.61/16.52 ((
% 98.61/16.52 (symdiffI2) =>
% 98.61/16.52 ((
% 98.61/16.52 (symdiffIneg1) =>
% 98.61/16.52 ((
% 98.61/16.52 (symdiffIneg2) =>
% 98.61/16.52 ((
% 98.61/16.52 (secondinupair) =>
% 98.61/16.52 ((
% 98.61/16.52 (setukpairIL) =>
% 98.61/16.52 ((
% 98.61/16.52 (setukpairIR) =>
% 98.61/16.52 ((
% 98.61/16.52 (kpairiskpair) =>
% 98.61/16.52 ((
% 98.61/16.52 (kpairp) =>
% 98.61/16.52 ((
% 98.61/16.52 (singletonsubset) =>
% 98.61/16.52 ((
% 98.61/16.52 (singletoninpowerset) =>
% 98.61/16.52 ((
% 98.61/16.52 (singletoninpowunion) =>
% 98.61/16.52 ((
% 98.61/16.52 (upairset2E) =>
% 98.61/16.52 ((
% 98.61/16.52 (upairsubunion) =>
% 98.61/16.52 ((
% 98.61/16.52 (upairinpowunion) =>
% 98.61/16.52 ((
% 98.61/16.52 (ubforcartprodlem1) =>
% 98.61/16.52 ((
% 98.61/16.52 (ubforcartprodlem2) =>
% 98.61/16.52 ((
% 98.61/16.52 (ubforcartprodlem3) =>
% 98.61/16.52 ((
% 98.61/16.52 (cartprodpairin) =>
% 98.61/16.52 ((
% 98.61/16.52 (cartprodmempair1) =>
% 98.61/16.52 ((
% 98.61/16.52 (cartprodmempair) =>
% 98.61/16.52 ((
% 98.61/16.52 (setunionE2) =>
% 98.61/16.52 ((
% 98.61/16.52 (setunionsingleton1) =>
% 98.61/16.52 ((
% 98.61/16.52 (setunionsingleton2) =>
% 98.61/16.52 ((
% 98.61/16.52 (setunionsingleton) =>
% 98.61/16.52 ((
% 98.61/16.52 (singletonprop) =>
% 98.61/16.52 ((
% 98.61/16.52 (ex1E1) =>
% 98.61/16.52 ((
% 98.61/16.52 (ex1I) =>
% 98.61/16.52 ((
% 98.61/16.52 (ex1I2) =>
% 98.61/16.52 ((
% 98.61/16.52 (singletonsuniq) =>
% 98.61/16.52 ((
% 98.61/16.52 (setukpairinjL1) =>
% 98.61/16.52 ((
% 98.61/16.52 (kfstsingleton) =>
% 98.61/16.52 ((
% 98.61/16.52 (theprop) =>
% 98.61/16.52 ((
% 98.61/16.52 (kfstpairEq) =>
% 98.61/16.52 ((
% 98.61/16.52 (cartprodfstin) =>
% 98.61/16.52 ((
% 98.61/16.52 (setukpairinjL2) =>
% 98.61/16.52 ((
% 98.61/16.52 (setukpairinjL) =>
% 98.61/16.52 ((
% 98.61/16.52 (setukpairinjR11) =>
% 98.61/16.52 ((
% 98.61/16.52 (setukpairinjR12) =>
% 98.61/16.52 ((
% 98.61/16.52 (setukpairinjR1) =>
% 98.61/16.52 ((
% 98.61/16.52 (upairequniteq) =>
% 98.61/16.52 ((
% 98.61/16.52 (setukpairinjR2) =>
% 98.61/16.52 ((
% 98.61/16.52 (setukpairinjR) =>
% 98.61/16.52 ((
% 98.61/16.52 (ksndsingleton) =>
% 98.61/16.52 ((
% 98.61/16.52 (ksndpairEq) =>
% 98.61/16.52 ((
% 98.61/16.52 (kpairsurjEq) =>
% 98.61/16.52 ((
% 98.61/16.52 (cartprodsndin) =>
% 98.61/16.52 ((
% 98.61/16.52 (cartprodpairmemEL) =>
% 98.61/16.52 ((
% 98.61/16.52 (cartprodpairmemER) =>
% 98.61/16.52 ((
% 98.61/16.52 (cartprodmempaircEq) =>
% 98.61/16.52 ((
% 98.61/16.52 (cartprodfstpairEq) =>
% 98.61/16.52 ((
% 98.61/16.52 (cartprodsndpairEq) =>
% 98.61/16.52 ((
% 98.61/16.52 (cartprodpairsurjEq) =>
% 98.61/16.52 ((
% 98.61/16.52 (dpsetconstrI) =>
% 98.61/16.52 ((
% 98.61/16.52 (dpsetconstrSub) =>
% 98.61/16.52 ((
% 98.61/16.52 (setOfPairsIsBReln) =>
% 98.61/16.52 ((
% 98.61/16.52 (dpsetconstrERa) =>
% 98.61/16.52 ((
% 98.61/16.52 (dpsetconstrEL1) =>
% 98.61/16.52 ((
% 98.61/16.52 (dpsetconstrEL2) =>
% 98.61/16.52 ((
% 98.61/16.52 (dpsetconstrER) =>
% 98.61/16.52 ((
% 98.61/16.52 (funcImageSingleton) =>
% 98.61/16.52 ((
% 98.61/16.52 (apProp) =>
% 98.61/16.52 ((
% 98.61/16.52 (app) =>
% 98.61/16.52 ((
% 98.61/16.52 (infuncsetfunc) =>
% 98.61/16.52 ((
% 98.61/16.52 (ap2p) =>
% 98.61/16.52 ((
% 98.61/16.52 (funcinfuncset) =>
% 98.61/16.52 ((
% 98.61/16.52 (lamProp) =>
% 98.61/16.52 ((
% 98.61/16.52 (lamp) =>
% 98.61/16.52 ((
% 98.61/16.52 (lam2p) =>
% 98.61/16.52 ((
% 98.61/16.52 (brelnall1) =>
% 98.61/16.52 ((
% 98.61/16.52 (brelnall2) =>
% 98.61/16.52 ((
% 98.61/16.52 (ex1E2) =>
% 98.61/16.52 ((
% 98.61/16.52 (funcGraphProp1) =>
% 98.61/16.52 ((
% 98.61/16.52 (funcGraphProp3) =>
% 98.61/16.52 ((
% 98.61/16.52 (funcGraphProp2) =>
% 98.61/16.52 ((
% 98.61/16.52 (funcextLem) =>
% 98.61/16.52 ((
% 98.61/16.52 (funcGraphProp4) =>
% 98.61/16.52 ((
% 98.61/16.52 (subbreln) =>
% 98.61/16.52 ((
% 98.61/16.52 (eqbreln) =>
% 98.61/16.52 ((
% 98.61/16.52 (funcext) =>
% 98.61/16.52 ((
% 98.61/16.52 (funcext2) =>
% 98.61/16.52 ((
% 98.61/16.52 (ap2apEq1) =>
% 98.61/16.52 ((
% 98.61/16.52 (ap2apEq2) =>
% 98.61/16.52 ((
% 98.61/16.52 (beta1) =>
% 98.61/16.52 ((
% 98.61/16.52 (eta1) =>
% 98.61/16.52 ((
% 98.61/16.52 (lam2lamEq) =>
% 98.61/16.52 ((
% 98.61/16.52 (beta2) =>
% 98.61/16.52 ((
% 98.61/16.52 (eta2) =>
% 98.61/16.52 ((
% 98.61/16.52 (iffalseProp1) =>
% 98.61/16.52 ((
% 98.61/16.52 (iffalseProp2) =>
% 98.61/16.52 ((
% 98.61/16.52 (iftrueProp1) =>
% 98.61/16.52 ((
% 98.61/16.52 (iftrueProp2) =>
% 98.61/16.52 ((
% 98.61/16.52 (ifSingleton) =>
% 98.61/16.52 ((
% 98.61/16.52 (ifp) =>
% 98.61/16.52 ((
% 98.61/16.52 (theeq) =>
% 98.61/16.52 ((
% 98.61/16.52 (iftrue) =>
% 98.61/16.52 ((
% 98.61/16.52 (iffalse) =>
% 98.61/16.52 ((
% 98.61/16.52 (iftrueorfalse) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectT_lem) =>
% 98.61/16.52 ((
% 98.61/16.52 (binunionT_lem) =>
% 98.61/16.52 ((
% 98.61/16.52 (powersetT_lem) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusT_lem) =>
% 98.61/16.52 ((
% 98.61/16.52 (complementT_lem) =>
% 98.61/16.52 ((
% 98.61/16.52 (setextT) =>
% 98.61/16.52 ((
% 98.61/16.52 (subsetTI) =>
% 98.61/16.52 ((
% 98.61/16.52 (powersetTI1) =>
% 98.61/16.52 ((
% 98.61/16.52 (powersetTE1) =>
% 98.61/16.52 ((
% 98.61/16.52 (complementTI1) =>
% 98.61/16.52 ((
% 98.61/16.52 (complementTE1) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectTELcontra) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectTERcontra) =>
% 98.61/16.52 ((
% 98.61/16.52 (contrasubsetT) =>
% 98.61/16.52 ((
% 98.61/16.52 (contrasubsetT1) =>
% 98.61/16.52 ((
% 98.61/16.52 (contrasubsetT2) =>
% 98.61/16.52 ((
% 98.61/16.52 (contrasubsetT3) =>
% 98.61/16.52 ((
% 98.61/16.52 (doubleComplementI1) =>
% 98.61/16.52 ((
% 98.61/16.52 (doubleComplementE1) =>
% 98.61/16.52 ((
% 98.61/16.52 (doubleComplementSub1) =>
% 98.61/16.52 ((
% 98.61/16.52 (doubleComplementSub2) =>
% 98.61/16.52 ((
% 98.61/16.52 (doubleComplementEq) =>
% 98.61/16.52 ((
% 98.61/16.52 (complementTnotintersectT) =>
% 98.61/16.52 ((
% 98.61/16.52 (complementImpComplementIntersect) =>
% 98.61/16.52 ((
% 98.61/16.52 (complementSubsetComplementIntersect) =>
% 98.61/16.52 ((
% 98.61/16.52 (complementInPowersetComplementIntersect) =>
% 98.61/16.52 ((
% 98.61/16.52 (contraSubsetComplement) =>
% 98.61/16.52 ((
% 98.61/16.52 (complementTcontraSubset) =>
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% 98.61/16.52 ((
% 98.61/16.52 (binunionTIRcontra) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (inIntersectImpInUnion2) =>
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% 98.61/16.52 (inIntersectImpInIntersectUnions) =>
% 98.61/16.52 ((
% 98.61/16.52 (intersectInPowersetIntersectUnions) =>
% 98.61/16.52 ((
% 98.61/16.52 (inComplementUnionImpNotIn1) =>
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% 98.61/16.52 (inComplementUnionImpInComplement1) =>
% 98.61/16.52 ((
% 98.61/16.52 (binunionTE) =>
% 98.61/16.52 ((
% 98.61/16.52 (binunionTEcontra) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (complementUnionInPowersetComplement) =>
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% 98.61/16.52 ((
% 98.61/16.52 (demorgan1a) =>
% 98.61/16.52 ((
% 98.61/16.52 (demorgan1b) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (demorgan2b2) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (demorgan2) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
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% 98.61/16.52 (breln1all2) =>
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% 98.61/16.52 (breln1SetBreln1) =>
% 98.61/16.52 ((
% 98.61/16.52 (choice2fnsingleton) =>
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% 98.61/16.52 (breln1compI) =>
% 98.61/16.52 ((
% 98.61/16.52 (breln1compE) =>
% 98.61/16.52 ((
% 98.61/16.52 (breln1compEex) =>
% 98.61/16.52 ((
% 98.61/16.52 (breln1unionprop) =>
% 98.61/16.52 ((
% 98.61/16.52 (breln1unionIL) =>
% 98.61/16.52 ((
% 98.61/16.52 (breln1unionIR) =>
% 98.61/16.52 ((
% 98.61/16.52 (breln1unionI) =>
% 98.61/16.52 ((
% 98.61/16.52 (breln1unionE) =>
% 98.61/16.52 ((
% 98.61/16.52 (breln1unionEcases) =>
% 98.61/16.52 ((
% 98.61/16.52 (breln1unionCommutes) =>
% 98.61/16.52 ((
% 98.61/16.52 (woz2Ex) =>
% 98.61/16.52 ((
% 98.61/16.52 (woz2W) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (woz2B) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (image1Ex1) =>
% 98.61/16.52 ((
% 98.61/16.52 (image1Equiv) =>
% 98.61/16.52 ((
% 98.61/16.52 (image1E) =>
% 98.61/16.52 ((
% 98.61/16.52 (image1I) =>
% 98.61/16.52 ((
% 98.61/16.52 (injFuncInInjFuncSet) =>
% 98.61/16.52 ((
% 98.61/16.52 (injFuncSetFuncIn) =>
% 98.61/16.52 ((
% 98.61/16.52 (injFuncSetFuncInj) =>
% 98.61/16.52 ((
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% 98.61/16.52 (('#B') @ (
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% 98.61/16.52 (
% 98.61/16.52 (
% 98.61/16.52 ('#B') @ (
% 98.61/16.52 (
% 98.61/16.52 ('#B') @ (
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% 98.61/16.52 (
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% 98.61/16.52 surjFuncSet)))))))) @
% 98.61/16.52 (
% 98.61/16.52 (
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% 98.61/16.52 (
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% 98.61/16.52 (
% 98.61/16.52 ('#C') @ in)))) @
% 98.61/16.52 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.61/16.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
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% 98.61/16.52 ((
% 98.61/16.52 (exuE2) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
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% 98.61/16.52 ((
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% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (quantDeMorgan1) =>
% 98.61/16.52 ((
% 98.61/16.52 (quantDeMorgan2) =>
% 98.61/16.52 ((
% 98.61/16.52 (quantDeMorgan3) =>
% 98.61/16.52 ((
% 98.61/16.52 (quantDeMorgan4) =>
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% 98.61/16.52 ((
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% 98.61/16.52 ((
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% 98.61/16.52 ((
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% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (exuE3u) =>
% 98.61/16.52 ((
% 98.61/16.52 (exu__Cong) =>
% 98.61/16.52 ((
% 98.61/16.52 (setadjoin__Cong) =>
% 98.61/16.52 ((
% 98.61/16.52 (powerset__Cong) =>
% 98.61/16.52 ((
% 98.61/16.52 (setunion__Cong) =>
% 98.61/16.52 ((
% 98.61/16.52 (exuEu) =>
% 98.61/16.52 ((
% 98.61/16.52 (descr__Cong) =>
% 98.61/16.52 ((
% 98.61/16.52 (dsetconstr__Cong) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
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% 98.61/16.52 ((
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% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (subsetE2) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (notequalI1) =>
% 98.61/16.52 ((
% 98.61/16.52 (notequalI2) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
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% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (powersetE1) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (powersetsubset) =>
% 98.61/16.52 ((
% 98.61/16.52 (sepInPowerset) =>
% 98.61/16.52 ((
% 98.61/16.52 (sepSubset) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (upairset2IR) =>
% 98.61/16.52 ((
% 98.61/16.52 (binunionIR) =>
% 98.61/16.52 ((
% 98.61/16.52 (binunionEcases) =>
% 98.61/16.52 ((
% 98.61/16.52 (binunionE) =>
% 98.61/16.52 ((
% 98.61/16.52 (binunionLsub) =>
% 98.61/16.52 ((
% 98.61/16.52 (binunionRsub) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectI) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectSubset5) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectEL) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectLsub) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectSubset2) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectSubset3) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectER) =>
% 98.61/16.52 ((
% 98.61/16.52 (disjointsetsI1) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectRsub) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectSubset4) =>
% 98.61/16.52 ((
% 98.61/16.52 (binintersectSubset1) =>
% 98.61/16.52 ((
% 98.61/16.52 (bs114d) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (setminusEL) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusER) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusSubset2) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusERneg) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusELneg) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusILneg) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusIRneg) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusLsub) =>
% 98.61/16.52 ((
% 98.61/16.52 (setminusSubset1) =>
% 98.61/16.52 ((
% 98.61/16.52 (symdiffE) =>
% 98.61/16.52 ((
% 98.61/16.52 (symdiffI1) =>
% 98.61/16.52 ((
% 98.61/16.52 (symdiffI2) =>
% 98.61/16.52 ((
% 98.61/16.52 (symdiffIneg1) =>
% 98.61/16.52 ((
% 98.61/16.52 (symdiffIneg2) =>
% 98.61/16.52 ((
% 98.61/16.52 (secondinupair) =>
% 98.61/16.52 ((
% 98.61/16.52 (setukpairIL) =>
% 98.61/16.52 ((
% 98.61/16.52 (setukpairIR) =>
% 98.61/16.52 ((
% 98.61/16.52 (kpairiskpair) =>
% 98.61/16.52 ((
% 98.61/16.52 (kpairp) =>
% 98.61/16.52 ((
% 98.61/16.52 (singletonsubset) =>
% 98.61/16.52 ((
% 98.61/16.52 (singletoninpowerset) =>
% 98.61/16.52 ((
% 98.61/16.52 (singletoninpowunion) =>
% 98.61/16.52 ((
% 98.61/16.52 (upairset2E) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
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% 98.61/16.52 (ubforcartprodlem2) =>
% 98.61/16.52 ((
% 98.61/16.52 (ubforcartprodlem3) =>
% 98.61/16.52 ((
% 98.61/16.52 (cartprodpairin) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (cartprodmempair) =>
% 98.61/16.52 ((
% 98.61/16.52 (setunionE2) =>
% 98.61/16.52 ((
% 98.61/16.52 (setunionsingleton1) =>
% 98.61/16.52 ((
% 98.61/16.52 (setunionsingleton2) =>
% 98.61/16.52 ((
% 98.61/16.52 (setunionsingleton) =>
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% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (kfstpairEq) =>
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% 98.61/16.52 ((
% 98.61/16.52 (setukpairinjL2) =>
% 98.61/16.52 ((
% 98.61/16.52 (setukpairinjL) =>
% 98.61/16.52 ((
% 98.61/16.52 (setukpairinjR11) =>
% 98.61/16.52 ((
% 98.61/16.52 (setukpairinjR12) =>
% 98.61/16.52 ((
% 98.61/16.52 (setukpairinjR1) =>
% 98.61/16.52 ((
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% 98.61/16.52 ((
% 98.61/16.52 (setukpairinjR) =>
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% 98.61/16.52 (kpairsurjEq) =>
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% 98.61/16.52 ((
% 98.61/16.52 (cartprodpairmemER) =>
% 98.61/16.52 ((
% 98.61/16.52 (cartprodmempaircEq) =>
% 98.61/16.52 ((
% 98.61/16.52 (cartprodfstpairEq) =>
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% 98.61/16.52 ((
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% 98.61/16.52 ((
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% 99.13/16.53 (dpsetconstrEL2) =>
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (funcinfuncset) =>
% 99.13/16.53 ((
% 99.13/16.53 (lamProp) =>
% 99.13/16.53 ((
% 99.13/16.53 (lamp) =>
% 99.13/16.53 ((
% 99.13/16.53 (lam2p) =>
% 99.13/16.53 ((
% 99.13/16.53 (brelnall1) =>
% 99.13/16.53 ((
% 99.13/16.53 (brelnall2) =>
% 99.13/16.53 ((
% 99.13/16.53 (ex1E2) =>
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% 99.13/16.53 (funcGraphProp1) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcGraphProp3) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcGraphProp2) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcextLem) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcGraphProp4) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (funcext2) =>
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% 99.13/16.53 ((
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% 99.13/16.53 (beta2) =>
% 99.13/16.53 ((
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% 99.13/16.53 (contrasubsetT2) =>
% 99.13/16.53 ((
% 99.13/16.53 (contrasubsetT3) =>
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% 99.13/16.53 ((
% 99.13/16.53 (doubleComplementE1) =>
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% 99.13/16.53 (doubleComplementSub2) =>
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% 99.13/16.53 (doubleComplementEq) =>
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% 99.13/16.53 (binunionTIRcontra) =>
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% 99.13/16.53 ((
% 99.13/16.53 (inIntersectImpInUnion2) =>
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% 99.13/16.53 (inIntersectImpInIntersectUnions) =>
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% 99.13/16.53 (intersectInPowersetIntersectUnions) =>
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% 99.13/16.53 (inComplementUnionImpNotIn1) =>
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (demorgan1) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan2a) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan2b2) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan2b) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan2) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz13rule0) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (woz13rule2) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz13rule3) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz13rule4) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz1_1) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz1_2) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz1_3) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz1_4) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz1_5) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1all2) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1SetBreln1) =>
% 99.13/16.53 ((
% 99.13/16.53 (choice2fnsingleton) =>
% 99.13/16.53 ((
% 99.13/16.53 (setOfPairsIsBReln1) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1all1) =>
% 99.13/16.53 ((
% 99.13/16.53 (subbreln1) =>
% 99.13/16.53 ((
% 99.13/16.53 (eqbreln1) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1invprop) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1invI) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1invE) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1compprop) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1compI) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1compE) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1compEex) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionprop) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionIL) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionIR) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionI) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionE) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionEcases) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionCommutes) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz2Ex) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz2W) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (woz2B) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (image1Ex1) =>
% 99.13/16.53 ((
% 99.13/16.53 (image1Equiv) =>
% 99.13/16.53 ((
% 99.13/16.53 (image1E) =>
% 99.13/16.53 ((
% 99.13/16.53 (image1I) =>
% 99.13/16.53 ((
% 99.13/16.53 (injFuncInInjFuncSet) =>
% 99.13/16.53 ((
% 99.13/16.53 (injFuncSetFuncIn) =>
% 99.13/16.53 ((
% 99.13/16.53 (injFuncSetFuncInj) =>
% 99.13/16.53 ((
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% 99.13/16.53 (('#B') @ (
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% 99.13/16.53 (
% 99.13/16.53 (
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% 99.13/16.53 (
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% 99.13/16.53 (
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% 99.13/16.53 (
% 99.13/16.53 (
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% 99.13/16.53 surjFuncSet)))))))) @
% 99.13/16.53 (
% 99.13/16.53 (
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% 99.13/16.53 (
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% 99.13/16.53 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])).
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (quantDeMorgan3) =>
% 99.13/16.53 ((
% 99.13/16.53 (quantDeMorgan4) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (exuEu) =>
% 99.13/16.53 ((
% 99.13/16.53 (descr__Cong) =>
% 99.13/16.53 ((
% 99.13/16.53 (dsetconstr__Cong) =>
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (binintersectSubset3) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (binintersectSubset4) =>
% 99.13/16.53 ((
% 99.13/16.53 (binintersectSubset1) =>
% 99.13/16.53 ((
% 99.13/16.53 (bs114d) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (setminusILneg) =>
% 99.13/16.53 ((
% 99.13/16.53 (setminusIRneg) =>
% 99.13/16.53 ((
% 99.13/16.53 (setminusLsub) =>
% 99.13/16.53 ((
% 99.13/16.53 (setminusSubset1) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (symdiffI2) =>
% 99.13/16.53 ((
% 99.13/16.53 (symdiffIneg1) =>
% 99.13/16.53 ((
% 99.13/16.53 (symdiffIneg2) =>
% 99.13/16.53 ((
% 99.13/16.53 (secondinupair) =>
% 99.13/16.53 ((
% 99.13/16.53 (setukpairIL) =>
% 99.13/16.53 ((
% 99.13/16.53 (setukpairIR) =>
% 99.13/16.53 ((
% 99.13/16.53 (kpairiskpair) =>
% 99.13/16.53 ((
% 99.13/16.53 (kpairp) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (singletoninpowerset) =>
% 99.13/16.53 ((
% 99.13/16.53 (singletoninpowunion) =>
% 99.13/16.53 ((
% 99.13/16.53 (upairset2E) =>
% 99.13/16.53 ((
% 99.13/16.53 (upairsubunion) =>
% 99.13/16.53 ((
% 99.13/16.53 (upairinpowunion) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (ubforcartprodlem2) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (cartprodmempaircEq) =>
% 99.13/16.53 ((
% 99.13/16.53 (cartprodfstpairEq) =>
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% 99.13/16.53 (cartprodsndpairEq) =>
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% 99.13/16.53 (cartprodpairsurjEq) =>
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% 99.13/16.53 (dpsetconstrEL2) =>
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (funcinfuncset) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (lamp) =>
% 99.13/16.53 ((
% 99.13/16.53 (lam2p) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (brelnall2) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (funcGraphProp3) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcGraphProp2) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcextLem) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcGraphProp4) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (funcext2) =>
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 (contrasubsetT2) =>
% 99.13/16.53 ((
% 99.13/16.53 (contrasubsetT3) =>
% 99.13/16.53 ((
% 99.13/16.53 (doubleComplementI1) =>
% 99.13/16.53 ((
% 99.13/16.53 (doubleComplementE1) =>
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% 99.13/16.53 (doubleComplementSub1) =>
% 99.13/16.53 ((
% 99.13/16.53 (doubleComplementSub2) =>
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% 99.13/16.53 (doubleComplementEq) =>
% 99.13/16.53 ((
% 99.13/16.53 (complementTnotintersectT) =>
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% 99.13/16.53 (complementImpComplementIntersect) =>
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% 99.13/16.53 (complementSubsetComplementIntersect) =>
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% 99.13/16.53 (complementInPowersetComplementIntersect) =>
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% 99.13/16.53 (binunionTIRcontra) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (inIntersectImpInUnion2) =>
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% 99.13/16.53 (inIntersectImpInIntersectUnions) =>
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% 99.13/16.53 (intersectInPowersetIntersectUnions) =>
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% 99.13/16.53 (inComplementUnionImpNotIn1) =>
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (demorgan2a) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan2b2) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan2b) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan2) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz13rule0) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (woz13rule2) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz13rule3) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz13rule4) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (woz1_2) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz1_3) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz1_4) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz1_5) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1all2) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1SetBreln1) =>
% 99.13/16.53 ((
% 99.13/16.53 (choice2fnsingleton) =>
% 99.13/16.53 ((
% 99.13/16.53 (setOfPairsIsBReln1) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1all1) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (breln1invI) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1invE) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1compprop) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1compI) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1compE) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1compEex) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionprop) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionIL) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionIR) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionI) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionE) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionEcases) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionCommutes) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (image1Ex1) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (image1E) =>
% 99.13/16.53 ((
% 99.13/16.53 (image1I) =>
% 99.13/16.53 ((
% 99.13/16.53 (injFuncInInjFuncSet) =>
% 99.13/16.53 ((
% 99.13/16.53 (injFuncSetFuncIn) =>
% 99.13/16.53 ((
% 99.13/16.53 (injFuncSetFuncInj) =>
% 99.13/16.53 ((
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% 99.13/16.53 (
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% 99.13/16.53 (
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% 99.13/16.53 (
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% 99.13/16.53 (
% 99.13/16.53 (
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% 99.13/16.53 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.13/16.53 ((
% 99.13/16.53 (quantDeMorgan3) =>
% 99.13/16.53 ((
% 99.13/16.53 (quantDeMorgan4) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (exu__Cong) =>
% 99.13/16.53 ((
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% 99.13/16.53 (powerset__Cong) =>
% 99.13/16.53 ((
% 99.13/16.53 (setunion__Cong) =>
% 99.13/16.53 ((
% 99.13/16.53 (exuEu) =>
% 99.13/16.53 ((
% 99.13/16.53 (descr__Cong) =>
% 99.13/16.53 ((
% 99.13/16.53 (dsetconstr__Cong) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 (binintersectSubset2) =>
% 99.13/16.53 ((
% 99.13/16.53 (binintersectSubset3) =>
% 99.13/16.53 ((
% 99.13/16.53 (binintersectER) =>
% 99.13/16.53 ((
% 99.13/16.53 (disjointsetsI1) =>
% 99.13/16.53 ((
% 99.13/16.53 (binintersectRsub) =>
% 99.13/16.53 ((
% 99.13/16.53 (binintersectSubset4) =>
% 99.13/16.53 ((
% 99.13/16.53 (binintersectSubset1) =>
% 99.13/16.53 ((
% 99.13/16.53 (bs114d) =>
% 99.13/16.53 ((
% 99.13/16.53 (setminusI) =>
% 99.13/16.53 ((
% 99.13/16.53 (setminusEL) =>
% 99.13/16.53 ((
% 99.13/16.53 (setminusER) =>
% 99.13/16.53 ((
% 99.13/16.53 (setminusSubset2) =>
% 99.13/16.53 ((
% 99.13/16.53 (setminusERneg) =>
% 99.13/16.53 ((
% 99.13/16.53 (setminusELneg) =>
% 99.13/16.53 ((
% 99.13/16.53 (setminusILneg) =>
% 99.13/16.53 ((
% 99.13/16.53 (setminusIRneg) =>
% 99.13/16.53 ((
% 99.13/16.53 (setminusLsub) =>
% 99.13/16.53 ((
% 99.13/16.53 (setminusSubset1) =>
% 99.13/16.53 ((
% 99.13/16.53 (symdiffE) =>
% 99.13/16.53 ((
% 99.13/16.53 (symdiffI1) =>
% 99.13/16.53 ((
% 99.13/16.53 (symdiffI2) =>
% 99.13/16.53 ((
% 99.13/16.53 (symdiffIneg1) =>
% 99.13/16.53 ((
% 99.13/16.53 (symdiffIneg2) =>
% 99.13/16.53 ((
% 99.13/16.53 (secondinupair) =>
% 99.13/16.53 ((
% 99.13/16.53 (setukpairIL) =>
% 99.13/16.53 ((
% 99.13/16.53 (setukpairIR) =>
% 99.13/16.53 ((
% 99.13/16.53 (kpairiskpair) =>
% 99.13/16.53 ((
% 99.13/16.53 (kpairp) =>
% 99.13/16.53 ((
% 99.13/16.53 (singletonsubset) =>
% 99.13/16.53 ((
% 99.13/16.53 (singletoninpowerset) =>
% 99.13/16.53 ((
% 99.13/16.53 (singletoninpowunion) =>
% 99.13/16.53 ((
% 99.13/16.53 (upairset2E) =>
% 99.13/16.53 ((
% 99.13/16.53 (upairsubunion) =>
% 99.13/16.53 ((
% 99.13/16.53 (upairinpowunion) =>
% 99.13/16.53 ((
% 99.13/16.53 (ubforcartprodlem1) =>
% 99.13/16.53 ((
% 99.13/16.53 (ubforcartprodlem2) =>
% 99.13/16.53 ((
% 99.13/16.53 (ubforcartprodlem3) =>
% 99.13/16.53 ((
% 99.13/16.53 (cartprodpairin) =>
% 99.13/16.53 ((
% 99.13/16.53 (cartprodmempair1) =>
% 99.13/16.53 ((
% 99.13/16.53 (cartprodmempair) =>
% 99.13/16.53 ((
% 99.13/16.53 (setunionE2) =>
% 99.13/16.53 ((
% 99.13/16.53 (setunionsingleton1) =>
% 99.13/16.53 ((
% 99.13/16.53 (setunionsingleton2) =>
% 99.13/16.53 ((
% 99.13/16.53 (setunionsingleton) =>
% 99.13/16.53 ((
% 99.13/16.53 (singletonprop) =>
% 99.13/16.53 ((
% 99.13/16.53 (ex1E1) =>
% 99.13/16.53 ((
% 99.13/16.53 (ex1I) =>
% 99.13/16.53 ((
% 99.13/16.53 (ex1I2) =>
% 99.13/16.53 ((
% 99.13/16.53 (singletonsuniq) =>
% 99.13/16.53 ((
% 99.13/16.53 (setukpairinjL1) =>
% 99.13/16.53 ((
% 99.13/16.53 (kfstsingleton) =>
% 99.13/16.53 ((
% 99.13/16.53 (theprop) =>
% 99.13/16.53 ((
% 99.13/16.53 (kfstpairEq) =>
% 99.13/16.53 ((
% 99.13/16.53 (cartprodfstin) =>
% 99.13/16.53 ((
% 99.13/16.53 (setukpairinjL2) =>
% 99.13/16.53 ((
% 99.13/16.53 (setukpairinjL) =>
% 99.13/16.53 ((
% 99.13/16.53 (setukpairinjR11) =>
% 99.13/16.53 ((
% 99.13/16.53 (setukpairinjR12) =>
% 99.13/16.53 ((
% 99.13/16.53 (setukpairinjR1) =>
% 99.13/16.53 ((
% 99.13/16.53 (upairequniteq) =>
% 99.13/16.53 ((
% 99.13/16.53 (setukpairinjR2) =>
% 99.13/16.53 ((
% 99.13/16.53 (setukpairinjR) =>
% 99.13/16.53 ((
% 99.13/16.53 (ksndsingleton) =>
% 99.13/16.53 ((
% 99.13/16.53 (ksndpairEq) =>
% 99.13/16.53 ((
% 99.13/16.53 (kpairsurjEq) =>
% 99.13/16.53 ((
% 99.13/16.53 (cartprodsndin) =>
% 99.13/16.53 ((
% 99.13/16.53 (cartprodpairmemEL) =>
% 99.13/16.53 ((
% 99.13/16.53 (cartprodpairmemER) =>
% 99.13/16.53 ((
% 99.13/16.53 (cartprodmempaircEq) =>
% 99.13/16.53 ((
% 99.13/16.53 (cartprodfstpairEq) =>
% 99.13/16.53 ((
% 99.13/16.53 (cartprodsndpairEq) =>
% 99.13/16.53 ((
% 99.13/16.53 (cartprodpairsurjEq) =>
% 99.13/16.53 ((
% 99.13/16.53 (dpsetconstrI) =>
% 99.13/16.53 ((
% 99.13/16.53 (dpsetconstrSub) =>
% 99.13/16.53 ((
% 99.13/16.53 (setOfPairsIsBReln) =>
% 99.13/16.53 ((
% 99.13/16.53 (dpsetconstrERa) =>
% 99.13/16.53 ((
% 99.13/16.53 (dpsetconstrEL1) =>
% 99.13/16.53 ((
% 99.13/16.53 (dpsetconstrEL2) =>
% 99.13/16.53 ((
% 99.13/16.53 (dpsetconstrER) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcImageSingleton) =>
% 99.13/16.53 ((
% 99.13/16.53 (apProp) =>
% 99.13/16.53 ((
% 99.13/16.53 (app) =>
% 99.13/16.53 ((
% 99.13/16.53 (infuncsetfunc) =>
% 99.13/16.53 ((
% 99.13/16.53 (ap2p) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcinfuncset) =>
% 99.13/16.53 ((
% 99.13/16.53 (lamProp) =>
% 99.13/16.53 ((
% 99.13/16.53 (lamp) =>
% 99.13/16.53 ((
% 99.13/16.53 (lam2p) =>
% 99.13/16.53 ((
% 99.13/16.53 (brelnall1) =>
% 99.13/16.53 ((
% 99.13/16.53 (brelnall2) =>
% 99.13/16.53 ((
% 99.13/16.53 (ex1E2) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcGraphProp1) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcGraphProp3) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcGraphProp2) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcextLem) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcGraphProp4) =>
% 99.13/16.53 ((
% 99.13/16.53 (subbreln) =>
% 99.13/16.53 ((
% 99.13/16.53 (eqbreln) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcext) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcext2) =>
% 99.13/16.53 ((
% 99.13/16.53 (ap2apEq1) =>
% 99.13/16.53 ((
% 99.13/16.53 (ap2apEq2) =>
% 99.13/16.53 ((
% 99.13/16.53 (beta1) =>
% 99.13/16.53 ((
% 99.13/16.53 (eta1) =>
% 99.13/16.53 ((
% 99.13/16.53 (lam2lamEq) =>
% 99.13/16.53 ((
% 99.13/16.53 (beta2) =>
% 99.13/16.53 ((
% 99.13/16.53 (eta2) =>
% 99.13/16.53 ((
% 99.13/16.53 (iffalseProp1) =>
% 99.13/16.53 ((
% 99.13/16.53 (iffalseProp2) =>
% 99.13/16.53 ((
% 99.13/16.53 (iftrueProp1) =>
% 99.13/16.53 ((
% 99.13/16.53 (iftrueProp2) =>
% 99.13/16.53 ((
% 99.13/16.53 (ifSingleton) =>
% 99.13/16.53 ((
% 99.13/16.53 (ifp) =>
% 99.13/16.53 ((
% 99.13/16.53 (theeq) =>
% 99.13/16.53 ((
% 99.13/16.53 (iftrue) =>
% 99.13/16.53 ((
% 99.13/16.53 (iffalse) =>
% 99.13/16.53 ((
% 99.13/16.53 (iftrueorfalse) =>
% 99.13/16.53 ((
% 99.13/16.53 (binintersectT_lem) =>
% 99.13/16.53 ((
% 99.13/16.53 (binunionT_lem) =>
% 99.13/16.53 ((
% 99.13/16.53 (powersetT_lem) =>
% 99.13/16.53 ((
% 99.13/16.53 (setminusT_lem) =>
% 99.13/16.53 ((
% 99.13/16.53 (complementT_lem) =>
% 99.13/16.53 ((
% 99.13/16.53 (setextT) =>
% 99.13/16.53 ((
% 99.13/16.53 (subsetTI) =>
% 99.13/16.53 ((
% 99.13/16.53 (powersetTI1) =>
% 99.13/16.53 ((
% 99.13/16.53 (powersetTE1) =>
% 99.13/16.53 ((
% 99.13/16.53 (complementTI1) =>
% 99.13/16.53 ((
% 99.13/16.53 (complementTE1) =>
% 99.13/16.53 ((
% 99.13/16.53 (binintersectTELcontra) =>
% 99.13/16.53 ((
% 99.13/16.53 (binintersectTERcontra) =>
% 99.13/16.53 ((
% 99.13/16.53 (contrasubsetT) =>
% 99.13/16.53 ((
% 99.13/16.53 (contrasubsetT1) =>
% 99.13/16.53 ((
% 99.13/16.53 (contrasubsetT2) =>
% 99.13/16.53 ((
% 99.13/16.53 (contrasubsetT3) =>
% 99.13/16.53 ((
% 99.13/16.53 (doubleComplementI1) =>
% 99.13/16.53 ((
% 99.13/16.53 (doubleComplementE1) =>
% 99.13/16.53 ((
% 99.13/16.53 (doubleComplementSub1) =>
% 99.13/16.53 ((
% 99.13/16.53 (doubleComplementSub2) =>
% 99.13/16.53 ((
% 99.13/16.53 (doubleComplementEq) =>
% 99.13/16.53 ((
% 99.13/16.53 (complementTnotintersectT) =>
% 99.13/16.53 ((
% 99.13/16.53 (complementImpComplementIntersect) =>
% 99.13/16.53 ((
% 99.13/16.53 (complementSubsetComplementIntersect) =>
% 99.13/16.53 ((
% 99.13/16.53 (complementInPowersetComplementIntersect) =>
% 99.13/16.53 ((
% 99.13/16.53 (contraSubsetComplement) =>
% 99.13/16.53 ((
% 99.13/16.53 (complementTcontraSubset) =>
% 99.13/16.53 ((
% 99.13/16.53 (binunionTILcontra) =>
% 99.13/16.53 ((
% 99.13/16.53 (binunionTIRcontra) =>
% 99.13/16.53 ((
% 99.13/16.53 (inIntersectImpInUnion) =>
% 99.13/16.53 ((
% 99.13/16.53 (inIntersectImpInUnion2) =>
% 99.13/16.53 ((
% 99.13/16.53 (inIntersectImpInIntersectUnions) =>
% 99.13/16.53 ((
% 99.13/16.53 (intersectInPowersetIntersectUnions) =>
% 99.13/16.53 ((
% 99.13/16.53 (inComplementUnionImpNotIn1) =>
% 99.13/16.53 ((
% 99.13/16.53 (inComplementUnionImpInComplement1) =>
% 99.13/16.53 ((
% 99.13/16.53 (binunionTE) =>
% 99.13/16.53 ((
% 99.13/16.53 (binunionTEcontra) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan2a1) =>
% 99.13/16.53 ((
% 99.13/16.53 (complementUnionInPowersetComplement) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan2a2) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan1a) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan1b) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan1) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan2a) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan2b2) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan2b) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan2) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz13rule0) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz13rule1) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz13rule2) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz13rule3) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz13rule4) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz1_1) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz1_2) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz1_3) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz1_4) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz1_5) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1all2) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1SetBreln1) =>
% 99.13/16.53 ((
% 99.13/16.53 (choice2fnsingleton) =>
% 99.13/16.53 ((
% 99.13/16.53 (setOfPairsIsBReln1) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1all1) =>
% 99.13/16.53 ((
% 99.13/16.53 (subbreln1) =>
% 99.13/16.53 ((
% 99.13/16.53 (eqbreln1) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1invprop) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1invI) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1invE) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1compprop) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1compI) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1compE) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1compEex) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionprop) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionIL) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionIR) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionI) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionE) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionEcases) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionCommutes) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz2Ex) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz2W) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz2A) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz2B) =>
% 99.13/16.53 ((
% 99.13/16.53 (image1Ex) =>
% 99.13/16.53 ((
% 99.13/16.53 (image1Ex1) =>
% 99.13/16.53 ((
% 99.13/16.53 (image1Equiv) =>
% 99.13/16.53 ((
% 99.13/16.53 (image1E) =>
% 99.13/16.53 ((
% 99.13/16.53 (image1I) =>
% 99.13/16.53 ((
% 99.13/16.53 (injFuncInInjFuncSet) =>
% 99.13/16.53 ((
% 99.13/16.53 (injFuncSetFuncIn) =>
% 99.13/16.53 ((
% 99.13/16.53 (injFuncSetFuncInj) =>
% 99.13/16.53 ((
% 99.13/16.53 (!!) @ (
% 99.13/16.53 (('#B') @ (
% 99.13/16.53 !!) @
% 99.13/16.53 (
% 99.13/16.53 (
% 99.13/16.53 ('#B') @ (
% 99.13/16.53 (
% 99.13/16.53 ('#B') @ (
% 99.13/16.53 !!))) @
% 99.13/16.53 (
% 99.13/16.53 (
% 99.13/16.53 ('#S') @ (
% 99.13/16.53 (
% 99.13/16.53 ('#B') @ (
% 99.13/16.53 '#S') @
% 99.13/16.53 (
% 99.13/16.53 (
% 99.13/16.53 ('#B') @ (
% 99.13/16.53 (
% 99.13/16.53 ('#B') @ (
% 99.13/16.53 '#S'))) @
% 99.13/16.53 (
% 99.13/16.53 (
% 99.13/16.53 ('#B') @ (
% 99.13/16.53 (
% 99.13/16.53 ('#B') @ (
% 99.13/16.53 (
% 99.13/16.53 ('#B') @ (
% 99.13/16.53 =>))))) @
% 99.13/16.53 (
% 99.13/16.53 (
% 99.13/16.53 ('#B') @ (
% 99.13/16.53 (
% 99.13/16.53 ('#B') @ (
% 99.13/16.53 (
% 99.13/16.53 ('#C') @ in)))) @
% 99.13/16.53 surjFuncSet)))))))) @
% 99.13/16.53 (
% 99.13/16.53 (
% 99.13/16.53 ('#B') @ (
% 99.13/16.53 (
% 99.13/16.53 ('#B') @ (
% 99.13/16.53 (
% 99.13/16.53 ('#C') @ in)))) @
% 99.13/16.53 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])).
% 99.13/16.53 thf(zip_derived_cl79, plain,
% 99.13/16.53 (~ (((dsetconstrEL) =>
% 99.13/16.53 (((dsetconstrER) =>
% 99.13/16.53 (((exuE1) =>
% 99.13/16.53 (((prop2setE) =>
% 99.13/16.53 (((emptysetE) =>
% 99.13/16.53 (((emptysetimpfalse) =>
% 99.13/16.53 (((notinemptyset) =>
% 99.13/16.53 (((exuE3e) =>
% 99.13/16.53 (((setext) =>
% 99.13/16.53 (((emptyI) =>
% 99.13/16.53 (((noeltsimpempty) =>
% 99.13/16.53 (((setbeta) =>
% 99.13/16.53 (((nonemptyE1) =>
% 99.13/16.53 (((nonemptyI) =>
% 99.13/16.53 (((nonemptyI1) =>
% 99.13/16.53 (((setadjoinIL) =>
% 99.13/16.53 (((in @ emptyset @
% 99.13/16.53 (setadjoin @ emptyset @ emptyset)) =>
% 99.13/16.53 (((setadjoinIR) =>
% 99.13/16.53 (((setadjoinE) =>
% 99.13/16.53 (((setadjoinOr) =>
% 99.13/16.53 (((setoftrueEq) =>
% 99.13/16.53 (((powersetI) =>
% 99.13/16.53 (((emptyinPowerset) =>
% 99.13/16.53 (((emptyInPowerset) =>
% 99.13/16.53 (((powersetE) =>
% 99.13/16.53 (((setunionI) =>
% 99.13/16.53 (((setunionE) =>
% 99.13/16.53 (((subPowSU) =>
% 99.13/16.53 (((exuE2) =>
% 99.13/16.53 (((nonemptyImpWitness) =>
% 99.13/16.53 ((
% 99.13/16.53 (uniqinunit) =>
% 99.13/16.53 ((
% 99.13/16.53 (notinsingleton) =>
% 99.13/16.53 ((
% 99.13/16.53 (eqinunit) =>
% 99.13/16.53 ((
% 99.13/16.53 (singletonsswitch) =>
% 99.13/16.53 ((
% 99.13/16.53 (upairsetE) =>
% 99.13/16.53 ((
% 99.13/16.53 (upairsetIL) =>
% 99.13/16.53 ((
% 99.13/16.53 (upairsetIR) =>
% 99.13/16.53 ((
% 99.13/16.53 (emptyE1) =>
% 99.13/16.53 ((
% 99.13/16.53 (vacuousDall) =>
% 99.13/16.53 ((
% 99.13/16.53 (quantDeMorgan1) =>
% 99.13/16.53 ((
% 99.13/16.53 (quantDeMorgan2) =>
% 99.13/16.53 ((
% 99.13/16.53 (quantDeMorgan3) =>
% 99.13/16.53 ((
% 99.13/16.53 (quantDeMorgan4) =>
% 99.13/16.53 ((
% 99.13/16.53 (prop2setI) =>
% 99.13/16.53 ((
% 99.13/16.53 (prop2set2propI) =>
% 99.13/16.53 ((
% 99.13/16.53 (notdexE) =>
% 99.13/16.53 ((
% 99.13/16.53 (notdallE) =>
% 99.13/16.53 ((
% 99.13/16.53 (exuI1) =>
% 99.13/16.53 ((
% 99.13/16.53 (exuI3) =>
% 99.13/16.53 ((
% 99.13/16.53 (exuI2) =>
% 99.13/16.53 ((
% 99.13/16.53 (inCongP) =>
% 99.13/16.53 ((
% 99.13/16.53 (in__Cong) =>
% 99.13/16.53 ((
% 99.13/16.53 (exuE3u) =>
% 99.13/16.53 ((
% 99.13/16.53 (exu__Cong) =>
% 99.13/16.53 ((
% 99.13/16.53 (setadjoin__Cong) =>
% 99.13/16.53 ((
% 99.13/16.53 (powerset__Cong) =>
% 99.13/16.53 ((
% 99.13/16.53 (setunion__Cong) =>
% 99.13/16.53 ((
% 99.13/16.53 (exuEu) =>
% 99.13/16.53 ((
% 99.13/16.53 (descr__Cong) =>
% 99.13/16.53 ((
% 99.13/16.53 (dsetconstr__Cong) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (setukpairinjR11) =>
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% 99.13/16.53 ((
% 99.13/16.53 (cartprodpairmemEL) =>
% 99.13/16.53 ((
% 99.13/16.53 (cartprodpairmemER) =>
% 99.13/16.53 ((
% 99.13/16.53 (cartprodmempaircEq) =>
% 99.13/16.53 ((
% 99.13/16.53 (cartprodfstpairEq) =>
% 99.13/16.53 ((
% 99.13/16.53 (cartprodsndpairEq) =>
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% 99.13/16.53 (cartprodpairsurjEq) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 (dpsetconstrEL2) =>
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (lamp) =>
% 99.13/16.53 ((
% 99.13/16.53 (lam2p) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (funcGraphProp3) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcGraphProp2) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcextLem) =>
% 99.13/16.53 ((
% 99.13/16.53 (funcGraphProp4) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (funcext2) =>
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (iffalseProp2) =>
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (contrasubsetT2) =>
% 99.13/16.53 ((
% 99.13/16.53 (contrasubsetT3) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (doubleComplementE1) =>
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% 99.13/16.53 (doubleComplementSub2) =>
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% 99.13/16.53 (complementTnotintersectT) =>
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% 99.13/16.53 (complementSubsetComplementIntersect) =>
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% 99.13/16.53 (contraSubsetComplement) =>
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% 99.13/16.53 (binunionTIRcontra) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (inIntersectImpInUnion2) =>
% 99.13/16.53 ((
% 99.13/16.53 (inIntersectImpInIntersectUnions) =>
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% 99.13/16.53 (intersectInPowersetIntersectUnions) =>
% 99.13/16.53 ((
% 99.13/16.53 (inComplementUnionImpNotIn1) =>
% 99.13/16.53 ((
% 99.13/16.53 (inComplementUnionImpInComplement1) =>
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% 99.13/16.53 ((
% 99.13/16.53 (complementUnionInPowersetComplement) =>
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (demorgan2b2) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan2b) =>
% 99.13/16.53 ((
% 99.13/16.53 (demorgan2) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (woz13rule2) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz13rule3) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz13rule4) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (woz1_2) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz1_3) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz1_4) =>
% 99.13/16.53 ((
% 99.13/16.53 (woz1_5) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1all2) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1SetBreln1) =>
% 99.13/16.53 ((
% 99.13/16.53 (choice2fnsingleton) =>
% 99.13/16.53 ((
% 99.13/16.53 (setOfPairsIsBReln1) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (breln1invI) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1invE) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1compprop) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1compI) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1compE) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1compEex) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionprop) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionIL) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionIR) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionI) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionE) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionEcases) =>
% 99.13/16.53 ((
% 99.13/16.53 (breln1unionCommutes) =>
% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
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% 99.13/16.53 ((
% 99.13/16.53 (image1Ex1) =>
% 99.13/16.53 ((
% 99.13/16.53 (image1Equiv) =>
% 99.13/16.53 ((
% 99.13/16.53 (image1E) =>
% 99.13/16.53 ((
% 99.13/16.53 (image1I) =>
% 99.13/16.53 ((
% 99.13/16.53 (injFuncInInjFuncSet) =>
% 99.13/16.53 ((
% 99.13/16.53 (injFuncSetFuncIn) =>
% 99.13/16.53 ((
% 99.13/16.53 (injFuncSetFuncInj) =>
% 99.13/16.53 ((
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% 99.13/16.53 (
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% 99.13/16.53 (
% 99.13/16.53 ('#B') @ (
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% 99.13/16.53 (
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% 99.13/16.53 (
% 99.13/16.53 (
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% 99.13/16.53 (
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% 99.13/16.53 (
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% 99.13/16.53 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.13/16.54 ('#B') @ (
% 99.13/16.54 '#S'))) @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 =>))))) @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#C') @ in)))) @
% 99.13/16.54 surjFuncSet)))))))) @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#C') @ in)))) @
% 99.13/16.54 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 99.13/16.54 thf(zip_derived_cl105, plain,
% 99.13/16.54 (~ (((exuE1) =>
% 99.13/16.54 (((prop2setE) =>
% 99.13/16.54 (((emptysetE) =>
% 99.13/16.54 (((emptysetimpfalse) =>
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% 99.13/16.54 (((noeltsimpempty) =>
% 99.13/16.54 (((setbeta) =>
% 99.13/16.54 (((nonemptyE1) =>
% 99.13/16.54 (((nonemptyI) =>
% 99.13/16.54 (((nonemptyI1) =>
% 99.13/16.54 (((setadjoinIL) =>
% 99.13/16.54 (((in @ emptyset @
% 99.13/16.54 (setadjoin @ emptyset @ emptyset)) =>
% 99.13/16.54 (((setadjoinIR) =>
% 99.13/16.54 (((setadjoinE) =>
% 99.13/16.54 (((setadjoinOr) =>
% 99.13/16.54 (((setoftrueEq) =>
% 99.13/16.54 (((powersetI) =>
% 99.13/16.54 (((emptyinPowerset) =>
% 99.13/16.54 (((emptyInPowerset) =>
% 99.13/16.54 (((powersetE) =>
% 99.13/16.54 (((setunionI) =>
% 99.13/16.54 (((setunionE) =>
% 99.13/16.54 (((subPowSU) =>
% 99.13/16.54 (((exuE2) =>
% 99.13/16.54 (((nonemptyImpWitness) =>
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% 99.13/16.54 (((notinsingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (eqinunit) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (upairsetE) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairsetIL) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairsetIR) =>
% 99.13/16.54 ((
% 99.13/16.54 (emptyE1) =>
% 99.13/16.54 ((
% 99.13/16.54 (vacuousDall) =>
% 99.13/16.54 ((
% 99.13/16.54 (quantDeMorgan1) =>
% 99.13/16.54 ((
% 99.13/16.54 (quantDeMorgan2) =>
% 99.13/16.54 ((
% 99.13/16.54 (quantDeMorgan3) =>
% 99.13/16.54 ((
% 99.13/16.54 (quantDeMorgan4) =>
% 99.13/16.54 ((
% 99.13/16.54 (prop2setI) =>
% 99.13/16.54 ((
% 99.13/16.54 (prop2set2propI) =>
% 99.13/16.54 ((
% 99.13/16.54 (notdexE) =>
% 99.13/16.54 ((
% 99.13/16.54 (notdallE) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuI3) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuI2) =>
% 99.13/16.54 ((
% 99.13/16.54 (inCongP) =>
% 99.13/16.54 ((
% 99.13/16.54 (in__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuE3u) =>
% 99.13/16.54 ((
% 99.13/16.54 (exu__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (setadjoin__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (powerset__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunion__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuEu) =>
% 99.13/16.54 ((
% 99.13/16.54 (descr__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (dsetconstr__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (eqimpsubset2) =>
% 99.13/16.54 ((
% 99.13/16.54 (eqimpsubset1) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetI2) =>
% 99.13/16.54 ((
% 99.13/16.54 (emptysetsubset) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetE) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetE2) =>
% 99.13/16.54 ((
% 99.13/16.54 (notsubsetI) =>
% 99.13/16.54 ((
% 99.13/16.54 (notequalI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (notequalI2) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetRefl) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetTrans) =>
% 99.13/16.54 ((
% 99.13/16.54 (setadjoinSub) =>
% 99.13/16.54 ((
% 99.13/16.54 (setadjoinSub2) =>
% 99.13/16.54 ((
% 99.13/16.54 (subset2powerset) =>
% 99.13/16.54 ((
% 99.13/16.54 (setextsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetemptysetimpeq) =>
% 99.13/16.54 ((
% 99.13/16.54 (powersetI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (powersetE1) =>
% 99.13/16.54 ((
% 99.13/16.54 (inPowerset) =>
% 99.13/16.54 ((
% 99.13/16.54 (powersetsubset) =>
% 99.13/16.54 ((
% 99.13/16.54 (sepInPowerset) =>
% 99.13/16.54 ((
% 99.13/16.54 (sepSubset) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionIL) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairset2IR) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionIR) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionEcases) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionE) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionLsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionRsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectI) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset5) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectEL) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectLsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset2) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset3) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectER) =>
% 99.13/16.54 ((
% 99.13/16.54 (disjointsetsI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectRsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset4) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset1) =>
% 99.13/16.54 ((
% 99.13/16.54 (bs114d) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusI) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusEL) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusER) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusSubset2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusERneg) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusELneg) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusILneg) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusIRneg) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusLsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusSubset1) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffE) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffI2) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffIneg1) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffIneg2) =>
% 99.13/16.54 ((
% 99.13/16.54 (secondinupair) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairIL) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairIR) =>
% 99.13/16.54 ((
% 99.13/16.54 (kpairiskpair) =>
% 99.13/16.54 ((
% 99.13/16.54 (kpairp) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletonsubset) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletoninpowerset) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletoninpowunion) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairset2E) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairsubunion) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairinpowunion) =>
% 99.13/16.54 ((
% 99.13/16.54 (ubforcartprodlem1) =>
% 99.13/16.54 ((
% 99.13/16.54 (ubforcartprodlem2) =>
% 99.13/16.54 ((
% 99.13/16.54 (ubforcartprodlem3) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodpairin) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodmempair1) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodmempair) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunionE2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunionsingleton1) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunionsingleton2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunionsingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletonprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (ex1E1) =>
% 99.13/16.54 ((
% 99.13/16.54 (ex1I) =>
% 99.13/16.54 ((
% 99.13/16.54 (ex1I2) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletonsuniq) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjL1) =>
% 99.13/16.54 ((
% 99.13/16.54 (kfstsingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (theprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (kfstpairEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodfstin) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjL2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjL) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR11) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR12) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR1) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairequniteq) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR) =>
% 99.13/16.54 ((
% 99.13/16.54 (ksndsingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (ksndpairEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (kpairsurjEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodsndin) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodpairmemEL) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodpairmemER) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodmempaircEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodfstpairEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodsndpairEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodpairsurjEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrI) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrSub) =>
% 99.13/16.54 ((
% 99.13/16.54 (setOfPairsIsBReln) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrERa) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrEL1) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrEL2) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrER) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcImageSingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (apProp) =>
% 99.13/16.54 ((
% 99.13/16.54 (app) =>
% 99.13/16.54 ((
% 99.13/16.54 (infuncsetfunc) =>
% 99.13/16.54 ((
% 99.13/16.54 (ap2p) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcinfuncset) =>
% 99.13/16.54 ((
% 99.13/16.54 (lamProp) =>
% 99.13/16.54 ((
% 99.13/16.54 (lamp) =>
% 99.13/16.54 ((
% 99.13/16.54 (lam2p) =>
% 99.13/16.54 ((
% 99.13/16.54 (brelnall1) =>
% 99.13/16.54 ((
% 99.13/16.54 (brelnall2) =>
% 99.13/16.54 ((
% 99.13/16.54 (ex1E2) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcGraphProp1) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcGraphProp3) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcGraphProp2) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcextLem) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcGraphProp4) =>
% 99.13/16.54 ((
% 99.13/16.54 (subbreln) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (funcext) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcext2) =>
% 99.13/16.54 ((
% 99.13/16.54 (ap2apEq1) =>
% 99.13/16.54 ((
% 99.13/16.54 (ap2apEq2) =>
% 99.13/16.54 ((
% 99.13/16.54 (beta1) =>
% 99.13/16.54 ((
% 99.13/16.54 (eta1) =>
% 99.13/16.54 ((
% 99.13/16.54 (lam2lamEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (beta2) =>
% 99.13/16.54 ((
% 99.13/16.54 (eta2) =>
% 99.13/16.54 ((
% 99.13/16.54 (iffalseProp1) =>
% 99.13/16.54 ((
% 99.13/16.54 (iffalseProp2) =>
% 99.13/16.54 ((
% 99.13/16.54 (iftrueProp1) =>
% 99.13/16.54 ((
% 99.13/16.54 (iftrueProp2) =>
% 99.13/16.54 ((
% 99.13/16.54 (ifSingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (ifp) =>
% 99.13/16.54 ((
% 99.13/16.54 (theeq) =>
% 99.13/16.54 ((
% 99.13/16.54 (iftrue) =>
% 99.13/16.54 ((
% 99.13/16.54 (iffalse) =>
% 99.13/16.54 ((
% 99.13/16.54 (iftrueorfalse) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectT_lem) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionT_lem) =>
% 99.13/16.54 ((
% 99.13/16.54 (powersetT_lem) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusT_lem) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementT_lem) =>
% 99.13/16.54 ((
% 99.13/16.54 (setextT) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetTI) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (powersetTE1) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (complementTE1) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectTELcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectTERcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (contrasubsetT) =>
% 99.13/16.54 ((
% 99.13/16.54 (contrasubsetT1) =>
% 99.13/16.54 ((
% 99.13/16.54 (contrasubsetT2) =>
% 99.13/16.54 ((
% 99.13/16.54 (contrasubsetT3) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementE1) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementSub1) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementSub2) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementTnotintersectT) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementImpComplementIntersect) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementSubsetComplementIntersect) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementInPowersetComplementIntersect) =>
% 99.13/16.54 ((
% 99.13/16.54 (contraSubsetComplement) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementTcontraSubset) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionTILcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionTIRcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (inIntersectImpInUnion) =>
% 99.13/16.54 ((
% 99.13/16.54 (inIntersectImpInUnion2) =>
% 99.13/16.54 ((
% 99.13/16.54 (inIntersectImpInIntersectUnions) =>
% 99.13/16.54 ((
% 99.13/16.54 (intersectInPowersetIntersectUnions) =>
% 99.13/16.54 ((
% 99.13/16.54 (inComplementUnionImpNotIn1) =>
% 99.13/16.54 ((
% 99.13/16.54 (inComplementUnionImpInComplement1) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionTE) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionTEcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2a1) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementUnionInPowersetComplement) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (demorgan2b2) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2b) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule0) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (woz13rule2) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (woz1_5) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1all2) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1SetBreln1) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (eqbreln1) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1invprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1invI) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1invE) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1compprop) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (breln1compE) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (descr__Cong) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (symdiffI2) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffIneg1) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffIneg2) =>
% 99.13/16.54 ((
% 99.13/16.54 (secondinupair) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (kpairp) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (singletoninpowerset) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (demorgan2a1) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementUnionInPowersetComplement) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2a2) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan1a) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan1b) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan1) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2a) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2b2) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2b) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule0) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule1) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule2) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule3) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule4) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_1) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_2) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_3) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_4) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_5) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1all2) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1SetBreln1) =>
% 99.13/16.54 ((
% 99.13/16.54 (choice2fnsingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (setOfPairsIsBReln1) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1all1) =>
% 99.13/16.54 ((
% 99.13/16.54 (subbreln1) =>
% 99.13/16.54 ((
% 99.13/16.54 (eqbreln1) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1invprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1invI) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1invE) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1compprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1compI) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1compE) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1compEex) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionIL) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionIR) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionI) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionE) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionEcases) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionCommutes) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz2Ex) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz2W) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz2A) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz2B) =>
% 99.13/16.54 ((
% 99.13/16.54 (image1Ex) =>
% 99.13/16.54 ((
% 99.13/16.54 (image1Ex1) =>
% 99.13/16.54 ((
% 99.13/16.54 (image1Equiv) =>
% 99.13/16.54 ((
% 99.13/16.54 (image1E) =>
% 99.13/16.54 ((
% 99.13/16.54 (image1I) =>
% 99.13/16.54 ((
% 99.13/16.54 (injFuncInInjFuncSet) =>
% 99.13/16.54 ((
% 99.13/16.54 (injFuncSetFuncIn) =>
% 99.13/16.54 ((
% 99.13/16.54 (injFuncSetFuncInj) =>
% 99.13/16.54 ((
% 99.13/16.54 (!!) @ (
% 99.13/16.54 (('#B') @ (
% 99.13/16.54 !!) @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 !!))) @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#S') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 '#S') @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 '#S'))) @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 =>))))) @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#C') @ in)))) @
% 99.13/16.54 surjFuncSet)))))))) @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#C') @ in)))) @
% 99.13/16.54 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])).
% 99.13/16.54 thf(zip_derived_cl142, plain,
% 99.13/16.54 (~ (((emptysetE) =>
% 99.13/16.54 (((emptysetimpfalse) =>
% 99.13/16.54 (((notinemptyset) =>
% 99.13/16.54 (((exuE3e) =>
% 99.13/16.54 (((setext) =>
% 99.13/16.54 (((emptyI) =>
% 99.13/16.54 (((noeltsimpempty) =>
% 99.13/16.54 (((setbeta) =>
% 99.13/16.54 (((nonemptyE1) =>
% 99.13/16.54 (((nonemptyI) =>
% 99.13/16.54 (((nonemptyI1) =>
% 99.13/16.54 (((setadjoinIL) =>
% 99.13/16.54 (((in @ emptyset @
% 99.13/16.54 (setadjoin @ emptyset @ emptyset)) =>
% 99.13/16.54 (((setadjoinIR) =>
% 99.13/16.54 (((setadjoinE) =>
% 99.13/16.54 (((setadjoinOr) =>
% 99.13/16.54 (((setoftrueEq) =>
% 99.13/16.54 (((powersetI) =>
% 99.13/16.54 (((emptyinPowerset) =>
% 99.13/16.54 (((emptyInPowerset) =>
% 99.13/16.54 (((powersetE) =>
% 99.13/16.54 (((setunionI) =>
% 99.13/16.54 (((setunionE) =>
% 99.13/16.54 (((subPowSU) =>
% 99.13/16.54 (((exuE2) =>
% 99.13/16.54 (((nonemptyImpWitness) =>
% 99.13/16.54 (((uniqinunit) =>
% 99.13/16.54 (((notinsingleton) =>
% 99.13/16.54 (((eqinunit) =>
% 99.13/16.54 (((singletonsswitch) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairsetE) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairsetIL) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairsetIR) =>
% 99.13/16.54 ((
% 99.13/16.54 (emptyE1) =>
% 99.13/16.54 ((
% 99.13/16.54 (vacuousDall) =>
% 99.13/16.54 ((
% 99.13/16.54 (quantDeMorgan1) =>
% 99.13/16.54 ((
% 99.13/16.54 (quantDeMorgan2) =>
% 99.13/16.54 ((
% 99.13/16.54 (quantDeMorgan3) =>
% 99.13/16.54 ((
% 99.13/16.54 (quantDeMorgan4) =>
% 99.13/16.54 ((
% 99.13/16.54 (prop2setI) =>
% 99.13/16.54 ((
% 99.13/16.54 (prop2set2propI) =>
% 99.13/16.54 ((
% 99.13/16.54 (notdexE) =>
% 99.13/16.54 ((
% 99.13/16.54 (notdallE) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuI3) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuI2) =>
% 99.13/16.54 ((
% 99.13/16.54 (inCongP) =>
% 99.13/16.54 ((
% 99.13/16.54 (in__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuE3u) =>
% 99.13/16.54 ((
% 99.13/16.54 (exu__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (setadjoin__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (powerset__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunion__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuEu) =>
% 99.13/16.54 ((
% 99.13/16.54 (descr__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (dsetconstr__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (eqimpsubset2) =>
% 99.13/16.54 ((
% 99.13/16.54 (eqimpsubset1) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetI2) =>
% 99.13/16.54 ((
% 99.13/16.54 (emptysetsubset) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetE) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetE2) =>
% 99.13/16.54 ((
% 99.13/16.54 (notsubsetI) =>
% 99.13/16.54 ((
% 99.13/16.54 (notequalI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (notequalI2) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetRefl) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetTrans) =>
% 99.13/16.54 ((
% 99.13/16.54 (setadjoinSub) =>
% 99.13/16.54 ((
% 99.13/16.54 (setadjoinSub2) =>
% 99.13/16.54 ((
% 99.13/16.54 (subset2powerset) =>
% 99.13/16.54 ((
% 99.13/16.54 (setextsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetemptysetimpeq) =>
% 99.13/16.54 ((
% 99.13/16.54 (powersetI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (powersetE1) =>
% 99.13/16.54 ((
% 99.13/16.54 (inPowerset) =>
% 99.13/16.54 ((
% 99.13/16.54 (powersetsubset) =>
% 99.13/16.54 ((
% 99.13/16.54 (sepInPowerset) =>
% 99.13/16.54 ((
% 99.13/16.54 (sepSubset) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionIL) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairset2IR) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionIR) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionEcases) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionE) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionLsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionRsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectI) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset5) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectEL) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectLsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset2) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset3) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectER) =>
% 99.13/16.54 ((
% 99.13/16.54 (disjointsetsI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectRsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset4) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset1) =>
% 99.13/16.54 ((
% 99.13/16.54 (bs114d) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusI) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusEL) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusER) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusSubset2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusERneg) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusELneg) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusILneg) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusIRneg) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusLsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusSubset1) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffE) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffI2) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffIneg1) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffIneg2) =>
% 99.13/16.54 ((
% 99.13/16.54 (secondinupair) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairIL) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairIR) =>
% 99.13/16.54 ((
% 99.13/16.54 (kpairiskpair) =>
% 99.13/16.54 ((
% 99.13/16.54 (kpairp) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletonsubset) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletoninpowerset) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletoninpowunion) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairset2E) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairsubunion) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairinpowunion) =>
% 99.13/16.54 ((
% 99.13/16.54 (ubforcartprodlem1) =>
% 99.13/16.54 ((
% 99.13/16.54 (ubforcartprodlem2) =>
% 99.13/16.54 ((
% 99.13/16.54 (ubforcartprodlem3) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodpairin) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodmempair1) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodmempair) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunionE2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunionsingleton1) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunionsingleton2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunionsingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletonprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (ex1E1) =>
% 99.13/16.54 ((
% 99.13/16.54 (ex1I) =>
% 99.13/16.54 ((
% 99.13/16.54 (ex1I2) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletonsuniq) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjL1) =>
% 99.13/16.54 ((
% 99.13/16.54 (kfstsingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (theprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (kfstpairEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodfstin) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjL2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjL) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR11) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR12) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR1) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairequniteq) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR) =>
% 99.13/16.54 ((
% 99.13/16.54 (ksndsingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (ksndpairEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (kpairsurjEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodsndin) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodpairmemEL) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodpairmemER) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodmempaircEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodfstpairEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodsndpairEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodpairsurjEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrI) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrSub) =>
% 99.13/16.54 ((
% 99.13/16.54 (setOfPairsIsBReln) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrERa) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrEL1) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrEL2) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrER) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcImageSingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (apProp) =>
% 99.13/16.54 ((
% 99.13/16.54 (app) =>
% 99.13/16.54 ((
% 99.13/16.54 (infuncsetfunc) =>
% 99.13/16.54 ((
% 99.13/16.54 (ap2p) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcinfuncset) =>
% 99.13/16.54 ((
% 99.13/16.54 (lamProp) =>
% 99.13/16.54 ((
% 99.13/16.54 (lamp) =>
% 99.13/16.54 ((
% 99.13/16.54 (lam2p) =>
% 99.13/16.54 ((
% 99.13/16.54 (brelnall1) =>
% 99.13/16.54 ((
% 99.13/16.54 (brelnall2) =>
% 99.13/16.54 ((
% 99.13/16.54 (ex1E2) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcGraphProp1) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcGraphProp3) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcGraphProp2) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcextLem) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcGraphProp4) =>
% 99.13/16.54 ((
% 99.13/16.54 (subbreln) =>
% 99.13/16.54 ((
% 99.13/16.54 (eqbreln) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcext) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcext2) =>
% 99.13/16.54 ((
% 99.13/16.54 (ap2apEq1) =>
% 99.13/16.54 ((
% 99.13/16.54 (ap2apEq2) =>
% 99.13/16.54 ((
% 99.13/16.54 (beta1) =>
% 99.13/16.54 ((
% 99.13/16.54 (eta1) =>
% 99.13/16.54 ((
% 99.13/16.54 (lam2lamEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (beta2) =>
% 99.13/16.54 ((
% 99.13/16.54 (eta2) =>
% 99.13/16.54 ((
% 99.13/16.54 (iffalseProp1) =>
% 99.13/16.54 ((
% 99.13/16.54 (iffalseProp2) =>
% 99.13/16.54 ((
% 99.13/16.54 (iftrueProp1) =>
% 99.13/16.54 ((
% 99.13/16.54 (iftrueProp2) =>
% 99.13/16.54 ((
% 99.13/16.54 (ifSingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (ifp) =>
% 99.13/16.54 ((
% 99.13/16.54 (theeq) =>
% 99.13/16.54 ((
% 99.13/16.54 (iftrue) =>
% 99.13/16.54 ((
% 99.13/16.54 (iffalse) =>
% 99.13/16.54 ((
% 99.13/16.54 (iftrueorfalse) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectT_lem) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionT_lem) =>
% 99.13/16.54 ((
% 99.13/16.54 (powersetT_lem) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusT_lem) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementT_lem) =>
% 99.13/16.54 ((
% 99.13/16.54 (setextT) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetTI) =>
% 99.13/16.54 ((
% 99.13/16.54 (powersetTI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (powersetTE1) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementTI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementTE1) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectTELcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectTERcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (contrasubsetT) =>
% 99.13/16.54 ((
% 99.13/16.54 (contrasubsetT1) =>
% 99.13/16.54 ((
% 99.13/16.54 (contrasubsetT2) =>
% 99.13/16.54 ((
% 99.13/16.54 (contrasubsetT3) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementE1) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementSub1) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementSub2) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementTnotintersectT) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementImpComplementIntersect) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementSubsetComplementIntersect) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementInPowersetComplementIntersect) =>
% 99.13/16.54 ((
% 99.13/16.54 (contraSubsetComplement) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementTcontraSubset) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionTILcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionTIRcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (inIntersectImpInUnion) =>
% 99.13/16.54 ((
% 99.13/16.54 (inIntersectImpInUnion2) =>
% 99.13/16.54 ((
% 99.13/16.54 (inIntersectImpInIntersectUnions) =>
% 99.13/16.54 ((
% 99.13/16.54 (intersectInPowersetIntersectUnions) =>
% 99.13/16.54 ((
% 99.13/16.54 (inComplementUnionImpNotIn1) =>
% 99.13/16.54 ((
% 99.13/16.54 (inComplementUnionImpInComplement1) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionTE) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionTEcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2a1) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementUnionInPowersetComplement) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2a2) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan1a) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan1b) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan1) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2a) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2b2) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2b) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule0) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule1) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule2) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule3) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule4) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_1) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_2) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_3) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_4) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_5) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1all2) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1SetBreln1) =>
% 99.13/16.54 ((
% 99.13/16.54 (choice2fnsingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (setOfPairsIsBReln1) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1all1) =>
% 99.13/16.54 ((
% 99.13/16.54 (subbreln1) =>
% 99.13/16.54 ((
% 99.13/16.54 (eqbreln1) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1invprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1invI) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1invE) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1compprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1compI) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1compE) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1compEex) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionIL) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionIR) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionI) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionE) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionEcases) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionCommutes) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz2Ex) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz2W) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz2A) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz2B) =>
% 99.13/16.54 ((
% 99.13/16.54 (image1Ex) =>
% 99.13/16.54 ((
% 99.13/16.54 (image1Ex1) =>
% 99.13/16.54 ((
% 99.13/16.54 (image1Equiv) =>
% 99.13/16.54 ((
% 99.13/16.54 (image1E) =>
% 99.13/16.54 ((
% 99.13/16.54 (image1I) =>
% 99.13/16.54 ((
% 99.13/16.54 (injFuncInInjFuncSet) =>
% 99.13/16.54 ((
% 99.13/16.54 (injFuncSetFuncIn) =>
% 99.13/16.54 ((
% 99.13/16.54 (injFuncSetFuncInj) =>
% 99.13/16.54 ((
% 99.13/16.54 (!!) @ (
% 99.13/16.54 (('#B') @ (
% 99.13/16.54 !!) @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 !!))) @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#S') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 '#S') @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 '#S'))) @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 =>))))) @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#C') @ in)))) @
% 99.13/16.54 surjFuncSet)))))))) @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#C') @ in)))) @
% 99.13/16.54 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])).
% 99.13/16.54 thf(zip_derived_cl158, plain,
% 99.13/16.54 (~ (((emptysetimpfalse) =>
% 99.13/16.54 (((notinemptyset) =>
% 99.13/16.54 (((exuE3e) =>
% 99.13/16.54 (((setext) =>
% 99.13/16.54 (((emptyI) =>
% 99.13/16.54 (((noeltsimpempty) =>
% 99.13/16.54 (((setbeta) =>
% 99.13/16.54 (((nonemptyE1) =>
% 99.13/16.54 (((nonemptyI) =>
% 99.13/16.54 (((nonemptyI1) =>
% 99.13/16.54 (((setadjoinIL) =>
% 99.13/16.54 (((in @ emptyset @
% 99.13/16.54 (setadjoin @ emptyset @ emptyset)) =>
% 99.13/16.54 (((setadjoinIR) =>
% 99.13/16.54 (((setadjoinE) =>
% 99.13/16.54 (((setadjoinOr) =>
% 99.13/16.54 (((setoftrueEq) =>
% 99.13/16.54 (((powersetI) =>
% 99.13/16.54 (((emptyinPowerset) =>
% 99.13/16.54 (((emptyInPowerset) =>
% 99.13/16.54 (((powersetE) =>
% 99.13/16.54 (((setunionI) =>
% 99.13/16.54 (((setunionE) =>
% 99.13/16.54 (((subPowSU) =>
% 99.13/16.54 (((exuE2) =>
% 99.13/16.54 (((nonemptyImpWitness) =>
% 99.13/16.54 (((uniqinunit) =>
% 99.13/16.54 (((notinsingleton) =>
% 99.13/16.54 (((eqinunit) =>
% 99.13/16.54 (((singletonsswitch) =>
% 99.13/16.54 (((upairsetE) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairsetIL) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairsetIR) =>
% 99.13/16.54 ((
% 99.13/16.54 (emptyE1) =>
% 99.13/16.54 ((
% 99.13/16.54 (vacuousDall) =>
% 99.13/16.54 ((
% 99.13/16.54 (quantDeMorgan1) =>
% 99.13/16.54 ((
% 99.13/16.54 (quantDeMorgan2) =>
% 99.13/16.54 ((
% 99.13/16.54 (quantDeMorgan3) =>
% 99.13/16.54 ((
% 99.13/16.54 (quantDeMorgan4) =>
% 99.13/16.54 ((
% 99.13/16.54 (prop2setI) =>
% 99.13/16.54 ((
% 99.13/16.54 (prop2set2propI) =>
% 99.13/16.54 ((
% 99.13/16.54 (notdexE) =>
% 99.13/16.54 ((
% 99.13/16.54 (notdallE) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuI3) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuI2) =>
% 99.13/16.54 ((
% 99.13/16.54 (inCongP) =>
% 99.13/16.54 ((
% 99.13/16.54 (in__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuE3u) =>
% 99.13/16.54 ((
% 99.13/16.54 (exu__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (setadjoin__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (powerset__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunion__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuEu) =>
% 99.13/16.54 ((
% 99.13/16.54 (descr__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (dsetconstr__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (eqimpsubset2) =>
% 99.13/16.54 ((
% 99.13/16.54 (eqimpsubset1) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetI2) =>
% 99.13/16.54 ((
% 99.13/16.54 (emptysetsubset) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetE) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetE2) =>
% 99.13/16.54 ((
% 99.13/16.54 (notsubsetI) =>
% 99.13/16.54 ((
% 99.13/16.54 (notequalI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (notequalI2) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetRefl) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetTrans) =>
% 99.13/16.54 ((
% 99.13/16.54 (setadjoinSub) =>
% 99.13/16.54 ((
% 99.13/16.54 (setadjoinSub2) =>
% 99.13/16.54 ((
% 99.13/16.54 (subset2powerset) =>
% 99.13/16.54 ((
% 99.13/16.54 (setextsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetemptysetimpeq) =>
% 99.13/16.54 ((
% 99.13/16.54 (powersetI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (powersetE1) =>
% 99.13/16.54 ((
% 99.13/16.54 (inPowerset) =>
% 99.13/16.54 ((
% 99.13/16.54 (powersetsubset) =>
% 99.13/16.54 ((
% 99.13/16.54 (sepInPowerset) =>
% 99.13/16.54 ((
% 99.13/16.54 (sepSubset) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionIL) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairset2IR) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionIR) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionEcases) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionE) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionLsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionRsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectI) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset5) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectEL) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectLsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset2) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset3) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectER) =>
% 99.13/16.54 ((
% 99.13/16.54 (disjointsetsI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectRsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset4) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset1) =>
% 99.13/16.54 ((
% 99.13/16.54 (bs114d) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusI) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusEL) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusER) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusSubset2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusERneg) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusELneg) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusILneg) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusIRneg) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusLsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusSubset1) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffE) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffI2) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffIneg1) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffIneg2) =>
% 99.13/16.54 ((
% 99.13/16.54 (secondinupair) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairIL) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairIR) =>
% 99.13/16.54 ((
% 99.13/16.54 (kpairiskpair) =>
% 99.13/16.54 ((
% 99.13/16.54 (kpairp) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletonsubset) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletoninpowerset) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletoninpowunion) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairset2E) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairsubunion) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairinpowunion) =>
% 99.13/16.54 ((
% 99.13/16.54 (ubforcartprodlem1) =>
% 99.13/16.54 ((
% 99.13/16.54 (ubforcartprodlem2) =>
% 99.13/16.54 ((
% 99.13/16.54 (ubforcartprodlem3) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodpairin) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodmempair1) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodmempair) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunionE2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunionsingleton1) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunionsingleton2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunionsingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletonprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (ex1E1) =>
% 99.13/16.54 ((
% 99.13/16.54 (ex1I) =>
% 99.13/16.54 ((
% 99.13/16.54 (ex1I2) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletonsuniq) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjL1) =>
% 99.13/16.54 ((
% 99.13/16.54 (kfstsingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (theprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (kfstpairEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodfstin) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjL2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjL) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR11) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR12) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR1) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairequniteq) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR) =>
% 99.13/16.54 ((
% 99.13/16.54 (ksndsingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (ksndpairEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (kpairsurjEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodsndin) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodpairmemEL) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodpairmemER) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodmempaircEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodfstpairEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodsndpairEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodpairsurjEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrI) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrSub) =>
% 99.13/16.54 ((
% 99.13/16.54 (setOfPairsIsBReln) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrERa) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrEL1) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrEL2) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrER) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcImageSingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (apProp) =>
% 99.13/16.54 ((
% 99.13/16.54 (app) =>
% 99.13/16.54 ((
% 99.13/16.54 (infuncsetfunc) =>
% 99.13/16.54 ((
% 99.13/16.54 (ap2p) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcinfuncset) =>
% 99.13/16.54 ((
% 99.13/16.54 (lamProp) =>
% 99.13/16.54 ((
% 99.13/16.54 (lamp) =>
% 99.13/16.54 ((
% 99.13/16.54 (lam2p) =>
% 99.13/16.54 ((
% 99.13/16.54 (brelnall1) =>
% 99.13/16.54 ((
% 99.13/16.54 (brelnall2) =>
% 99.13/16.54 ((
% 99.13/16.54 (ex1E2) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcGraphProp1) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcGraphProp3) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcGraphProp2) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcextLem) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcGraphProp4) =>
% 99.13/16.54 ((
% 99.13/16.54 (subbreln) =>
% 99.13/16.54 ((
% 99.13/16.54 (eqbreln) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcext) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcext2) =>
% 99.13/16.54 ((
% 99.13/16.54 (ap2apEq1) =>
% 99.13/16.54 ((
% 99.13/16.54 (ap2apEq2) =>
% 99.13/16.54 ((
% 99.13/16.54 (beta1) =>
% 99.13/16.54 ((
% 99.13/16.54 (eta1) =>
% 99.13/16.54 ((
% 99.13/16.54 (lam2lamEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (beta2) =>
% 99.13/16.54 ((
% 99.13/16.54 (eta2) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (iffalseProp2) =>
% 99.13/16.54 ((
% 99.13/16.54 (iftrueProp1) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (ifp) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (complementTE1) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (binintersectTERcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (contrasubsetT) =>
% 99.13/16.54 ((
% 99.13/16.54 (contrasubsetT1) =>
% 99.13/16.54 ((
% 99.13/16.54 (contrasubsetT2) =>
% 99.13/16.54 ((
% 99.13/16.54 (contrasubsetT3) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementE1) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementSub1) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementSub2) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementTnotintersectT) =>
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% 99.13/16.54 (complementImpComplementIntersect) =>
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% 99.13/16.54 (complementSubsetComplementIntersect) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementInPowersetComplementIntersect) =>
% 99.13/16.54 ((
% 99.13/16.54 (contraSubsetComplement) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementTcontraSubset) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (binunionTIRcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (inIntersectImpInUnion) =>
% 99.13/16.54 ((
% 99.13/16.54 (inIntersectImpInUnion2) =>
% 99.13/16.54 ((
% 99.13/16.54 (inIntersectImpInIntersectUnions) =>
% 99.13/16.54 ((
% 99.13/16.54 (intersectInPowersetIntersectUnions) =>
% 99.13/16.54 ((
% 99.13/16.54 (inComplementUnionImpNotIn1) =>
% 99.13/16.54 ((
% 99.13/16.54 (inComplementUnionImpInComplement1) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (binunionTEcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2a1) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementUnionInPowersetComplement) =>
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% 99.13/16.54 ((
% 99.13/16.54 (demorgan1a) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan1b) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan1) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2a) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2b2) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2b) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule0) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule1) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule2) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule3) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule4) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_1) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_2) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_3) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_4) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_5) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1all2) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1SetBreln1) =>
% 99.13/16.54 ((
% 99.13/16.54 (choice2fnsingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (setOfPairsIsBReln1) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1all1) =>
% 99.13/16.54 ((
% 99.13/16.54 (subbreln1) =>
% 99.13/16.54 ((
% 99.13/16.54 (eqbreln1) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1invprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1invI) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1invE) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1compprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1compI) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1compE) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1compEex) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionIL) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionIR) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionI) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionE) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionEcases) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionCommutes) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz2Ex) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz2W) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz2A) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz2B) =>
% 99.13/16.54 ((
% 99.13/16.54 (image1Ex) =>
% 99.13/16.54 ((
% 99.13/16.54 (image1Ex1) =>
% 99.13/16.54 ((
% 99.13/16.54 (image1Equiv) =>
% 99.13/16.54 ((
% 99.13/16.54 (image1E) =>
% 99.13/16.54 ((
% 99.13/16.54 (image1I) =>
% 99.13/16.54 ((
% 99.13/16.54 (injFuncInInjFuncSet) =>
% 99.13/16.54 ((
% 99.13/16.54 (injFuncSetFuncIn) =>
% 99.13/16.54 ((
% 99.13/16.54 (injFuncSetFuncInj) =>
% 99.13/16.54 ((
% 99.13/16.54 (!!) @ (
% 99.13/16.54 (('#B') @ (
% 99.13/16.54 !!) @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 !!))) @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#S') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 '#S') @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
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% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 =>))))) @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#C') @ in)))) @
% 99.13/16.54 surjFuncSet)))))))) @
% 99.13/16.54 (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#B') @ (
% 99.13/16.54 (
% 99.13/16.54 ('#C') @ in)))) @
% 99.13/16.54 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])).
% 99.13/16.54 thf(zip_derived_cl174, plain,
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% 99.13/16.54 (((in @ emptyset @
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% 99.13/16.54 (((setadjoinIR) =>
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% 99.13/16.54 (((setunionE) =>
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (quantDeMorgan1) =>
% 99.13/16.54 ((
% 99.13/16.54 (quantDeMorgan2) =>
% 99.13/16.54 ((
% 99.13/16.54 (quantDeMorgan3) =>
% 99.13/16.54 ((
% 99.13/16.54 (quantDeMorgan4) =>
% 99.13/16.54 ((
% 99.13/16.54 (prop2setI) =>
% 99.13/16.54 ((
% 99.13/16.54 (prop2set2propI) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (notdallE) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuI3) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuI2) =>
% 99.13/16.54 ((
% 99.13/16.54 (inCongP) =>
% 99.13/16.54 ((
% 99.13/16.54 (in__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuE3u) =>
% 99.13/16.54 ((
% 99.13/16.54 (exu__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (setadjoin__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (powerset__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunion__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (exuEu) =>
% 99.13/16.54 ((
% 99.13/16.54 (descr__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (dsetconstr__Cong) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetI1) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (eqimpsubset1) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (subsetE) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetE2) =>
% 99.13/16.54 ((
% 99.13/16.54 (notsubsetI) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (notequalI2) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (sepInPowerset) =>
% 99.13/16.54 ((
% 99.13/16.54 (sepSubset) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (upairset2IR) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionIR) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionEcases) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionE) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionLsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionRsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectI) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset5) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset2) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset3) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectER) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (binintersectRsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset4) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectSubset1) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (setminusI) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusEL) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusER) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusSubset2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusERneg) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusELneg) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusILneg) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusIRneg) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusLsub) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusSubset1) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffE) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (symdiffI2) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffIneg1) =>
% 99.13/16.54 ((
% 99.13/16.54 (symdiffIneg2) =>
% 99.13/16.54 ((
% 99.13/16.54 (secondinupair) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairIL) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairIR) =>
% 99.13/16.54 ((
% 99.13/16.54 (kpairiskpair) =>
% 99.13/16.54 ((
% 99.13/16.54 (kpairp) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletonsubset) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletoninpowerset) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletoninpowunion) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairset2E) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairsubunion) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairinpowunion) =>
% 99.13/16.54 ((
% 99.13/16.54 (ubforcartprodlem1) =>
% 99.13/16.54 ((
% 99.13/16.54 (ubforcartprodlem2) =>
% 99.13/16.54 ((
% 99.13/16.54 (ubforcartprodlem3) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodpairin) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodmempair1) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodmempair) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunionE2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunionsingleton1) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunionsingleton2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setunionsingleton) =>
% 99.13/16.54 ((
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% 99.13/16.54 ((
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% 99.13/16.54 ((
% 99.13/16.54 (ex1I) =>
% 99.13/16.54 ((
% 99.13/16.54 (ex1I2) =>
% 99.13/16.54 ((
% 99.13/16.54 (singletonsuniq) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjL1) =>
% 99.13/16.54 ((
% 99.13/16.54 (kfstsingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (theprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (kfstpairEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodfstin) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjL2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjL) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR11) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR12) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR1) =>
% 99.13/16.54 ((
% 99.13/16.54 (upairequniteq) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR2) =>
% 99.13/16.54 ((
% 99.13/16.54 (setukpairinjR) =>
% 99.13/16.54 ((
% 99.13/16.54 (ksndsingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (ksndpairEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (kpairsurjEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodsndin) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodpairmemEL) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodpairmemER) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodmempaircEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodfstpairEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodsndpairEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (cartprodpairsurjEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrI) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrSub) =>
% 99.13/16.54 ((
% 99.13/16.54 (setOfPairsIsBReln) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrERa) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrEL1) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrEL2) =>
% 99.13/16.54 ((
% 99.13/16.54 (dpsetconstrER) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcImageSingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (apProp) =>
% 99.13/16.54 ((
% 99.13/16.54 (app) =>
% 99.13/16.54 ((
% 99.13/16.54 (infuncsetfunc) =>
% 99.13/16.54 ((
% 99.13/16.54 (ap2p) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcinfuncset) =>
% 99.13/16.54 ((
% 99.13/16.54 (lamProp) =>
% 99.13/16.54 ((
% 99.13/16.54 (lamp) =>
% 99.13/16.54 ((
% 99.13/16.54 (lam2p) =>
% 99.13/16.54 ((
% 99.13/16.54 (brelnall1) =>
% 99.13/16.54 ((
% 99.13/16.54 (brelnall2) =>
% 99.13/16.54 ((
% 99.13/16.54 (ex1E2) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcGraphProp1) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcGraphProp3) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcGraphProp2) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcextLem) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcGraphProp4) =>
% 99.13/16.54 ((
% 99.13/16.54 (subbreln) =>
% 99.13/16.54 ((
% 99.13/16.54 (eqbreln) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcext) =>
% 99.13/16.54 ((
% 99.13/16.54 (funcext2) =>
% 99.13/16.54 ((
% 99.13/16.54 (ap2apEq1) =>
% 99.13/16.54 ((
% 99.13/16.54 (ap2apEq2) =>
% 99.13/16.54 ((
% 99.13/16.54 (beta1) =>
% 99.13/16.54 ((
% 99.13/16.54 (eta1) =>
% 99.13/16.54 ((
% 99.13/16.54 (lam2lamEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (beta2) =>
% 99.13/16.54 ((
% 99.13/16.54 (eta2) =>
% 99.13/16.54 ((
% 99.13/16.54 (iffalseProp1) =>
% 99.13/16.54 ((
% 99.13/16.54 (iffalseProp2) =>
% 99.13/16.54 ((
% 99.13/16.54 (iftrueProp1) =>
% 99.13/16.54 ((
% 99.13/16.54 (iftrueProp2) =>
% 99.13/16.54 ((
% 99.13/16.54 (ifSingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (ifp) =>
% 99.13/16.54 ((
% 99.13/16.54 (theeq) =>
% 99.13/16.54 ((
% 99.13/16.54 (iftrue) =>
% 99.13/16.54 ((
% 99.13/16.54 (iffalse) =>
% 99.13/16.54 ((
% 99.13/16.54 (iftrueorfalse) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectT_lem) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionT_lem) =>
% 99.13/16.54 ((
% 99.13/16.54 (powersetT_lem) =>
% 99.13/16.54 ((
% 99.13/16.54 (setminusT_lem) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementT_lem) =>
% 99.13/16.54 ((
% 99.13/16.54 (setextT) =>
% 99.13/16.54 ((
% 99.13/16.54 (subsetTI) =>
% 99.13/16.54 ((
% 99.13/16.54 (powersetTI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (powersetTE1) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementTI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementTE1) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectTELcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (binintersectTERcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (contrasubsetT) =>
% 99.13/16.54 ((
% 99.13/16.54 (contrasubsetT1) =>
% 99.13/16.54 ((
% 99.13/16.54 (contrasubsetT2) =>
% 99.13/16.54 ((
% 99.13/16.54 (contrasubsetT3) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementI1) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementE1) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementSub1) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementSub2) =>
% 99.13/16.54 ((
% 99.13/16.54 (doubleComplementEq) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementTnotintersectT) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementImpComplementIntersect) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementSubsetComplementIntersect) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementInPowersetComplementIntersect) =>
% 99.13/16.54 ((
% 99.13/16.54 (contraSubsetComplement) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementTcontraSubset) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionTILcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionTIRcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (inIntersectImpInUnion) =>
% 99.13/16.54 ((
% 99.13/16.54 (inIntersectImpInUnion2) =>
% 99.13/16.54 ((
% 99.13/16.54 (inIntersectImpInIntersectUnions) =>
% 99.13/16.54 ((
% 99.13/16.54 (intersectInPowersetIntersectUnions) =>
% 99.13/16.54 ((
% 99.13/16.54 (inComplementUnionImpNotIn1) =>
% 99.13/16.54 ((
% 99.13/16.54 (inComplementUnionImpInComplement1) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionTE) =>
% 99.13/16.54 ((
% 99.13/16.54 (binunionTEcontra) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2a1) =>
% 99.13/16.54 ((
% 99.13/16.54 (complementUnionInPowersetComplement) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2a2) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan1a) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan1b) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan1) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2a) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2b2) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2b) =>
% 99.13/16.54 ((
% 99.13/16.54 (demorgan2) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule0) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule1) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule2) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule3) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz13rule4) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_1) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_2) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_3) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_4) =>
% 99.13/16.54 ((
% 99.13/16.54 (woz1_5) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1all2) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1SetBreln1) =>
% 99.13/16.54 ((
% 99.13/16.54 (choice2fnsingleton) =>
% 99.13/16.54 ((
% 99.13/16.54 (setOfPairsIsBReln1) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1all1) =>
% 99.13/16.54 ((
% 99.13/16.54 (subbreln1) =>
% 99.13/16.54 ((
% 99.13/16.54 (eqbreln1) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1invprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1invI) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1invE) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1compprop) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1compI) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1compE) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1compEex) =>
% 99.13/16.54 ((
% 99.13/16.54 (breln1unionprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionIL) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionIR) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionI) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionE) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionEcases) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionCommutes) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2Ex) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2W) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2A) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2B) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1Ex) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1Ex1) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1Equiv) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1E) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1I) =>
% 99.13/16.55 ((
% 99.13/16.55 (injFuncInInjFuncSet) =>
% 99.13/16.55 ((
% 99.13/16.55 (injFuncSetFuncIn) =>
% 99.13/16.55 ((
% 99.13/16.55 (injFuncSetFuncInj) =>
% 99.13/16.55 ((
% 99.13/16.55 (!!) @ (
% 99.13/16.55 (('#B') @ (
% 99.13/16.55 !!) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 !!))) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#S') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 '#S') @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 '#S'))) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 =>))))) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#C') @ in)))) @
% 99.13/16.55 surjFuncSet)))))))) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#C') @ in)))) @
% 99.13/16.55 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])).
% 99.13/16.55 thf(zip_derived_cl189, plain,
% 99.13/16.55 (~ (((exuE3e) =>
% 99.13/16.55 (((setext) =>
% 99.13/16.55 (((emptyI) =>
% 99.13/16.55 (((noeltsimpempty) =>
% 99.13/16.55 (((setbeta) =>
% 99.13/16.55 (((nonemptyE1) =>
% 99.13/16.55 (((nonemptyI) =>
% 99.13/16.55 (((nonemptyI1) =>
% 99.13/16.55 (((setadjoinIL) =>
% 99.13/16.55 (((in @ emptyset @
% 99.13/16.55 (setadjoin @ emptyset @ emptyset)) =>
% 99.13/16.55 (((setadjoinIR) =>
% 99.13/16.55 (((setadjoinE) =>
% 99.13/16.55 (((setadjoinOr) =>
% 99.13/16.55 (((setoftrueEq) =>
% 99.13/16.55 (((powersetI) =>
% 99.13/16.55 (((emptyinPowerset) =>
% 99.13/16.55 (((emptyInPowerset) =>
% 99.13/16.55 (((powersetE) =>
% 99.13/16.55 (((setunionI) =>
% 99.13/16.55 (((setunionE) =>
% 99.13/16.55 (((subPowSU) =>
% 99.13/16.55 (((exuE2) =>
% 99.13/16.55 (((nonemptyImpWitness) =>
% 99.13/16.55 (((uniqinunit) =>
% 99.13/16.55 (((notinsingleton) =>
% 99.13/16.55 (((eqinunit) =>
% 99.13/16.55 (((singletonsswitch) =>
% 99.13/16.55 (((upairsetE) =>
% 99.13/16.55 (((upairsetIL) =>
% 99.13/16.55 (((upairsetIR) =>
% 99.13/16.55 ((
% 99.13/16.55 (emptyE1) =>
% 99.13/16.55 ((
% 99.13/16.55 (vacuousDall) =>
% 99.13/16.55 ((
% 99.13/16.55 (quantDeMorgan1) =>
% 99.13/16.55 ((
% 99.13/16.55 (quantDeMorgan2) =>
% 99.13/16.55 ((
% 99.13/16.55 (quantDeMorgan3) =>
% 99.13/16.55 ((
% 99.13/16.55 (quantDeMorgan4) =>
% 99.13/16.55 ((
% 99.13/16.55 (prop2setI) =>
% 99.13/16.55 ((
% 99.13/16.55 (prop2set2propI) =>
% 99.13/16.55 ((
% 99.13/16.55 (notdexE) =>
% 99.13/16.55 ((
% 99.13/16.55 (notdallE) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuI3) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuI2) =>
% 99.13/16.55 ((
% 99.13/16.55 (inCongP) =>
% 99.13/16.55 ((
% 99.13/16.55 (in__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuE3u) =>
% 99.13/16.55 ((
% 99.13/16.55 (exu__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (setadjoin__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (powerset__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunion__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuEu) =>
% 99.13/16.55 ((
% 99.13/16.55 (descr__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (dsetconstr__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (eqimpsubset2) =>
% 99.13/16.55 ((
% 99.13/16.55 (eqimpsubset1) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetI2) =>
% 99.13/16.55 ((
% 99.13/16.55 (emptysetsubset) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetE) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetE2) =>
% 99.13/16.55 ((
% 99.13/16.55 (notsubsetI) =>
% 99.13/16.55 ((
% 99.13/16.55 (notequalI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (notequalI2) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetRefl) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetTrans) =>
% 99.13/16.55 ((
% 99.13/16.55 (setadjoinSub) =>
% 99.13/16.55 ((
% 99.13/16.55 (setadjoinSub2) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (setextsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetemptysetimpeq) =>
% 99.13/16.55 ((
% 99.13/16.55 (powersetI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (powersetE1) =>
% 99.13/16.55 ((
% 99.13/16.55 (inPowerset) =>
% 99.13/16.55 ((
% 99.13/16.55 (powersetsubset) =>
% 99.13/16.55 ((
% 99.13/16.55 (sepInPowerset) =>
% 99.13/16.55 ((
% 99.13/16.55 (sepSubset) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionIL) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairset2IR) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionIR) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionEcases) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionE) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionLsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionRsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectI) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset5) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectEL) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectLsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset2) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset3) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectER) =>
% 99.13/16.55 ((
% 99.13/16.55 (disjointsetsI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectRsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset4) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset1) =>
% 99.13/16.55 ((
% 99.13/16.55 (bs114d) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusI) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusEL) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusER) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusSubset2) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusERneg) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusELneg) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusILneg) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusIRneg) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusLsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusSubset1) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffE) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffI2) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffIneg1) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffIneg2) =>
% 99.13/16.55 ((
% 99.13/16.55 (secondinupair) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairIL) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairIR) =>
% 99.13/16.55 ((
% 99.13/16.55 (kpairiskpair) =>
% 99.13/16.55 ((
% 99.13/16.55 (kpairp) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletonsubset) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletoninpowerset) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletoninpowunion) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairset2E) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairsubunion) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairinpowunion) =>
% 99.13/16.55 ((
% 99.13/16.55 (ubforcartprodlem1) =>
% 99.13/16.55 ((
% 99.13/16.55 (ubforcartprodlem2) =>
% 99.13/16.55 ((
% 99.13/16.55 (ubforcartprodlem3) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodpairin) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodmempair1) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodmempair) =>
% 99.13/16.55 ((
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% 99.13/16.55 (cartprodpairmemER) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodmempaircEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodfstpairEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodsndpairEq) =>
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% 99.13/16.55 (cartprodpairsurjEq) =>
% 99.13/16.55 ((
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% 99.13/16.55 (dpsetconstrSub) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrEL2) =>
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% 99.13/16.55 (dpsetconstrER) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcImageSingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (apProp) =>
% 99.13/16.55 ((
% 99.13/16.55 (app) =>
% 99.13/16.55 ((
% 99.13/16.55 (infuncsetfunc) =>
% 99.13/16.55 ((
% 99.13/16.55 (ap2p) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcinfuncset) =>
% 99.13/16.55 ((
% 99.13/16.55 (lamProp) =>
% 99.13/16.55 ((
% 99.13/16.55 (lamp) =>
% 99.13/16.55 ((
% 99.13/16.55 (lam2p) =>
% 99.13/16.55 ((
% 99.13/16.55 (brelnall1) =>
% 99.13/16.55 ((
% 99.13/16.55 (brelnall2) =>
% 99.13/16.55 ((
% 99.13/16.55 (ex1E2) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcGraphProp1) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcGraphProp3) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcGraphProp2) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcextLem) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcGraphProp4) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (funcext2) =>
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% 99.13/16.55 (ap2apEq2) =>
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% 99.13/16.55 ((
% 99.13/16.55 (eta1) =>
% 99.13/16.55 ((
% 99.13/16.55 (lam2lamEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (beta2) =>
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% 99.13/16.55 ((
% 99.13/16.55 (iffalseProp1) =>
% 99.13/16.55 ((
% 99.13/16.55 (iffalseProp2) =>
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (iftrue) =>
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% 99.13/16.55 ((
% 99.13/16.55 (powersetTE1) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementTI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementTE1) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectTELcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectTERcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (contrasubsetT) =>
% 99.13/16.55 ((
% 99.13/16.55 (contrasubsetT1) =>
% 99.13/16.55 ((
% 99.13/16.55 (contrasubsetT2) =>
% 99.13/16.55 ((
% 99.13/16.55 (contrasubsetT3) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementE1) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementSub1) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementSub2) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementEq) =>
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% 99.13/16.55 (complementTnotintersectT) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementImpComplementIntersect) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementSubsetComplementIntersect) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementInPowersetComplementIntersect) =>
% 99.13/16.55 ((
% 99.13/16.55 (contraSubsetComplement) =>
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% 99.13/16.55 (complementTcontraSubset) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionTILcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionTIRcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (inIntersectImpInUnion) =>
% 99.13/16.55 ((
% 99.13/16.55 (inIntersectImpInUnion2) =>
% 99.13/16.55 ((
% 99.13/16.55 (inIntersectImpInIntersectUnions) =>
% 99.13/16.55 ((
% 99.13/16.55 (intersectInPowersetIntersectUnions) =>
% 99.13/16.55 ((
% 99.13/16.55 (inComplementUnionImpNotIn1) =>
% 99.13/16.55 ((
% 99.13/16.55 (inComplementUnionImpInComplement1) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (binunionTEcontra) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (complementUnionInPowersetComplement) =>
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% 99.13/16.55 ((
% 99.13/16.55 (demorgan1a) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan1b) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan1) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2a) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2b2) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2b) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule0) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule1) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule2) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule3) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule4) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_1) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_2) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_3) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_4) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_5) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1all2) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1SetBreln1) =>
% 99.13/16.55 ((
% 99.13/16.55 (choice2fnsingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (setOfPairsIsBReln1) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1all1) =>
% 99.13/16.55 ((
% 99.13/16.55 (subbreln1) =>
% 99.13/16.55 ((
% 99.13/16.55 (eqbreln1) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1invprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1invI) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1invE) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1compprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1compI) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1compE) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1compEex) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionIL) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionIR) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionI) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionE) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionEcases) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionCommutes) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2Ex) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2W) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (woz2B) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (image1Ex1) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1Equiv) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1E) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1I) =>
% 99.13/16.55 ((
% 99.13/16.55 (injFuncInInjFuncSet) =>
% 99.13/16.55 ((
% 99.13/16.55 (injFuncSetFuncIn) =>
% 99.13/16.55 ((
% 99.13/16.55 (injFuncSetFuncInj) =>
% 99.13/16.55 ((
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% 99.13/16.55 (('#B') @ (
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% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
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% 99.13/16.55 (
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% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 '#S') @
% 99.13/16.55 (
% 99.13/16.55 (
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% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
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% 99.13/16.55 (
% 99.13/16.55 (
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% 99.13/16.55 (
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% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
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% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#C') @ in)))) @
% 99.13/16.55 surjFuncSet)))))))) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#C') @ in)))) @
% 99.13/16.55 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl174])).
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% 99.13/16.55 (((in @ emptyset @
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% 99.13/16.55 (((setadjoinIR) =>
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% 99.13/16.55 ((
% 99.13/16.55 (quantDeMorgan2) =>
% 99.13/16.55 ((
% 99.13/16.55 (quantDeMorgan3) =>
% 99.13/16.55 ((
% 99.13/16.55 (quantDeMorgan4) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (prop2set2propI) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (notdallE) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (exuI3) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuI2) =>
% 99.13/16.55 ((
% 99.13/16.55 (inCongP) =>
% 99.13/16.55 ((
% 99.13/16.55 (in__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuE3u) =>
% 99.13/16.55 ((
% 99.13/16.55 (exu__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (setadjoin__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (powerset__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunion__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuEu) =>
% 99.13/16.55 ((
% 99.13/16.55 (descr__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (dsetconstr__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetI1) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (subsetE2) =>
% 99.13/16.55 ((
% 99.13/16.55 (notsubsetI) =>
% 99.13/16.55 ((
% 99.13/16.55 (notequalI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (notequalI2) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (subsetTrans) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (setadjoinSub2) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (sepSubset) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (upairset2IR) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionIR) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionEcases) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionE) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionLsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionRsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectI) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset5) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectEL) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset3) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectER) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (binintersectRsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset4) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset1) =>
% 99.13/16.55 ((
% 99.13/16.55 (bs114d) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (setminusEL) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusER) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusSubset2) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusERneg) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusELneg) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusILneg) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusIRneg) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusLsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusSubset1) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffE) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffI2) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffIneg1) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffIneg2) =>
% 99.13/16.55 ((
% 99.13/16.55 (secondinupair) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairIL) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairIR) =>
% 99.13/16.55 ((
% 99.13/16.55 (kpairiskpair) =>
% 99.13/16.55 ((
% 99.13/16.55 (kpairp) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletonsubset) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletoninpowerset) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletoninpowunion) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairset2E) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairsubunion) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairinpowunion) =>
% 99.13/16.55 ((
% 99.13/16.55 (ubforcartprodlem1) =>
% 99.13/16.55 ((
% 99.13/16.55 (ubforcartprodlem2) =>
% 99.13/16.55 ((
% 99.13/16.55 (ubforcartprodlem3) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodpairin) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodmempair1) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodmempair) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunionE2) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunionsingleton1) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunionsingleton2) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunionsingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletonprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (ex1E1) =>
% 99.13/16.55 ((
% 99.13/16.55 (ex1I) =>
% 99.13/16.55 ((
% 99.13/16.55 (ex1I2) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletonsuniq) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjL1) =>
% 99.13/16.55 ((
% 99.13/16.55 (kfstsingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (theprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (kfstpairEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodfstin) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjL2) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjL) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR11) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR12) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR1) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairequniteq) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR2) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR) =>
% 99.13/16.55 ((
% 99.13/16.55 (ksndsingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (ksndpairEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (kpairsurjEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodsndin) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodpairmemEL) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodpairmemER) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodmempaircEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodfstpairEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodsndpairEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodpairsurjEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrI) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrSub) =>
% 99.13/16.55 ((
% 99.13/16.55 (setOfPairsIsBReln) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrERa) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrEL1) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrEL2) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrER) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcImageSingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (apProp) =>
% 99.13/16.55 ((
% 99.13/16.55 (app) =>
% 99.13/16.55 ((
% 99.13/16.55 (infuncsetfunc) =>
% 99.13/16.55 ((
% 99.13/16.55 (ap2p) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcinfuncset) =>
% 99.13/16.55 ((
% 99.13/16.55 (lamProp) =>
% 99.13/16.55 ((
% 99.13/16.55 (lamp) =>
% 99.13/16.55 ((
% 99.13/16.55 (lam2p) =>
% 99.13/16.55 ((
% 99.13/16.55 (brelnall1) =>
% 99.13/16.55 ((
% 99.13/16.55 (brelnall2) =>
% 99.13/16.55 ((
% 99.13/16.55 (ex1E2) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcGraphProp1) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcGraphProp3) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcGraphProp2) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcextLem) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcGraphProp4) =>
% 99.13/16.55 ((
% 99.13/16.55 (subbreln) =>
% 99.13/16.55 ((
% 99.13/16.55 (eqbreln) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcext) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcext2) =>
% 99.13/16.55 ((
% 99.13/16.55 (ap2apEq1) =>
% 99.13/16.55 ((
% 99.13/16.55 (ap2apEq2) =>
% 99.13/16.55 ((
% 99.13/16.55 (beta1) =>
% 99.13/16.55 ((
% 99.13/16.55 (eta1) =>
% 99.13/16.55 ((
% 99.13/16.55 (lam2lamEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (beta2) =>
% 99.13/16.55 ((
% 99.13/16.55 (eta2) =>
% 99.13/16.55 ((
% 99.13/16.55 (iffalseProp1) =>
% 99.13/16.55 ((
% 99.13/16.55 (iffalseProp2) =>
% 99.13/16.55 ((
% 99.13/16.55 (iftrueProp1) =>
% 99.13/16.55 ((
% 99.13/16.55 (iftrueProp2) =>
% 99.13/16.55 ((
% 99.13/16.55 (ifSingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (ifp) =>
% 99.13/16.55 ((
% 99.13/16.55 (theeq) =>
% 99.13/16.55 ((
% 99.13/16.55 (iftrue) =>
% 99.13/16.55 ((
% 99.13/16.55 (iffalse) =>
% 99.13/16.55 ((
% 99.13/16.55 (iftrueorfalse) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectT_lem) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionT_lem) =>
% 99.13/16.55 ((
% 99.13/16.55 (powersetT_lem) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusT_lem) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementT_lem) =>
% 99.13/16.55 ((
% 99.13/16.55 (setextT) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetTI) =>
% 99.13/16.55 ((
% 99.13/16.55 (powersetTI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (powersetTE1) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementTI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementTE1) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectTELcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectTERcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (contrasubsetT) =>
% 99.13/16.55 ((
% 99.13/16.55 (contrasubsetT1) =>
% 99.13/16.55 ((
% 99.13/16.55 (contrasubsetT2) =>
% 99.13/16.55 ((
% 99.13/16.55 (contrasubsetT3) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementE1) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementSub1) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementSub2) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementTnotintersectT) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementImpComplementIntersect) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementSubsetComplementIntersect) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementInPowersetComplementIntersect) =>
% 99.13/16.55 ((
% 99.13/16.55 (contraSubsetComplement) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementTcontraSubset) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionTILcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionTIRcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (inIntersectImpInUnion) =>
% 99.13/16.55 ((
% 99.13/16.55 (inIntersectImpInUnion2) =>
% 99.13/16.55 ((
% 99.13/16.55 (inIntersectImpInIntersectUnions) =>
% 99.13/16.55 ((
% 99.13/16.55 (intersectInPowersetIntersectUnions) =>
% 99.13/16.55 ((
% 99.13/16.55 (inComplementUnionImpNotIn1) =>
% 99.13/16.55 ((
% 99.13/16.55 (inComplementUnionImpInComplement1) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionTE) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionTEcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2a1) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementUnionInPowersetComplement) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2a2) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan1a) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan1b) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan1) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2a) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2b2) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2b) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule0) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule1) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule2) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule3) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule4) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_1) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_2) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_3) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_4) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_5) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1all2) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1SetBreln1) =>
% 99.13/16.55 ((
% 99.13/16.55 (choice2fnsingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (setOfPairsIsBReln1) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1all1) =>
% 99.13/16.55 ((
% 99.13/16.55 (subbreln1) =>
% 99.13/16.55 ((
% 99.13/16.55 (eqbreln1) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1invprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1invI) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1invE) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1compprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1compI) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1compE) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1compEex) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionIL) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionIR) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionI) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionE) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionEcases) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionCommutes) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2Ex) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2W) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2A) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2B) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1Ex) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1Ex1) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1Equiv) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1E) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1I) =>
% 99.13/16.55 ((
% 99.13/16.55 (injFuncInInjFuncSet) =>
% 99.13/16.55 ((
% 99.13/16.55 (injFuncSetFuncIn) =>
% 99.13/16.55 ((
% 99.13/16.55 (injFuncSetFuncInj) =>
% 99.13/16.55 ((
% 99.13/16.55 (!!) @ (
% 99.13/16.55 (('#B') @ (
% 99.13/16.55 !!) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 !!))) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#S') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 '#S') @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 '#S'))) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 =>))))) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#C') @ in)))) @
% 99.13/16.55 surjFuncSet)))))))) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#C') @ in)))) @
% 99.13/16.55 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl189])).
% 99.13/16.55 thf(zip_derived_cl222, plain,
% 99.13/16.55 (~ (((emptyI) =>
% 99.13/16.55 (((noeltsimpempty) =>
% 99.13/16.55 (((setbeta) =>
% 99.13/16.55 (((nonemptyE1) =>
% 99.13/16.55 (((nonemptyI) =>
% 99.13/16.55 (((nonemptyI1) =>
% 99.13/16.55 (((setadjoinIL) =>
% 99.13/16.55 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 99.13/16.55 (((setadjoinIR) =>
% 99.13/16.55 (((setadjoinE) =>
% 99.13/16.55 (((setadjoinOr) =>
% 99.13/16.55 (((setoftrueEq) =>
% 99.13/16.55 (((powersetI) =>
% 99.13/16.55 (((emptyinPowerset) =>
% 99.13/16.55 (((emptyInPowerset) =>
% 99.13/16.55 (((powersetE) =>
% 99.13/16.55 (((setunionI) =>
% 99.13/16.55 (((setunionE) =>
% 99.13/16.55 (((subPowSU) =>
% 99.13/16.55 (((exuE2) =>
% 99.13/16.55 (((nonemptyImpWitness) =>
% 99.13/16.55 (((uniqinunit) =>
% 99.13/16.55 (((notinsingleton) =>
% 99.13/16.55 (((eqinunit) =>
% 99.13/16.55 (((singletonsswitch) =>
% 99.13/16.55 (((upairsetE) =>
% 99.13/16.55 (((upairsetIL) =>
% 99.13/16.55 (((upairsetIR) =>
% 99.13/16.55 (((emptyE1) =>
% 99.13/16.55 (((vacuousDall) =>
% 99.13/16.55 ((
% 99.13/16.55 (quantDeMorgan1) =>
% 99.13/16.55 ((
% 99.13/16.55 (quantDeMorgan2) =>
% 99.13/16.55 ((
% 99.13/16.55 (quantDeMorgan3) =>
% 99.13/16.55 ((
% 99.13/16.55 (quantDeMorgan4) =>
% 99.13/16.55 ((
% 99.13/16.55 (prop2setI) =>
% 99.13/16.55 ((
% 99.13/16.55 (prop2set2propI) =>
% 99.13/16.55 ((
% 99.13/16.55 (notdexE) =>
% 99.13/16.55 ((
% 99.13/16.55 (notdallE) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuI3) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuI2) =>
% 99.13/16.55 ((
% 99.13/16.55 (inCongP) =>
% 99.13/16.55 ((
% 99.13/16.55 (in__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuE3u) =>
% 99.13/16.55 ((
% 99.13/16.55 (exu__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (setadjoin__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (powerset__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunion__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuEu) =>
% 99.13/16.55 ((
% 99.13/16.55 (descr__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (dsetconstr__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (eqimpsubset2) =>
% 99.13/16.55 ((
% 99.13/16.55 (eqimpsubset1) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetI2) =>
% 99.13/16.55 ((
% 99.13/16.55 (emptysetsubset) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetE) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetE2) =>
% 99.13/16.55 ((
% 99.13/16.55 (notsubsetI) =>
% 99.13/16.55 ((
% 99.13/16.55 (notequalI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (notequalI2) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetRefl) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetTrans) =>
% 99.13/16.55 ((
% 99.13/16.55 (setadjoinSub) =>
% 99.13/16.55 ((
% 99.13/16.55 (setadjoinSub2) =>
% 99.13/16.55 ((
% 99.13/16.55 (subset2powerset) =>
% 99.13/16.55 ((
% 99.13/16.55 (setextsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetemptysetimpeq) =>
% 99.13/16.55 ((
% 99.13/16.55 (powersetI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (powersetE1) =>
% 99.13/16.55 ((
% 99.13/16.55 (inPowerset) =>
% 99.13/16.55 ((
% 99.13/16.55 (powersetsubset) =>
% 99.13/16.55 ((
% 99.13/16.55 (sepInPowerset) =>
% 99.13/16.55 ((
% 99.13/16.55 (sepSubset) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionIL) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairset2IR) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionIR) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionEcases) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionE) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionLsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionRsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectI) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset5) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectEL) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectLsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset2) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset3) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectER) =>
% 99.13/16.55 ((
% 99.13/16.55 (disjointsetsI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectRsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset4) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset1) =>
% 99.13/16.55 ((
% 99.13/16.55 (bs114d) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusI) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusEL) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusER) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusSubset2) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusERneg) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusELneg) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusILneg) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusIRneg) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusLsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusSubset1) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffE) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffI2) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffIneg1) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffIneg2) =>
% 99.13/16.55 ((
% 99.13/16.55 (secondinupair) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairIL) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairIR) =>
% 99.13/16.55 ((
% 99.13/16.55 (kpairiskpair) =>
% 99.13/16.55 ((
% 99.13/16.55 (kpairp) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletonsubset) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletoninpowerset) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletoninpowunion) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairset2E) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairsubunion) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairinpowunion) =>
% 99.13/16.55 ((
% 99.13/16.55 (ubforcartprodlem1) =>
% 99.13/16.55 ((
% 99.13/16.55 (ubforcartprodlem2) =>
% 99.13/16.55 ((
% 99.13/16.55 (ubforcartprodlem3) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodpairin) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodmempair1) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodmempair) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunionE2) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunionsingleton1) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunionsingleton2) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunionsingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletonprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (ex1E1) =>
% 99.13/16.55 ((
% 99.13/16.55 (ex1I) =>
% 99.13/16.55 ((
% 99.13/16.55 (ex1I2) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletonsuniq) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjL1) =>
% 99.13/16.55 ((
% 99.13/16.55 (kfstsingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (theprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (kfstpairEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodfstin) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjL2) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjL) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR11) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR12) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR1) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairequniteq) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR2) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR) =>
% 99.13/16.55 ((
% 99.13/16.55 (ksndsingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (ksndpairEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (kpairsurjEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodsndin) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodpairmemEL) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodpairmemER) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodmempaircEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodfstpairEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodsndpairEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodpairsurjEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrI) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrSub) =>
% 99.13/16.55 ((
% 99.13/16.55 (setOfPairsIsBReln) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrERa) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrEL1) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrEL2) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrER) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcImageSingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (apProp) =>
% 99.13/16.55 ((
% 99.13/16.55 (app) =>
% 99.13/16.55 ((
% 99.13/16.55 (infuncsetfunc) =>
% 99.13/16.55 ((
% 99.13/16.55 (ap2p) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcinfuncset) =>
% 99.13/16.55 ((
% 99.13/16.55 (lamProp) =>
% 99.13/16.55 ((
% 99.13/16.55 (lamp) =>
% 99.13/16.55 ((
% 99.13/16.55 (lam2p) =>
% 99.13/16.55 ((
% 99.13/16.55 (brelnall1) =>
% 99.13/16.55 ((
% 99.13/16.55 (brelnall2) =>
% 99.13/16.55 ((
% 99.13/16.55 (ex1E2) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcGraphProp1) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcGraphProp3) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcGraphProp2) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcextLem) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcGraphProp4) =>
% 99.13/16.55 ((
% 99.13/16.55 (subbreln) =>
% 99.13/16.55 ((
% 99.13/16.55 (eqbreln) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcext) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcext2) =>
% 99.13/16.55 ((
% 99.13/16.55 (ap2apEq1) =>
% 99.13/16.55 ((
% 99.13/16.55 (ap2apEq2) =>
% 99.13/16.55 ((
% 99.13/16.55 (beta1) =>
% 99.13/16.55 ((
% 99.13/16.55 (eta1) =>
% 99.13/16.55 ((
% 99.13/16.55 (lam2lamEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (beta2) =>
% 99.13/16.55 ((
% 99.13/16.55 (eta2) =>
% 99.13/16.55 ((
% 99.13/16.55 (iffalseProp1) =>
% 99.13/16.55 ((
% 99.13/16.55 (iffalseProp2) =>
% 99.13/16.55 ((
% 99.13/16.55 (iftrueProp1) =>
% 99.13/16.55 ((
% 99.13/16.55 (iftrueProp2) =>
% 99.13/16.55 ((
% 99.13/16.55 (ifSingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (ifp) =>
% 99.13/16.55 ((
% 99.13/16.55 (theeq) =>
% 99.13/16.55 ((
% 99.13/16.55 (iftrue) =>
% 99.13/16.55 ((
% 99.13/16.55 (iffalse) =>
% 99.13/16.55 ((
% 99.13/16.55 (iftrueorfalse) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectT_lem) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionT_lem) =>
% 99.13/16.55 ((
% 99.13/16.55 (powersetT_lem) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusT_lem) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementT_lem) =>
% 99.13/16.55 ((
% 99.13/16.55 (setextT) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetTI) =>
% 99.13/16.55 ((
% 99.13/16.55 (powersetTI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (powersetTE1) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementTI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementTE1) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectTELcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectTERcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (contrasubsetT) =>
% 99.13/16.55 ((
% 99.13/16.55 (contrasubsetT1) =>
% 99.13/16.55 ((
% 99.13/16.55 (contrasubsetT2) =>
% 99.13/16.55 ((
% 99.13/16.55 (contrasubsetT3) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementE1) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementSub1) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementSub2) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementTnotintersectT) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementImpComplementIntersect) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementSubsetComplementIntersect) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementInPowersetComplementIntersect) =>
% 99.13/16.55 ((
% 99.13/16.55 (contraSubsetComplement) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementTcontraSubset) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionTILcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionTIRcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (inIntersectImpInUnion) =>
% 99.13/16.55 ((
% 99.13/16.55 (inIntersectImpInUnion2) =>
% 99.13/16.55 ((
% 99.13/16.55 (inIntersectImpInIntersectUnions) =>
% 99.13/16.55 ((
% 99.13/16.55 (intersectInPowersetIntersectUnions) =>
% 99.13/16.55 ((
% 99.13/16.55 (inComplementUnionImpNotIn1) =>
% 99.13/16.55 ((
% 99.13/16.55 (inComplementUnionImpInComplement1) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionTE) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionTEcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2a1) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementUnionInPowersetComplement) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2a2) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan1a) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan1b) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan1) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2a) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2b2) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2b) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule0) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule1) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule2) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule3) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule4) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_1) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_2) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_3) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_4) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_5) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1all2) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1SetBreln1) =>
% 99.13/16.55 ((
% 99.13/16.55 (choice2fnsingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (setOfPairsIsBReln1) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1all1) =>
% 99.13/16.55 ((
% 99.13/16.55 (subbreln1) =>
% 99.13/16.55 ((
% 99.13/16.55 (eqbreln1) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1invprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1invI) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1invE) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1compprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1compI) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1compE) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1compEex) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionIL) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionIR) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionI) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionE) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionEcases) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionCommutes) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2Ex) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2W) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2A) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2B) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1Ex) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1Ex1) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1Equiv) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1E) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1I) =>
% 99.13/16.55 ((
% 99.13/16.55 (injFuncInInjFuncSet) =>
% 99.13/16.55 ((
% 99.13/16.55 (injFuncSetFuncIn) =>
% 99.13/16.55 ((
% 99.13/16.55 (injFuncSetFuncInj) =>
% 99.13/16.55 ((
% 99.13/16.55 (!!) @ (
% 99.13/16.55 (('#B') @ (
% 99.13/16.55 !!) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 !!))) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#S') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 '#S') @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 '#S'))) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 =>))))) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#C') @ in)))) @
% 99.13/16.55 surjFuncSet)))))))) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#C') @ in)))) @
% 99.13/16.55 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])).
% 99.13/16.55 thf(zip_derived_cl236, plain,
% 99.13/16.55 (~ (((noeltsimpempty) =>
% 99.13/16.55 (((setbeta) =>
% 99.13/16.55 (((nonemptyE1) =>
% 99.13/16.55 (((nonemptyI) =>
% 99.13/16.55 (((nonemptyI1) =>
% 99.13/16.55 (((setadjoinIL) =>
% 99.13/16.55 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 99.13/16.55 (((setadjoinIR) =>
% 99.13/16.55 (((setadjoinE) =>
% 99.13/16.55 (((setadjoinOr) =>
% 99.13/16.55 (((setoftrueEq) =>
% 99.13/16.55 (((powersetI) =>
% 99.13/16.55 (((emptyinPowerset) =>
% 99.13/16.55 (((emptyInPowerset) =>
% 99.13/16.55 (((powersetE) =>
% 99.13/16.55 (((setunionI) =>
% 99.13/16.55 (((setunionE) =>
% 99.13/16.55 (((subPowSU) =>
% 99.13/16.55 (((exuE2) =>
% 99.13/16.55 (((nonemptyImpWitness) =>
% 99.13/16.55 (((uniqinunit) =>
% 99.13/16.55 (((notinsingleton) =>
% 99.13/16.55 (((eqinunit) =>
% 99.13/16.55 (((singletonsswitch) =>
% 99.13/16.55 (((upairsetE) =>
% 99.13/16.55 (((upairsetIL) =>
% 99.13/16.55 (((upairsetIR) =>
% 99.13/16.55 (((emptyE1) =>
% 99.13/16.55 (((vacuousDall) =>
% 99.13/16.55 (((quantDeMorgan1) =>
% 99.13/16.55 ((
% 99.13/16.55 (quantDeMorgan2) =>
% 99.13/16.55 ((
% 99.13/16.55 (quantDeMorgan3) =>
% 99.13/16.55 ((
% 99.13/16.55 (quantDeMorgan4) =>
% 99.13/16.55 ((
% 99.13/16.55 (prop2setI) =>
% 99.13/16.55 ((
% 99.13/16.55 (prop2set2propI) =>
% 99.13/16.55 ((
% 99.13/16.55 (notdexE) =>
% 99.13/16.55 ((
% 99.13/16.55 (notdallE) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuI3) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuI2) =>
% 99.13/16.55 ((
% 99.13/16.55 (inCongP) =>
% 99.13/16.55 ((
% 99.13/16.55 (in__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuE3u) =>
% 99.13/16.55 ((
% 99.13/16.55 (exu__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (setadjoin__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (powerset__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunion__Cong) =>
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% 99.13/16.55 (binintersectSubset3) =>
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% 99.13/16.55 ((
% 99.13/16.55 (setminusEL) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusER) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusSubset2) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (setminusILneg) =>
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% 99.13/16.55 (setminusIRneg) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 (symdiffI2) =>
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% 99.13/16.55 ((
% 99.13/16.55 (kpairp) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletonsubset) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletoninpowerset) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletoninpowunion) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairset2E) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairsubunion) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairinpowunion) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (ubforcartprodlem2) =>
% 99.13/16.55 ((
% 99.13/16.55 (ubforcartprodlem3) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodpairin) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodmempair1) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodmempair) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunionE2) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunionsingleton1) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunionsingleton2) =>
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% 99.13/16.55 (setunionsingleton) =>
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% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (ex1I2) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletonsuniq) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjL1) =>
% 99.13/16.55 ((
% 99.13/16.55 (kfstsingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (theprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (kfstpairEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodfstin) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjL2) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjL) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR11) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR12) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR1) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairequniteq) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR2) =>
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% 99.13/16.55 (setukpairinjR) =>
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% 99.13/16.55 (ksndsingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (ksndpairEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (kpairsurjEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodsndin) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodpairmemEL) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodpairmemER) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodmempaircEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodfstpairEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodsndpairEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodpairsurjEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrI) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrSub) =>
% 99.13/16.55 ((
% 99.13/16.55 (setOfPairsIsBReln) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrERa) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrEL1) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrEL2) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrER) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcImageSingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (apProp) =>
% 99.13/16.55 ((
% 99.13/16.55 (app) =>
% 99.13/16.55 ((
% 99.13/16.55 (infuncsetfunc) =>
% 99.13/16.55 ((
% 99.13/16.55 (ap2p) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcinfuncset) =>
% 99.13/16.55 ((
% 99.13/16.55 (lamProp) =>
% 99.13/16.55 ((
% 99.13/16.55 (lamp) =>
% 99.13/16.55 ((
% 99.13/16.55 (lam2p) =>
% 99.13/16.55 ((
% 99.13/16.55 (brelnall1) =>
% 99.13/16.55 ((
% 99.13/16.55 (brelnall2) =>
% 99.13/16.55 ((
% 99.13/16.55 (ex1E2) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcGraphProp1) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcGraphProp3) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcGraphProp2) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcextLem) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcGraphProp4) =>
% 99.13/16.55 ((
% 99.13/16.55 (subbreln) =>
% 99.13/16.55 ((
% 99.13/16.55 (eqbreln) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcext) =>
% 99.13/16.55 ((
% 99.13/16.55 (funcext2) =>
% 99.13/16.55 ((
% 99.13/16.55 (ap2apEq1) =>
% 99.13/16.55 ((
% 99.13/16.55 (ap2apEq2) =>
% 99.13/16.55 ((
% 99.13/16.55 (beta1) =>
% 99.13/16.55 ((
% 99.13/16.55 (eta1) =>
% 99.13/16.55 ((
% 99.13/16.55 (lam2lamEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (beta2) =>
% 99.13/16.55 ((
% 99.13/16.55 (eta2) =>
% 99.13/16.55 ((
% 99.13/16.55 (iffalseProp1) =>
% 99.13/16.55 ((
% 99.13/16.55 (iffalseProp2) =>
% 99.13/16.55 ((
% 99.13/16.55 (iftrueProp1) =>
% 99.13/16.55 ((
% 99.13/16.55 (iftrueProp2) =>
% 99.13/16.55 ((
% 99.13/16.55 (ifSingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (ifp) =>
% 99.13/16.55 ((
% 99.13/16.55 (theeq) =>
% 99.13/16.55 ((
% 99.13/16.55 (iftrue) =>
% 99.13/16.55 ((
% 99.13/16.55 (iffalse) =>
% 99.13/16.55 ((
% 99.13/16.55 (iftrueorfalse) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (binunionT_lem) =>
% 99.13/16.55 ((
% 99.13/16.55 (powersetT_lem) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusT_lem) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementT_lem) =>
% 99.13/16.55 ((
% 99.13/16.55 (setextT) =>
% 99.13/16.55 ((
% 99.13/16.55 (subsetTI) =>
% 99.13/16.55 ((
% 99.13/16.55 (powersetTI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (powersetTE1) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementTI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementTE1) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectTELcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectTERcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (contrasubsetT) =>
% 99.13/16.55 ((
% 99.13/16.55 (contrasubsetT1) =>
% 99.13/16.55 ((
% 99.13/16.55 (contrasubsetT2) =>
% 99.13/16.55 ((
% 99.13/16.55 (contrasubsetT3) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementE1) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementSub1) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementSub2) =>
% 99.13/16.55 ((
% 99.13/16.55 (doubleComplementEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementTnotintersectT) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementImpComplementIntersect) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementSubsetComplementIntersect) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementInPowersetComplementIntersect) =>
% 99.13/16.55 ((
% 99.13/16.55 (contraSubsetComplement) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementTcontraSubset) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionTILcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionTIRcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (inIntersectImpInUnion) =>
% 99.13/16.55 ((
% 99.13/16.55 (inIntersectImpInUnion2) =>
% 99.13/16.55 ((
% 99.13/16.55 (inIntersectImpInIntersectUnions) =>
% 99.13/16.55 ((
% 99.13/16.55 (intersectInPowersetIntersectUnions) =>
% 99.13/16.55 ((
% 99.13/16.55 (inComplementUnionImpNotIn1) =>
% 99.13/16.55 ((
% 99.13/16.55 (inComplementUnionImpInComplement1) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionTE) =>
% 99.13/16.55 ((
% 99.13/16.55 (binunionTEcontra) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2a1) =>
% 99.13/16.55 ((
% 99.13/16.55 (complementUnionInPowersetComplement) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2a2) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan1a) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan1b) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan1) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2a) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2b2) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2b) =>
% 99.13/16.55 ((
% 99.13/16.55 (demorgan2) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule0) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule1) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule2) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule3) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz13rule4) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_1) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_2) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_3) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_4) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz1_5) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1all2) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1SetBreln1) =>
% 99.13/16.55 ((
% 99.13/16.55 (choice2fnsingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (setOfPairsIsBReln1) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1all1) =>
% 99.13/16.55 ((
% 99.13/16.55 (subbreln1) =>
% 99.13/16.55 ((
% 99.13/16.55 (eqbreln1) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1invprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1invI) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1invE) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1compprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1compI) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1compE) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1compEex) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionprop) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionIL) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionIR) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionI) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionE) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionEcases) =>
% 99.13/16.55 ((
% 99.13/16.55 (breln1unionCommutes) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2Ex) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2W) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2A) =>
% 99.13/16.55 ((
% 99.13/16.55 (woz2B) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1Ex) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1Ex1) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1Equiv) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1E) =>
% 99.13/16.55 ((
% 99.13/16.55 (image1I) =>
% 99.13/16.55 ((
% 99.13/16.55 (injFuncInInjFuncSet) =>
% 99.13/16.55 ((
% 99.13/16.55 (injFuncSetFuncIn) =>
% 99.13/16.55 ((
% 99.13/16.55 (injFuncSetFuncInj) =>
% 99.13/16.55 ((
% 99.13/16.55 (!!) @ (
% 99.13/16.55 (('#B') @ (
% 99.13/16.55 !!) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 !!))) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#S') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 '#S') @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
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% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 =>))))) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#C') @ in)))) @
% 99.13/16.55 surjFuncSet)))))))) @
% 99.13/16.55 (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#C') @ in)))) @
% 99.13/16.55 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl222])).
% 99.13/16.55 thf(zip_derived_cl251, plain,
% 99.13/16.55 (~ (((setbeta) =>
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% 99.13/16.55 (((nonemptyI1) =>
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% 99.13/16.55 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 99.13/16.55 (((setadjoinIR) =>
% 99.13/16.55 (((setadjoinE) =>
% 99.13/16.55 (((setadjoinOr) =>
% 99.13/16.55 (((setoftrueEq) =>
% 99.13/16.55 (((powersetI) =>
% 99.13/16.55 (((emptyinPowerset) =>
% 99.13/16.55 (((emptyInPowerset) =>
% 99.13/16.55 (((powersetE) =>
% 99.13/16.55 (((setunionI) =>
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% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
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% 99.13/16.55 surjFuncSet)))))))) @
% 99.13/16.55 (
% 99.13/16.55 (
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% 99.13/16.55 (
% 99.13/16.55 ('#B') @ (
% 99.13/16.55 (
% 99.13/16.55 ('#C') @ in)))) @
% 99.13/16.55 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl236])).
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (exu__Cong) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (powerset__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunion__Cong) =>
% 99.13/16.55 ((
% 99.13/16.55 (exuEu) =>
% 99.13/16.55 ((
% 99.13/16.55 (descr__Cong) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (notequalI2) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (binunionRsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectI) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset5) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectEL) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectLsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset2) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset3) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectER) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (binintersectRsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset4) =>
% 99.13/16.55 ((
% 99.13/16.55 (binintersectSubset1) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (setminusER) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusSubset2) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (setminusILneg) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusIRneg) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusLsub) =>
% 99.13/16.55 ((
% 99.13/16.55 (setminusSubset1) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffE) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffI1) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffI2) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffIneg1) =>
% 99.13/16.55 ((
% 99.13/16.55 (symdiffIneg2) =>
% 99.13/16.55 ((
% 99.13/16.55 (secondinupair) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairIL) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairIR) =>
% 99.13/16.55 ((
% 99.13/16.55 (kpairiskpair) =>
% 99.13/16.55 ((
% 99.13/16.55 (kpairp) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletonsubset) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletoninpowerset) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletoninpowunion) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairset2E) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairsubunion) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairinpowunion) =>
% 99.13/16.55 ((
% 99.13/16.55 (ubforcartprodlem1) =>
% 99.13/16.55 ((
% 99.13/16.55 (ubforcartprodlem2) =>
% 99.13/16.55 ((
% 99.13/16.55 (ubforcartprodlem3) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodpairin) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodmempair1) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodmempair) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunionE2) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunionsingleton1) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunionsingleton2) =>
% 99.13/16.55 ((
% 99.13/16.55 (setunionsingleton) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (ex1I) =>
% 99.13/16.55 ((
% 99.13/16.55 (ex1I2) =>
% 99.13/16.55 ((
% 99.13/16.55 (singletonsuniq) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (kfstpairEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodfstin) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjL2) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjL) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR11) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR12) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR1) =>
% 99.13/16.55 ((
% 99.13/16.55 (upairequniteq) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR2) =>
% 99.13/16.55 ((
% 99.13/16.55 (setukpairinjR) =>
% 99.13/16.55 ((
% 99.13/16.55 (ksndsingleton) =>
% 99.13/16.55 ((
% 99.13/16.55 (ksndpairEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (kpairsurjEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodsndin) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodpairmemEL) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodpairmemER) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodmempaircEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodfstpairEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodsndpairEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (cartprodpairsurjEq) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrI) =>
% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrSub) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
% 99.13/16.55 (dpsetconstrERa) =>
% 99.13/16.55 ((
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% 99.13/16.55 (dpsetconstrEL2) =>
% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.55 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 (descr__Cong) =>
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% 99.13/16.56 ((
% 99.13/16.56 (ubforcartprodlem3) =>
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% 99.13/16.56 (demorgan2a) =>
% 99.13/16.56 ((
% 99.13/16.56 (demorgan2b2) =>
% 99.13/16.56 ((
% 99.13/16.56 (demorgan2b) =>
% 99.13/16.56 ((
% 99.13/16.56 (demorgan2) =>
% 99.13/16.56 ((
% 99.13/16.56 (woz13rule0) =>
% 99.13/16.56 ((
% 99.13/16.56 (woz13rule1) =>
% 99.13/16.56 ((
% 99.13/16.56 (woz13rule2) =>
% 99.13/16.56 ((
% 99.13/16.56 (woz13rule3) =>
% 99.13/16.56 ((
% 99.13/16.56 (woz13rule4) =>
% 99.13/16.56 ((
% 99.13/16.56 (woz1_1) =>
% 99.13/16.56 ((
% 99.13/16.56 (woz1_2) =>
% 99.13/16.56 ((
% 99.13/16.56 (woz1_3) =>
% 99.13/16.56 ((
% 99.13/16.56 (woz1_4) =>
% 99.13/16.56 ((
% 99.13/16.56 (woz1_5) =>
% 99.13/16.56 ((
% 99.13/16.56 (breln1all2) =>
% 99.13/16.56 ((
% 99.13/16.56 (breln1SetBreln1) =>
% 99.13/16.56 ((
% 99.13/16.56 (choice2fnsingleton) =>
% 99.13/16.56 ((
% 99.13/16.56 (setOfPairsIsBReln1) =>
% 99.13/16.56 ((
% 99.13/16.56 (breln1all1) =>
% 99.13/16.56 ((
% 99.13/16.56 (subbreln1) =>
% 99.13/16.56 ((
% 99.13/16.56 (eqbreln1) =>
% 99.13/16.56 ((
% 99.13/16.56 (breln1invprop) =>
% 99.13/16.56 ((
% 99.13/16.56 (breln1invI) =>
% 99.13/16.56 ((
% 99.13/16.56 (breln1invE) =>
% 99.13/16.56 ((
% 99.13/16.56 (breln1compprop) =>
% 99.13/16.56 ((
% 99.13/16.56 (breln1compI) =>
% 99.13/16.56 ((
% 99.13/16.56 (breln1compE) =>
% 99.13/16.56 ((
% 99.13/16.56 (breln1compEex) =>
% 99.13/16.56 ((
% 99.13/16.56 (breln1unionprop) =>
% 99.13/16.56 ((
% 99.13/16.56 (breln1unionIL) =>
% 99.13/16.56 ((
% 99.13/16.56 (breln1unionIR) =>
% 99.13/16.56 ((
% 99.13/16.56 (breln1unionI) =>
% 99.13/16.56 ((
% 99.13/16.56 (breln1unionE) =>
% 99.13/16.56 ((
% 99.13/16.56 (breln1unionEcases) =>
% 99.13/16.56 ((
% 99.13/16.56 (breln1unionCommutes) =>
% 99.13/16.56 ((
% 99.13/16.56 (woz2Ex) =>
% 99.13/16.56 ((
% 99.13/16.56 (woz2W) =>
% 99.13/16.56 ((
% 99.13/16.56 (woz2A) =>
% 99.13/16.56 ((
% 99.13/16.56 (woz2B) =>
% 99.13/16.56 ((
% 99.13/16.56 (image1Ex) =>
% 99.13/16.56 ((
% 99.13/16.56 (image1Ex1) =>
% 99.13/16.56 ((
% 99.13/16.56 (image1Equiv) =>
% 99.13/16.56 ((
% 99.13/16.56 (image1E) =>
% 99.13/16.56 ((
% 99.13/16.56 (image1I) =>
% 99.13/16.56 ((
% 99.13/16.56 (injFuncInInjFuncSet) =>
% 99.13/16.56 ((
% 99.13/16.56 (injFuncSetFuncIn) =>
% 99.13/16.56 ((
% 99.13/16.56 (injFuncSetFuncInj) =>
% 99.13/16.56 ((
% 99.13/16.56 (!!) @ (
% 99.13/16.56 (('#B') @ (
% 99.13/16.56 !!) @
% 99.13/16.56 (
% 99.13/16.56 (
% 99.13/16.56 ('#B') @ (
% 99.13/16.56 (
% 99.13/16.56 ('#B') @ (
% 99.13/16.56 !!))) @
% 99.13/16.56 (
% 99.13/16.56 (
% 99.13/16.56 ('#S') @ (
% 99.13/16.56 (
% 99.13/16.56 ('#B') @ (
% 99.13/16.56 '#S') @
% 99.13/16.56 (
% 99.13/16.56 (
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% 99.13/16.56 (
% 99.13/16.56 ('#B') @ (
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% 99.13/16.56 (
% 99.13/16.56 (
% 99.13/16.56 ('#B') @ (
% 99.13/16.56 (
% 99.13/16.56 ('#B') @ (
% 99.13/16.56 (
% 99.13/16.56 ('#B') @ (
% 99.13/16.56 =>))))) @
% 99.13/16.56 (
% 99.13/16.56 (
% 99.13/16.56 ('#B') @ (
% 99.13/16.56 (
% 99.13/16.56 ('#B') @ (
% 99.13/16.56 (
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% 99.13/16.56 surjFuncSet)))))))) @
% 99.13/16.56 (
% 99.13/16.56 (
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% 99.13/16.56 (
% 99.13/16.56 ('#B') @ (
% 99.13/16.56 (
% 99.13/16.56 ('#C') @ in)))) @
% 99.13/16.56 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl280])).
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% 99.13/16.56 (((setadjoinIR) =>
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% 99.13/16.56 (((quantDeMorgan1) =>
% 99.13/16.56 (((quantDeMorgan2) =>
% 99.13/16.56 (((quantDeMorgan3) =>
% 99.13/16.56 (((quantDeMorgan4) =>
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% 99.13/16.56 ((
% 99.13/16.56 (notdallE) =>
% 99.13/16.56 ((
% 99.13/16.56 (exuI1) =>
% 99.13/16.56 ((
% 99.13/16.56 (exuI3) =>
% 99.13/16.56 ((
% 99.13/16.56 (exuI2) =>
% 99.13/16.56 ((
% 99.13/16.56 (inCongP) =>
% 99.13/16.56 ((
% 99.13/16.56 (in__Cong) =>
% 99.13/16.56 ((
% 99.13/16.56 (exuE3u) =>
% 99.13/16.56 ((
% 99.13/16.56 (exu__Cong) =>
% 99.13/16.56 ((
% 99.13/16.56 (setadjoin__Cong) =>
% 99.13/16.56 ((
% 99.13/16.56 (powerset__Cong) =>
% 99.13/16.56 ((
% 99.13/16.56 (setunion__Cong) =>
% 99.13/16.56 ((
% 99.13/16.56 (exuEu) =>
% 99.13/16.56 ((
% 99.13/16.56 (descr__Cong) =>
% 99.13/16.56 ((
% 99.13/16.56 (dsetconstr__Cong) =>
% 99.13/16.56 ((
% 99.13/16.56 (subsetI1) =>
% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
% 99.13/16.56 (subsetRefl) =>
% 99.13/16.56 ((
% 99.13/16.56 (subsetTrans) =>
% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
% 99.13/16.56 (setextsub) =>
% 99.13/16.56 ((
% 99.13/16.56 (subsetemptysetimpeq) =>
% 99.13/16.56 ((
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% 99.13/16.56 ((
% 99.13/16.56 (powersetE1) =>
% 99.13/16.56 ((
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% 99.13/16.56 ((
% 99.13/16.56 (powersetsubset) =>
% 99.13/16.56 ((
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% 99.13/16.56 ((
% 99.13/16.56 (sepSubset) =>
% 99.13/16.56 ((
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% 99.13/16.56 ((
% 99.13/16.56 (upairset2IR) =>
% 99.13/16.56 ((
% 99.13/16.56 (binunionIR) =>
% 99.13/16.56 ((
% 99.13/16.56 (binunionEcases) =>
% 99.13/16.56 ((
% 99.13/16.56 (binunionE) =>
% 99.13/16.56 ((
% 99.13/16.56 (binunionLsub) =>
% 99.13/16.56 ((
% 99.13/16.56 (binunionRsub) =>
% 99.13/16.56 ((
% 99.13/16.56 (binintersectI) =>
% 99.13/16.56 ((
% 99.13/16.56 (binintersectSubset5) =>
% 99.13/16.56 ((
% 99.13/16.56 (binintersectEL) =>
% 99.13/16.56 ((
% 99.13/16.56 (binintersectLsub) =>
% 99.13/16.56 ((
% 99.13/16.56 (binintersectSubset2) =>
% 99.13/16.56 ((
% 99.13/16.56 (binintersectSubset3) =>
% 99.13/16.56 ((
% 99.13/16.56 (binintersectER) =>
% 99.13/16.56 ((
% 99.13/16.56 (disjointsetsI1) =>
% 99.13/16.56 ((
% 99.13/16.56 (binintersectRsub) =>
% 99.13/16.56 ((
% 99.13/16.56 (binintersectSubset4) =>
% 99.13/16.56 ((
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% 99.13/16.56 ((
% 99.13/16.56 (bs114d) =>
% 99.13/16.56 ((
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% 99.13/16.56 ((
% 99.13/16.56 (setminusEL) =>
% 99.13/16.56 ((
% 99.13/16.56 (setminusER) =>
% 99.13/16.56 ((
% 99.13/16.56 (setminusSubset2) =>
% 99.13/16.56 ((
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% 99.13/16.56 ((
% 99.13/16.56 (setminusELneg) =>
% 99.13/16.56 ((
% 99.13/16.56 (setminusILneg) =>
% 99.13/16.56 ((
% 99.13/16.56 (setminusIRneg) =>
% 99.13/16.56 ((
% 99.13/16.56 (setminusLsub) =>
% 99.13/16.56 ((
% 99.13/16.56 (setminusSubset1) =>
% 99.13/16.56 ((
% 99.13/16.56 (symdiffE) =>
% 99.13/16.56 ((
% 99.13/16.56 (symdiffI1) =>
% 99.13/16.56 ((
% 99.13/16.56 (symdiffI2) =>
% 99.13/16.56 ((
% 99.13/16.56 (symdiffIneg1) =>
% 99.13/16.56 ((
% 99.13/16.56 (symdiffIneg2) =>
% 99.13/16.56 ((
% 99.13/16.56 (secondinupair) =>
% 99.13/16.56 ((
% 99.13/16.56 (setukpairIL) =>
% 99.13/16.56 ((
% 99.13/16.56 (setukpairIR) =>
% 99.13/16.56 ((
% 99.13/16.56 (kpairiskpair) =>
% 99.13/16.56 ((
% 99.13/16.56 (kpairp) =>
% 99.13/16.56 ((
% 99.13/16.56 (singletonsubset) =>
% 99.13/16.56 ((
% 99.13/16.56 (singletoninpowerset) =>
% 99.13/16.56 ((
% 99.13/16.56 (singletoninpowunion) =>
% 99.13/16.56 ((
% 99.13/16.56 (upairset2E) =>
% 99.13/16.56 ((
% 99.13/16.56 (upairsubunion) =>
% 99.13/16.56 ((
% 99.13/16.56 (upairinpowunion) =>
% 99.13/16.56 ((
% 99.13/16.56 (ubforcartprodlem1) =>
% 99.13/16.56 ((
% 99.13/16.56 (ubforcartprodlem2) =>
% 99.13/16.56 ((
% 99.13/16.56 (ubforcartprodlem3) =>
% 99.13/16.56 ((
% 99.13/16.56 (cartprodpairin) =>
% 99.13/16.56 ((
% 99.13/16.56 (cartprodmempair1) =>
% 99.13/16.56 ((
% 99.13/16.56 (cartprodmempair) =>
% 99.13/16.56 ((
% 99.13/16.56 (setunionE2) =>
% 99.13/16.56 ((
% 99.13/16.56 (setunionsingleton1) =>
% 99.13/16.56 ((
% 99.13/16.56 (setunionsingleton2) =>
% 99.13/16.56 ((
% 99.13/16.56 (setunionsingleton) =>
% 99.13/16.56 ((
% 99.13/16.56 (singletonprop) =>
% 99.13/16.56 ((
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% 99.13/16.56 ((
% 99.13/16.56 (ex1I) =>
% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
% 99.13/16.56 (kfstpairEq) =>
% 99.13/16.56 ((
% 99.13/16.56 (cartprodfstin) =>
% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
% 99.13/16.56 (setukpairinjR12) =>
% 99.13/16.56 ((
% 99.13/16.56 (setukpairinjR1) =>
% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
% 99.13/16.56 (setukpairinjR) =>
% 99.13/16.56 ((
% 99.13/16.56 (ksndsingleton) =>
% 99.13/16.56 ((
% 99.13/16.56 (ksndpairEq) =>
% 99.13/16.56 ((
% 99.13/16.56 (kpairsurjEq) =>
% 99.13/16.56 ((
% 99.13/16.56 (cartprodsndin) =>
% 99.13/16.56 ((
% 99.13/16.56 (cartprodpairmemEL) =>
% 99.13/16.56 ((
% 99.13/16.56 (cartprodpairmemER) =>
% 99.13/16.56 ((
% 99.13/16.56 (cartprodmempaircEq) =>
% 99.13/16.56 ((
% 99.13/16.56 (cartprodfstpairEq) =>
% 99.13/16.56 ((
% 99.13/16.56 (cartprodsndpairEq) =>
% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
% 99.13/16.56 (setOfPairsIsBReln) =>
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% 99.13/16.56 (dpsetconstrEL2) =>
% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
% 99.13/16.56 (breln1unionE) =>
% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
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% 99.13/16.56 ((
% 99.13/16.56 (descr__Cong) =>
% 99.13/16.56 ((
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% 99.13/16.57 (funcGraphProp3) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcGraphProp2) =>
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (demorgan2b2) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (demorgan2) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (woz13rule2) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule3) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule4) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_1) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_2) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_3) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_4) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_5) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1all2) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1SetBreln1) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (breln1invI) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1invE) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compprop) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compI) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compE) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compEex) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionprop) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionIL) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionIR) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionI) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionE) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionEcases) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionCommutes) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz2Ex) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (image1Ex1) =>
% 99.13/16.57 ((
% 99.13/16.57 (image1Equiv) =>
% 99.13/16.57 ((
% 99.13/16.57 (image1E) =>
% 99.13/16.57 ((
% 99.13/16.57 (image1I) =>
% 99.13/16.57 ((
% 99.13/16.57 (injFuncInInjFuncSet) =>
% 99.13/16.57 ((
% 99.13/16.57 (injFuncSetFuncIn) =>
% 99.13/16.57 ((
% 99.13/16.57 (injFuncSetFuncInj) =>
% 99.13/16.57 ((
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% 99.13/16.57 (
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% 99.13/16.57 (
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% 99.13/16.57 surjFuncSet)))))))) @
% 99.13/16.57 (
% 99.13/16.57 (
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% 99.13/16.57 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (descr__Cong) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (ubforcartprodlem2) =>
% 99.13/16.57 ((
% 99.13/16.57 (ubforcartprodlem3) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (cartprodmempair) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 (setunionsingleton) =>
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (dpsetconstrEL2) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (funcImageSingleton) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 (ap2p) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcinfuncset) =>
% 99.13/16.57 ((
% 99.13/16.57 (lamProp) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (lam2p) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (brelnall2) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (funcGraphProp1) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcGraphProp3) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcGraphProp2) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcextLem) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcGraphProp4) =>
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (contrasubsetT2) =>
% 99.13/16.57 ((
% 99.13/16.57 (contrasubsetT3) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (doubleComplementE1) =>
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% 99.13/16.57 (doubleComplementSub2) =>
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% 99.13/16.57 (doubleComplementEq) =>
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% 99.13/16.57 (binunionTIRcontra) =>
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% 99.13/16.57 ((
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% 99.13/16.57 (intersectInPowersetIntersectUnions) =>
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% 99.13/16.57 ((
% 99.13/16.57 (inComplementUnionImpInComplement1) =>
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (demorgan1b) =>
% 99.13/16.57 ((
% 99.13/16.57 (demorgan1) =>
% 99.13/16.57 ((
% 99.13/16.57 (demorgan2a) =>
% 99.13/16.57 ((
% 99.13/16.57 (demorgan2b2) =>
% 99.13/16.57 ((
% 99.13/16.57 (demorgan2b) =>
% 99.13/16.57 ((
% 99.13/16.57 (demorgan2) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule0) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule1) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule2) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule3) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule4) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_1) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_2) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_3) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_4) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_5) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1all2) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1SetBreln1) =>
% 99.13/16.57 ((
% 99.13/16.57 (choice2fnsingleton) =>
% 99.13/16.57 ((
% 99.13/16.57 (setOfPairsIsBReln1) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1all1) =>
% 99.13/16.57 ((
% 99.13/16.57 (subbreln1) =>
% 99.13/16.57 ((
% 99.13/16.57 (eqbreln1) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1invprop) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1invI) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1invE) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compprop) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compI) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compE) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compEex) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionprop) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionIL) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionIR) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionI) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionE) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionEcases) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionCommutes) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz2Ex) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz2W) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (woz2B) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (image1Ex1) =>
% 99.13/16.57 ((
% 99.13/16.57 (image1Equiv) =>
% 99.13/16.57 ((
% 99.13/16.57 (image1E) =>
% 99.13/16.57 ((
% 99.13/16.57 (image1I) =>
% 99.13/16.57 ((
% 99.13/16.57 (injFuncInInjFuncSet) =>
% 99.13/16.57 ((
% 99.13/16.57 (injFuncSetFuncIn) =>
% 99.13/16.57 ((
% 99.13/16.57 (injFuncSetFuncInj) =>
% 99.13/16.57 ((
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% 99.13/16.57 (
% 99.13/16.57 (
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% 99.13/16.57 (
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% 99.13/16.57 (
% 99.13/16.57 (
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% 99.13/16.57 (
% 99.13/16.57 (
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% 99.13/16.57 (
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% 99.13/16.57 surjFuncSet)))))))) @
% 99.13/16.57 (
% 99.13/16.57 (
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% 99.13/16.57 (
% 99.13/16.57 ('#B') @ (
% 99.13/16.57 (
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% 99.13/16.57 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (exuE3u) =>
% 99.13/16.57 ((
% 99.13/16.57 (exu__Cong) =>
% 99.13/16.57 ((
% 99.13/16.57 (setadjoin__Cong) =>
% 99.13/16.57 ((
% 99.13/16.57 (powerset__Cong) =>
% 99.13/16.57 ((
% 99.13/16.57 (setunion__Cong) =>
% 99.13/16.57 ((
% 99.13/16.57 (exuEu) =>
% 99.13/16.57 ((
% 99.13/16.57 (descr__Cong) =>
% 99.13/16.57 ((
% 99.13/16.57 (dsetconstr__Cong) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (subsetE2) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (binintersectSubset3) =>
% 99.13/16.57 ((
% 99.13/16.57 (binintersectER) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (setminusEL) =>
% 99.13/16.57 ((
% 99.13/16.57 (setminusER) =>
% 99.13/16.57 ((
% 99.13/16.57 (setminusSubset2) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (setukpairIR) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (kpairp) =>
% 99.13/16.57 ((
% 99.13/16.57 (singletonsubset) =>
% 99.13/16.57 ((
% 99.13/16.57 (singletoninpowerset) =>
% 99.13/16.57 ((
% 99.13/16.57 (singletoninpowunion) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (upairsubunion) =>
% 99.13/16.57 ((
% 99.13/16.57 (upairinpowunion) =>
% 99.13/16.57 ((
% 99.13/16.57 (ubforcartprodlem1) =>
% 99.13/16.57 ((
% 99.13/16.57 (ubforcartprodlem2) =>
% 99.13/16.57 ((
% 99.13/16.57 (ubforcartprodlem3) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodpairin) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodmempair1) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodmempair) =>
% 99.13/16.57 ((
% 99.13/16.57 (setunionE2) =>
% 99.13/16.57 ((
% 99.13/16.57 (setunionsingleton1) =>
% 99.13/16.57 ((
% 99.13/16.57 (setunionsingleton2) =>
% 99.13/16.57 ((
% 99.13/16.57 (setunionsingleton) =>
% 99.13/16.57 ((
% 99.13/16.57 (singletonprop) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (ex1I) =>
% 99.13/16.57 ((
% 99.13/16.57 (ex1I2) =>
% 99.13/16.57 ((
% 99.13/16.57 (singletonsuniq) =>
% 99.13/16.57 ((
% 99.13/16.57 (setukpairinjL1) =>
% 99.13/16.57 ((
% 99.13/16.57 (kfstsingleton) =>
% 99.13/16.57 ((
% 99.13/16.57 (theprop) =>
% 99.13/16.57 ((
% 99.13/16.57 (kfstpairEq) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodfstin) =>
% 99.13/16.57 ((
% 99.13/16.57 (setukpairinjL2) =>
% 99.13/16.57 ((
% 99.13/16.57 (setukpairinjL) =>
% 99.13/16.57 ((
% 99.13/16.57 (setukpairinjR11) =>
% 99.13/16.57 ((
% 99.13/16.57 (setukpairinjR12) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 (cartprodpairmemER) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodmempaircEq) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodfstpairEq) =>
% 99.13/16.57 ((
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% 99.13/16.57 (cartprodpairsurjEq) =>
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (brelnall2) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (funcGraphProp3) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcGraphProp2) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcextLem) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcGraphProp4) =>
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (contrasubsetT3) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (doubleComplementE1) =>
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% 99.13/16.57 (doubleComplementSub2) =>
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% 99.13/16.57 (doubleComplementEq) =>
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% 99.13/16.57 (complementTnotintersectT) =>
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% 99.13/16.57 (inIntersectImpInUnion) =>
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% 99.13/16.57 (inIntersectImpInIntersectUnions) =>
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% 99.13/16.57 (intersectInPowersetIntersectUnions) =>
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (demorgan1b) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (demorgan2a) =>
% 99.13/16.57 ((
% 99.13/16.57 (demorgan2b2) =>
% 99.13/16.57 ((
% 99.13/16.57 (demorgan2b) =>
% 99.13/16.57 ((
% 99.13/16.57 (demorgan2) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule0) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule1) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule2) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule3) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule4) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_1) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_2) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_3) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_4) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_5) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1all2) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1SetBreln1) =>
% 99.13/16.57 ((
% 99.13/16.57 (choice2fnsingleton) =>
% 99.13/16.57 ((
% 99.13/16.57 (setOfPairsIsBReln1) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1all1) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (eqbreln1) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1invprop) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1invI) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1invE) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compprop) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compI) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compE) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compEex) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionprop) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionIL) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionIR) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionI) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionE) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionEcases) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionCommutes) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz2Ex) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz2W) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (woz2B) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (image1Ex1) =>
% 99.13/16.57 ((
% 99.13/16.57 (image1Equiv) =>
% 99.13/16.57 ((
% 99.13/16.57 (image1E) =>
% 99.13/16.57 ((
% 99.13/16.57 (image1I) =>
% 99.13/16.57 ((
% 99.13/16.57 (injFuncInInjFuncSet) =>
% 99.13/16.57 ((
% 99.13/16.57 (injFuncSetFuncIn) =>
% 99.13/16.57 ((
% 99.13/16.57 (injFuncSetFuncInj) =>
% 99.13/16.57 ((
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% 99.13/16.57 (
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% 99.13/16.57 (
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% 99.13/16.57 surjFuncSet)))))))) @
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% 99.13/16.57 (
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% 99.13/16.57 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (exu__Cong) =>
% 99.13/16.57 ((
% 99.13/16.57 (setadjoin__Cong) =>
% 99.13/16.57 ((
% 99.13/16.57 (powerset__Cong) =>
% 99.13/16.57 ((
% 99.13/16.57 (setunion__Cong) =>
% 99.13/16.57 ((
% 99.13/16.57 (exuEu) =>
% 99.13/16.57 ((
% 99.13/16.57 (descr__Cong) =>
% 99.13/16.57 ((
% 99.13/16.57 (dsetconstr__Cong) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (binintersectSubset3) =>
% 99.13/16.57 ((
% 99.13/16.57 (binintersectER) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (binintersectSubset4) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (kpairp) =>
% 99.13/16.57 ((
% 99.13/16.57 (singletonsubset) =>
% 99.13/16.57 ((
% 99.13/16.57 (singletoninpowerset) =>
% 99.13/16.57 ((
% 99.13/16.57 (singletoninpowunion) =>
% 99.13/16.57 ((
% 99.13/16.57 (upairset2E) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (upairinpowunion) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (ubforcartprodlem2) =>
% 99.13/16.57 ((
% 99.13/16.57 (ubforcartprodlem3) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodpairin) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodmempair1) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodmempair) =>
% 99.13/16.57 ((
% 99.13/16.57 (setunionE2) =>
% 99.13/16.57 ((
% 99.13/16.57 (setunionsingleton1) =>
% 99.13/16.57 ((
% 99.13/16.57 (setunionsingleton2) =>
% 99.13/16.57 ((
% 99.13/16.57 (setunionsingleton) =>
% 99.13/16.57 ((
% 99.13/16.57 (singletonprop) =>
% 99.13/16.57 ((
% 99.13/16.57 (ex1E1) =>
% 99.13/16.57 ((
% 99.13/16.57 (ex1I) =>
% 99.13/16.57 ((
% 99.13/16.57 (ex1I2) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (demorgan2) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (woz13rule2) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule3) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule4) =>
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% 99.13/16.57 ((
% 99.13/16.57 (woz1_2) =>
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% 99.13/16.57 (woz1_3) =>
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% 99.13/16.57 (woz1_4) =>
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% 99.13/16.57 (woz1_5) =>
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% 99.13/16.57 ((
% 99.13/16.57 (breln1SetBreln1) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (breln1invE) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compprop) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (breln1compE) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compEex) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 (descr__Cong) =>
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% 99.13/16.57 (cartprodpairmemER) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodmempaircEq) =>
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% 99.13/16.57 (cartprodfstpairEq) =>
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% 99.13/16.57 (cartprodsndpairEq) =>
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% 99.13/16.57 (cartprodpairsurjEq) =>
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% 99.13/16.57 (funcImageSingleton) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (funcinfuncset) =>
% 99.13/16.57 ((
% 99.13/16.57 (lamProp) =>
% 99.13/16.57 ((
% 99.13/16.57 (lamp) =>
% 99.13/16.57 ((
% 99.13/16.57 (lam2p) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (brelnall2) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (funcGraphProp3) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcGraphProp2) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcextLem) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcGraphProp4) =>
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% 99.13/16.57 (eta1) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 (binintersectTERcontra) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (contrasubsetT2) =>
% 99.13/16.57 ((
% 99.13/16.57 (contrasubsetT3) =>
% 99.13/16.57 ((
% 99.13/16.57 (doubleComplementI1) =>
% 99.13/16.57 ((
% 99.13/16.57 (doubleComplementE1) =>
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% 99.13/16.57 ((
% 99.13/16.57 (doubleComplementSub2) =>
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% 99.13/16.57 (doubleComplementEq) =>
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% 99.13/16.57 (complementTnotintersectT) =>
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% 99.13/16.57 (complementSubsetComplementIntersect) =>
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% 99.13/16.57 (complementInPowersetComplementIntersect) =>
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% 99.13/16.57 ((
% 99.13/16.57 (binunionTIRcontra) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (inIntersectImpInUnion2) =>
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% 99.13/16.57 (inIntersectImpInIntersectUnions) =>
% 99.13/16.57 ((
% 99.13/16.57 (intersectInPowersetIntersectUnions) =>
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% 99.13/16.57 (inComplementUnionImpNotIn1) =>
% 99.13/16.57 ((
% 99.13/16.57 (inComplementUnionImpInComplement1) =>
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% 99.13/16.57 ((
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% 99.13/16.57 (demorgan2a2) =>
% 99.13/16.57 ((
% 99.13/16.57 (demorgan1a) =>
% 99.13/16.57 ((
% 99.13/16.57 (demorgan1b) =>
% 99.13/16.57 ((
% 99.13/16.57 (demorgan1) =>
% 99.13/16.57 ((
% 99.13/16.57 (demorgan2a) =>
% 99.13/16.57 ((
% 99.13/16.57 (demorgan2b2) =>
% 99.13/16.57 ((
% 99.13/16.57 (demorgan2b) =>
% 99.13/16.57 ((
% 99.13/16.57 (demorgan2) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule0) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule1) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule2) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule3) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz13rule4) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_1) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_2) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_3) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_4) =>
% 99.13/16.57 ((
% 99.13/16.57 (woz1_5) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1all2) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1SetBreln1) =>
% 99.13/16.57 ((
% 99.13/16.57 (choice2fnsingleton) =>
% 99.13/16.57 ((
% 99.13/16.57 (setOfPairsIsBReln1) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1all1) =>
% 99.13/16.57 ((
% 99.13/16.57 (subbreln1) =>
% 99.13/16.57 ((
% 99.13/16.57 (eqbreln1) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (breln1invI) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1invE) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compprop) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compI) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compE) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1compEex) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionprop) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionIL) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionIR) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionI) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionE) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionEcases) =>
% 99.13/16.57 ((
% 99.13/16.57 (breln1unionCommutes) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
% 99.13/16.57 (image1Ex1) =>
% 99.13/16.57 ((
% 99.13/16.57 (image1Equiv) =>
% 99.13/16.57 ((
% 99.13/16.57 (image1E) =>
% 99.13/16.57 ((
% 99.13/16.57 (image1I) =>
% 99.13/16.57 ((
% 99.13/16.57 (injFuncInInjFuncSet) =>
% 99.13/16.57 ((
% 99.13/16.57 (injFuncSetFuncIn) =>
% 99.13/16.57 ((
% 99.13/16.57 (injFuncSetFuncInj) =>
% 99.13/16.57 ((
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% 99.13/16.57 (
% 99.13/16.57 (
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% 99.13/16.57 surjFuncSet)))))))) @
% 99.13/16.57 (
% 99.13/16.57 (
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% 99.13/16.57 (
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% 99.13/16.57 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl376])).
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% 99.13/16.57 ((
% 99.13/16.57 (exuEu) =>
% 99.13/16.57 ((
% 99.13/16.57 (descr__Cong) =>
% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 ((
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% 99.13/16.57 (setminusIRneg) =>
% 99.13/16.57 ((
% 99.13/16.57 (setminusLsub) =>
% 99.13/16.57 ((
% 99.13/16.57 (setminusSubset1) =>
% 99.13/16.57 ((
% 99.13/16.57 (symdiffE) =>
% 99.13/16.57 ((
% 99.13/16.57 (symdiffI1) =>
% 99.13/16.57 ((
% 99.13/16.57 (symdiffI2) =>
% 99.13/16.57 ((
% 99.13/16.57 (symdiffIneg1) =>
% 99.13/16.57 ((
% 99.13/16.57 (symdiffIneg2) =>
% 99.13/16.57 ((
% 99.13/16.57 (secondinupair) =>
% 99.13/16.57 ((
% 99.13/16.57 (setukpairIL) =>
% 99.13/16.57 ((
% 99.13/16.57 (setukpairIR) =>
% 99.13/16.57 ((
% 99.13/16.57 (kpairiskpair) =>
% 99.13/16.57 ((
% 99.13/16.57 (kpairp) =>
% 99.13/16.57 ((
% 99.13/16.57 (singletonsubset) =>
% 99.13/16.57 ((
% 99.13/16.57 (singletoninpowerset) =>
% 99.13/16.57 ((
% 99.13/16.57 (singletoninpowunion) =>
% 99.13/16.57 ((
% 99.13/16.57 (upairset2E) =>
% 99.13/16.57 ((
% 99.13/16.57 (upairsubunion) =>
% 99.13/16.57 ((
% 99.13/16.57 (upairinpowunion) =>
% 99.13/16.57 ((
% 99.13/16.57 (ubforcartprodlem1) =>
% 99.13/16.57 ((
% 99.13/16.57 (ubforcartprodlem2) =>
% 99.13/16.57 ((
% 99.13/16.57 (ubforcartprodlem3) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodpairin) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodmempair1) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodmempair) =>
% 99.13/16.57 ((
% 99.13/16.57 (setunionE2) =>
% 99.13/16.57 ((
% 99.13/16.57 (setunionsingleton1) =>
% 99.13/16.57 ((
% 99.13/16.57 (setunionsingleton2) =>
% 99.13/16.57 ((
% 99.13/16.57 (setunionsingleton) =>
% 99.13/16.57 ((
% 99.13/16.57 (singletonprop) =>
% 99.13/16.57 ((
% 99.13/16.57 (ex1E1) =>
% 99.13/16.57 ((
% 99.13/16.57 (ex1I) =>
% 99.13/16.57 ((
% 99.13/16.57 (ex1I2) =>
% 99.13/16.57 ((
% 99.13/16.57 (singletonsuniq) =>
% 99.13/16.57 ((
% 99.13/16.57 (setukpairinjL1) =>
% 99.13/16.57 ((
% 99.13/16.57 (kfstsingleton) =>
% 99.13/16.57 ((
% 99.13/16.57 (theprop) =>
% 99.13/16.57 ((
% 99.13/16.57 (kfstpairEq) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodfstin) =>
% 99.13/16.57 ((
% 99.13/16.57 (setukpairinjL2) =>
% 99.13/16.57 ((
% 99.13/16.57 (setukpairinjL) =>
% 99.13/16.57 ((
% 99.13/16.57 (setukpairinjR11) =>
% 99.13/16.57 ((
% 99.13/16.57 (setukpairinjR12) =>
% 99.13/16.57 ((
% 99.13/16.57 (setukpairinjR1) =>
% 99.13/16.57 ((
% 99.13/16.57 (upairequniteq) =>
% 99.13/16.57 ((
% 99.13/16.57 (setukpairinjR2) =>
% 99.13/16.57 ((
% 99.13/16.57 (setukpairinjR) =>
% 99.13/16.57 ((
% 99.13/16.57 (ksndsingleton) =>
% 99.13/16.57 ((
% 99.13/16.57 (ksndpairEq) =>
% 99.13/16.57 ((
% 99.13/16.57 (kpairsurjEq) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodsndin) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodpairmemEL) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodpairmemER) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodmempaircEq) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodfstpairEq) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodsndpairEq) =>
% 99.13/16.57 ((
% 99.13/16.57 (cartprodpairsurjEq) =>
% 99.13/16.57 ((
% 99.13/16.57 (dpsetconstrI) =>
% 99.13/16.57 ((
% 99.13/16.57 (dpsetconstrSub) =>
% 99.13/16.57 ((
% 99.13/16.57 (setOfPairsIsBReln) =>
% 99.13/16.57 ((
% 99.13/16.57 (dpsetconstrERa) =>
% 99.13/16.57 ((
% 99.13/16.57 (dpsetconstrEL1) =>
% 99.13/16.57 ((
% 99.13/16.57 (dpsetconstrEL2) =>
% 99.13/16.57 ((
% 99.13/16.57 (dpsetconstrER) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcImageSingleton) =>
% 99.13/16.57 ((
% 99.13/16.57 (apProp) =>
% 99.13/16.57 ((
% 99.13/16.57 (app) =>
% 99.13/16.57 ((
% 99.13/16.57 (infuncsetfunc) =>
% 99.13/16.57 ((
% 99.13/16.57 (ap2p) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcinfuncset) =>
% 99.13/16.57 ((
% 99.13/16.57 (lamProp) =>
% 99.13/16.57 ((
% 99.13/16.57 (lamp) =>
% 99.13/16.57 ((
% 99.13/16.57 (lam2p) =>
% 99.13/16.57 ((
% 99.13/16.57 (brelnall1) =>
% 99.13/16.57 ((
% 99.13/16.57 (brelnall2) =>
% 99.13/16.57 ((
% 99.13/16.57 (ex1E2) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcGraphProp1) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcGraphProp3) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcGraphProp2) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcextLem) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcGraphProp4) =>
% 99.13/16.57 ((
% 99.13/16.57 (subbreln) =>
% 99.13/16.57 ((
% 99.13/16.57 (eqbreln) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcext) =>
% 99.13/16.57 ((
% 99.13/16.57 (funcext2) =>
% 99.13/16.57 ((
% 99.13/16.57 (ap2apEq1) =>
% 99.13/16.57 ((
% 99.13/16.57 (ap2apEq2) =>
% 99.13/16.57 ((
% 99.13/16.57 (beta1) =>
% 99.13/16.57 ((
% 99.13/16.57 (eta1) =>
% 99.13/16.57 ((
% 99.13/16.57 (lam2lamEq) =>
% 99.13/16.57 ((
% 99.13/16.57 (beta2) =>
% 99.13/16.57 ((
% 99.13/16.57 (eta2) =>
% 99.13/16.57 ((
% 99.13/16.58 (iffalseProp1) =>
% 99.13/16.58 ((
% 99.13/16.58 (iffalseProp2) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrueProp1) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrueProp2) =>
% 99.13/16.58 ((
% 99.13/16.58 (ifSingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (ifp) =>
% 99.13/16.58 ((
% 99.13/16.58 (theeq) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrue) =>
% 99.13/16.58 ((
% 99.13/16.58 (iffalse) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrueorfalse) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (setextT) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetTI) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetTI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetTE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectTELcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectTERcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT1) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT2) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT3) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementSub1) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementSub2) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTnotintersectT) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementImpComplementIntersect) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementSubsetComplementIntersect) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementInPowersetComplementIntersect) =>
% 99.13/16.58 ((
% 99.13/16.58 (contraSubsetComplement) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTcontraSubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTILcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTIRcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (inIntersectImpInUnion) =>
% 99.13/16.58 ((
% 99.13/16.58 (inIntersectImpInUnion2) =>
% 99.13/16.58 ((
% 99.13/16.58 (inIntersectImpInIntersectUnions) =>
% 99.13/16.58 ((
% 99.13/16.58 (intersectInPowersetIntersectUnions) =>
% 99.13/16.58 ((
% 99.13/16.58 (inComplementUnionImpNotIn1) =>
% 99.13/16.58 ((
% 99.13/16.58 (inComplementUnionImpInComplement1) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTE) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTEcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2a1) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementUnionInPowersetComplement) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2a2) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan1a) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan1b) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan1) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2a) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2b2) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2b) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule0) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule1) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule2) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule3) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule4) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_1) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_2) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_3) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_4) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_5) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1all2) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1SetBreln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (choice2fnsingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (setOfPairsIsBReln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1all1) =>
% 99.13/16.58 ((
% 99.13/16.58 (subbreln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqbreln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1invprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1invI) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1invE) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compI) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compE) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compEex) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionIL) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionIR) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionI) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionE) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionEcases) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionCommutes) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2Ex) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2W) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2A) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2B) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1Ex) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1Ex1) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1Equiv) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1E) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1I) =>
% 99.13/16.58 ((
% 99.13/16.58 (injFuncInInjFuncSet) =>
% 99.13/16.58 ((
% 99.13/16.58 (injFuncSetFuncIn) =>
% 99.13/16.58 ((
% 99.13/16.58 (injFuncSetFuncInj) =>
% 99.13/16.58 ((
% 99.13/16.58 (!!) @ (
% 99.13/16.58 (('#B') @ (
% 99.13/16.58 !!) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 !!))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#S') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 '#S') @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 '#S'))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 =>))))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#C') @ in)))) @
% 99.13/16.58 surjFuncSet)))))))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#C') @ in)))) @
% 99.13/16.58 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl384])).
% 99.13/16.58 thf(zip_derived_cl400, plain,
% 99.13/16.58 (~ (((setunionI) =>
% 99.13/16.58 (((setunionE) =>
% 99.13/16.58 (((subPowSU) =>
% 99.13/16.58 (((exuE2) =>
% 99.13/16.58 (((nonemptyImpWitness) =>
% 99.13/16.58 (((uniqinunit) =>
% 99.13/16.58 (((notinsingleton) =>
% 99.13/16.58 (((eqinunit) =>
% 99.13/16.58 (((singletonsswitch) =>
% 99.13/16.58 (((upairsetE) =>
% 99.13/16.58 (((upairsetIL) =>
% 99.13/16.58 (((upairsetIR) =>
% 99.13/16.58 (((emptyE1) =>
% 99.13/16.58 (((vacuousDall) =>
% 99.13/16.58 (((quantDeMorgan1) =>
% 99.13/16.58 (((quantDeMorgan2) =>
% 99.13/16.58 (((quantDeMorgan3) =>
% 99.13/16.58 (((quantDeMorgan4) =>
% 99.13/16.58 (((prop2setI) =>
% 99.13/16.58 (((prop2set2propI) =>
% 99.13/16.58 (((notdexE) =>
% 99.13/16.58 (((notdallE) =>
% 99.13/16.58 (((exuI1) =>
% 99.13/16.58 (((exuI3) =>
% 99.13/16.58 (((exuI2) =>
% 99.13/16.58 (((inCongP) =>
% 99.13/16.58 (((in__Cong) =>
% 99.13/16.58 (((exuE3u) =>
% 99.13/16.58 (((exu__Cong) =>
% 99.13/16.58 (((setadjoin__Cong) =>
% 99.13/16.58 ((
% 99.13/16.58 (powerset__Cong) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunion__Cong) =>
% 99.13/16.58 ((
% 99.13/16.58 (exuEu) =>
% 99.13/16.58 ((
% 99.13/16.58 (descr__Cong) =>
% 99.13/16.58 ((
% 99.13/16.58 (dsetconstr__Cong) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqimpsubset2) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqimpsubset1) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetI2) =>
% 99.13/16.58 ((
% 99.13/16.58 (emptysetsubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetE) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetE2) =>
% 99.13/16.58 ((
% 99.13/16.58 (notsubsetI) =>
% 99.13/16.58 ((
% 99.13/16.58 (notequalI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (notequalI2) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetRefl) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetTrans) =>
% 99.13/16.58 ((
% 99.13/16.58 (setadjoinSub) =>
% 99.13/16.58 ((
% 99.13/16.58 (setadjoinSub2) =>
% 99.13/16.58 ((
% 99.13/16.58 (subset2powerset) =>
% 99.13/16.58 ((
% 99.13/16.58 (setextsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetemptysetimpeq) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (inPowerset) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetsubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (sepInPowerset) =>
% 99.13/16.58 ((
% 99.13/16.58 (sepSubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionIL) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairset2IR) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionIR) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionEcases) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionE) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionLsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionRsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectI) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset5) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectEL) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectLsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset2) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset3) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectER) =>
% 99.13/16.58 ((
% 99.13/16.58 (disjointsetsI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectRsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset4) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset1) =>
% 99.13/16.58 ((
% 99.13/16.58 (bs114d) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusI) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusEL) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusER) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusSubset2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusERneg) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusELneg) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusILneg) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusIRneg) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusLsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusSubset1) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffE) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffI2) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffIneg1) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffIneg2) =>
% 99.13/16.58 ((
% 99.13/16.58 (secondinupair) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairIL) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairIR) =>
% 99.13/16.58 ((
% 99.13/16.58 (kpairiskpair) =>
% 99.13/16.58 ((
% 99.13/16.58 (kpairp) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletonsubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletoninpowerset) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletoninpowunion) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairset2E) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairsubunion) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairinpowunion) =>
% 99.13/16.58 ((
% 99.13/16.58 (ubforcartprodlem1) =>
% 99.13/16.58 ((
% 99.13/16.58 (ubforcartprodlem2) =>
% 99.13/16.58 ((
% 99.13/16.58 (ubforcartprodlem3) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodpairin) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodmempair1) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodmempair) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunionE2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunionsingleton1) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunionsingleton2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunionsingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletonprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (ex1E1) =>
% 99.13/16.58 ((
% 99.13/16.58 (ex1I) =>
% 99.13/16.58 ((
% 99.13/16.58 (ex1I2) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletonsuniq) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjL1) =>
% 99.13/16.58 ((
% 99.13/16.58 (kfstsingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (theprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (kfstpairEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodfstin) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjL2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjL) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR11) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR12) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR1) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairequniteq) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR) =>
% 99.13/16.58 ((
% 99.13/16.58 (ksndsingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (ksndpairEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (kpairsurjEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodsndin) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodpairmemEL) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodpairmemER) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodmempaircEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodfstpairEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodsndpairEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodpairsurjEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrI) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrSub) =>
% 99.13/16.58 ((
% 99.13/16.58 (setOfPairsIsBReln) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrERa) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrEL1) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrEL2) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrER) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcImageSingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (apProp) =>
% 99.13/16.58 ((
% 99.13/16.58 (app) =>
% 99.13/16.58 ((
% 99.13/16.58 (infuncsetfunc) =>
% 99.13/16.58 ((
% 99.13/16.58 (ap2p) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcinfuncset) =>
% 99.13/16.58 ((
% 99.13/16.58 (lamProp) =>
% 99.13/16.58 ((
% 99.13/16.58 (lamp) =>
% 99.13/16.58 ((
% 99.13/16.58 (lam2p) =>
% 99.13/16.58 ((
% 99.13/16.58 (brelnall1) =>
% 99.13/16.58 ((
% 99.13/16.58 (brelnall2) =>
% 99.13/16.58 ((
% 99.13/16.58 (ex1E2) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcGraphProp1) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcGraphProp3) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcGraphProp2) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcextLem) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcGraphProp4) =>
% 99.13/16.58 ((
% 99.13/16.58 (subbreln) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqbreln) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcext) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcext2) =>
% 99.13/16.58 ((
% 99.13/16.58 (ap2apEq1) =>
% 99.13/16.58 ((
% 99.13/16.58 (ap2apEq2) =>
% 99.13/16.58 ((
% 99.13/16.58 (beta1) =>
% 99.13/16.58 ((
% 99.13/16.58 (eta1) =>
% 99.13/16.58 ((
% 99.13/16.58 (lam2lamEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (beta2) =>
% 99.13/16.58 ((
% 99.13/16.58 (eta2) =>
% 99.13/16.58 ((
% 99.13/16.58 (iffalseProp1) =>
% 99.13/16.58 ((
% 99.13/16.58 (iffalseProp2) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrueProp1) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrueProp2) =>
% 99.13/16.58 ((
% 99.13/16.58 (ifSingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (ifp) =>
% 99.13/16.58 ((
% 99.13/16.58 (theeq) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrue) =>
% 99.13/16.58 ((
% 99.13/16.58 (iffalse) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrueorfalse) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (setextT) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetTI) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetTI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetTE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectTELcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectTERcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT1) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT2) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT3) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementSub1) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementSub2) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTnotintersectT) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementImpComplementIntersect) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementSubsetComplementIntersect) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementInPowersetComplementIntersect) =>
% 99.13/16.58 ((
% 99.13/16.58 (contraSubsetComplement) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTcontraSubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTILcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTIRcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (inIntersectImpInUnion) =>
% 99.13/16.58 ((
% 99.13/16.58 (inIntersectImpInUnion2) =>
% 99.13/16.58 ((
% 99.13/16.58 (inIntersectImpInIntersectUnions) =>
% 99.13/16.58 ((
% 99.13/16.58 (intersectInPowersetIntersectUnions) =>
% 99.13/16.58 ((
% 99.13/16.58 (inComplementUnionImpNotIn1) =>
% 99.13/16.58 ((
% 99.13/16.58 (inComplementUnionImpInComplement1) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTE) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTEcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2a1) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementUnionInPowersetComplement) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2a2) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan1a) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan1b) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan1) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2a) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2b2) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2b) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule0) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule1) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule2) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule3) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule4) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_1) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_2) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_3) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_4) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_5) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1all2) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1SetBreln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (choice2fnsingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (setOfPairsIsBReln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1all1) =>
% 99.13/16.58 ((
% 99.13/16.58 (subbreln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqbreln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1invprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1invI) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1invE) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compI) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compE) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compEex) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionIL) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionIR) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionI) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionE) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionEcases) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionCommutes) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2Ex) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2W) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2A) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2B) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1Ex) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1Ex1) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1Equiv) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1E) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1I) =>
% 99.13/16.58 ((
% 99.13/16.58 (injFuncInInjFuncSet) =>
% 99.13/16.58 ((
% 99.13/16.58 (injFuncSetFuncIn) =>
% 99.13/16.58 ((
% 99.13/16.58 (injFuncSetFuncInj) =>
% 99.13/16.58 ((
% 99.13/16.58 (!!) @ (
% 99.13/16.58 (('#B') @ (
% 99.13/16.58 !!) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 !!))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#S') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 '#S') @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 '#S'))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 =>))))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#C') @ in)))) @
% 99.13/16.58 surjFuncSet)))))))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#C') @ in)))) @
% 99.13/16.58 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl392])).
% 99.13/16.58 thf(zip_derived_cl408, plain,
% 99.13/16.58 (~ (((setunionE) =>
% 99.13/16.58 (((subPowSU) =>
% 99.13/16.58 (((exuE2) =>
% 99.13/16.58 (((nonemptyImpWitness) =>
% 99.13/16.58 (((uniqinunit) =>
% 99.13/16.58 (((notinsingleton) =>
% 99.13/16.58 (((eqinunit) =>
% 99.13/16.58 (((singletonsswitch) =>
% 99.13/16.58 (((upairsetE) =>
% 99.13/16.58 (((upairsetIL) =>
% 99.13/16.58 (((upairsetIR) =>
% 99.13/16.58 (((emptyE1) =>
% 99.13/16.58 (((vacuousDall) =>
% 99.13/16.58 (((quantDeMorgan1) =>
% 99.13/16.58 (((quantDeMorgan2) =>
% 99.13/16.58 (((quantDeMorgan3) =>
% 99.13/16.58 (((quantDeMorgan4) =>
% 99.13/16.58 (((prop2setI) =>
% 99.13/16.58 (((prop2set2propI) =>
% 99.13/16.58 (((notdexE) =>
% 99.13/16.58 (((notdallE) =>
% 99.13/16.58 (((exuI1) =>
% 99.13/16.58 (((exuI3) =>
% 99.13/16.58 (((exuI2) =>
% 99.13/16.58 (((inCongP) =>
% 99.13/16.58 (((in__Cong) =>
% 99.13/16.58 (((exuE3u) =>
% 99.13/16.58 (((exu__Cong) =>
% 99.13/16.58 (((setadjoin__Cong) =>
% 99.13/16.58 (((powerset__Cong) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunion__Cong) =>
% 99.13/16.58 ((
% 99.13/16.58 (exuEu) =>
% 99.13/16.58 ((
% 99.13/16.58 (descr__Cong) =>
% 99.13/16.58 ((
% 99.13/16.58 (dsetconstr__Cong) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqimpsubset2) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqimpsubset1) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetI2) =>
% 99.13/16.58 ((
% 99.13/16.58 (emptysetsubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetE) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetE2) =>
% 99.13/16.58 ((
% 99.13/16.58 (notsubsetI) =>
% 99.13/16.58 ((
% 99.13/16.58 (notequalI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (notequalI2) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetRefl) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetTrans) =>
% 99.13/16.58 ((
% 99.13/16.58 (setadjoinSub) =>
% 99.13/16.58 ((
% 99.13/16.58 (setadjoinSub2) =>
% 99.13/16.58 ((
% 99.13/16.58 (subset2powerset) =>
% 99.13/16.58 ((
% 99.13/16.58 (setextsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetemptysetimpeq) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (inPowerset) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetsubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (sepInPowerset) =>
% 99.13/16.58 ((
% 99.13/16.58 (sepSubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionIL) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairset2IR) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionIR) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionEcases) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionE) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionLsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionRsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectI) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset5) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectEL) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectLsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset2) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset3) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectER) =>
% 99.13/16.58 ((
% 99.13/16.58 (disjointsetsI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectRsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset4) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset1) =>
% 99.13/16.58 ((
% 99.13/16.58 (bs114d) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusI) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusEL) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusER) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusSubset2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusERneg) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusELneg) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusILneg) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusIRneg) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusLsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusSubset1) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffE) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffI2) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffIneg1) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffIneg2) =>
% 99.13/16.58 ((
% 99.13/16.58 (secondinupair) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairIL) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairIR) =>
% 99.13/16.58 ((
% 99.13/16.58 (kpairiskpair) =>
% 99.13/16.58 ((
% 99.13/16.58 (kpairp) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletonsubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletoninpowerset) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletoninpowunion) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairset2E) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairsubunion) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairinpowunion) =>
% 99.13/16.58 ((
% 99.13/16.58 (ubforcartprodlem1) =>
% 99.13/16.58 ((
% 99.13/16.58 (ubforcartprodlem2) =>
% 99.13/16.58 ((
% 99.13/16.58 (ubforcartprodlem3) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodpairin) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodmempair1) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodmempair) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunionE2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunionsingleton1) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunionsingleton2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunionsingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletonprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (ex1E1) =>
% 99.13/16.58 ((
% 99.13/16.58 (ex1I) =>
% 99.13/16.58 ((
% 99.13/16.58 (ex1I2) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletonsuniq) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjL1) =>
% 99.13/16.58 ((
% 99.13/16.58 (kfstsingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (theprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (kfstpairEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodfstin) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjL2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjL) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR11) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR12) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR1) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairequniteq) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR) =>
% 99.13/16.58 ((
% 99.13/16.58 (ksndsingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (ksndpairEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (kpairsurjEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodsndin) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodpairmemEL) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodpairmemER) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodmempaircEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodfstpairEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodsndpairEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodpairsurjEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrI) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrSub) =>
% 99.13/16.58 ((
% 99.13/16.58 (setOfPairsIsBReln) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrERa) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrEL1) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrEL2) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrER) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcImageSingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (apProp) =>
% 99.13/16.58 ((
% 99.13/16.58 (app) =>
% 99.13/16.58 ((
% 99.13/16.58 (infuncsetfunc) =>
% 99.13/16.58 ((
% 99.13/16.58 (ap2p) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcinfuncset) =>
% 99.13/16.58 ((
% 99.13/16.58 (lamProp) =>
% 99.13/16.58 ((
% 99.13/16.58 (lamp) =>
% 99.13/16.58 ((
% 99.13/16.58 (lam2p) =>
% 99.13/16.58 ((
% 99.13/16.58 (brelnall1) =>
% 99.13/16.58 ((
% 99.13/16.58 (brelnall2) =>
% 99.13/16.58 ((
% 99.13/16.58 (ex1E2) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcGraphProp1) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcGraphProp3) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcGraphProp2) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcextLem) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcGraphProp4) =>
% 99.13/16.58 ((
% 99.13/16.58 (subbreln) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqbreln) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcext) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcext2) =>
% 99.13/16.58 ((
% 99.13/16.58 (ap2apEq1) =>
% 99.13/16.58 ((
% 99.13/16.58 (ap2apEq2) =>
% 99.13/16.58 ((
% 99.13/16.58 (beta1) =>
% 99.13/16.58 ((
% 99.13/16.58 (eta1) =>
% 99.13/16.58 ((
% 99.13/16.58 (lam2lamEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (beta2) =>
% 99.13/16.58 ((
% 99.13/16.58 (eta2) =>
% 99.13/16.58 ((
% 99.13/16.58 (iffalseProp1) =>
% 99.13/16.58 ((
% 99.13/16.58 (iffalseProp2) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrueProp1) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrueProp2) =>
% 99.13/16.58 ((
% 99.13/16.58 (ifSingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (ifp) =>
% 99.13/16.58 ((
% 99.13/16.58 (theeq) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrue) =>
% 99.13/16.58 ((
% 99.13/16.58 (iffalse) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrueorfalse) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (setextT) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetTI) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetTI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetTE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectTELcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectTERcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT1) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT2) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT3) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementSub1) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementSub2) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTnotintersectT) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementImpComplementIntersect) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementSubsetComplementIntersect) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementInPowersetComplementIntersect) =>
% 99.13/16.58 ((
% 99.13/16.58 (contraSubsetComplement) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTcontraSubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTILcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTIRcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (inIntersectImpInUnion) =>
% 99.13/16.58 ((
% 99.13/16.58 (inIntersectImpInUnion2) =>
% 99.13/16.58 ((
% 99.13/16.58 (inIntersectImpInIntersectUnions) =>
% 99.13/16.58 ((
% 99.13/16.58 (intersectInPowersetIntersectUnions) =>
% 99.13/16.58 ((
% 99.13/16.58 (inComplementUnionImpNotIn1) =>
% 99.13/16.58 ((
% 99.13/16.58 (inComplementUnionImpInComplement1) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTE) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTEcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2a1) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementUnionInPowersetComplement) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2a2) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan1a) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan1b) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan1) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2a) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2b2) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2b) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule0) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule1) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule2) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule3) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule4) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_1) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_2) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_3) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_4) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_5) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1all2) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1SetBreln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (choice2fnsingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (setOfPairsIsBReln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1all1) =>
% 99.13/16.58 ((
% 99.13/16.58 (subbreln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqbreln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1invprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1invI) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1invE) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compI) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compE) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compEex) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionIL) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionIR) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionI) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionE) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionEcases) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionCommutes) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2Ex) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2W) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2A) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2B) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1Ex) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1Ex1) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1Equiv) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1E) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1I) =>
% 99.13/16.58 ((
% 99.13/16.58 (injFuncInInjFuncSet) =>
% 99.13/16.58 ((
% 99.13/16.58 (injFuncSetFuncIn) =>
% 99.13/16.58 ((
% 99.13/16.58 (injFuncSetFuncInj) =>
% 99.13/16.58 ((
% 99.13/16.58 (!!) @ (
% 99.13/16.58 (('#B') @ (
% 99.13/16.58 !!) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 !!))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#S') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 '#S') @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 '#S'))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 =>))))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#C') @ in)))) @
% 99.13/16.58 surjFuncSet)))))))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#C') @ in)))) @
% 99.13/16.58 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl400])).
% 99.13/16.58 thf(zip_derived_cl417, plain,
% 99.13/16.58 (~ (((subPowSU) =>
% 99.13/16.58 (((exuE2) =>
% 99.13/16.58 (((nonemptyImpWitness) =>
% 99.13/16.58 (((uniqinunit) =>
% 99.13/16.58 (((notinsingleton) =>
% 99.13/16.58 (((eqinunit) =>
% 99.13/16.58 (((singletonsswitch) =>
% 99.13/16.58 (((upairsetE) =>
% 99.13/16.58 (((upairsetIL) =>
% 99.13/16.58 (((upairsetIR) =>
% 99.13/16.58 (((emptyE1) =>
% 99.13/16.58 (((vacuousDall) =>
% 99.13/16.58 (((quantDeMorgan1) =>
% 99.13/16.58 (((quantDeMorgan2) =>
% 99.13/16.58 (((quantDeMorgan3) =>
% 99.13/16.58 (((quantDeMorgan4) =>
% 99.13/16.58 (((prop2setI) =>
% 99.13/16.58 (((prop2set2propI) =>
% 99.13/16.58 (((notdexE) =>
% 99.13/16.58 (((notdallE) =>
% 99.13/16.58 (((exuI1) =>
% 99.13/16.58 (((exuI3) =>
% 99.13/16.58 (((exuI2) =>
% 99.13/16.58 (((inCongP) =>
% 99.13/16.58 (((in__Cong) =>
% 99.13/16.58 (((exuE3u) =>
% 99.13/16.58 (((exu__Cong) =>
% 99.13/16.58 (((setadjoin__Cong) =>
% 99.13/16.58 (((powerset__Cong) =>
% 99.13/16.58 (((setunion__Cong) =>
% 99.13/16.58 ((
% 99.13/16.58 (exuEu) =>
% 99.13/16.58 ((
% 99.13/16.58 (descr__Cong) =>
% 99.13/16.58 ((
% 99.13/16.58 (dsetconstr__Cong) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqimpsubset2) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqimpsubset1) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetI2) =>
% 99.13/16.58 ((
% 99.13/16.58 (emptysetsubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetE) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetE2) =>
% 99.13/16.58 ((
% 99.13/16.58 (notsubsetI) =>
% 99.13/16.58 ((
% 99.13/16.58 (notequalI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (notequalI2) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetRefl) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetTrans) =>
% 99.13/16.58 ((
% 99.13/16.58 (setadjoinSub) =>
% 99.13/16.58 ((
% 99.13/16.58 (setadjoinSub2) =>
% 99.13/16.58 ((
% 99.13/16.58 (subset2powerset) =>
% 99.13/16.58 ((
% 99.13/16.58 (setextsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetemptysetimpeq) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (inPowerset) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetsubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (sepInPowerset) =>
% 99.13/16.58 ((
% 99.13/16.58 (sepSubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionIL) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairset2IR) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionIR) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionEcases) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionE) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionLsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionRsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectI) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset5) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectEL) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectLsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset2) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset3) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectER) =>
% 99.13/16.58 ((
% 99.13/16.58 (disjointsetsI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectRsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset4) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset1) =>
% 99.13/16.58 ((
% 99.13/16.58 (bs114d) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusI) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusEL) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusER) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusSubset2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusERneg) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusELneg) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusILneg) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusIRneg) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusLsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusSubset1) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffE) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffI2) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffIneg1) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffIneg2) =>
% 99.13/16.58 ((
% 99.13/16.58 (secondinupair) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairIL) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairIR) =>
% 99.13/16.58 ((
% 99.13/16.58 (kpairiskpair) =>
% 99.13/16.58 ((
% 99.13/16.58 (kpairp) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletonsubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletoninpowerset) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletoninpowunion) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairset2E) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairsubunion) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairinpowunion) =>
% 99.13/16.58 ((
% 99.13/16.58 (ubforcartprodlem1) =>
% 99.13/16.58 ((
% 99.13/16.58 (ubforcartprodlem2) =>
% 99.13/16.58 ((
% 99.13/16.58 (ubforcartprodlem3) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodpairin) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodmempair1) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodmempair) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunionE2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunionsingleton1) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunionsingleton2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunionsingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletonprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (ex1E1) =>
% 99.13/16.58 ((
% 99.13/16.58 (ex1I) =>
% 99.13/16.58 ((
% 99.13/16.58 (ex1I2) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletonsuniq) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjL1) =>
% 99.13/16.58 ((
% 99.13/16.58 (kfstsingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (theprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (kfstpairEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodfstin) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjL2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjL) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR11) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR12) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR1) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairequniteq) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR) =>
% 99.13/16.58 ((
% 99.13/16.58 (ksndsingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (ksndpairEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (kpairsurjEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodsndin) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodpairmemEL) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodpairmemER) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodmempaircEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodfstpairEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodsndpairEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodpairsurjEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrI) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrSub) =>
% 99.13/16.58 ((
% 99.13/16.58 (setOfPairsIsBReln) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrERa) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrEL1) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrEL2) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrER) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcImageSingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (apProp) =>
% 99.13/16.58 ((
% 99.13/16.58 (app) =>
% 99.13/16.58 ((
% 99.13/16.58 (infuncsetfunc) =>
% 99.13/16.58 ((
% 99.13/16.58 (ap2p) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcinfuncset) =>
% 99.13/16.58 ((
% 99.13/16.58 (lamProp) =>
% 99.13/16.58 ((
% 99.13/16.58 (lamp) =>
% 99.13/16.58 ((
% 99.13/16.58 (lam2p) =>
% 99.13/16.58 ((
% 99.13/16.58 (brelnall1) =>
% 99.13/16.58 ((
% 99.13/16.58 (brelnall2) =>
% 99.13/16.58 ((
% 99.13/16.58 (ex1E2) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcGraphProp1) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcGraphProp3) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcGraphProp2) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcextLem) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcGraphProp4) =>
% 99.13/16.58 ((
% 99.13/16.58 (subbreln) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqbreln) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcext) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcext2) =>
% 99.13/16.58 ((
% 99.13/16.58 (ap2apEq1) =>
% 99.13/16.58 ((
% 99.13/16.58 (ap2apEq2) =>
% 99.13/16.58 ((
% 99.13/16.58 (beta1) =>
% 99.13/16.58 ((
% 99.13/16.58 (eta1) =>
% 99.13/16.58 ((
% 99.13/16.58 (lam2lamEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (beta2) =>
% 99.13/16.58 ((
% 99.13/16.58 (eta2) =>
% 99.13/16.58 ((
% 99.13/16.58 (iffalseProp1) =>
% 99.13/16.58 ((
% 99.13/16.58 (iffalseProp2) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrueProp1) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrueProp2) =>
% 99.13/16.58 ((
% 99.13/16.58 (ifSingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (ifp) =>
% 99.13/16.58 ((
% 99.13/16.58 (theeq) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrue) =>
% 99.13/16.58 ((
% 99.13/16.58 (iffalse) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrueorfalse) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (setextT) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetTI) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetTI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetTE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectTELcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectTERcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT1) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT2) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT3) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementSub1) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementSub2) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTnotintersectT) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementImpComplementIntersect) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementSubsetComplementIntersect) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementInPowersetComplementIntersect) =>
% 99.13/16.58 ((
% 99.13/16.58 (contraSubsetComplement) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTcontraSubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTILcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTIRcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (inIntersectImpInUnion) =>
% 99.13/16.58 ((
% 99.13/16.58 (inIntersectImpInUnion2) =>
% 99.13/16.58 ((
% 99.13/16.58 (inIntersectImpInIntersectUnions) =>
% 99.13/16.58 ((
% 99.13/16.58 (intersectInPowersetIntersectUnions) =>
% 99.13/16.58 ((
% 99.13/16.58 (inComplementUnionImpNotIn1) =>
% 99.13/16.58 ((
% 99.13/16.58 (inComplementUnionImpInComplement1) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTE) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTEcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2a1) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementUnionInPowersetComplement) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2a2) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan1a) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan1b) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan1) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2a) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2b2) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2b) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule0) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule1) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule2) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule3) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule4) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_1) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_2) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_3) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_4) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_5) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1all2) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1SetBreln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (choice2fnsingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (setOfPairsIsBReln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1all1) =>
% 99.13/16.58 ((
% 99.13/16.58 (subbreln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqbreln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1invprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1invI) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1invE) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compI) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compE) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compEex) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionIL) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionIR) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionI) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionE) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionEcases) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionCommutes) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2Ex) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2W) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2A) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2B) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1Ex) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1Ex1) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1Equiv) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1E) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1I) =>
% 99.13/16.58 ((
% 99.13/16.58 (injFuncInInjFuncSet) =>
% 99.13/16.58 ((
% 99.13/16.58 (injFuncSetFuncIn) =>
% 99.13/16.58 ((
% 99.13/16.58 (injFuncSetFuncInj) =>
% 99.13/16.58 ((
% 99.13/16.58 (!!) @ (
% 99.13/16.58 (('#B') @ (
% 99.13/16.58 !!) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 !!))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#S') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 '#S') @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 '#S'))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 =>))))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#C') @ in)))) @
% 99.13/16.58 surjFuncSet)))))))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#C') @ in)))) @
% 99.13/16.58 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl408])).
% 99.13/16.58 thf(zip_derived_cl428, plain,
% 99.13/16.58 (~ (((exuE2) =>
% 99.13/16.58 (((nonemptyImpWitness) =>
% 99.13/16.58 (((uniqinunit) =>
% 99.13/16.58 (((notinsingleton) =>
% 99.13/16.58 (((eqinunit) =>
% 99.13/16.58 (((singletonsswitch) =>
% 99.13/16.58 (((upairsetE) =>
% 99.13/16.58 (((upairsetIL) =>
% 99.13/16.58 (((upairsetIR) =>
% 99.13/16.58 (((emptyE1) =>
% 99.13/16.58 (((vacuousDall) =>
% 99.13/16.58 (((quantDeMorgan1) =>
% 99.13/16.58 (((quantDeMorgan2) =>
% 99.13/16.58 (((quantDeMorgan3) =>
% 99.13/16.58 (((quantDeMorgan4) =>
% 99.13/16.58 (((prop2setI) =>
% 99.13/16.58 (((prop2set2propI) =>
% 99.13/16.58 (((notdexE) =>
% 99.13/16.58 (((notdallE) =>
% 99.13/16.58 (((exuI1) =>
% 99.13/16.58 (((exuI3) =>
% 99.13/16.58 (((exuI2) =>
% 99.13/16.58 (((inCongP) =>
% 99.13/16.58 (((in__Cong) =>
% 99.13/16.58 (((exuE3u) =>
% 99.13/16.58 (((exu__Cong) =>
% 99.13/16.58 (((setadjoin__Cong) =>
% 99.13/16.58 (((powerset__Cong) =>
% 99.13/16.58 (((setunion__Cong) =>
% 99.13/16.58 (((exuEu) =>
% 99.13/16.58 ((
% 99.13/16.58 (descr__Cong) =>
% 99.13/16.58 ((
% 99.13/16.58 (dsetconstr__Cong) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqimpsubset2) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqimpsubset1) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetI2) =>
% 99.13/16.58 ((
% 99.13/16.58 (emptysetsubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetE) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetE2) =>
% 99.13/16.58 ((
% 99.13/16.58 (notsubsetI) =>
% 99.13/16.58 ((
% 99.13/16.58 (notequalI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (notequalI2) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetRefl) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetTrans) =>
% 99.13/16.58 ((
% 99.13/16.58 (setadjoinSub) =>
% 99.13/16.58 ((
% 99.13/16.58 (setadjoinSub2) =>
% 99.13/16.58 ((
% 99.13/16.58 (subset2powerset) =>
% 99.13/16.58 ((
% 99.13/16.58 (setextsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetemptysetimpeq) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (inPowerset) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetsubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (sepInPowerset) =>
% 99.13/16.58 ((
% 99.13/16.58 (sepSubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionIL) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairset2IR) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionIR) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionEcases) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionE) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionLsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionRsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectI) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset5) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectEL) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectLsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset2) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset3) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectER) =>
% 99.13/16.58 ((
% 99.13/16.58 (disjointsetsI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectRsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset4) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectSubset1) =>
% 99.13/16.58 ((
% 99.13/16.58 (bs114d) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusI) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusEL) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusER) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusSubset2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusERneg) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusELneg) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusILneg) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusIRneg) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusLsub) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusSubset1) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffE) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffI2) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffIneg1) =>
% 99.13/16.58 ((
% 99.13/16.58 (symdiffIneg2) =>
% 99.13/16.58 ((
% 99.13/16.58 (secondinupair) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairIL) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairIR) =>
% 99.13/16.58 ((
% 99.13/16.58 (kpairiskpair) =>
% 99.13/16.58 ((
% 99.13/16.58 (kpairp) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletonsubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletoninpowerset) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletoninpowunion) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairset2E) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairsubunion) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairinpowunion) =>
% 99.13/16.58 ((
% 99.13/16.58 (ubforcartprodlem1) =>
% 99.13/16.58 ((
% 99.13/16.58 (ubforcartprodlem2) =>
% 99.13/16.58 ((
% 99.13/16.58 (ubforcartprodlem3) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodpairin) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodmempair1) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodmempair) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunionE2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunionsingleton1) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunionsingleton2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setunionsingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletonprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (ex1E1) =>
% 99.13/16.58 ((
% 99.13/16.58 (ex1I) =>
% 99.13/16.58 ((
% 99.13/16.58 (ex1I2) =>
% 99.13/16.58 ((
% 99.13/16.58 (singletonsuniq) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjL1) =>
% 99.13/16.58 ((
% 99.13/16.58 (kfstsingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (theprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (kfstpairEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodfstin) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjL2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjL) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR11) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR12) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR1) =>
% 99.13/16.58 ((
% 99.13/16.58 (upairequniteq) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR2) =>
% 99.13/16.58 ((
% 99.13/16.58 (setukpairinjR) =>
% 99.13/16.58 ((
% 99.13/16.58 (ksndsingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (ksndpairEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (kpairsurjEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodsndin) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodpairmemEL) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodpairmemER) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodmempaircEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodfstpairEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodsndpairEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (cartprodpairsurjEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrI) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrSub) =>
% 99.13/16.58 ((
% 99.13/16.58 (setOfPairsIsBReln) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrERa) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrEL1) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrEL2) =>
% 99.13/16.58 ((
% 99.13/16.58 (dpsetconstrER) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcImageSingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (apProp) =>
% 99.13/16.58 ((
% 99.13/16.58 (app) =>
% 99.13/16.58 ((
% 99.13/16.58 (infuncsetfunc) =>
% 99.13/16.58 ((
% 99.13/16.58 (ap2p) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcinfuncset) =>
% 99.13/16.58 ((
% 99.13/16.58 (lamProp) =>
% 99.13/16.58 ((
% 99.13/16.58 (lamp) =>
% 99.13/16.58 ((
% 99.13/16.58 (lam2p) =>
% 99.13/16.58 ((
% 99.13/16.58 (brelnall1) =>
% 99.13/16.58 ((
% 99.13/16.58 (brelnall2) =>
% 99.13/16.58 ((
% 99.13/16.58 (ex1E2) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcGraphProp1) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcGraphProp3) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcGraphProp2) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcextLem) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcGraphProp4) =>
% 99.13/16.58 ((
% 99.13/16.58 (subbreln) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqbreln) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcext) =>
% 99.13/16.58 ((
% 99.13/16.58 (funcext2) =>
% 99.13/16.58 ((
% 99.13/16.58 (ap2apEq1) =>
% 99.13/16.58 ((
% 99.13/16.58 (ap2apEq2) =>
% 99.13/16.58 ((
% 99.13/16.58 (beta1) =>
% 99.13/16.58 ((
% 99.13/16.58 (eta1) =>
% 99.13/16.58 ((
% 99.13/16.58 (lam2lamEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (beta2) =>
% 99.13/16.58 ((
% 99.13/16.58 (eta2) =>
% 99.13/16.58 ((
% 99.13/16.58 (iffalseProp1) =>
% 99.13/16.58 ((
% 99.13/16.58 (iffalseProp2) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrueProp1) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrueProp2) =>
% 99.13/16.58 ((
% 99.13/16.58 (ifSingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (ifp) =>
% 99.13/16.58 ((
% 99.13/16.58 (theeq) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrue) =>
% 99.13/16.58 ((
% 99.13/16.58 (iffalse) =>
% 99.13/16.58 ((
% 99.13/16.58 (iftrueorfalse) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (setminusT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementT_lem) =>
% 99.13/16.58 ((
% 99.13/16.58 (setextT) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetTI) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetTI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (powersetTE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectTELcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (binintersectTERcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT1) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT2) =>
% 99.13/16.58 ((
% 99.13/16.58 (contrasubsetT3) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementE1) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementSub1) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementSub2) =>
% 99.13/16.58 ((
% 99.13/16.58 (doubleComplementEq) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTnotintersectT) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementImpComplementIntersect) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementSubsetComplementIntersect) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementInPowersetComplementIntersect) =>
% 99.13/16.58 ((
% 99.13/16.58 (contraSubsetComplement) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementTcontraSubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTILcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTIRcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (inIntersectImpInUnion) =>
% 99.13/16.58 ((
% 99.13/16.58 (inIntersectImpInUnion2) =>
% 99.13/16.58 ((
% 99.13/16.58 (inIntersectImpInIntersectUnions) =>
% 99.13/16.58 ((
% 99.13/16.58 (intersectInPowersetIntersectUnions) =>
% 99.13/16.58 ((
% 99.13/16.58 (inComplementUnionImpNotIn1) =>
% 99.13/16.58 ((
% 99.13/16.58 (inComplementUnionImpInComplement1) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTE) =>
% 99.13/16.58 ((
% 99.13/16.58 (binunionTEcontra) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2a1) =>
% 99.13/16.58 ((
% 99.13/16.58 (complementUnionInPowersetComplement) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2a2) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan1a) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan1b) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan1) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2a) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2b2) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2b) =>
% 99.13/16.58 ((
% 99.13/16.58 (demorgan2) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule0) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule1) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule2) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule3) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz13rule4) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_1) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_2) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_3) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_4) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz1_5) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1all2) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1SetBreln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (choice2fnsingleton) =>
% 99.13/16.58 ((
% 99.13/16.58 (setOfPairsIsBReln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1all1) =>
% 99.13/16.58 ((
% 99.13/16.58 (subbreln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqbreln1) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1invprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1invI) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1invE) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compI) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compE) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1compEex) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionprop) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionIL) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionIR) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionI) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionE) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionEcases) =>
% 99.13/16.58 ((
% 99.13/16.58 (breln1unionCommutes) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2Ex) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2W) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2A) =>
% 99.13/16.58 ((
% 99.13/16.58 (woz2B) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1Ex) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1Ex1) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1Equiv) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1E) =>
% 99.13/16.58 ((
% 99.13/16.58 (image1I) =>
% 99.13/16.58 ((
% 99.13/16.58 (injFuncInInjFuncSet) =>
% 99.13/16.58 ((
% 99.13/16.58 (injFuncSetFuncIn) =>
% 99.13/16.58 ((
% 99.13/16.58 (injFuncSetFuncInj) =>
% 99.13/16.58 ((
% 99.13/16.58 (!!) @ (
% 99.13/16.58 (('#B') @ (
% 99.13/16.58 !!) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 !!))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#S') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 '#S') @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 '#S'))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 =>))))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#C') @ in)))) @
% 99.13/16.58 surjFuncSet)))))))) @
% 99.13/16.58 (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#B') @ (
% 99.13/16.58 (
% 99.13/16.58 ('#C') @ in)))) @
% 99.13/16.58 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.13/16.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl417])).
% 99.13/16.58 thf(zip_derived_cl439, plain,
% 99.13/16.58 (~ (((nonemptyImpWitness) =>
% 99.13/16.58 (((uniqinunit) =>
% 99.13/16.58 (((notinsingleton) =>
% 99.13/16.58 (((eqinunit) =>
% 99.13/16.58 (((singletonsswitch) =>
% 99.13/16.58 (((upairsetE) =>
% 99.13/16.58 (((upairsetIL) =>
% 99.13/16.58 (((upairsetIR) =>
% 99.13/16.58 (((emptyE1) =>
% 99.13/16.58 (((vacuousDall) =>
% 99.13/16.58 (((quantDeMorgan1) =>
% 99.13/16.58 (((quantDeMorgan2) =>
% 99.13/16.58 (((quantDeMorgan3) =>
% 99.13/16.58 (((quantDeMorgan4) =>
% 99.13/16.58 (((prop2setI) =>
% 99.13/16.58 (((prop2set2propI) =>
% 99.13/16.58 (((notdexE) =>
% 99.13/16.58 (((notdallE) =>
% 99.13/16.58 (((exuI1) =>
% 99.13/16.58 (((exuI3) =>
% 99.13/16.58 (((exuI2) =>
% 99.13/16.58 (((inCongP) =>
% 99.13/16.58 (((in__Cong) =>
% 99.13/16.58 (((exuE3u) =>
% 99.13/16.58 (((exu__Cong) =>
% 99.13/16.58 (((setadjoin__Cong) =>
% 99.13/16.58 (((powerset__Cong) =>
% 99.13/16.58 (((setunion__Cong) =>
% 99.13/16.58 (((exuEu) =>
% 99.13/16.58 (((descr__Cong) =>
% 99.13/16.58 ((
% 99.13/16.58 (dsetconstr__Cong) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqimpsubset2) =>
% 99.13/16.58 ((
% 99.13/16.58 (eqimpsubset1) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetI2) =>
% 99.13/16.58 ((
% 99.13/16.58 (emptysetsubset) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetE) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetE2) =>
% 99.13/16.58 ((
% 99.13/16.58 (notsubsetI) =>
% 99.13/16.58 ((
% 99.13/16.58 (notequalI1) =>
% 99.13/16.58 ((
% 99.13/16.58 (notequalI2) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetRefl) =>
% 99.13/16.58 ((
% 99.13/16.58 (subsetTrans) =>
% 99.13/16.58 ((
% 99.13/16.58 (setadjoinSub) =>
% 99.13/16.58 ((
% 99.42/16.58 (setadjoinSub2) =>
% 99.42/16.58 ((
% 99.42/16.58 (subset2powerset) =>
% 99.42/16.58 ((
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% 99.42/16.58 ((
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% 99.42/16.58 (setukpairinjL) =>
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% 99.42/16.58 (setukpairinjR12) =>
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% 99.42/16.58 (kpairsurjEq) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodsndin) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodpairmemEL) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodpairmemER) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodmempaircEq) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodfstpairEq) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodsndpairEq) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodpairsurjEq) =>
% 99.42/16.58 ((
% 99.42/16.58 (dpsetconstrI) =>
% 99.42/16.58 ((
% 99.42/16.58 (dpsetconstrSub) =>
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% 99.42/16.58 (setOfPairsIsBReln) =>
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% 99.42/16.58 (dpsetconstrERa) =>
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% 99.42/16.58 (dpsetconstrEL2) =>
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% 99.42/16.58 (dpsetconstrER) =>
% 99.42/16.58 ((
% 99.42/16.58 (funcImageSingleton) =>
% 99.42/16.58 ((
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% 99.42/16.58 ((
% 99.42/16.58 (app) =>
% 99.42/16.58 ((
% 99.42/16.58 (infuncsetfunc) =>
% 99.42/16.58 ((
% 99.42/16.58 (ap2p) =>
% 99.42/16.58 ((
% 99.42/16.58 (funcinfuncset) =>
% 99.42/16.58 ((
% 99.42/16.58 (lamProp) =>
% 99.42/16.58 ((
% 99.42/16.58 (lamp) =>
% 99.42/16.58 ((
% 99.42/16.58 (lam2p) =>
% 99.42/16.58 ((
% 99.42/16.58 (brelnall1) =>
% 99.42/16.58 ((
% 99.42/16.58 (brelnall2) =>
% 99.42/16.58 ((
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% 99.42/16.58 (funcGraphProp1) =>
% 99.42/16.58 ((
% 99.42/16.58 (funcGraphProp3) =>
% 99.42/16.58 ((
% 99.42/16.58 (funcGraphProp2) =>
% 99.42/16.58 ((
% 99.42/16.58 (funcextLem) =>
% 99.42/16.58 ((
% 99.42/16.58 (funcGraphProp4) =>
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% 99.42/16.58 ((
% 99.42/16.58 (eta1) =>
% 99.42/16.58 ((
% 99.42/16.58 (lam2lamEq) =>
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% 99.42/16.58 (beta2) =>
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% 99.42/16.58 ((
% 99.42/16.58 (iffalseProp2) =>
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% 99.42/16.58 (iftrueProp2) =>
% 99.42/16.58 ((
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% 99.42/16.58 ((
% 99.42/16.58 (ifp) =>
% 99.42/16.58 ((
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% 99.42/16.58 ((
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% 99.42/16.58 ((
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% 99.42/16.58 ((
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% 99.42/16.58 ((
% 99.42/16.58 (powersetTI1) =>
% 99.42/16.58 ((
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% 99.42/16.58 ((
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% 99.42/16.58 ((
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% 99.42/16.58 ((
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% 99.42/16.58 ((
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% 99.42/16.58 ((
% 99.42/16.58 (contrasubsetT2) =>
% 99.42/16.58 ((
% 99.42/16.58 (contrasubsetT3) =>
% 99.42/16.58 ((
% 99.42/16.58 (doubleComplementI1) =>
% 99.42/16.58 ((
% 99.42/16.58 (doubleComplementE1) =>
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% 99.42/16.58 (doubleComplementSub1) =>
% 99.42/16.58 ((
% 99.42/16.58 (doubleComplementSub2) =>
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% 99.42/16.58 (doubleComplementEq) =>
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% 99.42/16.58 (complementTnotintersectT) =>
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% 99.42/16.58 (complementImpComplementIntersect) =>
% 99.42/16.58 ((
% 99.42/16.58 (complementSubsetComplementIntersect) =>
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% 99.42/16.58 (complementInPowersetComplementIntersect) =>
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% 99.42/16.58 (contraSubsetComplement) =>
% 99.42/16.58 ((
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% 99.42/16.58 (binunionTIRcontra) =>
% 99.42/16.58 ((
% 99.42/16.58 (inIntersectImpInUnion) =>
% 99.42/16.58 ((
% 99.42/16.58 (inIntersectImpInUnion2) =>
% 99.42/16.58 ((
% 99.42/16.58 (inIntersectImpInIntersectUnions) =>
% 99.42/16.58 ((
% 99.42/16.58 (intersectInPowersetIntersectUnions) =>
% 99.42/16.58 ((
% 99.42/16.58 (inComplementUnionImpNotIn1) =>
% 99.42/16.58 ((
% 99.42/16.58 (inComplementUnionImpInComplement1) =>
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% 99.42/16.58 ((
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% 99.42/16.58 ((
% 99.42/16.58 (complementUnionInPowersetComplement) =>
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% 99.42/16.58 (demorgan2a2) =>
% 99.42/16.58 ((
% 99.42/16.58 (demorgan1a) =>
% 99.42/16.58 ((
% 99.42/16.58 (demorgan1b) =>
% 99.42/16.58 ((
% 99.42/16.58 (demorgan1) =>
% 99.42/16.58 ((
% 99.42/16.58 (demorgan2a) =>
% 99.42/16.58 ((
% 99.42/16.58 (demorgan2b2) =>
% 99.42/16.58 ((
% 99.42/16.58 (demorgan2b) =>
% 99.42/16.58 ((
% 99.42/16.58 (demorgan2) =>
% 99.42/16.58 ((
% 99.42/16.58 (woz13rule0) =>
% 99.42/16.58 ((
% 99.42/16.58 (woz13rule1) =>
% 99.42/16.58 ((
% 99.42/16.58 (woz13rule2) =>
% 99.42/16.58 ((
% 99.42/16.58 (woz13rule3) =>
% 99.42/16.58 ((
% 99.42/16.58 (woz13rule4) =>
% 99.42/16.58 ((
% 99.42/16.58 (woz1_1) =>
% 99.42/16.58 ((
% 99.42/16.58 (woz1_2) =>
% 99.42/16.58 ((
% 99.42/16.58 (woz1_3) =>
% 99.42/16.58 ((
% 99.42/16.58 (woz1_4) =>
% 99.42/16.58 ((
% 99.42/16.58 (woz1_5) =>
% 99.42/16.58 ((
% 99.42/16.58 (breln1all2) =>
% 99.42/16.58 ((
% 99.42/16.58 (breln1SetBreln1) =>
% 99.42/16.58 ((
% 99.42/16.58 (choice2fnsingleton) =>
% 99.42/16.58 ((
% 99.42/16.58 (setOfPairsIsBReln1) =>
% 99.42/16.58 ((
% 99.42/16.58 (breln1all1) =>
% 99.42/16.58 ((
% 99.42/16.58 (subbreln1) =>
% 99.42/16.58 ((
% 99.42/16.58 (eqbreln1) =>
% 99.42/16.58 ((
% 99.42/16.58 (breln1invprop) =>
% 99.42/16.58 ((
% 99.42/16.58 (breln1invI) =>
% 99.42/16.58 ((
% 99.42/16.58 (breln1invE) =>
% 99.42/16.58 ((
% 99.42/16.58 (breln1compprop) =>
% 99.42/16.58 ((
% 99.42/16.58 (breln1compI) =>
% 99.42/16.58 ((
% 99.42/16.58 (breln1compE) =>
% 99.42/16.58 ((
% 99.42/16.58 (breln1compEex) =>
% 99.42/16.58 ((
% 99.42/16.58 (breln1unionprop) =>
% 99.42/16.58 ((
% 99.42/16.58 (breln1unionIL) =>
% 99.42/16.58 ((
% 99.42/16.58 (breln1unionIR) =>
% 99.42/16.58 ((
% 99.42/16.58 (breln1unionI) =>
% 99.42/16.58 ((
% 99.42/16.58 (breln1unionE) =>
% 99.42/16.58 ((
% 99.42/16.58 (breln1unionEcases) =>
% 99.42/16.58 ((
% 99.42/16.58 (breln1unionCommutes) =>
% 99.42/16.58 ((
% 99.42/16.58 (woz2Ex) =>
% 99.42/16.58 ((
% 99.42/16.58 (woz2W) =>
% 99.42/16.58 ((
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% 99.42/16.58 ((
% 99.42/16.58 (woz2B) =>
% 99.42/16.58 ((
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% 99.42/16.58 ((
% 99.42/16.58 (image1Ex1) =>
% 99.42/16.58 ((
% 99.42/16.58 (image1Equiv) =>
% 99.42/16.58 ((
% 99.42/16.58 (image1E) =>
% 99.42/16.58 ((
% 99.42/16.58 (image1I) =>
% 99.42/16.58 ((
% 99.42/16.58 (injFuncInInjFuncSet) =>
% 99.42/16.58 ((
% 99.42/16.58 (injFuncSetFuncIn) =>
% 99.42/16.58 ((
% 99.42/16.58 (injFuncSetFuncInj) =>
% 99.42/16.58 ((
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% 99.42/16.58 (('#B') @ (
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% 99.42/16.58 (
% 99.42/16.58 (
% 99.42/16.58 ('#B') @ (
% 99.42/16.58 (
% 99.42/16.58 ('#B') @ (
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% 99.42/16.58 (
% 99.42/16.58 (
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% 99.42/16.58 (
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% 99.42/16.58 (
% 99.42/16.58 (
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% 99.42/16.58 (
% 99.42/16.58 (
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% 99.42/16.58 (
% 99.42/16.58 ('#B') @ (
% 99.42/16.58 (
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% 99.42/16.58 (
% 99.42/16.58 (
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% 99.42/16.58 (
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% 99.42/16.58 surjFuncSet)))))))) @
% 99.42/16.58 (
% 99.42/16.58 (
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% 99.42/16.58 (
% 99.42/16.58 ('#B') @ (
% 99.42/16.58 (
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% 99.42/16.58 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])).
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% 99.42/16.58 (((exuE3u) =>
% 99.42/16.58 (((exu__Cong) =>
% 99.42/16.58 (((setadjoin__Cong) =>
% 99.42/16.58 (((powerset__Cong) =>
% 99.42/16.58 (((setunion__Cong) =>
% 99.42/16.58 (((exuEu) =>
% 99.42/16.58 (((descr__Cong) =>
% 99.42/16.58 (((dsetconstr__Cong) =>
% 99.42/16.58 ((
% 99.42/16.58 (subsetI1) =>
% 99.42/16.58 ((
% 99.42/16.58 (eqimpsubset2) =>
% 99.42/16.58 ((
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% 99.42/16.58 ((
% 99.42/16.58 (subsetE2) =>
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% 99.42/16.58 ((
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% 99.42/16.58 ((
% 99.42/16.58 (notequalI2) =>
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% 99.42/16.58 ((
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% 99.42/16.58 ((
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% 99.42/16.58 ((
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% 99.42/16.58 ((
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% 99.42/16.58 ((
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% 99.42/16.58 ((
% 99.42/16.58 (binunionEcases) =>
% 99.42/16.58 ((
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% 99.42/16.58 ((
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% 99.42/16.58 ((
% 99.42/16.58 (binunionRsub) =>
% 99.42/16.58 ((
% 99.42/16.58 (binintersectI) =>
% 99.42/16.58 ((
% 99.42/16.58 (binintersectSubset5) =>
% 99.42/16.58 ((
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% 99.42/16.58 ((
% 99.42/16.58 (binintersectLsub) =>
% 99.42/16.58 ((
% 99.42/16.58 (binintersectSubset2) =>
% 99.42/16.58 ((
% 99.42/16.58 (binintersectSubset3) =>
% 99.42/16.58 ((
% 99.42/16.58 (binintersectER) =>
% 99.42/16.58 ((
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% 99.42/16.58 ((
% 99.42/16.58 (binintersectRsub) =>
% 99.42/16.58 ((
% 99.42/16.58 (binintersectSubset4) =>
% 99.42/16.58 ((
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% 99.42/16.58 ((
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% 99.42/16.58 ((
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% 99.42/16.58 ((
% 99.42/16.58 (setminusEL) =>
% 99.42/16.58 ((
% 99.42/16.58 (setminusER) =>
% 99.42/16.58 ((
% 99.42/16.58 (setminusSubset2) =>
% 99.42/16.58 ((
% 99.42/16.58 (setminusERneg) =>
% 99.42/16.58 ((
% 99.42/16.58 (setminusELneg) =>
% 99.42/16.58 ((
% 99.42/16.58 (setminusILneg) =>
% 99.42/16.58 ((
% 99.42/16.58 (setminusIRneg) =>
% 99.42/16.58 ((
% 99.42/16.58 (setminusLsub) =>
% 99.42/16.58 ((
% 99.42/16.58 (setminusSubset1) =>
% 99.42/16.58 ((
% 99.42/16.58 (symdiffE) =>
% 99.42/16.58 ((
% 99.42/16.58 (symdiffI1) =>
% 99.42/16.58 ((
% 99.42/16.58 (symdiffI2) =>
% 99.42/16.58 ((
% 99.42/16.58 (symdiffIneg1) =>
% 99.42/16.58 ((
% 99.42/16.58 (symdiffIneg2) =>
% 99.42/16.58 ((
% 99.42/16.58 (secondinupair) =>
% 99.42/16.58 ((
% 99.42/16.58 (setukpairIL) =>
% 99.42/16.58 ((
% 99.42/16.58 (setukpairIR) =>
% 99.42/16.58 ((
% 99.42/16.58 (kpairiskpair) =>
% 99.42/16.58 ((
% 99.42/16.58 (kpairp) =>
% 99.42/16.58 ((
% 99.42/16.58 (singletonsubset) =>
% 99.42/16.58 ((
% 99.42/16.58 (singletoninpowerset) =>
% 99.42/16.58 ((
% 99.42/16.58 (singletoninpowunion) =>
% 99.42/16.58 ((
% 99.42/16.58 (upairset2E) =>
% 99.42/16.58 ((
% 99.42/16.58 (upairsubunion) =>
% 99.42/16.58 ((
% 99.42/16.58 (upairinpowunion) =>
% 99.42/16.58 ((
% 99.42/16.58 (ubforcartprodlem1) =>
% 99.42/16.58 ((
% 99.42/16.58 (ubforcartprodlem2) =>
% 99.42/16.58 ((
% 99.42/16.58 (ubforcartprodlem3) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodpairin) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodmempair1) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodmempair) =>
% 99.42/16.58 ((
% 99.42/16.58 (setunionE2) =>
% 99.42/16.58 ((
% 99.42/16.58 (setunionsingleton1) =>
% 99.42/16.58 ((
% 99.42/16.58 (setunionsingleton2) =>
% 99.42/16.58 ((
% 99.42/16.58 (setunionsingleton) =>
% 99.42/16.58 ((
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% 99.42/16.58 ((
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% 99.42/16.58 ((
% 99.42/16.58 (ex1I) =>
% 99.42/16.58 ((
% 99.42/16.58 (ex1I2) =>
% 99.42/16.58 ((
% 99.42/16.58 (singletonsuniq) =>
% 99.42/16.58 ((
% 99.42/16.58 (setukpairinjL1) =>
% 99.42/16.58 ((
% 99.42/16.58 (kfstsingleton) =>
% 99.42/16.58 ((
% 99.42/16.58 (theprop) =>
% 99.42/16.58 ((
% 99.42/16.58 (kfstpairEq) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodfstin) =>
% 99.42/16.58 ((
% 99.42/16.58 (setukpairinjL2) =>
% 99.42/16.58 ((
% 99.42/16.58 (setukpairinjL) =>
% 99.42/16.58 ((
% 99.42/16.58 (setukpairinjR11) =>
% 99.42/16.58 ((
% 99.42/16.58 (setukpairinjR12) =>
% 99.42/16.58 ((
% 99.42/16.58 (setukpairinjR1) =>
% 99.42/16.58 ((
% 99.42/16.58 (upairequniteq) =>
% 99.42/16.58 ((
% 99.42/16.58 (setukpairinjR2) =>
% 99.42/16.58 ((
% 99.42/16.58 (setukpairinjR) =>
% 99.42/16.58 ((
% 99.42/16.58 (ksndsingleton) =>
% 99.42/16.58 ((
% 99.42/16.58 (ksndpairEq) =>
% 99.42/16.58 ((
% 99.42/16.58 (kpairsurjEq) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodsndin) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodpairmemEL) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodpairmemER) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodmempaircEq) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodfstpairEq) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodsndpairEq) =>
% 99.42/16.58 ((
% 99.42/16.58 (cartprodpairsurjEq) =>
% 99.42/16.58 ((
% 99.42/16.58 (dpsetconstrI) =>
% 99.42/16.58 ((
% 99.42/16.58 (dpsetconstrSub) =>
% 99.42/16.58 ((
% 99.42/16.58 (setOfPairsIsBReln) =>
% 99.42/16.58 ((
% 99.42/16.58 (dpsetconstrERa) =>
% 99.42/16.58 ((
% 99.42/16.58 (dpsetconstrEL1) =>
% 99.42/16.58 ((
% 99.42/16.58 (dpsetconstrEL2) =>
% 99.42/16.58 ((
% 99.42/16.58 (dpsetconstrER) =>
% 99.42/16.58 ((
% 99.42/16.58 (funcImageSingleton) =>
% 99.42/16.58 ((
% 99.42/16.58 (apProp) =>
% 99.42/16.58 ((
% 99.42/16.58 (app) =>
% 99.42/16.58 ((
% 99.42/16.58 (infuncsetfunc) =>
% 99.42/16.58 ((
% 99.42/16.58 (ap2p) =>
% 99.42/16.58 ((
% 99.42/16.58 (funcinfuncset) =>
% 99.42/16.58 ((
% 99.42/16.58 (lamProp) =>
% 99.42/16.58 ((
% 99.42/16.58 (lamp) =>
% 99.42/16.58 ((
% 99.42/16.58 (lam2p) =>
% 99.42/16.58 ((
% 99.42/16.58 (brelnall1) =>
% 99.42/16.58 ((
% 99.42/16.58 (brelnall2) =>
% 99.42/16.58 ((
% 99.42/16.58 (ex1E2) =>
% 99.42/16.58 ((
% 99.42/16.58 (funcGraphProp1) =>
% 99.42/16.58 ((
% 99.42/16.58 (funcGraphProp3) =>
% 99.42/16.58 ((
% 99.42/16.58 (funcGraphProp2) =>
% 99.42/16.58 ((
% 99.42/16.58 (funcextLem) =>
% 99.42/16.58 ((
% 99.42/16.58 (funcGraphProp4) =>
% 99.42/16.58 ((
% 99.42/16.58 (subbreln) =>
% 99.42/16.58 ((
% 99.42/16.58 (eqbreln) =>
% 99.42/16.58 ((
% 99.42/16.58 (funcext) =>
% 99.42/16.58 ((
% 99.42/16.58 (funcext2) =>
% 99.42/16.58 ((
% 99.42/16.58 (ap2apEq1) =>
% 99.42/16.58 ((
% 99.42/16.58 (ap2apEq2) =>
% 99.42/16.58 ((
% 99.42/16.58 (beta1) =>
% 99.42/16.58 ((
% 99.42/16.58 (eta1) =>
% 99.42/16.58 ((
% 99.42/16.58 (lam2lamEq) =>
% 99.42/16.58 ((
% 99.42/16.58 (beta2) =>
% 99.42/16.58 ((
% 99.42/16.58 (eta2) =>
% 99.42/16.58 ((
% 99.42/16.58 (iffalseProp1) =>
% 99.42/16.58 ((
% 99.42/16.58 (iffalseProp2) =>
% 99.42/16.58 ((
% 99.42/16.58 (iftrueProp1) =>
% 99.42/16.58 ((
% 99.42/16.58 (iftrueProp2) =>
% 99.42/16.58 ((
% 99.42/16.58 (ifSingleton) =>
% 99.42/16.58 ((
% 99.42/16.58 (ifp) =>
% 99.42/16.58 ((
% 99.42/16.58 (theeq) =>
% 99.42/16.58 ((
% 99.42/16.58 (iftrue) =>
% 99.42/16.58 ((
% 99.42/16.58 (iffalse) =>
% 99.42/16.58 ((
% 99.42/16.58 (iftrueorfalse) =>
% 99.42/16.58 ((
% 99.42/16.58 (binintersectT_lem) =>
% 99.42/16.58 ((
% 99.42/16.58 (binunionT_lem) =>
% 99.42/16.58 ((
% 99.42/16.58 (powersetT_lem) =>
% 99.42/16.58 ((
% 99.42/16.58 (setminusT_lem) =>
% 99.42/16.58 ((
% 99.42/16.58 (complementT_lem) =>
% 99.42/16.58 ((
% 99.42/16.58 (setextT) =>
% 99.42/16.58 ((
% 99.42/16.58 (subsetTI) =>
% 99.42/16.58 ((
% 99.42/16.58 (powersetTI1) =>
% 99.42/16.58 ((
% 99.42/16.58 (powersetTE1) =>
% 99.42/16.58 ((
% 99.42/16.58 (complementTI1) =>
% 99.42/16.58 ((
% 99.42/16.58 (complementTE1) =>
% 99.42/16.58 ((
% 99.42/16.58 (binintersectTELcontra) =>
% 99.42/16.58 ((
% 99.42/16.58 (binintersectTERcontra) =>
% 99.42/16.58 ((
% 99.42/16.58 (contrasubsetT) =>
% 99.42/16.58 ((
% 99.42/16.58 (contrasubsetT1) =>
% 99.42/16.58 ((
% 99.42/16.58 (contrasubsetT2) =>
% 99.42/16.58 ((
% 99.42/16.58 (contrasubsetT3) =>
% 99.42/16.58 ((
% 99.42/16.58 (doubleComplementI1) =>
% 99.42/16.58 ((
% 99.42/16.58 (doubleComplementE1) =>
% 99.42/16.58 ((
% 99.42/16.58 (doubleComplementSub1) =>
% 99.42/16.58 ((
% 99.42/16.58 (doubleComplementSub2) =>
% 99.42/16.58 ((
% 99.42/16.58 (doubleComplementEq) =>
% 99.42/16.58 ((
% 99.42/16.58 (complementTnotintersectT) =>
% 99.42/16.58 ((
% 99.42/16.58 (complementImpComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementSubsetComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementInPowersetComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (contraSubsetComplement) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTcontraSubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTILcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTIRcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInUnion) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInUnion2) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInIntersectUnions) =>
% 99.42/16.59 ((
% 99.42/16.59 (intersectInPowersetIntersectUnions) =>
% 99.42/16.59 ((
% 99.42/16.59 (inComplementUnionImpNotIn1) =>
% 99.42/16.59 ((
% 99.42/16.59 (inComplementUnionImpInComplement1) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTE) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTEcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementUnionInPowersetComplement) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a2) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1a) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1b) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2b2) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2b) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule0) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule1) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule3) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule4) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_1) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_3) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_4) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_5) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1all2) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1SetBreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (choice2fnsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (setOfPairsIsBReln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1all1) =>
% 99.42/16.59 ((
% 99.42/16.59 (subbreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (eqbreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compEex) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionIL) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionIR) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionEcases) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionCommutes) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2Ex) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2W) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2A) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2B) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Ex) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Ex1) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Equiv) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1E) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1I) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncInInjFuncSet) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncSetFuncIn) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncSetFuncInj) =>
% 99.42/16.59 ((
% 99.42/16.59 (!!) @ (
% 99.42/16.59 (('#B') @ (
% 99.42/16.59 !!) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 !!))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#S') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 '#S') @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 '#S'))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 =>))))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#C') @ in)))) @
% 99.42/16.59 surjFuncSet)))))))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#C') @ in)))) @
% 99.42/16.59 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl439])).
% 99.42/16.59 thf(zip_derived_cl458, plain,
% 99.42/16.59 (~ (((notinsingleton) =>
% 99.42/16.59 (((eqinunit) =>
% 99.42/16.59 (((singletonsswitch) =>
% 99.42/16.59 (((upairsetE) =>
% 99.42/16.59 (((upairsetIL) =>
% 99.42/16.59 (((upairsetIR) =>
% 99.42/16.59 (((emptyE1) =>
% 99.42/16.59 (((vacuousDall) =>
% 99.42/16.59 (((quantDeMorgan1) =>
% 99.42/16.59 (((quantDeMorgan2) =>
% 99.42/16.59 (((quantDeMorgan3) =>
% 99.42/16.59 (((quantDeMorgan4) =>
% 99.42/16.59 (((prop2setI) =>
% 99.42/16.59 (((prop2set2propI) =>
% 99.42/16.59 (((notdexE) =>
% 99.42/16.59 (((notdallE) =>
% 99.42/16.59 (((exuI1) =>
% 99.42/16.59 (((exuI3) =>
% 99.42/16.59 (((exuI2) =>
% 99.42/16.59 (((inCongP) =>
% 99.42/16.59 (((in__Cong) =>
% 99.42/16.59 (((exuE3u) =>
% 99.42/16.59 (((exu__Cong) =>
% 99.42/16.59 (((setadjoin__Cong) =>
% 99.42/16.59 (((powerset__Cong) =>
% 99.42/16.59 (((setunion__Cong) =>
% 99.42/16.59 (((exuEu) =>
% 99.42/16.59 (((descr__Cong) =>
% 99.42/16.59 (((dsetconstr__Cong) =>
% 99.42/16.59 (((subsetI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (eqimpsubset2) =>
% 99.42/16.59 ((
% 99.42/16.59 (eqimpsubset1) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetI2) =>
% 99.42/16.59 ((
% 99.42/16.59 (emptysetsubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetE) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetE2) =>
% 99.42/16.59 ((
% 99.42/16.59 (notsubsetI) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (binunionEcases) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (binunionRsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectI) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset5) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (binintersectLsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset2) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset3) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (setminusEL) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusER) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusSubset2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusERneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusELneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusILneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusIRneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusLsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusSubset1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffE) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffI2) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffIneg1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffIneg2) =>
% 99.42/16.59 ((
% 99.42/16.59 (secondinupair) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairIL) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (kpairiskpair) =>
% 99.42/16.59 ((
% 99.42/16.59 (kpairp) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletonsubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletoninpowerset) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletoninpowunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairset2E) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairsubunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairinpowunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem1) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem3) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairin) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempair1) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempair) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionE2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton1) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (ex1I) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1I2) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletonsuniq) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL1) =>
% 99.42/16.59 ((
% 99.42/16.59 (kfstsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (theprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (kfstpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodfstin) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR11) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR12) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR1) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairequniteq) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR) =>
% 99.42/16.59 ((
% 99.42/16.59 (ksndsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (ksndpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (kpairsurjEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodsndin) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairmemEL) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairmemER) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempaircEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodfstpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodsndpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairsurjEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrI) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrSub) =>
% 99.42/16.59 ((
% 99.42/16.59 (setOfPairsIsBReln) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrERa) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrEL1) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrEL2) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrER) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcImageSingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (apProp) =>
% 99.42/16.59 ((
% 99.42/16.59 (app) =>
% 99.42/16.59 ((
% 99.42/16.59 (infuncsetfunc) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2p) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcinfuncset) =>
% 99.42/16.59 ((
% 99.42/16.59 (lamProp) =>
% 99.42/16.59 ((
% 99.42/16.59 (lamp) =>
% 99.42/16.59 ((
% 99.42/16.59 (lam2p) =>
% 99.42/16.59 ((
% 99.42/16.59 (brelnall1) =>
% 99.42/16.59 ((
% 99.42/16.59 (brelnall2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1E2) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp3) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcextLem) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp4) =>
% 99.42/16.59 ((
% 99.42/16.59 (subbreln) =>
% 99.42/16.59 ((
% 99.42/16.59 (eqbreln) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcext) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcext2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2apEq1) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2apEq2) =>
% 99.42/16.59 ((
% 99.42/16.59 (beta1) =>
% 99.42/16.59 ((
% 99.42/16.59 (eta1) =>
% 99.42/16.59 ((
% 99.42/16.59 (lam2lamEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (beta2) =>
% 99.42/16.59 ((
% 99.42/16.59 (eta2) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalseProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalseProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ifSingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (ifp) =>
% 99.42/16.59 ((
% 99.42/16.59 (theeq) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrue) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalse) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueorfalse) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (setextT) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetTI) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetTI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetTE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectTELcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectTERcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT1) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT2) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT3) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementSub1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementSub2) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTnotintersectT) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementImpComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementSubsetComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementInPowersetComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (contraSubsetComplement) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTcontraSubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTILcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTIRcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInUnion) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInUnion2) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInIntersectUnions) =>
% 99.42/16.59 ((
% 99.42/16.59 (intersectInPowersetIntersectUnions) =>
% 99.42/16.59 ((
% 99.42/16.59 (inComplementUnionImpNotIn1) =>
% 99.42/16.59 ((
% 99.42/16.59 (inComplementUnionImpInComplement1) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTE) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTEcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementUnionInPowersetComplement) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a2) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1a) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1b) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2b2) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2b) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule0) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule1) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule3) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule4) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_1) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_3) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_4) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_5) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1all2) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1SetBreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (choice2fnsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (setOfPairsIsBReln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1all1) =>
% 99.42/16.59 ((
% 99.42/16.59 (subbreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (eqbreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compEex) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionIL) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionIR) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionEcases) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionCommutes) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2Ex) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2W) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2A) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2B) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Ex) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Ex1) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Equiv) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1E) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1I) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncInInjFuncSet) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncSetFuncIn) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncSetFuncInj) =>
% 99.42/16.59 ((
% 99.42/16.59 (!!) @ (
% 99.42/16.59 (('#B') @ (
% 99.42/16.59 !!) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 !!))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#S') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 '#S') @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 '#S'))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 =>))))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#C') @ in)))) @
% 99.42/16.59 surjFuncSet)))))))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#C') @ in)))) @
% 99.42/16.59 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl449])).
% 99.42/16.59 thf(zip_derived_cl467, plain,
% 99.42/16.59 (~ (((eqinunit) =>
% 99.42/16.59 (((singletonsswitch) =>
% 99.42/16.59 (((upairsetE) =>
% 99.42/16.59 (((upairsetIL) =>
% 99.42/16.59 (((upairsetIR) =>
% 99.42/16.59 (((emptyE1) =>
% 99.42/16.59 (((vacuousDall) =>
% 99.42/16.59 (((quantDeMorgan1) =>
% 99.42/16.59 (((quantDeMorgan2) =>
% 99.42/16.59 (((quantDeMorgan3) =>
% 99.42/16.59 (((quantDeMorgan4) =>
% 99.42/16.59 (((prop2setI) =>
% 99.42/16.59 (((prop2set2propI) =>
% 99.42/16.59 (((notdexE) =>
% 99.42/16.59 (((notdallE) =>
% 99.42/16.59 (((exuI1) =>
% 99.42/16.59 (((exuI3) =>
% 99.42/16.59 (((exuI2) =>
% 99.42/16.59 (((inCongP) =>
% 99.42/16.59 (((in__Cong) =>
% 99.42/16.59 (((exuE3u) =>
% 99.42/16.59 (((exu__Cong) =>
% 99.42/16.59 (((setadjoin__Cong) =>
% 99.42/16.59 (((powerset__Cong) =>
% 99.42/16.59 (((setunion__Cong) =>
% 99.42/16.59 (((exuEu) =>
% 99.42/16.59 (((descr__Cong) =>
% 99.42/16.59 (((dsetconstr__Cong) =>
% 99.42/16.59 (((subsetI1) =>
% 99.42/16.59 (((eqimpsubset2) =>
% 99.42/16.59 ((
% 99.42/16.59 (eqimpsubset1) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetI2) =>
% 99.42/16.59 ((
% 99.42/16.59 (emptysetsubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetE) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetE2) =>
% 99.42/16.59 ((
% 99.42/16.59 (notsubsetI) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (notequalI2) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (sepSubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionIL) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairset2IR) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionIR) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionEcases) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionE) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionLsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionRsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectI) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset5) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectEL) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectLsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset2) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset3) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectER) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (binintersectRsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset4) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset1) =>
% 99.42/16.59 ((
% 99.42/16.59 (bs114d) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusI) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusEL) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusER) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusSubset2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusERneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusELneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusILneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusIRneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusLsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusSubset1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffE) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffI2) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffIneg1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffIneg2) =>
% 99.42/16.59 ((
% 99.42/16.59 (secondinupair) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairIL) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairIR) =>
% 99.42/16.59 ((
% 99.42/16.59 (kpairiskpair) =>
% 99.42/16.59 ((
% 99.42/16.59 (kpairp) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletonsubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletoninpowerset) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletoninpowunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairset2E) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairsubunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairinpowunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem1) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem3) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairin) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempair1) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempair) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionE2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton1) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletonprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1E1) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1I) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1I2) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletonsuniq) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL1) =>
% 99.42/16.59 ((
% 99.42/16.59 (kfstsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (theprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (kfstpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodfstin) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR11) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR12) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR1) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairequniteq) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR) =>
% 99.42/16.59 ((
% 99.42/16.59 (ksndsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (ksndpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (kpairsurjEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodsndin) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairmemEL) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairmemER) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempaircEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodfstpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodsndpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairsurjEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrI) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrSub) =>
% 99.42/16.59 ((
% 99.42/16.59 (setOfPairsIsBReln) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrERa) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrEL1) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrEL2) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrER) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcImageSingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (apProp) =>
% 99.42/16.59 ((
% 99.42/16.59 (app) =>
% 99.42/16.59 ((
% 99.42/16.59 (infuncsetfunc) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2p) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcinfuncset) =>
% 99.42/16.59 ((
% 99.42/16.59 (lamProp) =>
% 99.42/16.59 ((
% 99.42/16.59 (lamp) =>
% 99.42/16.59 ((
% 99.42/16.59 (lam2p) =>
% 99.42/16.59 ((
% 99.42/16.59 (brelnall1) =>
% 99.42/16.59 ((
% 99.42/16.59 (brelnall2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1E2) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp3) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcextLem) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp4) =>
% 99.42/16.59 ((
% 99.42/16.59 (subbreln) =>
% 99.42/16.59 ((
% 99.42/16.59 (eqbreln) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcext) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcext2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2apEq1) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2apEq2) =>
% 99.42/16.59 ((
% 99.42/16.59 (beta1) =>
% 99.42/16.59 ((
% 99.42/16.59 (eta1) =>
% 99.42/16.59 ((
% 99.42/16.59 (lam2lamEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (beta2) =>
% 99.42/16.59 ((
% 99.42/16.59 (eta2) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalseProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalseProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ifSingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (ifp) =>
% 99.42/16.59 ((
% 99.42/16.59 (theeq) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrue) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalse) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueorfalse) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (setextT) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetTI) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetTI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetTE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectTELcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectTERcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT1) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT2) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT3) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementSub1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementSub2) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTnotintersectT) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementImpComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementSubsetComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementInPowersetComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (contraSubsetComplement) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTcontraSubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTILcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTIRcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInUnion) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInUnion2) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInIntersectUnions) =>
% 99.42/16.59 ((
% 99.42/16.59 (intersectInPowersetIntersectUnions) =>
% 99.42/16.59 ((
% 99.42/16.59 (inComplementUnionImpNotIn1) =>
% 99.42/16.59 ((
% 99.42/16.59 (inComplementUnionImpInComplement1) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTE) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTEcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementUnionInPowersetComplement) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a2) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1a) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1b) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2b2) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2b) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule0) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule1) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule3) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule4) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_1) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_3) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_4) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_5) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1all2) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1SetBreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (choice2fnsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (setOfPairsIsBReln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1all1) =>
% 99.42/16.59 ((
% 99.42/16.59 (subbreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (eqbreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compEex) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionIL) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionIR) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionEcases) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionCommutes) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2Ex) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2W) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2A) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2B) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Ex) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Ex1) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Equiv) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1E) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1I) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncInInjFuncSet) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncSetFuncIn) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncSetFuncInj) =>
% 99.42/16.59 ((
% 99.42/16.59 (!!) @ (
% 99.42/16.59 (('#B') @ (
% 99.42/16.59 !!) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 !!))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#S') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 '#S') @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 '#S'))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 =>))))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#C') @ in)))) @
% 99.42/16.59 surjFuncSet)))))))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#C') @ in)))) @
% 99.42/16.59 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl458])).
% 99.42/16.59 thf(zip_derived_cl475, plain,
% 99.42/16.59 (~ (((singletonsswitch) =>
% 99.42/16.59 (((upairsetE) =>
% 99.42/16.59 (((upairsetIL) =>
% 99.42/16.59 (((upairsetIR) =>
% 99.42/16.59 (((emptyE1) =>
% 99.42/16.59 (((vacuousDall) =>
% 99.42/16.59 (((quantDeMorgan1) =>
% 99.42/16.59 (((quantDeMorgan2) =>
% 99.42/16.59 (((quantDeMorgan3) =>
% 99.42/16.59 (((quantDeMorgan4) =>
% 99.42/16.59 (((prop2setI) =>
% 99.42/16.59 (((prop2set2propI) =>
% 99.42/16.59 (((notdexE) =>
% 99.42/16.59 (((notdallE) =>
% 99.42/16.59 (((exuI1) =>
% 99.42/16.59 (((exuI3) =>
% 99.42/16.59 (((exuI2) =>
% 99.42/16.59 (((inCongP) =>
% 99.42/16.59 (((in__Cong) =>
% 99.42/16.59 (((exuE3u) =>
% 99.42/16.59 (((exu__Cong) =>
% 99.42/16.59 (((setadjoin__Cong) =>
% 99.42/16.59 (((powerset__Cong) =>
% 99.42/16.59 (((setunion__Cong) =>
% 99.42/16.59 (((exuEu) =>
% 99.42/16.59 (((descr__Cong) =>
% 99.42/16.59 (((dsetconstr__Cong) =>
% 99.42/16.59 (((subsetI1) =>
% 99.42/16.59 (((eqimpsubset2) =>
% 99.42/16.59 (((eqimpsubset1) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetI2) =>
% 99.42/16.59 ((
% 99.42/16.59 (emptysetsubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetE) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetE2) =>
% 99.42/16.59 ((
% 99.42/16.59 (notsubsetI) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (upairset2IR) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionIR) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionEcases) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionE) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionLsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionRsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectI) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset5) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectEL) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectLsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset2) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset3) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectER) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (binintersectRsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset4) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset1) =>
% 99.42/16.59 ((
% 99.42/16.59 (bs114d) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusI) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusEL) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusER) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusSubset2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusERneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusELneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusILneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusIRneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusLsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusSubset1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffE) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffI2) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffIneg1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffIneg2) =>
% 99.42/16.59 ((
% 99.42/16.59 (secondinupair) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairIL) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairIR) =>
% 99.42/16.59 ((
% 99.42/16.59 (kpairiskpair) =>
% 99.42/16.59 ((
% 99.42/16.59 (kpairp) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletonsubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletoninpowerset) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletoninpowunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairset2E) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairsubunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairinpowunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem1) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem3) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairin) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempair1) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempair) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionE2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton1) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletonprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1E1) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1I) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1I2) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletonsuniq) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL1) =>
% 99.42/16.59 ((
% 99.42/16.59 (kfstsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (theprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (kfstpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodfstin) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR11) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR12) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR1) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairequniteq) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR) =>
% 99.42/16.59 ((
% 99.42/16.59 (ksndsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (ksndpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (kpairsurjEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodsndin) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairmemEL) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairmemER) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempaircEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodfstpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodsndpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairsurjEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrI) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrSub) =>
% 99.42/16.59 ((
% 99.42/16.59 (setOfPairsIsBReln) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrERa) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrEL1) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrEL2) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrER) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcImageSingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (apProp) =>
% 99.42/16.59 ((
% 99.42/16.59 (app) =>
% 99.42/16.59 ((
% 99.42/16.59 (infuncsetfunc) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2p) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcinfuncset) =>
% 99.42/16.59 ((
% 99.42/16.59 (lamProp) =>
% 99.42/16.59 ((
% 99.42/16.59 (lamp) =>
% 99.42/16.59 ((
% 99.42/16.59 (lam2p) =>
% 99.42/16.59 ((
% 99.42/16.59 (brelnall1) =>
% 99.42/16.59 ((
% 99.42/16.59 (brelnall2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1E2) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp3) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcextLem) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp4) =>
% 99.42/16.59 ((
% 99.42/16.59 (subbreln) =>
% 99.42/16.59 ((
% 99.42/16.59 (eqbreln) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcext) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcext2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2apEq1) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2apEq2) =>
% 99.42/16.59 ((
% 99.42/16.59 (beta1) =>
% 99.42/16.59 ((
% 99.42/16.59 (eta1) =>
% 99.42/16.59 ((
% 99.42/16.59 (lam2lamEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (beta2) =>
% 99.42/16.59 ((
% 99.42/16.59 (eta2) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalseProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalseProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ifSingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (ifp) =>
% 99.42/16.59 ((
% 99.42/16.59 (theeq) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrue) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalse) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueorfalse) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (setextT) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetTI) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetTI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetTE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectTELcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectTERcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT1) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT2) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT3) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementSub1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementSub2) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTnotintersectT) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementImpComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementSubsetComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementInPowersetComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (contraSubsetComplement) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTcontraSubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTILcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTIRcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInUnion) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInUnion2) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInIntersectUnions) =>
% 99.42/16.59 ((
% 99.42/16.59 (intersectInPowersetIntersectUnions) =>
% 99.42/16.59 ((
% 99.42/16.59 (inComplementUnionImpNotIn1) =>
% 99.42/16.59 ((
% 99.42/16.59 (inComplementUnionImpInComplement1) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTE) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTEcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementUnionInPowersetComplement) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a2) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1a) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1b) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2b2) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2b) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule0) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule1) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule3) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule4) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_1) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_3) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_4) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_5) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1all2) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1SetBreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (choice2fnsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (setOfPairsIsBReln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1all1) =>
% 99.42/16.59 ((
% 99.42/16.59 (subbreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (eqbreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compEex) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionIL) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionIR) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionEcases) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionCommutes) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2Ex) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2W) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2A) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2B) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Ex) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Ex1) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Equiv) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1E) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1I) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncInInjFuncSet) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncSetFuncIn) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncSetFuncInj) =>
% 99.42/16.59 ((
% 99.42/16.59 (!!) @ (
% 99.42/16.59 (('#B') @ (
% 99.42/16.59 !!) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 !!))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#S') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 '#S') @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 '#S'))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 =>))))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#C') @ in)))) @
% 99.42/16.59 surjFuncSet)))))))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#C') @ in)))) @
% 99.42/16.59 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl467])).
% 99.42/16.59 thf(zip_derived_cl485, plain,
% 99.42/16.59 (~ (((upairsetE) =>
% 99.42/16.59 (((upairsetIL) =>
% 99.42/16.59 (((upairsetIR) =>
% 99.42/16.59 (((emptyE1) =>
% 99.42/16.59 (((vacuousDall) =>
% 99.42/16.59 (((quantDeMorgan1) =>
% 99.42/16.59 (((quantDeMorgan2) =>
% 99.42/16.59 (((quantDeMorgan3) =>
% 99.42/16.59 (((quantDeMorgan4) =>
% 99.42/16.59 (((prop2setI) =>
% 99.42/16.59 (((prop2set2propI) =>
% 99.42/16.59 (((notdexE) =>
% 99.42/16.59 (((notdallE) =>
% 99.42/16.59 (((exuI1) =>
% 99.42/16.59 (((exuI3) =>
% 99.42/16.59 (((exuI2) =>
% 99.42/16.59 (((inCongP) =>
% 99.42/16.59 (((in__Cong) =>
% 99.42/16.59 (((exuE3u) =>
% 99.42/16.59 (((exu__Cong) =>
% 99.42/16.59 (((setadjoin__Cong) =>
% 99.42/16.59 (((powerset__Cong) =>
% 99.42/16.59 (((setunion__Cong) =>
% 99.42/16.59 (((exuEu) =>
% 99.42/16.59 (((descr__Cong) =>
% 99.42/16.59 (((dsetconstr__Cong) =>
% 99.42/16.59 (((subsetI1) =>
% 99.42/16.59 (((eqimpsubset2) =>
% 99.42/16.59 (((eqimpsubset1) =>
% 99.42/16.59 (((subsetI2) =>
% 99.42/16.59 ((
% 99.42/16.59 (emptysetsubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetE) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetE2) =>
% 99.42/16.59 ((
% 99.42/16.59 (notsubsetI) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (notequalI2) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetRefl) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetTrans) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (powersetE1) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (powersetsubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (sepInPowerset) =>
% 99.42/16.59 ((
% 99.42/16.59 (sepSubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionIL) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairset2IR) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionIR) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionEcases) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionE) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionLsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionRsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectI) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset5) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectEL) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectLsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset2) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset3) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectER) =>
% 99.42/16.59 ((
% 99.42/16.59 (disjointsetsI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectRsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset4) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset1) =>
% 99.42/16.59 ((
% 99.42/16.59 (bs114d) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusI) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusEL) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusER) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusSubset2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusERneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusELneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusILneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusIRneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusLsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusSubset1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffE) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffI2) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffIneg1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffIneg2) =>
% 99.42/16.59 ((
% 99.42/16.59 (secondinupair) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairIL) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairIR) =>
% 99.42/16.59 ((
% 99.42/16.59 (kpairiskpair) =>
% 99.42/16.59 ((
% 99.42/16.59 (kpairp) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletonsubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletoninpowerset) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletoninpowunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairset2E) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairsubunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairinpowunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem1) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem3) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairin) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempair1) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempair) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionE2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton1) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletonprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1E1) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1I) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1I2) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletonsuniq) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL1) =>
% 99.42/16.59 ((
% 99.42/16.59 (kfstsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (theprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (kfstpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodfstin) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR11) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR12) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR1) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairequniteq) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR) =>
% 99.42/16.59 ((
% 99.42/16.59 (ksndsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (ksndpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (kpairsurjEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodsndin) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairmemEL) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairmemER) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempaircEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodfstpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodsndpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairsurjEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrI) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrSub) =>
% 99.42/16.59 ((
% 99.42/16.59 (setOfPairsIsBReln) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrERa) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrEL1) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrEL2) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrER) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcImageSingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (apProp) =>
% 99.42/16.59 ((
% 99.42/16.59 (app) =>
% 99.42/16.59 ((
% 99.42/16.59 (infuncsetfunc) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2p) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcinfuncset) =>
% 99.42/16.59 ((
% 99.42/16.59 (lamProp) =>
% 99.42/16.59 ((
% 99.42/16.59 (lamp) =>
% 99.42/16.59 ((
% 99.42/16.59 (lam2p) =>
% 99.42/16.59 ((
% 99.42/16.59 (brelnall1) =>
% 99.42/16.59 ((
% 99.42/16.59 (brelnall2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1E2) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp3) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcextLem) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp4) =>
% 99.42/16.59 ((
% 99.42/16.59 (subbreln) =>
% 99.42/16.59 ((
% 99.42/16.59 (eqbreln) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcext) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcext2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2apEq1) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2apEq2) =>
% 99.42/16.59 ((
% 99.42/16.59 (beta1) =>
% 99.42/16.59 ((
% 99.42/16.59 (eta1) =>
% 99.42/16.59 ((
% 99.42/16.59 (lam2lamEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (beta2) =>
% 99.42/16.59 ((
% 99.42/16.59 (eta2) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalseProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalseProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ifSingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (ifp) =>
% 99.42/16.59 ((
% 99.42/16.59 (theeq) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrue) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalse) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueorfalse) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (setextT) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetTI) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetTI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetTE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectTELcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectTERcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT1) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT2) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT3) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementSub1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementSub2) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTnotintersectT) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementImpComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementSubsetComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementInPowersetComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (contraSubsetComplement) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTcontraSubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTILcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTIRcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInUnion) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInUnion2) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInIntersectUnions) =>
% 99.42/16.59 ((
% 99.42/16.59 (intersectInPowersetIntersectUnions) =>
% 99.42/16.59 ((
% 99.42/16.59 (inComplementUnionImpNotIn1) =>
% 99.42/16.59 ((
% 99.42/16.59 (inComplementUnionImpInComplement1) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTE) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTEcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementUnionInPowersetComplement) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a2) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1a) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1b) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2b2) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2b) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule0) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule1) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule3) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule4) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_1) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_3) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_4) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_5) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1all2) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1SetBreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (choice2fnsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (setOfPairsIsBReln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1all1) =>
% 99.42/16.59 ((
% 99.42/16.59 (subbreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (eqbreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compEex) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionIL) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionIR) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionEcases) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionCommutes) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2Ex) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2W) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2A) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2B) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Ex) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Ex1) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Equiv) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1E) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1I) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncInInjFuncSet) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncSetFuncIn) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncSetFuncInj) =>
% 99.42/16.59 ((
% 99.42/16.59 (!!) @ (
% 99.42/16.59 (('#B') @ (
% 99.42/16.59 !!) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 !!))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#S') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 '#S') @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 '#S'))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 =>))))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#C') @ in)))) @
% 99.42/16.59 surjFuncSet)))))))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#C') @ in)))) @
% 99.42/16.59 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl475])).
% 99.42/16.59 thf(zip_derived_cl496, plain,
% 99.42/16.59 (~ (((upairsetIL) =>
% 99.42/16.59 (((upairsetIR) =>
% 99.42/16.59 (((emptyE1) =>
% 99.42/16.59 (((vacuousDall) =>
% 99.42/16.59 (((quantDeMorgan1) =>
% 99.42/16.59 (((quantDeMorgan2) =>
% 99.42/16.59 (((quantDeMorgan3) =>
% 99.42/16.59 (((quantDeMorgan4) =>
% 99.42/16.59 (((prop2setI) =>
% 99.42/16.59 (((prop2set2propI) =>
% 99.42/16.59 (((notdexE) =>
% 99.42/16.59 (((notdallE) =>
% 99.42/16.59 (((exuI1) =>
% 99.42/16.59 (((exuI3) =>
% 99.42/16.59 (((exuI2) =>
% 99.42/16.59 (((inCongP) =>
% 99.42/16.59 (((in__Cong) =>
% 99.42/16.59 (((exuE3u) =>
% 99.42/16.59 (((exu__Cong) =>
% 99.42/16.59 (((setadjoin__Cong) =>
% 99.42/16.59 (((powerset__Cong) =>
% 99.42/16.59 (((setunion__Cong) =>
% 99.42/16.59 (((exuEu) =>
% 99.42/16.59 (((descr__Cong) =>
% 99.42/16.59 (((dsetconstr__Cong) =>
% 99.42/16.59 (((subsetI1) =>
% 99.42/16.59 (((eqimpsubset2) =>
% 99.42/16.59 (((eqimpsubset1) =>
% 99.42/16.59 (((subsetI2) =>
% 99.42/16.59 (((emptysetsubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetE) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetE2) =>
% 99.42/16.59 ((
% 99.42/16.59 (notsubsetI) =>
% 99.42/16.59 ((
% 99.42/16.59 (notequalI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (notequalI2) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetRefl) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetTrans) =>
% 99.42/16.59 ((
% 99.42/16.59 (setadjoinSub) =>
% 99.42/16.59 ((
% 99.42/16.59 (setadjoinSub2) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (setextsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetemptysetimpeq) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (powersetE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (inPowerset) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetsubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (sepInPowerset) =>
% 99.42/16.59 ((
% 99.42/16.59 (sepSubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionIL) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairset2IR) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionIR) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionEcases) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionE) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionLsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionRsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectI) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset5) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectEL) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectLsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset2) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset3) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectER) =>
% 99.42/16.59 ((
% 99.42/16.59 (disjointsetsI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectRsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset4) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset1) =>
% 99.42/16.59 ((
% 99.42/16.59 (bs114d) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusI) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusEL) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusER) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusSubset2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusERneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusELneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusILneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusIRneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusLsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusSubset1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffE) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffI2) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffIneg1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffIneg2) =>
% 99.42/16.59 ((
% 99.42/16.59 (secondinupair) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairIL) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairIR) =>
% 99.42/16.59 ((
% 99.42/16.59 (kpairiskpair) =>
% 99.42/16.59 ((
% 99.42/16.59 (kpairp) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletonsubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletoninpowerset) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletoninpowunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairset2E) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairsubunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairinpowunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem1) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem3) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairin) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempair1) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempair) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionE2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton1) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletonprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1E1) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1I) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1I2) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletonsuniq) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL1) =>
% 99.42/16.59 ((
% 99.42/16.59 (kfstsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (theprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (kfstpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodfstin) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR11) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR12) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR1) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairequniteq) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR) =>
% 99.42/16.59 ((
% 99.42/16.59 (ksndsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (ksndpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (kpairsurjEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodsndin) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairmemEL) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairmemER) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempaircEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodfstpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodsndpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairsurjEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrI) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrSub) =>
% 99.42/16.59 ((
% 99.42/16.59 (setOfPairsIsBReln) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrERa) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrEL1) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrEL2) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrER) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcImageSingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (apProp) =>
% 99.42/16.59 ((
% 99.42/16.59 (app) =>
% 99.42/16.59 ((
% 99.42/16.59 (infuncsetfunc) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2p) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcinfuncset) =>
% 99.42/16.59 ((
% 99.42/16.59 (lamProp) =>
% 99.42/16.59 ((
% 99.42/16.59 (lamp) =>
% 99.42/16.59 ((
% 99.42/16.59 (lam2p) =>
% 99.42/16.59 ((
% 99.42/16.59 (brelnall1) =>
% 99.42/16.59 ((
% 99.42/16.59 (brelnall2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1E2) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp3) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcextLem) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp4) =>
% 99.42/16.59 ((
% 99.42/16.59 (subbreln) =>
% 99.42/16.59 ((
% 99.42/16.59 (eqbreln) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcext) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcext2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2apEq1) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2apEq2) =>
% 99.42/16.59 ((
% 99.42/16.59 (beta1) =>
% 99.42/16.59 ((
% 99.42/16.59 (eta1) =>
% 99.42/16.59 ((
% 99.42/16.59 (lam2lamEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (beta2) =>
% 99.42/16.59 ((
% 99.42/16.59 (eta2) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalseProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalseProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ifSingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (ifp) =>
% 99.42/16.59 ((
% 99.42/16.59 (theeq) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrue) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalse) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueorfalse) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (setextT) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetTI) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetTI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetTE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectTELcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectTERcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT1) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT2) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT3) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementSub1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementSub2) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTnotintersectT) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementImpComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementSubsetComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementInPowersetComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (contraSubsetComplement) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTcontraSubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTILcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTIRcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInUnion) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInUnion2) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInIntersectUnions) =>
% 99.42/16.59 ((
% 99.42/16.59 (intersectInPowersetIntersectUnions) =>
% 99.42/16.59 ((
% 99.42/16.59 (inComplementUnionImpNotIn1) =>
% 99.42/16.59 ((
% 99.42/16.59 (inComplementUnionImpInComplement1) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTE) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTEcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementUnionInPowersetComplement) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a2) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1a) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1b) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2b2) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2b) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule0) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule1) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule3) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule4) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_1) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_3) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_4) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_5) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1all2) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1SetBreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (choice2fnsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (setOfPairsIsBReln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1all1) =>
% 99.42/16.59 ((
% 99.42/16.59 (subbreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (eqbreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compEex) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionIL) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionIR) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionEcases) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionCommutes) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2Ex) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2W) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2A) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2B) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Ex) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Ex1) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Equiv) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1E) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1I) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncInInjFuncSet) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncSetFuncIn) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncSetFuncInj) =>
% 99.42/16.59 ((
% 99.42/16.59 (!!) @ (
% 99.42/16.59 (('#B') @ (
% 99.42/16.59 !!) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 !!))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#S') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 '#S') @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 '#S'))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 =>))))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#C') @ in)))) @
% 99.42/16.59 surjFuncSet)))))))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#C') @ in)))) @
% 99.42/16.59 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl485])).
% 99.42/16.59 thf(zip_derived_cl507, plain,
% 99.42/16.59 (~ (((upairsetIR) =>
% 99.42/16.59 (((emptyE1) =>
% 99.42/16.59 (((vacuousDall) =>
% 99.42/16.59 (((quantDeMorgan1) =>
% 99.42/16.59 (((quantDeMorgan2) =>
% 99.42/16.59 (((quantDeMorgan3) =>
% 99.42/16.59 (((quantDeMorgan4) =>
% 99.42/16.59 (((prop2setI) =>
% 99.42/16.59 (((prop2set2propI) =>
% 99.42/16.59 (((notdexE) =>
% 99.42/16.59 (((notdallE) =>
% 99.42/16.59 (((exuI1) =>
% 99.42/16.59 (((exuI3) =>
% 99.42/16.59 (((exuI2) =>
% 99.42/16.59 (((inCongP) =>
% 99.42/16.59 (((in__Cong) =>
% 99.42/16.59 (((exuE3u) =>
% 99.42/16.59 (((exu__Cong) =>
% 99.42/16.59 (((setadjoin__Cong) =>
% 99.42/16.59 (((powerset__Cong) =>
% 99.42/16.59 (((setunion__Cong) =>
% 99.42/16.59 (((exuEu) =>
% 99.42/16.59 (((descr__Cong) =>
% 99.42/16.59 (((dsetconstr__Cong) =>
% 99.42/16.59 (((subsetI1) =>
% 99.42/16.59 (((eqimpsubset2) =>
% 99.42/16.59 (((eqimpsubset1) =>
% 99.42/16.59 (((subsetI2) =>
% 99.42/16.59 (((emptysetsubset) =>
% 99.42/16.59 (((subsetE) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetE2) =>
% 99.42/16.59 ((
% 99.42/16.59 (notsubsetI) =>
% 99.42/16.59 ((
% 99.42/16.59 (notequalI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (notequalI2) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetRefl) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetTrans) =>
% 99.42/16.59 ((
% 99.42/16.59 (setadjoinSub) =>
% 99.42/16.59 ((
% 99.42/16.59 (setadjoinSub2) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (setextsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetemptysetimpeq) =>
% 99.42/16.59 ((
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% 99.42/16.59 ((
% 99.42/16.59 (powersetE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (inPowerset) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetsubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (sepInPowerset) =>
% 99.42/16.59 ((
% 99.42/16.59 (sepSubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionIL) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairset2IR) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionIR) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionEcases) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionE) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionLsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionRsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectI) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset5) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectEL) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectLsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset2) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset3) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectER) =>
% 99.42/16.59 ((
% 99.42/16.59 (disjointsetsI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectRsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset4) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectSubset1) =>
% 99.42/16.59 ((
% 99.42/16.59 (bs114d) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusI) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusEL) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusER) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusSubset2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusERneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusELneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusILneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusIRneg) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusLsub) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusSubset1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffE) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffI2) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffIneg1) =>
% 99.42/16.59 ((
% 99.42/16.59 (symdiffIneg2) =>
% 99.42/16.59 ((
% 99.42/16.59 (secondinupair) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairIL) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairIR) =>
% 99.42/16.59 ((
% 99.42/16.59 (kpairiskpair) =>
% 99.42/16.59 ((
% 99.42/16.59 (kpairp) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletonsubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletoninpowerset) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletoninpowunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairset2E) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairsubunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairinpowunion) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem1) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ubforcartprodlem3) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairin) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempair1) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempair) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionE2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton1) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setunionsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletonprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1E1) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1I) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1I2) =>
% 99.42/16.59 ((
% 99.42/16.59 (singletonsuniq) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL1) =>
% 99.42/16.59 ((
% 99.42/16.59 (kfstsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (theprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (kfstpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodfstin) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjL) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR11) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR12) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR1) =>
% 99.42/16.59 ((
% 99.42/16.59 (upairequniteq) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR2) =>
% 99.42/16.59 ((
% 99.42/16.59 (setukpairinjR) =>
% 99.42/16.59 ((
% 99.42/16.59 (ksndsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (ksndpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (kpairsurjEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodsndin) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairmemEL) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairmemER) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodmempaircEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodfstpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodsndpairEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (cartprodpairsurjEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrI) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrSub) =>
% 99.42/16.59 ((
% 99.42/16.59 (setOfPairsIsBReln) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrERa) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrEL1) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrEL2) =>
% 99.42/16.59 ((
% 99.42/16.59 (dpsetconstrER) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcImageSingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (apProp) =>
% 99.42/16.59 ((
% 99.42/16.59 (app) =>
% 99.42/16.59 ((
% 99.42/16.59 (infuncsetfunc) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2p) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcinfuncset) =>
% 99.42/16.59 ((
% 99.42/16.59 (lamProp) =>
% 99.42/16.59 ((
% 99.42/16.59 (lamp) =>
% 99.42/16.59 ((
% 99.42/16.59 (lam2p) =>
% 99.42/16.59 ((
% 99.42/16.59 (brelnall1) =>
% 99.42/16.59 ((
% 99.42/16.59 (brelnall2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ex1E2) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp3) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcextLem) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcGraphProp4) =>
% 99.42/16.59 ((
% 99.42/16.59 (subbreln) =>
% 99.42/16.59 ((
% 99.42/16.59 (eqbreln) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcext) =>
% 99.42/16.59 ((
% 99.42/16.59 (funcext2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2apEq1) =>
% 99.42/16.59 ((
% 99.42/16.59 (ap2apEq2) =>
% 99.42/16.59 ((
% 99.42/16.59 (beta1) =>
% 99.42/16.59 ((
% 99.42/16.59 (eta1) =>
% 99.42/16.59 ((
% 99.42/16.59 (lam2lamEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (beta2) =>
% 99.42/16.59 ((
% 99.42/16.59 (eta2) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalseProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalseProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueProp1) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueProp2) =>
% 99.42/16.59 ((
% 99.42/16.59 (ifSingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (ifp) =>
% 99.42/16.59 ((
% 99.42/16.59 (theeq) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrue) =>
% 99.42/16.59 ((
% 99.42/16.59 (iffalse) =>
% 99.42/16.59 ((
% 99.42/16.59 (iftrueorfalse) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (setminusT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementT_lem) =>
% 99.42/16.59 ((
% 99.42/16.59 (setextT) =>
% 99.42/16.59 ((
% 99.42/16.59 (subsetTI) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetTI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (powersetTE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectTELcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (binintersectTERcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT1) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT2) =>
% 99.42/16.59 ((
% 99.42/16.59 (contrasubsetT3) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementI1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementE1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementSub1) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementSub2) =>
% 99.42/16.59 ((
% 99.42/16.59 (doubleComplementEq) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTnotintersectT) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementImpComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementSubsetComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementInPowersetComplementIntersect) =>
% 99.42/16.59 ((
% 99.42/16.59 (contraSubsetComplement) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementTcontraSubset) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTILcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTIRcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInUnion) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInUnion2) =>
% 99.42/16.59 ((
% 99.42/16.59 (inIntersectImpInIntersectUnions) =>
% 99.42/16.59 ((
% 99.42/16.59 (intersectInPowersetIntersectUnions) =>
% 99.42/16.59 ((
% 99.42/16.59 (inComplementUnionImpNotIn1) =>
% 99.42/16.59 ((
% 99.42/16.59 (inComplementUnionImpInComplement1) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTE) =>
% 99.42/16.59 ((
% 99.42/16.59 (binunionTEcontra) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a1) =>
% 99.42/16.59 ((
% 99.42/16.59 (complementUnionInPowersetComplement) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a2) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1a) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1b) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan1) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2a) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2b2) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2b) =>
% 99.42/16.59 ((
% 99.42/16.59 (demorgan2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule0) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule1) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule3) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz13rule4) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_1) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_2) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_3) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_4) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz1_5) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1all2) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1SetBreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (choice2fnsingleton) =>
% 99.42/16.59 ((
% 99.42/16.59 (setOfPairsIsBReln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1all1) =>
% 99.42/16.59 ((
% 99.42/16.59 (subbreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (eqbreln1) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1invE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1compEex) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionprop) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionIL) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionIR) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionI) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionE) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionEcases) =>
% 99.42/16.59 ((
% 99.42/16.59 (breln1unionCommutes) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2Ex) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2W) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2A) =>
% 99.42/16.59 ((
% 99.42/16.59 (woz2B) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Ex) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Ex1) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1Equiv) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1E) =>
% 99.42/16.59 ((
% 99.42/16.59 (image1I) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncInInjFuncSet) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncSetFuncIn) =>
% 99.42/16.59 ((
% 99.42/16.59 (injFuncSetFuncInj) =>
% 99.42/16.59 ((
% 99.42/16.59 (!!) @ (
% 99.42/16.59 (('#B') @ (
% 99.42/16.59 !!) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 !!))) @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#S') @ (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.59 '#S') @
% 99.42/16.59 (
% 99.42/16.59 (
% 99.42/16.59 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 '#S'))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 =>))))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#C') @ in)))) @
% 99.42/16.60 surjFuncSet)))))))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#C') @ in)))) @
% 99.42/16.60 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl496])).
% 99.42/16.60 thf(zip_derived_cl517, plain,
% 99.42/16.60 (~ (((emptyE1) =>
% 99.42/16.60 (((vacuousDall) =>
% 99.42/16.60 (((quantDeMorgan1) =>
% 99.42/16.60 (((quantDeMorgan2) =>
% 99.42/16.60 (((quantDeMorgan3) =>
% 99.42/16.60 (((quantDeMorgan4) =>
% 99.42/16.60 (((prop2setI) =>
% 99.42/16.60 (((prop2set2propI) =>
% 99.42/16.60 (((notdexE) =>
% 99.42/16.60 (((notdallE) =>
% 99.42/16.60 (((exuI1) =>
% 99.42/16.60 (((exuI3) =>
% 99.42/16.60 (((exuI2) =>
% 99.42/16.60 (((inCongP) =>
% 99.42/16.60 (((in__Cong) =>
% 99.42/16.60 (((exuE3u) =>
% 99.42/16.60 (((exu__Cong) =>
% 99.42/16.60 (((setadjoin__Cong) =>
% 99.42/16.60 (((powerset__Cong) =>
% 99.42/16.60 (((setunion__Cong) =>
% 99.42/16.60 (((exuEu) =>
% 99.42/16.60 (((descr__Cong) =>
% 99.42/16.60 (((dsetconstr__Cong) =>
% 99.42/16.60 (((subsetI1) =>
% 99.42/16.60 (((eqimpsubset2) =>
% 99.42/16.60 (((eqimpsubset1) =>
% 99.42/16.60 (((subsetI2) =>
% 99.42/16.60 (((emptysetsubset) =>
% 99.42/16.60 (((subsetE) =>
% 99.42/16.60 (((subsetE2) =>
% 99.42/16.60 ((
% 99.42/16.60 (notsubsetI) =>
% 99.42/16.60 ((
% 99.42/16.60 (notequalI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (notequalI2) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetRefl) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetTrans) =>
% 99.42/16.60 ((
% 99.42/16.60 (setadjoinSub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setadjoinSub2) =>
% 99.42/16.60 ((
% 99.42/16.60 (subset2powerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (setextsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetemptysetimpeq) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (inPowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetsubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (sepInPowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (sepSubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairset2IR) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionEcases) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionE) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionRsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectI) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset5) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset2) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset3) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectER) =>
% 99.42/16.60 ((
% 99.42/16.60 (disjointsetsI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectRsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset4) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset1) =>
% 99.42/16.60 ((
% 99.42/16.60 (bs114d) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusI) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusER) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusSubset2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusERneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusELneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusILneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusIRneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusSubset1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffE) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffI2) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffIneg1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffIneg2) =>
% 99.42/16.60 ((
% 99.42/16.60 (secondinupair) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairiskpair) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairp) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonsubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletoninpowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletoninpowunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairset2E) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairsubunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairinpowunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem3) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairin) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempair1) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempair) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionE2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton1) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1E1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1I) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1I2) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonsuniq) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL1) =>
% 99.42/16.60 ((
% 99.42/16.60 (kfstsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (theprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (kfstpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodfstin) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR11) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR12) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR1) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairequniteq) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR) =>
% 99.42/16.60 ((
% 99.42/16.60 (ksndsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (ksndpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairsurjEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodsndin) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairmemEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairmemER) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempaircEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodfstpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodsndpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairsurjEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrI) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrSub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setOfPairsIsBReln) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrERa) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrEL1) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrEL2) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrER) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcImageSingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (apProp) =>
% 99.42/16.60 ((
% 99.42/16.60 (app) =>
% 99.42/16.60 ((
% 99.42/16.60 (infuncsetfunc) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2p) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcinfuncset) =>
% 99.42/16.60 ((
% 99.42/16.60 (lamProp) =>
% 99.42/16.60 ((
% 99.42/16.60 (lamp) =>
% 99.42/16.60 ((
% 99.42/16.60 (lam2p) =>
% 99.42/16.60 ((
% 99.42/16.60 (brelnall1) =>
% 99.42/16.60 ((
% 99.42/16.60 (brelnall2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1E2) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp3) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcextLem) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp4) =>
% 99.42/16.60 ((
% 99.42/16.60 (subbreln) =>
% 99.42/16.60 ((
% 99.42/16.60 (eqbreln) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcext) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcext2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2apEq1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2apEq2) =>
% 99.42/16.60 ((
% 99.42/16.60 (beta1) =>
% 99.42/16.60 ((
% 99.42/16.60 (eta1) =>
% 99.42/16.60 ((
% 99.42/16.60 (lam2lamEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (beta2) =>
% 99.42/16.60 ((
% 99.42/16.60 (eta2) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalseProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalseProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ifSingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (ifp) =>
% 99.42/16.60 ((
% 99.42/16.60 (theeq) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrue) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalse) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueorfalse) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (setextT) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetTI) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetTI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetTE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectTELcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectTERcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT1) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT2) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT3) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementSub1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementSub2) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTnotintersectT) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementImpComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementSubsetComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementInPowersetComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (contraSubsetComplement) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTcontraSubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTILcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTIRcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInUnion) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInUnion2) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInIntersectUnions) =>
% 99.42/16.60 ((
% 99.42/16.60 (intersectInPowersetIntersectUnions) =>
% 99.42/16.60 ((
% 99.42/16.60 (inComplementUnionImpNotIn1) =>
% 99.42/16.60 ((
% 99.42/16.60 (inComplementUnionImpInComplement1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTE) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTEcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementUnionInPowersetComplement) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a2) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1a) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1b) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2b2) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2b) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule0) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule1) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule3) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule4) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_1) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_3) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_4) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_5) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1all2) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1SetBreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (choice2fnsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (setOfPairsIsBReln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1all1) =>
% 99.42/16.60 ((
% 99.42/16.60 (subbreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (eqbreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compEex) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionEcases) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionCommutes) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2Ex) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2W) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2A) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2B) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Ex) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Ex1) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Equiv) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1E) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1I) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncInInjFuncSet) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncSetFuncIn) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncSetFuncInj) =>
% 99.42/16.60 ((
% 99.42/16.60 (!!) @ (
% 99.42/16.60 (('#B') @ (
% 99.42/16.60 !!) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 !!))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#S') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 '#S') @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 '#S'))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 =>))))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#C') @ in)))) @
% 99.42/16.60 surjFuncSet)))))))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#C') @ in)))) @
% 99.42/16.60 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl507])).
% 99.42/16.60 thf(zip_derived_cl528, plain,
% 99.42/16.60 (~ (((vacuousDall) =>
% 99.42/16.60 (((quantDeMorgan1) =>
% 99.42/16.60 (((quantDeMorgan2) =>
% 99.42/16.60 (((quantDeMorgan3) =>
% 99.42/16.60 (((quantDeMorgan4) =>
% 99.42/16.60 (((prop2setI) =>
% 99.42/16.60 (((prop2set2propI) =>
% 99.42/16.60 (((notdexE) =>
% 99.42/16.60 (((notdallE) =>
% 99.42/16.60 (((exuI1) =>
% 99.42/16.60 (((exuI3) =>
% 99.42/16.60 (((exuI2) =>
% 99.42/16.60 (((inCongP) =>
% 99.42/16.60 (((in__Cong) =>
% 99.42/16.60 (((exuE3u) =>
% 99.42/16.60 (((exu__Cong) =>
% 99.42/16.60 (((setadjoin__Cong) =>
% 99.42/16.60 (((powerset__Cong) =>
% 99.42/16.60 (((setunion__Cong) =>
% 99.42/16.60 (((exuEu) =>
% 99.42/16.60 (((descr__Cong) =>
% 99.42/16.60 (((dsetconstr__Cong) =>
% 99.42/16.60 (((subsetI1) =>
% 99.42/16.60 (((eqimpsubset2) =>
% 99.42/16.60 (((eqimpsubset1) =>
% 99.42/16.60 (((subsetI2) =>
% 99.42/16.60 (((emptysetsubset) =>
% 99.42/16.60 (((subsetE) =>
% 99.42/16.60 (((subsetE2) =>
% 99.42/16.60 (((notsubsetI) =>
% 99.42/16.60 ((
% 99.42/16.60 (notequalI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (notequalI2) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetRefl) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetTrans) =>
% 99.42/16.60 ((
% 99.42/16.60 (setadjoinSub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setadjoinSub2) =>
% 99.42/16.60 ((
% 99.42/16.60 (subset2powerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (setextsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetemptysetimpeq) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (inPowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetsubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (sepInPowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (sepSubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairset2IR) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionEcases) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionE) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionRsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectI) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset5) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset2) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset3) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectER) =>
% 99.42/16.60 ((
% 99.42/16.60 (disjointsetsI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectRsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset4) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset1) =>
% 99.42/16.60 ((
% 99.42/16.60 (bs114d) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusI) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusER) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusSubset2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusERneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusELneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusILneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusIRneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusSubset1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffE) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffI2) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffIneg1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffIneg2) =>
% 99.42/16.60 ((
% 99.42/16.60 (secondinupair) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairiskpair) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairp) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonsubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletoninpowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletoninpowunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairset2E) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairsubunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairinpowunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem3) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairin) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempair1) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempair) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionE2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton1) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1E1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1I) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1I2) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonsuniq) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL1) =>
% 99.42/16.60 ((
% 99.42/16.60 (kfstsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (theprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (kfstpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodfstin) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR11) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR12) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR1) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairequniteq) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR) =>
% 99.42/16.60 ((
% 99.42/16.60 (ksndsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (ksndpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairsurjEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodsndin) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairmemEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairmemER) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempaircEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodfstpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodsndpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairsurjEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrI) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrSub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setOfPairsIsBReln) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrERa) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrEL1) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrEL2) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrER) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcImageSingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (apProp) =>
% 99.42/16.60 ((
% 99.42/16.60 (app) =>
% 99.42/16.60 ((
% 99.42/16.60 (infuncsetfunc) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2p) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcinfuncset) =>
% 99.42/16.60 ((
% 99.42/16.60 (lamProp) =>
% 99.42/16.60 ((
% 99.42/16.60 (lamp) =>
% 99.42/16.60 ((
% 99.42/16.60 (lam2p) =>
% 99.42/16.60 ((
% 99.42/16.60 (brelnall1) =>
% 99.42/16.60 ((
% 99.42/16.60 (brelnall2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1E2) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp3) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcextLem) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp4) =>
% 99.42/16.60 ((
% 99.42/16.60 (subbreln) =>
% 99.42/16.60 ((
% 99.42/16.60 (eqbreln) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcext) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcext2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2apEq1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2apEq2) =>
% 99.42/16.60 ((
% 99.42/16.60 (beta1) =>
% 99.42/16.60 ((
% 99.42/16.60 (eta1) =>
% 99.42/16.60 ((
% 99.42/16.60 (lam2lamEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (beta2) =>
% 99.42/16.60 ((
% 99.42/16.60 (eta2) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalseProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalseProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ifSingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (ifp) =>
% 99.42/16.60 ((
% 99.42/16.60 (theeq) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrue) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalse) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueorfalse) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (setextT) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetTI) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetTI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetTE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectTELcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectTERcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT1) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT2) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT3) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementSub1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementSub2) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTnotintersectT) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementImpComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementSubsetComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementInPowersetComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (contraSubsetComplement) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTcontraSubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTILcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTIRcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInUnion) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInUnion2) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInIntersectUnions) =>
% 99.42/16.60 ((
% 99.42/16.60 (intersectInPowersetIntersectUnions) =>
% 99.42/16.60 ((
% 99.42/16.60 (inComplementUnionImpNotIn1) =>
% 99.42/16.60 ((
% 99.42/16.60 (inComplementUnionImpInComplement1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTE) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTEcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementUnionInPowersetComplement) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a2) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1a) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1b) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2b2) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2b) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule0) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule1) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule3) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule4) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_1) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_3) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_4) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_5) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1all2) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1SetBreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (choice2fnsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (setOfPairsIsBReln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1all1) =>
% 99.42/16.60 ((
% 99.42/16.60 (subbreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (eqbreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compEex) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionEcases) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionCommutes) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2Ex) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2W) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2A) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2B) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Ex) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Ex1) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Equiv) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1E) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1I) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncInInjFuncSet) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncSetFuncIn) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncSetFuncInj) =>
% 99.42/16.60 ((
% 99.42/16.60 (!!) @ (
% 99.42/16.60 (('#B') @ (
% 99.42/16.60 !!) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 !!))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#S') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 '#S') @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 '#S'))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 =>))))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#C') @ in)))) @
% 99.42/16.60 surjFuncSet)))))))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#C') @ in)))) @
% 99.42/16.60 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl517])).
% 99.42/16.60 thf(zip_derived_cl537, plain,
% 99.42/16.60 (~ (((quantDeMorgan1) =>
% 99.42/16.60 (((quantDeMorgan2) =>
% 99.42/16.60 (((quantDeMorgan3) =>
% 99.42/16.60 (((quantDeMorgan4) =>
% 99.42/16.60 (((prop2setI) =>
% 99.42/16.60 (((prop2set2propI) =>
% 99.42/16.60 (((notdexE) =>
% 99.42/16.60 (((notdallE) =>
% 99.42/16.60 (((exuI1) =>
% 99.42/16.60 (((exuI3) =>
% 99.42/16.60 (((exuI2) =>
% 99.42/16.60 (((inCongP) =>
% 99.42/16.60 (((in__Cong) =>
% 99.42/16.60 (((exuE3u) =>
% 99.42/16.60 (((exu__Cong) =>
% 99.42/16.60 (((setadjoin__Cong) =>
% 99.42/16.60 (((powerset__Cong) =>
% 99.42/16.60 (((setunion__Cong) =>
% 99.42/16.60 (((exuEu) =>
% 99.42/16.60 (((descr__Cong) =>
% 99.42/16.60 (((dsetconstr__Cong) =>
% 99.42/16.60 (((subsetI1) =>
% 99.42/16.60 (((eqimpsubset2) =>
% 99.42/16.60 (((eqimpsubset1) =>
% 99.42/16.60 (((subsetI2) =>
% 99.42/16.60 (((emptysetsubset) =>
% 99.42/16.60 (((subsetE) =>
% 99.42/16.60 (((subsetE2) =>
% 99.42/16.60 (((notsubsetI) =>
% 99.42/16.60 (((notequalI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (notequalI2) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetRefl) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetTrans) =>
% 99.42/16.60 ((
% 99.42/16.60 (setadjoinSub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setadjoinSub2) =>
% 99.42/16.60 ((
% 99.42/16.60 (subset2powerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (setextsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetemptysetimpeq) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (inPowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetsubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (sepInPowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (sepSubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairset2IR) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionEcases) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionE) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionRsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectI) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset5) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset2) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset3) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectER) =>
% 99.42/16.60 ((
% 99.42/16.60 (disjointsetsI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectRsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset4) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset1) =>
% 99.42/16.60 ((
% 99.42/16.60 (bs114d) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusI) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusER) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusSubset2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusERneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusELneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusILneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusIRneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusSubset1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffE) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffI2) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffIneg1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffIneg2) =>
% 99.42/16.60 ((
% 99.42/16.60 (secondinupair) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairiskpair) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairp) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonsubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletoninpowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletoninpowunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairset2E) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairsubunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairinpowunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem3) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairin) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempair1) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempair) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionE2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton1) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1E1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1I) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1I2) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonsuniq) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL1) =>
% 99.42/16.60 ((
% 99.42/16.60 (kfstsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (theprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (kfstpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodfstin) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR11) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR12) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR1) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairequniteq) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR) =>
% 99.42/16.60 ((
% 99.42/16.60 (ksndsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (ksndpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairsurjEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodsndin) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairmemEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairmemER) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempaircEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodfstpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodsndpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairsurjEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrI) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrSub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setOfPairsIsBReln) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrERa) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrEL1) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrEL2) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrER) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcImageSingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (apProp) =>
% 99.42/16.60 ((
% 99.42/16.60 (app) =>
% 99.42/16.60 ((
% 99.42/16.60 (infuncsetfunc) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2p) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcinfuncset) =>
% 99.42/16.60 ((
% 99.42/16.60 (lamProp) =>
% 99.42/16.60 ((
% 99.42/16.60 (lamp) =>
% 99.42/16.60 ((
% 99.42/16.60 (lam2p) =>
% 99.42/16.60 ((
% 99.42/16.60 (brelnall1) =>
% 99.42/16.60 ((
% 99.42/16.60 (brelnall2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1E2) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp3) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcextLem) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp4) =>
% 99.42/16.60 ((
% 99.42/16.60 (subbreln) =>
% 99.42/16.60 ((
% 99.42/16.60 (eqbreln) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcext) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcext2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2apEq1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2apEq2) =>
% 99.42/16.60 ((
% 99.42/16.60 (beta1) =>
% 99.42/16.60 ((
% 99.42/16.60 (eta1) =>
% 99.42/16.60 ((
% 99.42/16.60 (lam2lamEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (beta2) =>
% 99.42/16.60 ((
% 99.42/16.60 (eta2) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalseProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalseProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ifSingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (ifp) =>
% 99.42/16.60 ((
% 99.42/16.60 (theeq) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrue) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalse) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueorfalse) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (setextT) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetTI) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetTI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetTE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectTELcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectTERcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT1) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT2) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT3) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementSub1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementSub2) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTnotintersectT) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementImpComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementSubsetComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementInPowersetComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (contraSubsetComplement) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTcontraSubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTILcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTIRcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInUnion) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInUnion2) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInIntersectUnions) =>
% 99.42/16.60 ((
% 99.42/16.60 (intersectInPowersetIntersectUnions) =>
% 99.42/16.60 ((
% 99.42/16.60 (inComplementUnionImpNotIn1) =>
% 99.42/16.60 ((
% 99.42/16.60 (inComplementUnionImpInComplement1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTE) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTEcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementUnionInPowersetComplement) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a2) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1a) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1b) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2b2) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2b) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule0) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule1) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule3) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule4) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_1) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_3) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_4) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_5) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1all2) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1SetBreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (choice2fnsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (setOfPairsIsBReln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1all1) =>
% 99.42/16.60 ((
% 99.42/16.60 (subbreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (eqbreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compEex) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionEcases) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionCommutes) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2Ex) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2W) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2A) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2B) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Ex) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Ex1) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Equiv) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1E) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1I) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncInInjFuncSet) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncSetFuncIn) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncSetFuncInj) =>
% 99.42/16.60 ((
% 99.42/16.60 (!!) @ (
% 99.42/16.60 (('#B') @ (
% 99.42/16.60 !!) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 !!))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#S') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 '#S') @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 '#S'))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 =>))))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#C') @ in)))) @
% 99.42/16.60 surjFuncSet)))))))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#C') @ in)))) @
% 99.42/16.60 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl528])).
% 99.42/16.60 thf(zip_derived_cl546, plain,
% 99.42/16.60 (~ (((quantDeMorgan2) =>
% 99.42/16.60 (((quantDeMorgan3) =>
% 99.42/16.60 (((quantDeMorgan4) =>
% 99.42/16.60 (((prop2setI) =>
% 99.42/16.60 (((prop2set2propI) =>
% 99.42/16.60 (((notdexE) =>
% 99.42/16.60 (((notdallE) =>
% 99.42/16.60 (((exuI1) =>
% 99.42/16.60 (((exuI3) =>
% 99.42/16.60 (((exuI2) =>
% 99.42/16.60 (((inCongP) =>
% 99.42/16.60 (((in__Cong) =>
% 99.42/16.60 (((exuE3u) =>
% 99.42/16.60 (((exu__Cong) =>
% 99.42/16.60 (((setadjoin__Cong) =>
% 99.42/16.60 (((powerset__Cong) =>
% 99.42/16.60 (((setunion__Cong) =>
% 99.42/16.60 (((exuEu) =>
% 99.42/16.60 (((descr__Cong) =>
% 99.42/16.60 (((dsetconstr__Cong) =>
% 99.42/16.60 (((subsetI1) =>
% 99.42/16.60 (((eqimpsubset2) =>
% 99.42/16.60 (((eqimpsubset1) =>
% 99.42/16.60 (((subsetI2) =>
% 99.42/16.60 (((emptysetsubset) =>
% 99.42/16.60 (((subsetE) =>
% 99.42/16.60 (((subsetE2) =>
% 99.42/16.60 (((notsubsetI) =>
% 99.42/16.60 (((notequalI1) =>
% 99.42/16.60 (((notequalI2) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetRefl) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetTrans) =>
% 99.42/16.60 ((
% 99.42/16.60 (setadjoinSub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setadjoinSub2) =>
% 99.42/16.60 ((
% 99.42/16.60 (subset2powerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (setextsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetemptysetimpeq) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (inPowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetsubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (sepInPowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (sepSubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairset2IR) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionEcases) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionE) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionRsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectI) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset5) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset2) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset3) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectER) =>
% 99.42/16.60 ((
% 99.42/16.60 (disjointsetsI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectRsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset4) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset1) =>
% 99.42/16.60 ((
% 99.42/16.60 (bs114d) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusI) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusER) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusSubset2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusERneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusELneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusILneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusIRneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusSubset1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffE) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffI2) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffIneg1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffIneg2) =>
% 99.42/16.60 ((
% 99.42/16.60 (secondinupair) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairiskpair) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairp) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonsubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletoninpowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletoninpowunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairset2E) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairsubunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairinpowunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem3) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairin) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempair1) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempair) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionE2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton1) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1E1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1I) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1I2) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonsuniq) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL1) =>
% 99.42/16.60 ((
% 99.42/16.60 (kfstsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (theprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (kfstpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodfstin) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR11) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR12) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR1) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairequniteq) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR) =>
% 99.42/16.60 ((
% 99.42/16.60 (ksndsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (ksndpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairsurjEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodsndin) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairmemEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairmemER) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempaircEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodfstpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodsndpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairsurjEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrI) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrSub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setOfPairsIsBReln) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrERa) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrEL1) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrEL2) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrER) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcImageSingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (apProp) =>
% 99.42/16.60 ((
% 99.42/16.60 (app) =>
% 99.42/16.60 ((
% 99.42/16.60 (infuncsetfunc) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2p) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcinfuncset) =>
% 99.42/16.60 ((
% 99.42/16.60 (lamProp) =>
% 99.42/16.60 ((
% 99.42/16.60 (lamp) =>
% 99.42/16.60 ((
% 99.42/16.60 (lam2p) =>
% 99.42/16.60 ((
% 99.42/16.60 (brelnall1) =>
% 99.42/16.60 ((
% 99.42/16.60 (brelnall2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1E2) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp3) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcextLem) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp4) =>
% 99.42/16.60 ((
% 99.42/16.60 (subbreln) =>
% 99.42/16.60 ((
% 99.42/16.60 (eqbreln) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcext) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcext2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2apEq1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2apEq2) =>
% 99.42/16.60 ((
% 99.42/16.60 (beta1) =>
% 99.42/16.60 ((
% 99.42/16.60 (eta1) =>
% 99.42/16.60 ((
% 99.42/16.60 (lam2lamEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (beta2) =>
% 99.42/16.60 ((
% 99.42/16.60 (eta2) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalseProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalseProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ifSingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (ifp) =>
% 99.42/16.60 ((
% 99.42/16.60 (theeq) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrue) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalse) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueorfalse) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (setextT) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetTI) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetTI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetTE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectTELcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectTERcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT1) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT2) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT3) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementSub1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementSub2) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTnotintersectT) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementImpComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementSubsetComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementInPowersetComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (contraSubsetComplement) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTcontraSubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTILcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTIRcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInUnion) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInUnion2) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInIntersectUnions) =>
% 99.42/16.60 ((
% 99.42/16.60 (intersectInPowersetIntersectUnions) =>
% 99.42/16.60 ((
% 99.42/16.60 (inComplementUnionImpNotIn1) =>
% 99.42/16.60 ((
% 99.42/16.60 (inComplementUnionImpInComplement1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTE) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTEcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementUnionInPowersetComplement) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a2) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1a) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1b) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2b2) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2b) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule0) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule1) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule3) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule4) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_1) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_3) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_4) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_5) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1all2) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1SetBreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (choice2fnsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (setOfPairsIsBReln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1all1) =>
% 99.42/16.60 ((
% 99.42/16.60 (subbreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (eqbreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compEex) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionEcases) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionCommutes) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2Ex) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2W) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2A) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2B) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Ex) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Ex1) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Equiv) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1E) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1I) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncInInjFuncSet) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncSetFuncIn) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncSetFuncInj) =>
% 99.42/16.60 ((
% 99.42/16.60 (!!) @ (
% 99.42/16.60 (('#B') @ (
% 99.42/16.60 !!) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 !!))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#S') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 '#S') @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 '#S'))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 =>))))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#C') @ in)))) @
% 99.42/16.60 surjFuncSet)))))))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#C') @ in)))) @
% 99.42/16.60 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl537])).
% 99.42/16.60 thf(zip_derived_cl553, plain,
% 99.42/16.60 (~ (((quantDeMorgan3) =>
% 99.42/16.60 (((quantDeMorgan4) =>
% 99.42/16.60 (((prop2setI) =>
% 99.42/16.60 (((prop2set2propI) =>
% 99.42/16.60 (((notdexE) =>
% 99.42/16.60 (((notdallE) =>
% 99.42/16.60 (((exuI1) =>
% 99.42/16.60 (((exuI3) =>
% 99.42/16.60 (((exuI2) =>
% 99.42/16.60 (((inCongP) =>
% 99.42/16.60 (((in__Cong) =>
% 99.42/16.60 (((exuE3u) =>
% 99.42/16.60 (((exu__Cong) =>
% 99.42/16.60 (((setadjoin__Cong) =>
% 99.42/16.60 (((powerset__Cong) =>
% 99.42/16.60 (((setunion__Cong) =>
% 99.42/16.60 (((exuEu) =>
% 99.42/16.60 (((descr__Cong) =>
% 99.42/16.60 (((dsetconstr__Cong) =>
% 99.42/16.60 (((subsetI1) =>
% 99.42/16.60 (((eqimpsubset2) =>
% 99.42/16.60 (((eqimpsubset1) =>
% 99.42/16.60 (((subsetI2) =>
% 99.42/16.60 (((emptysetsubset) =>
% 99.42/16.60 (((subsetE) =>
% 99.42/16.60 (((subsetE2) =>
% 99.42/16.60 (((notsubsetI) =>
% 99.42/16.60 (((notequalI1) =>
% 99.42/16.60 (((notequalI2) =>
% 99.42/16.60 (((subsetRefl) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetTrans) =>
% 99.42/16.60 ((
% 99.42/16.60 (setadjoinSub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setadjoinSub2) =>
% 99.42/16.60 ((
% 99.42/16.60 (subset2powerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (setextsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetemptysetimpeq) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (inPowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetsubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (sepInPowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (sepSubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairset2IR) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionEcases) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionE) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionRsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectI) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset5) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset2) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset3) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectER) =>
% 99.42/16.60 ((
% 99.42/16.60 (disjointsetsI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectRsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset4) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset1) =>
% 99.42/16.60 ((
% 99.42/16.60 (bs114d) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusI) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusER) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusSubset2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusERneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusELneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusILneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusIRneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusSubset1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffE) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffI2) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffIneg1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffIneg2) =>
% 99.42/16.60 ((
% 99.42/16.60 (secondinupair) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairiskpair) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairp) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonsubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletoninpowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletoninpowunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairset2E) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairsubunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairinpowunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem3) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairin) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempair1) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempair) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionE2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton1) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1E1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1I) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1I2) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonsuniq) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL1) =>
% 99.42/16.60 ((
% 99.42/16.60 (kfstsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (theprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (kfstpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodfstin) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR11) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR12) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR1) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairequniteq) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR) =>
% 99.42/16.60 ((
% 99.42/16.60 (ksndsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (ksndpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairsurjEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodsndin) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairmemEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairmemER) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempaircEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodfstpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodsndpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairsurjEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrI) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrSub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setOfPairsIsBReln) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrERa) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrEL1) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrEL2) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrER) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcImageSingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (apProp) =>
% 99.42/16.60 ((
% 99.42/16.60 (app) =>
% 99.42/16.60 ((
% 99.42/16.60 (infuncsetfunc) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2p) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcinfuncset) =>
% 99.42/16.60 ((
% 99.42/16.60 (lamProp) =>
% 99.42/16.60 ((
% 99.42/16.60 (lamp) =>
% 99.42/16.60 ((
% 99.42/16.60 (lam2p) =>
% 99.42/16.60 ((
% 99.42/16.60 (brelnall1) =>
% 99.42/16.60 ((
% 99.42/16.60 (brelnall2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1E2) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp3) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcextLem) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp4) =>
% 99.42/16.60 ((
% 99.42/16.60 (subbreln) =>
% 99.42/16.60 ((
% 99.42/16.60 (eqbreln) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcext) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcext2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2apEq1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2apEq2) =>
% 99.42/16.60 ((
% 99.42/16.60 (beta1) =>
% 99.42/16.60 ((
% 99.42/16.60 (eta1) =>
% 99.42/16.60 ((
% 99.42/16.60 (lam2lamEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (beta2) =>
% 99.42/16.60 ((
% 99.42/16.60 (eta2) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalseProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalseProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ifSingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (ifp) =>
% 99.42/16.60 ((
% 99.42/16.60 (theeq) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrue) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalse) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueorfalse) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (setextT) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetTI) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetTI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetTE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectTELcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectTERcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT1) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT2) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT3) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementSub1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementSub2) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTnotintersectT) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementImpComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementSubsetComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementInPowersetComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (contraSubsetComplement) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTcontraSubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTILcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTIRcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInUnion) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInUnion2) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInIntersectUnions) =>
% 99.42/16.60 ((
% 99.42/16.60 (intersectInPowersetIntersectUnions) =>
% 99.42/16.60 ((
% 99.42/16.60 (inComplementUnionImpNotIn1) =>
% 99.42/16.60 ((
% 99.42/16.60 (inComplementUnionImpInComplement1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTE) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTEcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementUnionInPowersetComplement) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a2) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1a) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1b) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2b2) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2b) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule0) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule1) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule3) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule4) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_1) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_3) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_4) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_5) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1all2) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1SetBreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (choice2fnsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (setOfPairsIsBReln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1all1) =>
% 99.42/16.60 ((
% 99.42/16.60 (subbreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (eqbreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compEex) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionEcases) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionCommutes) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2Ex) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2W) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2A) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2B) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Ex) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Ex1) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Equiv) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1E) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1I) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncInInjFuncSet) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncSetFuncIn) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncSetFuncInj) =>
% 99.42/16.60 ((
% 99.42/16.60 (!!) @ (
% 99.42/16.60 (('#B') @ (
% 99.42/16.60 !!) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 !!))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#S') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 '#S') @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 '#S'))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 =>))))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#C') @ in)))) @
% 99.42/16.60 surjFuncSet)))))))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#C') @ in)))) @
% 99.42/16.60 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl546])).
% 99.42/16.60 thf(zip_derived_cl561, plain,
% 99.42/16.60 (~ (((quantDeMorgan4) =>
% 99.42/16.60 (((prop2setI) =>
% 99.42/16.60 (((prop2set2propI) =>
% 99.42/16.60 (((notdexE) =>
% 99.42/16.60 (((notdallE) =>
% 99.42/16.60 (((exuI1) =>
% 99.42/16.60 (((exuI3) =>
% 99.42/16.60 (((exuI2) =>
% 99.42/16.60 (((inCongP) =>
% 99.42/16.60 (((in__Cong) =>
% 99.42/16.60 (((exuE3u) =>
% 99.42/16.60 (((exu__Cong) =>
% 99.42/16.60 (((setadjoin__Cong) =>
% 99.42/16.60 (((powerset__Cong) =>
% 99.42/16.60 (((setunion__Cong) =>
% 99.42/16.60 (((exuEu) =>
% 99.42/16.60 (((descr__Cong) =>
% 99.42/16.60 (((dsetconstr__Cong) =>
% 99.42/16.60 (((subsetI1) =>
% 99.42/16.60 (((eqimpsubset2) =>
% 99.42/16.60 (((eqimpsubset1) =>
% 99.42/16.60 (((subsetI2) =>
% 99.42/16.60 (((emptysetsubset) =>
% 99.42/16.60 (((subsetE) =>
% 99.42/16.60 (((subsetE2) =>
% 99.42/16.60 (((notsubsetI) =>
% 99.42/16.60 (((notequalI1) =>
% 99.42/16.60 (((notequalI2) =>
% 99.42/16.60 (((subsetRefl) =>
% 99.42/16.60 (((subsetTrans) =>
% 99.42/16.60 ((
% 99.42/16.60 (setadjoinSub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setadjoinSub2) =>
% 99.42/16.60 ((
% 99.42/16.60 (subset2powerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (setextsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetemptysetimpeq) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (inPowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetsubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (sepInPowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (sepSubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairset2IR) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionEcases) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionE) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionRsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectI) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset5) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset2) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset3) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectER) =>
% 99.42/16.60 ((
% 99.42/16.60 (disjointsetsI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectRsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset4) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset1) =>
% 99.42/16.60 ((
% 99.42/16.60 (bs114d) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusI) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusER) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusSubset2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusERneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusELneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusILneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusIRneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusSubset1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffE) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffI2) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffIneg1) =>
% 99.42/16.60 ((
% 99.42/16.60 (symdiffIneg2) =>
% 99.42/16.60 ((
% 99.42/16.60 (secondinupair) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairiskpair) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairp) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonsubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletoninpowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletoninpowunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairset2E) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairsubunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairinpowunion) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ubforcartprodlem3) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairin) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempair1) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempair) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionE2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton1) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setunionsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1E1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1I) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1I2) =>
% 99.42/16.60 ((
% 99.42/16.60 (singletonsuniq) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL1) =>
% 99.42/16.60 ((
% 99.42/16.60 (kfstsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (theprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (kfstpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodfstin) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR11) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR12) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR1) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairequniteq) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setukpairinjR) =>
% 99.42/16.60 ((
% 99.42/16.60 (ksndsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (ksndpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (kpairsurjEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodsndin) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairmemEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairmemER) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempaircEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodfstpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodsndpairEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairsurjEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrI) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrSub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setOfPairsIsBReln) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrERa) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrEL1) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrEL2) =>
% 99.42/16.60 ((
% 99.42/16.60 (dpsetconstrER) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcImageSingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (apProp) =>
% 99.42/16.60 ((
% 99.42/16.60 (app) =>
% 99.42/16.60 ((
% 99.42/16.60 (infuncsetfunc) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2p) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcinfuncset) =>
% 99.42/16.60 ((
% 99.42/16.60 (lamProp) =>
% 99.42/16.60 ((
% 99.42/16.60 (lamp) =>
% 99.42/16.60 ((
% 99.42/16.60 (lam2p) =>
% 99.42/16.60 ((
% 99.42/16.60 (brelnall1) =>
% 99.42/16.60 ((
% 99.42/16.60 (brelnall2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ex1E2) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp3) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcextLem) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcGraphProp4) =>
% 99.42/16.60 ((
% 99.42/16.60 (subbreln) =>
% 99.42/16.60 ((
% 99.42/16.60 (eqbreln) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcext) =>
% 99.42/16.60 ((
% 99.42/16.60 (funcext2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2apEq1) =>
% 99.42/16.60 ((
% 99.42/16.60 (ap2apEq2) =>
% 99.42/16.60 ((
% 99.42/16.60 (beta1) =>
% 99.42/16.60 ((
% 99.42/16.60 (eta1) =>
% 99.42/16.60 ((
% 99.42/16.60 (lam2lamEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (beta2) =>
% 99.42/16.60 ((
% 99.42/16.60 (eta2) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalseProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalseProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueProp1) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueProp2) =>
% 99.42/16.60 ((
% 99.42/16.60 (ifSingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (ifp) =>
% 99.42/16.60 ((
% 99.42/16.60 (theeq) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrue) =>
% 99.42/16.60 ((
% 99.42/16.60 (iffalse) =>
% 99.42/16.60 ((
% 99.42/16.60 (iftrueorfalse) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementT_lem) =>
% 99.42/16.60 ((
% 99.42/16.60 (setextT) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetTI) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetTI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetTE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectTELcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectTERcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT1) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT2) =>
% 99.42/16.60 ((
% 99.42/16.60 (contrasubsetT3) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementSub1) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementSub2) =>
% 99.42/16.60 ((
% 99.42/16.60 (doubleComplementEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTnotintersectT) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementImpComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementSubsetComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementInPowersetComplementIntersect) =>
% 99.42/16.60 ((
% 99.42/16.60 (contraSubsetComplement) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementTcontraSubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTILcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTIRcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInUnion) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInUnion2) =>
% 99.42/16.60 ((
% 99.42/16.60 (inIntersectImpInIntersectUnions) =>
% 99.42/16.60 ((
% 99.42/16.60 (intersectInPowersetIntersectUnions) =>
% 99.42/16.60 ((
% 99.42/16.60 (inComplementUnionImpNotIn1) =>
% 99.42/16.60 ((
% 99.42/16.60 (inComplementUnionImpInComplement1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTE) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionTEcontra) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a1) =>
% 99.42/16.60 ((
% 99.42/16.60 (complementUnionInPowersetComplement) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a2) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1a) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1b) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan1) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2a) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2b2) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2b) =>
% 99.42/16.60 ((
% 99.42/16.60 (demorgan2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule0) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule1) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule3) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz13rule4) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_1) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_2) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_3) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_4) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz1_5) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1all2) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1SetBreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (choice2fnsingleton) =>
% 99.42/16.60 ((
% 99.42/16.60 (setOfPairsIsBReln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1all1) =>
% 99.42/16.60 ((
% 99.42/16.60 (subbreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (eqbreln1) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1invE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1compEex) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionprop) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionI) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionE) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionEcases) =>
% 99.42/16.60 ((
% 99.42/16.60 (breln1unionCommutes) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2Ex) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2W) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2A) =>
% 99.42/16.60 ((
% 99.42/16.60 (woz2B) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Ex) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Ex1) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1Equiv) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1E) =>
% 99.42/16.60 ((
% 99.42/16.60 (image1I) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncInInjFuncSet) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncSetFuncIn) =>
% 99.42/16.60 ((
% 99.42/16.60 (injFuncSetFuncInj) =>
% 99.42/16.60 ((
% 99.42/16.60 (!!) @ (
% 99.42/16.60 (('#B') @ (
% 99.42/16.60 !!) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 !!))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#S') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 '#S') @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 '#S'))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 =>))))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#C') @ in)))) @
% 99.42/16.60 surjFuncSet)))))))) @
% 99.42/16.60 (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#B') @ (
% 99.42/16.60 (
% 99.42/16.60 ('#C') @ in)))) @
% 99.42/16.60 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl553])).
% 99.42/16.60 thf(zip_derived_cl570, plain,
% 99.42/16.60 (~ (((prop2setI) =>
% 99.42/16.60 (((prop2set2propI) =>
% 99.42/16.60 (((notdexE) =>
% 99.42/16.60 (((notdallE) =>
% 99.42/16.60 (((exuI1) =>
% 99.42/16.60 (((exuI3) =>
% 99.42/16.60 (((exuI2) =>
% 99.42/16.60 (((inCongP) =>
% 99.42/16.60 (((in__Cong) =>
% 99.42/16.60 (((exuE3u) =>
% 99.42/16.60 (((exu__Cong) =>
% 99.42/16.60 (((setadjoin__Cong) =>
% 99.42/16.60 (((powerset__Cong) =>
% 99.42/16.60 (((setunion__Cong) =>
% 99.42/16.60 (((exuEu) =>
% 99.42/16.60 (((descr__Cong) =>
% 99.42/16.60 (((dsetconstr__Cong) =>
% 99.42/16.60 (((subsetI1) =>
% 99.42/16.60 (((eqimpsubset2) =>
% 99.42/16.60 (((eqimpsubset1) =>
% 99.42/16.60 (((subsetI2) =>
% 99.42/16.60 (((emptysetsubset) =>
% 99.42/16.60 (((subsetE) =>
% 99.42/16.60 (((subsetE2) =>
% 99.42/16.60 (((notsubsetI) =>
% 99.42/16.60 (((notequalI1) =>
% 99.42/16.60 (((notequalI2) =>
% 99.42/16.60 (((subsetRefl) =>
% 99.42/16.60 (((subsetTrans) =>
% 99.42/16.60 (((setadjoinSub) =>
% 99.42/16.60 ((
% 99.42/16.60 (setadjoinSub2) =>
% 99.42/16.60 ((
% 99.42/16.60 (subset2powerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (setextsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (subsetemptysetimpeq) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetE1) =>
% 99.42/16.60 ((
% 99.42/16.60 (inPowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (powersetsubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (sepInPowerset) =>
% 99.42/16.60 ((
% 99.42/16.60 (sepSubset) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionIL) =>
% 99.42/16.60 ((
% 99.42/16.60 (upairset2IR) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionIR) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionEcases) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionE) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binunionRsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectI) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset5) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectLsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset2) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset3) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectER) =>
% 99.42/16.60 ((
% 99.42/16.60 (disjointsetsI1) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectRsub) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset4) =>
% 99.42/16.60 ((
% 99.42/16.60 (binintersectSubset1) =>
% 99.42/16.60 ((
% 99.42/16.60 (bs114d) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusI) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusER) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusSubset2) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusERneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusELneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusILneg) =>
% 99.42/16.60 ((
% 99.42/16.60 (setminusIRneg) =>
% 99.42/16.60 ((
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% 99.42/16.60 ((
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% 99.42/16.60 (kpairsurjEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodsndin) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairmemEL) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodpairmemER) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodmempaircEq) =>
% 99.42/16.60 ((
% 99.42/16.60 (cartprodfstpairEq) =>
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% 99.42/16.60 (cartprodsndpairEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodpairsurjEq) =>
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% 99.42/16.61 (dpsetconstrEL2) =>
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% 99.42/16.61 ((
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% 99.42/16.61 (ap2p) =>
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% 99.42/16.61 (lamProp) =>
% 99.42/16.61 ((
% 99.42/16.61 (lamp) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (brelnall2) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp1) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp3) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp2) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp4) =>
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% 99.42/16.61 (contrasubsetT2) =>
% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT3) =>
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% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementE1) =>
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% 99.42/16.61 (doubleComplementSub2) =>
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% 99.42/16.61 (complementTnotintersectT) =>
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% 99.42/16.61 (complementSubsetComplementIntersect) =>
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% 99.42/16.61 (complementTcontraSubset) =>
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% 99.42/16.61 (binunionTIRcontra) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInUnion) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInUnion2) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInIntersectUnions) =>
% 99.42/16.61 ((
% 99.42/16.61 (intersectInPowersetIntersectUnions) =>
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% 99.42/16.61 (inComplementUnionImpNotIn1) =>
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% 99.42/16.61 (inComplementUnionImpInComplement1) =>
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% 99.42/16.61 ((
% 99.42/16.61 (demorgan2a1) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementUnionInPowersetComplement) =>
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% 99.42/16.61 ((
% 99.42/16.61 (demorgan1a) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan1b) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan1) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2a) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2b2) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2b) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (woz13rule1) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule2) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule3) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule4) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_1) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_2) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_3) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_4) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_5) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1all2) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1SetBreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (choice2fnsingleton) =>
% 99.42/16.61 ((
% 99.42/16.61 (setOfPairsIsBReln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1all1) =>
% 99.42/16.61 ((
% 99.42/16.61 (subbreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (eqbreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compEex) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionIL) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionIR) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionEcases) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionCommutes) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2Ex) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (image1Ex1) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1Equiv) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1E) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1I) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncInInjFuncSet) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncSetFuncIn) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncSetFuncInj) =>
% 99.42/16.61 ((
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% 99.42/16.61 (('#B') @ (
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% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
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% 99.42/16.61 (
% 99.42/16.61 (
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% 99.42/16.61 (
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% 99.42/16.61 (
% 99.42/16.61 (
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% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
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% 99.42/16.61 (
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% 99.42/16.61 (
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% 99.42/16.61 ('#B') @ (
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% 99.42/16.61 (
% 99.42/16.61 (
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% 99.42/16.61 surjFuncSet)))))))) @
% 99.42/16.61 (
% 99.42/16.61 (
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% 99.42/16.61 (
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% 99.42/16.61 (
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% 99.42/16.61 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl561])).
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% 99.42/16.61 (((exuE3u) =>
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% 99.42/16.61 (((setadjoin__Cong) =>
% 99.42/16.61 (((powerset__Cong) =>
% 99.42/16.61 (((setunion__Cong) =>
% 99.42/16.61 (((exuEu) =>
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 (symdiffIneg2) =>
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 (setukpairinjR11) =>
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% 99.42/16.61 (setukpairinjR1) =>
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% 99.42/16.61 (kpairsurjEq) =>
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% 99.42/16.61 (cartprodsndin) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodpairmemEL) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodpairmemER) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodmempaircEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodfstpairEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodsndpairEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodpairsurjEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (dpsetconstrI) =>
% 99.42/16.61 ((
% 99.42/16.61 (dpsetconstrSub) =>
% 99.42/16.61 ((
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% 99.42/16.61 (dpsetconstrEL2) =>
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% 99.42/16.61 (dpsetconstrER) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcImageSingleton) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (ap2p) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcinfuncset) =>
% 99.42/16.61 ((
% 99.42/16.61 (lamProp) =>
% 99.42/16.61 ((
% 99.42/16.61 (lamp) =>
% 99.42/16.61 ((
% 99.42/16.61 (lam2p) =>
% 99.42/16.61 ((
% 99.42/16.61 (brelnall1) =>
% 99.42/16.61 ((
% 99.42/16.61 (brelnall2) =>
% 99.42/16.61 ((
% 99.42/16.61 (ex1E2) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp1) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp3) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp2) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcextLem) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp4) =>
% 99.42/16.61 ((
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% 99.42/16.61 (funcext2) =>
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% 99.42/16.61 (ap2apEq2) =>
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% 99.42/16.61 ((
% 99.42/16.61 (eta1) =>
% 99.42/16.61 ((
% 99.42/16.61 (lam2lamEq) =>
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% 99.42/16.61 ((
% 99.42/16.61 (iffalseProp2) =>
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% 99.42/16.61 (ifSingleton) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (binintersectTERcontra) =>
% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT) =>
% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT1) =>
% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT2) =>
% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT3) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementI1) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementE1) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementSub1) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementSub2) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementTnotintersectT) =>
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% 99.42/16.61 (complementImpComplementIntersect) =>
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% 99.42/16.61 (complementSubsetComplementIntersect) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementInPowersetComplementIntersect) =>
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% 99.42/16.61 (contraSubsetComplement) =>
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% 99.42/16.61 (complementTcontraSubset) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (binunionTIRcontra) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInUnion) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInUnion2) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInIntersectUnions) =>
% 99.42/16.61 ((
% 99.42/16.61 (intersectInPowersetIntersectUnions) =>
% 99.42/16.61 ((
% 99.42/16.61 (inComplementUnionImpNotIn1) =>
% 99.42/16.61 ((
% 99.42/16.61 (inComplementUnionImpInComplement1) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (binunionTEcontra) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2a1) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementUnionInPowersetComplement) =>
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% 99.42/16.61 (demorgan2a2) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan1a) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan1b) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan1) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2a) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2b2) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2b) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule0) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule1) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule2) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule3) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule4) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_1) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_2) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_3) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_4) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_5) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1all2) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1SetBreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (choice2fnsingleton) =>
% 99.42/16.61 ((
% 99.42/16.61 (setOfPairsIsBReln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1all1) =>
% 99.42/16.61 ((
% 99.42/16.61 (subbreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (eqbreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compEex) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionIL) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionIR) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionEcases) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionCommutes) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2Ex) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2W) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (woz2B) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (image1Ex1) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1Equiv) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1E) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1I) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncInInjFuncSet) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncSetFuncIn) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncSetFuncInj) =>
% 99.42/16.61 ((
% 99.42/16.61 (!!) @ (
% 99.42/16.61 (('#B') @ (
% 99.42/16.61 !!) @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 !!))) @
% 99.42/16.61 (
% 99.42/16.61 (
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% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 '#S') @
% 99.42/16.61 (
% 99.42/16.61 (
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% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
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% 99.42/16.61 (
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% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
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% 99.42/16.61 (
% 99.42/16.61 (
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% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
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% 99.42/16.61 surjFuncSet)))))))) @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
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% 99.42/16.61 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl570])).
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% 99.42/16.61 (((exuE3u) =>
% 99.42/16.61 (((exu__Cong) =>
% 99.42/16.61 (((setadjoin__Cong) =>
% 99.42/16.61 (((powerset__Cong) =>
% 99.42/16.61 (((setunion__Cong) =>
% 99.42/16.61 (((exuEu) =>
% 99.42/16.61 (((descr__Cong) =>
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (powersetE1) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (powersetsubset) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (sepSubset) =>
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% 99.42/16.61 ((
% 99.42/16.61 (upairset2IR) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (binunionEcases) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (binunionRsub) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectI) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectSubset5) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (setminusEL) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (setminusSubset2) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (setminusILneg) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (symdiffIneg2) =>
% 99.42/16.61 ((
% 99.42/16.61 (secondinupair) =>
% 99.42/16.61 ((
% 99.42/16.61 (setukpairIL) =>
% 99.42/16.61 ((
% 99.42/16.61 (setukpairIR) =>
% 99.42/16.61 ((
% 99.42/16.61 (kpairiskpair) =>
% 99.42/16.61 ((
% 99.42/16.61 (kpairp) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (singletoninpowunion) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (upairsubunion) =>
% 99.42/16.61 ((
% 99.42/16.61 (upairinpowunion) =>
% 99.42/16.61 ((
% 99.42/16.61 (ubforcartprodlem1) =>
% 99.42/16.61 ((
% 99.42/16.61 (ubforcartprodlem2) =>
% 99.42/16.61 ((
% 99.42/16.61 (ubforcartprodlem3) =>
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% 99.42/16.61 ((
% 99.42/16.61 (cartprodfstin) =>
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% 99.42/16.61 (setukpairinjL2) =>
% 99.42/16.61 ((
% 99.42/16.61 (setukpairinjL) =>
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% 99.42/16.61 (cartprodsndin) =>
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% 99.42/16.61 (cartprodpairmemEL) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodpairmemER) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodmempaircEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodfstpairEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodsndpairEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodpairsurjEq) =>
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% 99.42/16.61 ((
% 99.42/16.61 (dpsetconstrSub) =>
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% 99.42/16.61 ((
% 99.42/16.61 (dpsetconstrEL2) =>
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% 99.42/16.61 (dpsetconstrER) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcImageSingleton) =>
% 99.42/16.61 ((
% 99.42/16.61 (apProp) =>
% 99.42/16.61 ((
% 99.42/16.61 (app) =>
% 99.42/16.61 ((
% 99.42/16.61 (infuncsetfunc) =>
% 99.42/16.61 ((
% 99.42/16.61 (ap2p) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcinfuncset) =>
% 99.42/16.61 ((
% 99.42/16.61 (lamProp) =>
% 99.42/16.61 ((
% 99.42/16.61 (lamp) =>
% 99.42/16.61 ((
% 99.42/16.61 (lam2p) =>
% 99.42/16.61 ((
% 99.42/16.61 (brelnall1) =>
% 99.42/16.61 ((
% 99.42/16.61 (brelnall2) =>
% 99.42/16.61 ((
% 99.42/16.61 (ex1E2) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp1) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp3) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp2) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcextLem) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp4) =>
% 99.42/16.61 ((
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% 99.42/16.61 (funcext2) =>
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% 99.42/16.61 (ap2apEq2) =>
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (lam2lamEq) =>
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% 99.42/16.61 ((
% 99.42/16.61 (iffalseProp2) =>
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% 99.42/16.61 ((
% 99.42/16.61 (ifSingleton) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (binintersectTERcontra) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT1) =>
% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT2) =>
% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT3) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementI1) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementE1) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementSub1) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementSub2) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementTnotintersectT) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementImpComplementIntersect) =>
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% 99.42/16.61 (complementSubsetComplementIntersect) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementInPowersetComplementIntersect) =>
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% 99.42/16.61 (contraSubsetComplement) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementTcontraSubset) =>
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% 99.42/16.61 ((
% 99.42/16.61 (binunionTIRcontra) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInUnion) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInUnion2) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInIntersectUnions) =>
% 99.42/16.61 ((
% 99.42/16.61 (intersectInPowersetIntersectUnions) =>
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% 99.42/16.61 (inComplementUnionImpNotIn1) =>
% 99.42/16.61 ((
% 99.42/16.61 (inComplementUnionImpInComplement1) =>
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% 99.42/16.61 ((
% 99.42/16.61 (binunionTEcontra) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2a1) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementUnionInPowersetComplement) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2a2) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan1a) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan1b) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan1) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2a) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2b2) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2b) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule0) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule1) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule2) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule3) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule4) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_1) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_2) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_3) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_4) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_5) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1all2) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1SetBreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (choice2fnsingleton) =>
% 99.42/16.61 ((
% 99.42/16.61 (setOfPairsIsBReln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1all1) =>
% 99.42/16.61 ((
% 99.42/16.61 (subbreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (eqbreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compEex) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionIL) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionIR) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionEcases) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionCommutes) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2Ex) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2W) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2A) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2B) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1Ex) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1Ex1) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1Equiv) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1E) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1I) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncInInjFuncSet) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncSetFuncIn) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncSetFuncInj) =>
% 99.42/16.61 ((
% 99.42/16.61 (!!) @ (
% 99.42/16.61 (('#B') @ (
% 99.42/16.61 !!) @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 !!))) @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#S') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 '#S') @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
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% 99.42/16.61 (
% 99.42/16.61 (
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% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
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% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
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% 99.42/16.61 surjFuncSet)))))))) @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#C') @ in)))) @
% 99.42/16.61 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
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% 99.42/16.61 (((exuE3u) =>
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% 99.42/16.61 (((setadjoin__Cong) =>
% 99.42/16.61 (((powerset__Cong) =>
% 99.42/16.61 (((setunion__Cong) =>
% 99.42/16.61 (((exuEu) =>
% 99.42/16.61 (((descr__Cong) =>
% 99.42/16.61 (((dsetconstr__Cong) =>
% 99.42/16.61 (((subsetI1) =>
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% 99.42/16.61 ((
% 99.42/16.61 (powersetE1) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (powersetsubset) =>
% 99.42/16.61 ((
% 99.42/16.61 (sepInPowerset) =>
% 99.42/16.61 ((
% 99.42/16.61 (sepSubset) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (upairset2IR) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionIR) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionEcases) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionE) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionLsub) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionRsub) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectI) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectSubset5) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectEL) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectLsub) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (binintersectSubset3) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 (binintersectSubset4) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (setminusEL) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusER) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusSubset2) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusERneg) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusELneg) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusILneg) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusIRneg) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (setminusSubset1) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (symdiffIneg2) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (setukpairIL) =>
% 99.42/16.61 ((
% 99.42/16.61 (setukpairIR) =>
% 99.42/16.61 ((
% 99.42/16.61 (kpairiskpair) =>
% 99.42/16.61 ((
% 99.42/16.61 (kpairp) =>
% 99.42/16.61 ((
% 99.42/16.61 (singletonsubset) =>
% 99.42/16.61 ((
% 99.42/16.61 (singletoninpowerset) =>
% 99.42/16.61 ((
% 99.42/16.61 (singletoninpowunion) =>
% 99.42/16.61 ((
% 99.42/16.61 (upairset2E) =>
% 99.42/16.61 ((
% 99.42/16.61 (upairsubunion) =>
% 99.42/16.61 ((
% 99.42/16.61 (upairinpowunion) =>
% 99.42/16.61 ((
% 99.42/16.61 (ubforcartprodlem1) =>
% 99.42/16.61 ((
% 99.42/16.61 (ubforcartprodlem2) =>
% 99.42/16.61 ((
% 99.42/16.61 (ubforcartprodlem3) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodpairin) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodmempair1) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodmempair) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (cartprodpairmemER) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodmempaircEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodfstpairEq) =>
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% 99.42/16.61 (cartprodsndpairEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodpairsurjEq) =>
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% 99.42/16.61 ((
% 99.42/16.61 (dpsetconstrSub) =>
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (ap2p) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (lamProp) =>
% 99.42/16.61 ((
% 99.42/16.61 (lamp) =>
% 99.42/16.61 ((
% 99.42/16.61 (lam2p) =>
% 99.42/16.61 ((
% 99.42/16.61 (brelnall1) =>
% 99.42/16.61 ((
% 99.42/16.61 (brelnall2) =>
% 99.42/16.61 ((
% 99.42/16.61 (ex1E2) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp1) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp3) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp2) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp4) =>
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% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT2) =>
% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT3) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementE1) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementSub2) =>
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% 99.42/16.61 (doubleComplementEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementTnotintersectT) =>
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% 99.42/16.61 (complementSubsetComplementIntersect) =>
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% 99.42/16.61 (complementTcontraSubset) =>
% 99.42/16.61 ((
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% 99.42/16.61 (binunionTIRcontra) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInUnion) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInUnion2) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInIntersectUnions) =>
% 99.42/16.61 ((
% 99.42/16.61 (intersectInPowersetIntersectUnions) =>
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% 99.42/16.61 (inComplementUnionImpNotIn1) =>
% 99.42/16.61 ((
% 99.42/16.61 (inComplementUnionImpInComplement1) =>
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% 99.42/16.61 ((
% 99.42/16.61 (demorgan2a1) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementUnionInPowersetComplement) =>
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% 99.42/16.61 ((
% 99.42/16.61 (demorgan1a) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan1b) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan1) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2a) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2b2) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2b) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (woz13rule1) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule2) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule3) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule4) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_1) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_2) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_3) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_4) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_5) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1all2) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1SetBreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (choice2fnsingleton) =>
% 99.42/16.61 ((
% 99.42/16.61 (setOfPairsIsBReln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1all1) =>
% 99.42/16.61 ((
% 99.42/16.61 (subbreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (eqbreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compEex) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionIL) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionIR) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionEcases) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionCommutes) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2Ex) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2W) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2A) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2B) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1Ex) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1Ex1) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1Equiv) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1E) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1I) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncInInjFuncSet) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncSetFuncIn) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncSetFuncInj) =>
% 99.42/16.61 ((
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% 99.42/16.61 (('#B') @ (
% 99.42/16.61 !!) @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 !!))) @
% 99.42/16.61 (
% 99.42/16.61 (
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% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 '#S') @
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% 99.42/16.61 (
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% 99.42/16.61 (
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% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
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% 99.42/16.61 (
% 99.42/16.61 (
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% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
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% 99.42/16.61 surjFuncSet)))))))) @
% 99.42/16.61 (
% 99.42/16.61 (
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% 99.42/16.61 (
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% 99.42/16.61 (
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% 99.42/16.61 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl586])).
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% 99.42/16.61 (((setadjoin__Cong) =>
% 99.42/16.61 (((powerset__Cong) =>
% 99.42/16.61 (((setunion__Cong) =>
% 99.42/16.61 (((exuEu) =>
% 99.42/16.61 (((descr__Cong) =>
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (binintersectSubset5) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (setminusILneg) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusIRneg) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (setukpairIR) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (kpairp) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (upairsubunion) =>
% 99.42/16.61 ((
% 99.42/16.61 (upairinpowunion) =>
% 99.42/16.61 ((
% 99.42/16.61 (ubforcartprodlem1) =>
% 99.42/16.61 ((
% 99.42/16.61 (ubforcartprodlem2) =>
% 99.42/16.61 ((
% 99.42/16.61 (ubforcartprodlem3) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodpairin) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodmempair1) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodmempair) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (kfstpairEq) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (setukpairinjL2) =>
% 99.42/16.61 ((
% 99.42/16.61 (setukpairinjL) =>
% 99.42/16.61 ((
% 99.42/16.61 (setukpairinjR11) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (breln1invE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compEex) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionprop) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 (breln1unionI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionEcases) =>
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% 99.42/16.61 (breln1unionCommutes) =>
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% 99.42/16.61 ((
% 99.42/16.61 (image1Ex1) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1Equiv) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1E) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1I) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncInInjFuncSet) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncSetFuncIn) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncSetFuncInj) =>
% 99.42/16.61 ((
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% 99.42/16.61 (
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (kpairsurjEq) =>
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% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (cartprodpairmemER) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (cartprodfstpairEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodsndpairEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodpairsurjEq) =>
% 99.42/16.61 ((
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% 99.42/16.61 (setOfPairsIsBReln) =>
% 99.42/16.61 ((
% 99.42/16.61 (dpsetconstrERa) =>
% 99.42/16.61 ((
% 99.42/16.61 (dpsetconstrEL1) =>
% 99.42/16.61 ((
% 99.42/16.61 (dpsetconstrEL2) =>
% 99.42/16.61 ((
% 99.42/16.61 (dpsetconstrER) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcImageSingleton) =>
% 99.42/16.61 ((
% 99.42/16.61 (apProp) =>
% 99.42/16.61 ((
% 99.42/16.61 (app) =>
% 99.42/16.61 ((
% 99.42/16.61 (infuncsetfunc) =>
% 99.42/16.61 ((
% 99.42/16.61 (ap2p) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcinfuncset) =>
% 99.42/16.61 ((
% 99.42/16.61 (lamProp) =>
% 99.42/16.61 ((
% 99.42/16.61 (lamp) =>
% 99.42/16.61 ((
% 99.42/16.61 (lam2p) =>
% 99.42/16.61 ((
% 99.42/16.61 (brelnall1) =>
% 99.42/16.61 ((
% 99.42/16.61 (brelnall2) =>
% 99.42/16.61 ((
% 99.42/16.61 (ex1E2) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp1) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp3) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp2) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcextLem) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp4) =>
% 99.42/16.61 ((
% 99.42/16.61 (subbreln) =>
% 99.42/16.61 ((
% 99.42/16.61 (eqbreln) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcext) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcext2) =>
% 99.42/16.61 ((
% 99.42/16.61 (ap2apEq1) =>
% 99.42/16.61 ((
% 99.42/16.61 (ap2apEq2) =>
% 99.42/16.61 ((
% 99.42/16.61 (beta1) =>
% 99.42/16.61 ((
% 99.42/16.61 (eta1) =>
% 99.42/16.61 ((
% 99.42/16.61 (lam2lamEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (beta2) =>
% 99.42/16.61 ((
% 99.42/16.61 (eta2) =>
% 99.42/16.61 ((
% 99.42/16.61 (iffalseProp1) =>
% 99.42/16.61 ((
% 99.42/16.61 (iffalseProp2) =>
% 99.42/16.61 ((
% 99.42/16.61 (iftrueProp1) =>
% 99.42/16.61 ((
% 99.42/16.61 (iftrueProp2) =>
% 99.42/16.61 ((
% 99.42/16.61 (ifSingleton) =>
% 99.42/16.61 ((
% 99.42/16.61 (ifp) =>
% 99.42/16.61 ((
% 99.42/16.61 (theeq) =>
% 99.42/16.61 ((
% 99.42/16.61 (iftrue) =>
% 99.42/16.61 ((
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% 99.42/16.61 (iftrueorfalse) =>
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% 99.42/16.61 ((
% 99.42/16.61 (binunionT_lem) =>
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% 99.42/16.61 (powersetT_lem) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusT_lem) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementT_lem) =>
% 99.42/16.61 ((
% 99.42/16.61 (setextT) =>
% 99.42/16.61 ((
% 99.42/16.61 (subsetTI) =>
% 99.42/16.61 ((
% 99.42/16.61 (powersetTI1) =>
% 99.42/16.61 ((
% 99.42/16.61 (powersetTE1) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementTI1) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementTE1) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectTELcontra) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectTERcontra) =>
% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT) =>
% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT1) =>
% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT2) =>
% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT3) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementI1) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementE1) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementSub1) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementSub2) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementTnotintersectT) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementImpComplementIntersect) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementSubsetComplementIntersect) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementInPowersetComplementIntersect) =>
% 99.42/16.61 ((
% 99.42/16.61 (contraSubsetComplement) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementTcontraSubset) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionTILcontra) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionTIRcontra) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInUnion) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInUnion2) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInIntersectUnions) =>
% 99.42/16.61 ((
% 99.42/16.61 (intersectInPowersetIntersectUnions) =>
% 99.42/16.61 ((
% 99.42/16.61 (inComplementUnionImpNotIn1) =>
% 99.42/16.61 ((
% 99.42/16.61 (inComplementUnionImpInComplement1) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionTE) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionTEcontra) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2a1) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementUnionInPowersetComplement) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2a2) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan1a) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan1b) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan1) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2a) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2b2) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2b) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule0) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule1) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule2) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule3) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule4) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_1) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_2) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_3) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_4) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_5) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1all2) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1SetBreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (choice2fnsingleton) =>
% 99.42/16.61 ((
% 99.42/16.61 (setOfPairsIsBReln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1all1) =>
% 99.42/16.61 ((
% 99.42/16.61 (subbreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (eqbreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compEex) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionIL) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionIR) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionEcases) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionCommutes) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2Ex) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2W) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2A) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2B) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1Ex) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1Ex1) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1Equiv) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1E) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1I) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncInInjFuncSet) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncSetFuncIn) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncSetFuncInj) =>
% 99.42/16.61 ((
% 99.42/16.61 (!!) @ (
% 99.42/16.61 (('#B') @ (
% 99.42/16.61 !!) @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 !!))) @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#S') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 '#S') @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 '#S'))) @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 =>))))) @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#C') @ in)))) @
% 99.42/16.61 surjFuncSet)))))))) @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#C') @ in)))) @
% 99.42/16.61 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl606])).
% 99.42/16.61 thf(zip_derived_cl630, plain,
% 99.42/16.61 (~ (((exuI2) =>
% 99.42/16.61 (((inCongP) =>
% 99.42/16.61 (((in__Cong) =>
% 99.42/16.61 (((exuE3u) =>
% 99.42/16.61 (((exu__Cong) =>
% 99.42/16.61 (((setadjoin__Cong) =>
% 99.42/16.61 (((powerset__Cong) =>
% 99.42/16.61 (((setunion__Cong) =>
% 99.42/16.61 (((exuEu) =>
% 99.42/16.61 (((descr__Cong) =>
% 99.42/16.61 (((dsetconstr__Cong) =>
% 99.42/16.61 (((subsetI1) =>
% 99.42/16.61 (((eqimpsubset2) =>
% 99.42/16.61 (((eqimpsubset1) =>
% 99.42/16.61 (((subsetI2) =>
% 99.42/16.61 (((emptysetsubset) =>
% 99.42/16.61 (((subsetE) =>
% 99.42/16.61 (((subsetE2) =>
% 99.42/16.61 (((notsubsetI) =>
% 99.42/16.61 (((notequalI1) =>
% 99.42/16.61 (((notequalI2) =>
% 99.42/16.61 (((subsetRefl) =>
% 99.42/16.61 (((subsetTrans) =>
% 99.42/16.61 (((setadjoinSub) =>
% 99.42/16.61 (((setadjoinSub2) =>
% 99.42/16.61 (((subset2powerset) =>
% 99.42/16.61 (((setextsub) =>
% 99.42/16.61 (((subsetemptysetimpeq) =>
% 99.42/16.61 (((powersetI1) =>
% 99.42/16.61 (((powersetE1) =>
% 99.42/16.61 ((
% 99.42/16.61 (inPowerset) =>
% 99.42/16.61 ((
% 99.42/16.61 (powersetsubset) =>
% 99.42/16.61 ((
% 99.42/16.61 (sepInPowerset) =>
% 99.42/16.61 ((
% 99.42/16.61 (sepSubset) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionIL) =>
% 99.42/16.61 ((
% 99.42/16.61 (upairset2IR) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionIR) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionEcases) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionE) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionLsub) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionRsub) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectI) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectSubset5) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectEL) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectLsub) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectSubset2) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectSubset3) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectER) =>
% 99.42/16.61 ((
% 99.42/16.61 (disjointsetsI1) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectRsub) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectSubset4) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectSubset1) =>
% 99.42/16.61 ((
% 99.42/16.61 (bs114d) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusI) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusEL) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusER) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusSubset2) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusERneg) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusELneg) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusILneg) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusIRneg) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusLsub) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusSubset1) =>
% 99.42/16.61 ((
% 99.42/16.61 (symdiffE) =>
% 99.42/16.61 ((
% 99.42/16.61 (symdiffI1) =>
% 99.42/16.61 ((
% 99.42/16.61 (symdiffI2) =>
% 99.42/16.61 ((
% 99.42/16.61 (symdiffIneg1) =>
% 99.42/16.61 ((
% 99.42/16.61 (symdiffIneg2) =>
% 99.42/16.61 ((
% 99.42/16.61 (secondinupair) =>
% 99.42/16.61 ((
% 99.42/16.61 (setukpairIL) =>
% 99.42/16.61 ((
% 99.42/16.61 (setukpairIR) =>
% 99.42/16.61 ((
% 99.42/16.61 (kpairiskpair) =>
% 99.42/16.61 ((
% 99.42/16.61 (kpairp) =>
% 99.42/16.61 ((
% 99.42/16.61 (singletonsubset) =>
% 99.42/16.61 ((
% 99.42/16.61 (singletoninpowerset) =>
% 99.42/16.61 ((
% 99.42/16.61 (singletoninpowunion) =>
% 99.42/16.61 ((
% 99.42/16.61 (upairset2E) =>
% 99.42/16.61 ((
% 99.42/16.61 (upairsubunion) =>
% 99.42/16.61 ((
% 99.42/16.61 (upairinpowunion) =>
% 99.42/16.61 ((
% 99.42/16.61 (ubforcartprodlem1) =>
% 99.42/16.61 ((
% 99.42/16.61 (ubforcartprodlem2) =>
% 99.42/16.61 ((
% 99.42/16.61 (ubforcartprodlem3) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodpairin) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodmempair1) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodmempair) =>
% 99.42/16.61 ((
% 99.42/16.61 (setunionE2) =>
% 99.42/16.61 ((
% 99.42/16.61 (setunionsingleton1) =>
% 99.42/16.61 ((
% 99.42/16.61 (setunionsingleton2) =>
% 99.42/16.61 ((
% 99.42/16.61 (setunionsingleton) =>
% 99.42/16.61 ((
% 99.42/16.61 (singletonprop) =>
% 99.42/16.61 ((
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% 99.42/16.61 ((
% 99.42/16.61 (ex1I) =>
% 99.42/16.61 ((
% 99.42/16.61 (ex1I2) =>
% 99.42/16.61 ((
% 99.42/16.61 (singletonsuniq) =>
% 99.42/16.61 ((
% 99.42/16.61 (setukpairinjL1) =>
% 99.42/16.61 ((
% 99.42/16.61 (kfstsingleton) =>
% 99.42/16.61 ((
% 99.42/16.61 (theprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (kfstpairEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodfstin) =>
% 99.42/16.61 ((
% 99.42/16.61 (setukpairinjL2) =>
% 99.42/16.61 ((
% 99.42/16.61 (setukpairinjL) =>
% 99.42/16.61 ((
% 99.42/16.61 (setukpairinjR11) =>
% 99.42/16.61 ((
% 99.42/16.61 (setukpairinjR12) =>
% 99.42/16.61 ((
% 99.42/16.61 (setukpairinjR1) =>
% 99.42/16.61 ((
% 99.42/16.61 (upairequniteq) =>
% 99.42/16.61 ((
% 99.42/16.61 (setukpairinjR2) =>
% 99.42/16.61 ((
% 99.42/16.61 (setukpairinjR) =>
% 99.42/16.61 ((
% 99.42/16.61 (ksndsingleton) =>
% 99.42/16.61 ((
% 99.42/16.61 (ksndpairEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (kpairsurjEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodsndin) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodpairmemEL) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodpairmemER) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodmempaircEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodfstpairEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodsndpairEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (cartprodpairsurjEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (dpsetconstrI) =>
% 99.42/16.61 ((
% 99.42/16.61 (dpsetconstrSub) =>
% 99.42/16.61 ((
% 99.42/16.61 (setOfPairsIsBReln) =>
% 99.42/16.61 ((
% 99.42/16.61 (dpsetconstrERa) =>
% 99.42/16.61 ((
% 99.42/16.61 (dpsetconstrEL1) =>
% 99.42/16.61 ((
% 99.42/16.61 (dpsetconstrEL2) =>
% 99.42/16.61 ((
% 99.42/16.61 (dpsetconstrER) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcImageSingleton) =>
% 99.42/16.61 ((
% 99.42/16.61 (apProp) =>
% 99.42/16.61 ((
% 99.42/16.61 (app) =>
% 99.42/16.61 ((
% 99.42/16.61 (infuncsetfunc) =>
% 99.42/16.61 ((
% 99.42/16.61 (ap2p) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcinfuncset) =>
% 99.42/16.61 ((
% 99.42/16.61 (lamProp) =>
% 99.42/16.61 ((
% 99.42/16.61 (lamp) =>
% 99.42/16.61 ((
% 99.42/16.61 (lam2p) =>
% 99.42/16.61 ((
% 99.42/16.61 (brelnall1) =>
% 99.42/16.61 ((
% 99.42/16.61 (brelnall2) =>
% 99.42/16.61 ((
% 99.42/16.61 (ex1E2) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp1) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp3) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp2) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcextLem) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcGraphProp4) =>
% 99.42/16.61 ((
% 99.42/16.61 (subbreln) =>
% 99.42/16.61 ((
% 99.42/16.61 (eqbreln) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcext) =>
% 99.42/16.61 ((
% 99.42/16.61 (funcext2) =>
% 99.42/16.61 ((
% 99.42/16.61 (ap2apEq1) =>
% 99.42/16.61 ((
% 99.42/16.61 (ap2apEq2) =>
% 99.42/16.61 ((
% 99.42/16.61 (beta1) =>
% 99.42/16.61 ((
% 99.42/16.61 (eta1) =>
% 99.42/16.61 ((
% 99.42/16.61 (lam2lamEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (beta2) =>
% 99.42/16.61 ((
% 99.42/16.61 (eta2) =>
% 99.42/16.61 ((
% 99.42/16.61 (iffalseProp1) =>
% 99.42/16.61 ((
% 99.42/16.61 (iffalseProp2) =>
% 99.42/16.61 ((
% 99.42/16.61 (iftrueProp1) =>
% 99.42/16.61 ((
% 99.42/16.61 (iftrueProp2) =>
% 99.42/16.61 ((
% 99.42/16.61 (ifSingleton) =>
% 99.42/16.61 ((
% 99.42/16.61 (ifp) =>
% 99.42/16.61 ((
% 99.42/16.61 (theeq) =>
% 99.42/16.61 ((
% 99.42/16.61 (iftrue) =>
% 99.42/16.61 ((
% 99.42/16.61 (iffalse) =>
% 99.42/16.61 ((
% 99.42/16.61 (iftrueorfalse) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectT_lem) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionT_lem) =>
% 99.42/16.61 ((
% 99.42/16.61 (powersetT_lem) =>
% 99.42/16.61 ((
% 99.42/16.61 (setminusT_lem) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementT_lem) =>
% 99.42/16.61 ((
% 99.42/16.61 (setextT) =>
% 99.42/16.61 ((
% 99.42/16.61 (subsetTI) =>
% 99.42/16.61 ((
% 99.42/16.61 (powersetTI1) =>
% 99.42/16.61 ((
% 99.42/16.61 (powersetTE1) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementTI1) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementTE1) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectTELcontra) =>
% 99.42/16.61 ((
% 99.42/16.61 (binintersectTERcontra) =>
% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT) =>
% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT1) =>
% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT2) =>
% 99.42/16.61 ((
% 99.42/16.61 (contrasubsetT3) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementI1) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementE1) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementSub1) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementSub2) =>
% 99.42/16.61 ((
% 99.42/16.61 (doubleComplementEq) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementTnotintersectT) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementImpComplementIntersect) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementSubsetComplementIntersect) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementInPowersetComplementIntersect) =>
% 99.42/16.61 ((
% 99.42/16.61 (contraSubsetComplement) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementTcontraSubset) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionTILcontra) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionTIRcontra) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInUnion) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInUnion2) =>
% 99.42/16.61 ((
% 99.42/16.61 (inIntersectImpInIntersectUnions) =>
% 99.42/16.61 ((
% 99.42/16.61 (intersectInPowersetIntersectUnions) =>
% 99.42/16.61 ((
% 99.42/16.61 (inComplementUnionImpNotIn1) =>
% 99.42/16.61 ((
% 99.42/16.61 (inComplementUnionImpInComplement1) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionTE) =>
% 99.42/16.61 ((
% 99.42/16.61 (binunionTEcontra) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2a1) =>
% 99.42/16.61 ((
% 99.42/16.61 (complementUnionInPowersetComplement) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2a2) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan1a) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan1b) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan1) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2a) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2b2) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2b) =>
% 99.42/16.61 ((
% 99.42/16.61 (demorgan2) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule0) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule1) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule2) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule3) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz13rule4) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_1) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_2) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_3) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_4) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz1_5) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1all2) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1SetBreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (choice2fnsingleton) =>
% 99.42/16.61 ((
% 99.42/16.61 (setOfPairsIsBReln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1all1) =>
% 99.42/16.61 ((
% 99.42/16.61 (subbreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (eqbreln1) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1invE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1compEex) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionprop) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionIL) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionIR) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionI) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionE) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionEcases) =>
% 99.42/16.61 ((
% 99.42/16.61 (breln1unionCommutes) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2Ex) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2W) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2A) =>
% 99.42/16.61 ((
% 99.42/16.61 (woz2B) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1Ex) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1Ex1) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1Equiv) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1E) =>
% 99.42/16.61 ((
% 99.42/16.61 (image1I) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncInInjFuncSet) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncSetFuncIn) =>
% 99.42/16.61 ((
% 99.42/16.61 (injFuncSetFuncInj) =>
% 99.42/16.61 ((
% 99.42/16.61 (!!) @ (
% 99.42/16.61 (('#B') @ (
% 99.42/16.61 !!) @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 !!))) @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#S') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 '#S') @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 '#S'))) @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 =>))))) @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#C') @ in)))) @
% 99.42/16.61 surjFuncSet)))))))) @
% 99.42/16.61 (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#B') @ (
% 99.42/16.61 (
% 99.42/16.61 ('#C') @ in)))) @
% 99.42/16.61 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl619])).
% 99.42/16.62 thf(zip_derived_cl640, plain,
% 99.42/16.62 (~ (((inCongP) =>
% 99.42/16.62 (((in__Cong) =>
% 99.42/16.62 (((exuE3u) =>
% 99.42/16.62 (((exu__Cong) =>
% 99.42/16.62 (((setadjoin__Cong) =>
% 99.42/16.62 (((powerset__Cong) =>
% 99.42/16.62 (((setunion__Cong) =>
% 99.42/16.62 (((exuEu) =>
% 99.42/16.62 (((descr__Cong) =>
% 99.42/16.62 (((dsetconstr__Cong) =>
% 99.42/16.62 (((subsetI1) =>
% 99.42/16.62 (((eqimpsubset2) =>
% 99.42/16.62 (((eqimpsubset1) =>
% 99.42/16.62 (((subsetI2) =>
% 99.42/16.62 (((emptysetsubset) =>
% 99.42/16.62 (((subsetE) =>
% 99.42/16.62 (((subsetE2) =>
% 99.42/16.62 (((notsubsetI) =>
% 99.42/16.62 (((notequalI1) =>
% 99.42/16.62 (((notequalI2) =>
% 99.42/16.62 (((subsetRefl) =>
% 99.42/16.62 (((subsetTrans) =>
% 99.42/16.62 (((setadjoinSub) =>
% 99.42/16.62 (((setadjoinSub2) =>
% 99.42/16.62 (((subset2powerset) =>
% 99.42/16.62 (((setextsub) =>
% 99.42/16.62 (((subsetemptysetimpeq) =>
% 99.42/16.62 (((powersetI1) =>
% 99.42/16.62 (((powersetE1) =>
% 99.42/16.62 (((inPowerset) =>
% 99.42/16.62 ((
% 99.42/16.62 (powersetsubset) =>
% 99.42/16.62 ((
% 99.42/16.62 (sepInPowerset) =>
% 99.42/16.62 ((
% 99.42/16.62 (sepSubset) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionIL) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairset2IR) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionEcases) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionE) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionRsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectI) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset5) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset2) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset3) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectER) =>
% 99.42/16.62 ((
% 99.42/16.62 (disjointsetsI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectRsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset4) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset1) =>
% 99.42/16.62 ((
% 99.42/16.62 (bs114d) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusI) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusER) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusSubset2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusERneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusELneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusILneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusIRneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusSubset1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffE) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffI2) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffIneg1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffIneg2) =>
% 99.42/16.62 ((
% 99.42/16.62 (secondinupair) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairIL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairiskpair) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairp) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletonsubset) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletoninpowerset) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletoninpowunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairset2E) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairsubunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairinpowunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem1) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem3) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairin) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempair1) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempair) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionE2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton1) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletonprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1E1) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1I) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1I2) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletonsuniq) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjL1) =>
% 99.42/16.62 ((
% 99.42/16.62 (kfstsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (theprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (kfstpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodfstin) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjL2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR11) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR12) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR1) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairequniteq) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR) =>
% 99.42/16.62 ((
% 99.42/16.62 (ksndsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (ksndpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairsurjEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodsndin) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairmemEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairmemER) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempaircEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodfstpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodsndpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairsurjEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrI) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrSub) =>
% 99.42/16.62 ((
% 99.42/16.62 (setOfPairsIsBReln) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrERa) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrEL1) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrEL2) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrER) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcImageSingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (apProp) =>
% 99.42/16.62 ((
% 99.42/16.62 (app) =>
% 99.42/16.62 ((
% 99.42/16.62 (infuncsetfunc) =>
% 99.42/16.62 ((
% 99.42/16.62 (ap2p) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcinfuncset) =>
% 99.42/16.62 ((
% 99.42/16.62 (lamProp) =>
% 99.42/16.62 ((
% 99.42/16.62 (lamp) =>
% 99.42/16.62 ((
% 99.42/16.62 (lam2p) =>
% 99.42/16.62 ((
% 99.42/16.62 (brelnall1) =>
% 99.42/16.62 ((
% 99.42/16.62 (brelnall2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1E2) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp1) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp3) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp2) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcextLem) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp4) =>
% 99.42/16.62 ((
% 99.42/16.62 (subbreln) =>
% 99.42/16.62 ((
% 99.42/16.62 (eqbreln) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcext) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcext2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ap2apEq1) =>
% 99.42/16.62 ((
% 99.42/16.62 (ap2apEq2) =>
% 99.42/16.62 ((
% 99.42/16.62 (beta1) =>
% 99.42/16.62 ((
% 99.42/16.62 (eta1) =>
% 99.42/16.62 ((
% 99.42/16.62 (lam2lamEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (beta2) =>
% 99.42/16.62 ((
% 99.42/16.62 (eta2) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (iffalseProp2) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (iftrueProp2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ifSingleton) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (powersetTE1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTE1) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (binintersectTERcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT1) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT2) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT3) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementE1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementSub1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementSub2) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTnotintersectT) =>
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% 99.42/16.62 (complementImpComplementIntersect) =>
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% 99.42/16.62 ((
% 99.42/16.62 (complementInPowersetComplementIntersect) =>
% 99.42/16.62 ((
% 99.42/16.62 (contraSubsetComplement) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTcontraSubset) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (binunionTIRcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInUnion) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInUnion2) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInIntersectUnions) =>
% 99.42/16.62 ((
% 99.42/16.62 (intersectInPowersetIntersectUnions) =>
% 99.42/16.62 ((
% 99.42/16.62 (inComplementUnionImpNotIn1) =>
% 99.42/16.62 ((
% 99.42/16.62 (inComplementUnionImpInComplement1) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTE) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTEcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2a1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementUnionInPowersetComplement) =>
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% 99.42/16.62 (demorgan2a2) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1a) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1b) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2a) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2b2) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2b) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule0) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule1) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule2) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule3) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule4) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_1) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_2) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_3) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_4) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_5) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1all2) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1SetBreln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (choice2fnsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (setOfPairsIsBReln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1all1) =>
% 99.42/16.62 ((
% 99.42/16.62 (subbreln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (eqbreln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1invprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1invI) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1invE) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compI) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compE) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compEex) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionIL) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionI) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionE) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionEcases) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionCommutes) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2Ex) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2W) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2A) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2B) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1Ex) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1Ex1) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1Equiv) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1E) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1I) =>
% 99.42/16.62 ((
% 99.42/16.62 (injFuncInInjFuncSet) =>
% 99.42/16.62 ((
% 99.42/16.62 (injFuncSetFuncIn) =>
% 99.42/16.62 ((
% 99.42/16.62 (injFuncSetFuncInj) =>
% 99.42/16.62 ((
% 99.42/16.62 (!!) @ (
% 99.42/16.62 (('#B') @ (
% 99.42/16.62 !!) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 !!))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#S') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 '#S') @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
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% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 =>))))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#C') @ in)))) @
% 99.42/16.62 surjFuncSet)))))))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#C') @ in)))) @
% 99.42/16.62 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl630])).
% 99.42/16.62 thf(zip_derived_cl650, plain,
% 99.42/16.62 (~ (((in__Cong) =>
% 99.42/16.62 (((exuE3u) =>
% 99.42/16.62 (((exu__Cong) =>
% 99.42/16.62 (((setadjoin__Cong) =>
% 99.42/16.62 (((powerset__Cong) =>
% 99.42/16.62 (((setunion__Cong) =>
% 99.42/16.62 (((exuEu) =>
% 99.42/16.62 (((descr__Cong) =>
% 99.42/16.62 (((dsetconstr__Cong) =>
% 99.42/16.62 (((subsetI1) =>
% 99.42/16.62 (((eqimpsubset2) =>
% 99.42/16.62 (((eqimpsubset1) =>
% 99.42/16.62 (((subsetI2) =>
% 99.42/16.62 (((emptysetsubset) =>
% 99.42/16.62 (((subsetE) =>
% 99.42/16.62 (((subsetE2) =>
% 99.42/16.62 (((notsubsetI) =>
% 99.42/16.62 (((notequalI1) =>
% 99.42/16.62 (((notequalI2) =>
% 99.42/16.62 (((subsetRefl) =>
% 99.42/16.62 (((subsetTrans) =>
% 99.42/16.62 (((setadjoinSub) =>
% 99.42/16.62 (((setadjoinSub2) =>
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% 99.42/16.62 ((
% 99.42/16.62 (sepInPowerset) =>
% 99.42/16.62 ((
% 99.42/16.62 (sepSubset) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionIL) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairset2IR) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionEcases) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionE) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionRsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectI) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset5) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset2) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset3) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectER) =>
% 99.42/16.62 ((
% 99.42/16.62 (disjointsetsI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectRsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset4) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset1) =>
% 99.42/16.62 ((
% 99.42/16.62 (bs114d) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (setminusEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusER) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusSubset2) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (setminusELneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusILneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusIRneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusSubset1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffE) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffI2) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffIneg1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffIneg2) =>
% 99.42/16.62 ((
% 99.42/16.62 (secondinupair) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairIL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairiskpair) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairp) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletonsubset) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletoninpowerset) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletoninpowunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairset2E) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairsubunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairinpowunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem1) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem3) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairin) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempair1) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempair) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionE2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton1) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (kfstpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodfstin) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjL2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR11) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR12) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR1) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairequniteq) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR) =>
% 99.42/16.62 ((
% 99.42/16.62 (ksndsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (ksndpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairsurjEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodsndin) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairmemEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairmemER) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempaircEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodfstpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodsndpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairsurjEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrI) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrSub) =>
% 99.42/16.62 ((
% 99.42/16.62 (setOfPairsIsBReln) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrERa) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrEL1) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrEL2) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrER) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcImageSingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (apProp) =>
% 99.42/16.62 ((
% 99.42/16.62 (app) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (ap2p) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcinfuncset) =>
% 99.42/16.62 ((
% 99.42/16.62 (lamProp) =>
% 99.42/16.62 ((
% 99.42/16.62 (lamp) =>
% 99.42/16.62 ((
% 99.42/16.62 (lam2p) =>
% 99.42/16.62 ((
% 99.42/16.62 (brelnall1) =>
% 99.42/16.62 ((
% 99.42/16.62 (brelnall2) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp3) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp2) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcextLem) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp4) =>
% 99.42/16.62 ((
% 99.42/16.62 (subbreln) =>
% 99.42/16.62 ((
% 99.42/16.62 (eqbreln) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcext) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcext2) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (ap2apEq2) =>
% 99.42/16.62 ((
% 99.42/16.62 (beta1) =>
% 99.42/16.62 ((
% 99.42/16.62 (eta1) =>
% 99.42/16.62 ((
% 99.42/16.62 (lam2lamEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (beta2) =>
% 99.42/16.62 ((
% 99.42/16.62 (eta2) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (iftrueProp2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ifSingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (ifp) =>
% 99.42/16.62 ((
% 99.42/16.62 (theeq) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrue) =>
% 99.42/16.62 ((
% 99.42/16.62 (iffalse) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrueorfalse) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectT_lem) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 (subsetTI) =>
% 99.42/16.62 ((
% 99.42/16.62 (powersetTI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (powersetTE1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTE1) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectTELcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectTERcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT1) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT2) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT3) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementE1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementSub1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementSub2) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTnotintersectT) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementImpComplementIntersect) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementSubsetComplementIntersect) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementInPowersetComplementIntersect) =>
% 99.42/16.62 ((
% 99.42/16.62 (contraSubsetComplement) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTcontraSubset) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTILcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTIRcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInUnion) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInUnion2) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInIntersectUnions) =>
% 99.42/16.62 ((
% 99.42/16.62 (intersectInPowersetIntersectUnions) =>
% 99.42/16.62 ((
% 99.42/16.62 (inComplementUnionImpNotIn1) =>
% 99.42/16.62 ((
% 99.42/16.62 (inComplementUnionImpInComplement1) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTE) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTEcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2a1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementUnionInPowersetComplement) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2a2) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1a) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1b) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2a) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2b2) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2b) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule0) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule1) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule2) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule3) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule4) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_1) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_2) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_3) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_4) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_5) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1all2) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1SetBreln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (choice2fnsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (setOfPairsIsBReln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1all1) =>
% 99.42/16.62 ((
% 99.42/16.62 (subbreln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (eqbreln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1invprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1invI) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1invE) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compI) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compE) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compEex) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionIL) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionI) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionE) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionEcases) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionCommutes) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2Ex) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2W) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2A) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2B) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1Ex) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1Ex1) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1Equiv) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1E) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1I) =>
% 99.42/16.62 ((
% 99.42/16.62 (injFuncInInjFuncSet) =>
% 99.42/16.62 ((
% 99.42/16.62 (injFuncSetFuncIn) =>
% 99.42/16.62 ((
% 99.42/16.62 (injFuncSetFuncInj) =>
% 99.42/16.62 ((
% 99.42/16.62 (!!) @ (
% 99.42/16.62 (('#B') @ (
% 99.42/16.62 !!) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 !!))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#S') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 '#S') @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 '#S'))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 =>))))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#C') @ in)))) @
% 99.42/16.62 surjFuncSet)))))))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#C') @ in)))) @
% 99.42/16.62 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl640])).
% 99.42/16.62 thf(zip_derived_cl660, plain,
% 99.42/16.62 (~ (((exuE3u) =>
% 99.42/16.62 (((exu__Cong) =>
% 99.42/16.62 (((setadjoin__Cong) =>
% 99.42/16.62 (((powerset__Cong) =>
% 99.42/16.62 (((setunion__Cong) =>
% 99.42/16.62 (((exuEu) =>
% 99.42/16.62 (((descr__Cong) =>
% 99.42/16.62 (((dsetconstr__Cong) =>
% 99.42/16.62 (((subsetI1) =>
% 99.42/16.62 (((eqimpsubset2) =>
% 99.42/16.62 (((eqimpsubset1) =>
% 99.42/16.62 (((subsetI2) =>
% 99.42/16.62 (((emptysetsubset) =>
% 99.42/16.62 (((subsetE) =>
% 99.42/16.62 (((subsetE2) =>
% 99.42/16.62 (((notsubsetI) =>
% 99.42/16.62 (((notequalI1) =>
% 99.42/16.62 (((notequalI2) =>
% 99.42/16.62 (((subsetRefl) =>
% 99.42/16.62 (((subsetTrans) =>
% 99.42/16.62 (((setadjoinSub) =>
% 99.42/16.62 (((setadjoinSub2) =>
% 99.42/16.62 (((subset2powerset) =>
% 99.42/16.62 (((setextsub) =>
% 99.42/16.62 (((subsetemptysetimpeq) =>
% 99.42/16.62 (((powersetI1) =>
% 99.42/16.62 (((powersetE1) =>
% 99.42/16.62 (((inPowerset) =>
% 99.42/16.62 (((powersetsubset) =>
% 99.42/16.62 (((sepInPowerset) =>
% 99.42/16.62 ((
% 99.42/16.62 (sepSubset) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionIL) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairset2IR) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionEcases) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionE) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionRsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectI) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset5) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset2) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset3) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectER) =>
% 99.42/16.62 ((
% 99.42/16.62 (disjointsetsI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectRsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset4) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset1) =>
% 99.42/16.62 ((
% 99.42/16.62 (bs114d) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusI) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusER) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusSubset2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusERneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusELneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusILneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusIRneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusSubset1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffE) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffI2) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffIneg1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffIneg2) =>
% 99.42/16.62 ((
% 99.42/16.62 (secondinupair) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairIL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairiskpair) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairp) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletonsubset) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletoninpowerset) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletoninpowunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairset2E) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairsubunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairinpowunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem1) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem3) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairin) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempair1) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempair) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionE2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton1) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletonprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1E1) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1I) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1I2) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletonsuniq) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjL1) =>
% 99.42/16.62 ((
% 99.42/16.62 (kfstsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (theprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (kfstpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodfstin) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjL2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR11) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR12) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR1) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairequniteq) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR) =>
% 99.42/16.62 ((
% 99.42/16.62 (ksndsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (ksndpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairsurjEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodsndin) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairmemEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairmemER) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempaircEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodfstpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodsndpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairsurjEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrI) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrSub) =>
% 99.42/16.62 ((
% 99.42/16.62 (setOfPairsIsBReln) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrERa) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrEL1) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrEL2) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrER) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcImageSingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (apProp) =>
% 99.42/16.62 ((
% 99.42/16.62 (app) =>
% 99.42/16.62 ((
% 99.42/16.62 (infuncsetfunc) =>
% 99.42/16.62 ((
% 99.42/16.62 (ap2p) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcinfuncset) =>
% 99.42/16.62 ((
% 99.42/16.62 (lamProp) =>
% 99.42/16.62 ((
% 99.42/16.62 (lamp) =>
% 99.42/16.62 ((
% 99.42/16.62 (lam2p) =>
% 99.42/16.62 ((
% 99.42/16.62 (brelnall1) =>
% 99.42/16.62 ((
% 99.42/16.62 (brelnall2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1E2) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp1) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp3) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp2) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcextLem) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp4) =>
% 99.42/16.62 ((
% 99.42/16.62 (subbreln) =>
% 99.42/16.62 ((
% 99.42/16.62 (eqbreln) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcext) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcext2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ap2apEq1) =>
% 99.42/16.62 ((
% 99.42/16.62 (ap2apEq2) =>
% 99.42/16.62 ((
% 99.42/16.62 (beta1) =>
% 99.42/16.62 ((
% 99.42/16.62 (eta1) =>
% 99.42/16.62 ((
% 99.42/16.62 (lam2lamEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (beta2) =>
% 99.42/16.62 ((
% 99.42/16.62 (eta2) =>
% 99.42/16.62 ((
% 99.42/16.62 (iffalseProp1) =>
% 99.42/16.62 ((
% 99.42/16.62 (iffalseProp2) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrueProp1) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrueProp2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ifSingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (ifp) =>
% 99.42/16.62 ((
% 99.42/16.62 (theeq) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrue) =>
% 99.42/16.62 ((
% 99.42/16.62 (iffalse) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrueorfalse) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (powersetT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (setextT) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (powersetTI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (powersetTE1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTE1) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (binintersectTERcontra) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT2) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT3) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementE1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementSub1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementSub2) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTnotintersectT) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementImpComplementIntersect) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementSubsetComplementIntersect) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementInPowersetComplementIntersect) =>
% 99.42/16.62 ((
% 99.42/16.62 (contraSubsetComplement) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTcontraSubset) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTILcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTIRcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInUnion) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInUnion2) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInIntersectUnions) =>
% 99.42/16.62 ((
% 99.42/16.62 (intersectInPowersetIntersectUnions) =>
% 99.42/16.62 ((
% 99.42/16.62 (inComplementUnionImpNotIn1) =>
% 99.42/16.62 ((
% 99.42/16.62 (inComplementUnionImpInComplement1) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTE) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTEcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2a1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementUnionInPowersetComplement) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2a2) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1a) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1b) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2a) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2b2) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2b) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule0) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule1) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule2) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule3) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule4) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_1) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_2) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_3) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_4) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_5) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1all2) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1SetBreln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (choice2fnsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (setOfPairsIsBReln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1all1) =>
% 99.42/16.62 ((
% 99.42/16.62 (subbreln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (eqbreln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1invprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1invI) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1invE) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compI) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compE) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compEex) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionIL) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionI) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionE) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionEcases) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionCommutes) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2Ex) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2W) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2A) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2B) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1Ex) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1Ex1) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1Equiv) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1E) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1I) =>
% 99.42/16.62 ((
% 99.42/16.62 (injFuncInInjFuncSet) =>
% 99.42/16.62 ((
% 99.42/16.62 (injFuncSetFuncIn) =>
% 99.42/16.62 ((
% 99.42/16.62 (injFuncSetFuncInj) =>
% 99.42/16.62 ((
% 99.42/16.62 (!!) @ (
% 99.42/16.62 (('#B') @ (
% 99.42/16.62 !!) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 !!))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#S') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 '#S') @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 '#S'))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 =>))))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#C') @ in)))) @
% 99.42/16.62 surjFuncSet)))))))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#C') @ in)))) @
% 99.42/16.62 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl650])).
% 99.42/16.62 thf(zip_derived_cl672, plain,
% 99.42/16.62 (~ (((exu__Cong) =>
% 99.42/16.62 (((setadjoin__Cong) =>
% 99.42/16.62 (((powerset__Cong) =>
% 99.42/16.62 (((setunion__Cong) =>
% 99.42/16.62 (((exuEu) =>
% 99.42/16.62 (((descr__Cong) =>
% 99.42/16.62 (((dsetconstr__Cong) =>
% 99.42/16.62 (((subsetI1) =>
% 99.42/16.62 (((eqimpsubset2) =>
% 99.42/16.62 (((eqimpsubset1) =>
% 99.42/16.62 (((subsetI2) =>
% 99.42/16.62 (((emptysetsubset) =>
% 99.42/16.62 (((subsetE) =>
% 99.42/16.62 (((subsetE2) =>
% 99.42/16.62 (((notsubsetI) =>
% 99.42/16.62 (((notequalI1) =>
% 99.42/16.62 (((notequalI2) =>
% 99.42/16.62 (((subsetRefl) =>
% 99.42/16.62 (((subsetTrans) =>
% 99.42/16.62 (((setadjoinSub) =>
% 99.42/16.62 (((setadjoinSub2) =>
% 99.42/16.62 (((subset2powerset) =>
% 99.42/16.62 (((setextsub) =>
% 99.42/16.62 (((subsetemptysetimpeq) =>
% 99.42/16.62 (((powersetI1) =>
% 99.42/16.62 (((powersetE1) =>
% 99.42/16.62 (((inPowerset) =>
% 99.42/16.62 (((powersetsubset) =>
% 99.42/16.62 (((sepInPowerset) =>
% 99.42/16.62 (((sepSubset) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionIL) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairset2IR) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionEcases) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionE) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionRsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectI) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset5) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset2) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset3) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectER) =>
% 99.42/16.62 ((
% 99.42/16.62 (disjointsetsI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectRsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset4) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset1) =>
% 99.42/16.62 ((
% 99.42/16.62 (bs114d) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusI) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusER) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusSubset2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusERneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusELneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusILneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusIRneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusSubset1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffE) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffI2) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffIneg1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffIneg2) =>
% 99.42/16.62 ((
% 99.42/16.62 (secondinupair) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairIL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairiskpair) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairp) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletonsubset) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletoninpowerset) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletoninpowunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairset2E) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairsubunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairinpowunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem1) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem3) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairin) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempair1) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempair) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionE2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton1) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletonprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1E1) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1I) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1I2) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletonsuniq) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjL1) =>
% 99.42/16.62 ((
% 99.42/16.62 (kfstsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (theprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (kfstpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodfstin) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjL2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR11) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR12) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR1) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairequniteq) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR) =>
% 99.42/16.62 ((
% 99.42/16.62 (ksndsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (ksndpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairsurjEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodsndin) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairmemEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairmemER) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempaircEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodfstpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodsndpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairsurjEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrI) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrSub) =>
% 99.42/16.62 ((
% 99.42/16.62 (setOfPairsIsBReln) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrERa) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrEL1) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrEL2) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrER) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcImageSingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (apProp) =>
% 99.42/16.62 ((
% 99.42/16.62 (app) =>
% 99.42/16.62 ((
% 99.42/16.62 (infuncsetfunc) =>
% 99.42/16.62 ((
% 99.42/16.62 (ap2p) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcinfuncset) =>
% 99.42/16.62 ((
% 99.42/16.62 (lamProp) =>
% 99.42/16.62 ((
% 99.42/16.62 (lamp) =>
% 99.42/16.62 ((
% 99.42/16.62 (lam2p) =>
% 99.42/16.62 ((
% 99.42/16.62 (brelnall1) =>
% 99.42/16.62 ((
% 99.42/16.62 (brelnall2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1E2) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp1) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp3) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp2) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcextLem) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp4) =>
% 99.42/16.62 ((
% 99.42/16.62 (subbreln) =>
% 99.42/16.62 ((
% 99.42/16.62 (eqbreln) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcext) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcext2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ap2apEq1) =>
% 99.42/16.62 ((
% 99.42/16.62 (ap2apEq2) =>
% 99.42/16.62 ((
% 99.42/16.62 (beta1) =>
% 99.42/16.62 ((
% 99.42/16.62 (eta1) =>
% 99.42/16.62 ((
% 99.42/16.62 (lam2lamEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (beta2) =>
% 99.42/16.62 ((
% 99.42/16.62 (eta2) =>
% 99.42/16.62 ((
% 99.42/16.62 (iffalseProp1) =>
% 99.42/16.62 ((
% 99.42/16.62 (iffalseProp2) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrueProp1) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrueProp2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ifSingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (ifp) =>
% 99.42/16.62 ((
% 99.42/16.62 (theeq) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrue) =>
% 99.42/16.62 ((
% 99.42/16.62 (iffalse) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrueorfalse) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (powersetT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (setextT) =>
% 99.42/16.62 ((
% 99.42/16.62 (subsetTI) =>
% 99.42/16.62 ((
% 99.42/16.62 (powersetTI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (powersetTE1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTE1) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectTELcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectTERcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT1) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT2) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT3) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementE1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementSub1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementSub2) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTnotintersectT) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementImpComplementIntersect) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementSubsetComplementIntersect) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementInPowersetComplementIntersect) =>
% 99.42/16.62 ((
% 99.42/16.62 (contraSubsetComplement) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTcontraSubset) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTILcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTIRcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInUnion) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInUnion2) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInIntersectUnions) =>
% 99.42/16.62 ((
% 99.42/16.62 (intersectInPowersetIntersectUnions) =>
% 99.42/16.62 ((
% 99.42/16.62 (inComplementUnionImpNotIn1) =>
% 99.42/16.62 ((
% 99.42/16.62 (inComplementUnionImpInComplement1) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTE) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTEcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2a1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementUnionInPowersetComplement) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2a2) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1a) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1b) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2a) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2b2) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2b) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule0) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule1) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule2) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule3) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule4) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_1) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_2) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_3) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_4) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_5) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1all2) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1SetBreln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (choice2fnsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (setOfPairsIsBReln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1all1) =>
% 99.42/16.62 ((
% 99.42/16.62 (subbreln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (eqbreln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1invprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1invI) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1invE) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compI) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compE) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compEex) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionIL) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionI) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionE) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionEcases) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionCommutes) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2Ex) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2W) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2A) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2B) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1Ex) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1Ex1) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1Equiv) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1E) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1I) =>
% 99.42/16.62 ((
% 99.42/16.62 (injFuncInInjFuncSet) =>
% 99.42/16.62 ((
% 99.42/16.62 (injFuncSetFuncIn) =>
% 99.42/16.62 ((
% 99.42/16.62 (injFuncSetFuncInj) =>
% 99.42/16.62 ((
% 99.42/16.62 (!!) @ (
% 99.42/16.62 (('#B') @ (
% 99.42/16.62 !!) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 !!))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#S') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 '#S') @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 '#S'))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 =>))))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#C') @ in)))) @
% 99.42/16.62 surjFuncSet)))))))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#C') @ in)))) @
% 99.42/16.62 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl660])).
% 99.42/16.62 thf(zip_derived_cl685, plain,
% 99.42/16.62 (~ (((setadjoin__Cong) =>
% 99.42/16.62 (((powerset__Cong) =>
% 99.42/16.62 (((setunion__Cong) =>
% 99.42/16.62 (((exuEu) =>
% 99.42/16.62 (((descr__Cong) =>
% 99.42/16.62 (((dsetconstr__Cong) =>
% 99.42/16.62 (((subsetI1) =>
% 99.42/16.62 (((eqimpsubset2) =>
% 99.42/16.62 (((eqimpsubset1) =>
% 99.42/16.62 (((subsetI2) =>
% 99.42/16.62 (((emptysetsubset) =>
% 99.42/16.62 (((subsetE) =>
% 99.42/16.62 (((subsetE2) =>
% 99.42/16.62 (((notsubsetI) =>
% 99.42/16.62 (((notequalI1) =>
% 99.42/16.62 (((notequalI2) =>
% 99.42/16.62 (((subsetRefl) =>
% 99.42/16.62 (((subsetTrans) =>
% 99.42/16.62 (((setadjoinSub) =>
% 99.42/16.62 (((setadjoinSub2) =>
% 99.42/16.62 (((subset2powerset) =>
% 99.42/16.62 (((setextsub) =>
% 99.42/16.62 (((subsetemptysetimpeq) =>
% 99.42/16.62 (((powersetI1) =>
% 99.42/16.62 (((powersetE1) =>
% 99.42/16.62 (((inPowerset) =>
% 99.42/16.62 (((powersetsubset) =>
% 99.42/16.62 (((sepInPowerset) =>
% 99.42/16.62 (((sepSubset) =>
% 99.42/16.62 (((binunionIL) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairset2IR) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionEcases) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionE) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionRsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectI) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset5) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset2) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset3) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectER) =>
% 99.42/16.62 ((
% 99.42/16.62 (disjointsetsI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectRsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset4) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset1) =>
% 99.42/16.62 ((
% 99.42/16.62 (bs114d) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusI) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusER) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusSubset2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusERneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusELneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusILneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusIRneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusSubset1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffE) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffI2) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffIneg1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffIneg2) =>
% 99.42/16.62 ((
% 99.42/16.62 (secondinupair) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairIL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairiskpair) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairp) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletonsubset) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletoninpowerset) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletoninpowunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairset2E) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairsubunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairinpowunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem1) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem3) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairin) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempair1) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempair) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionE2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton1) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletonprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1E1) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1I) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1I2) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletonsuniq) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjL1) =>
% 99.42/16.62 ((
% 99.42/16.62 (kfstsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (theprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (kfstpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodfstin) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjL2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR11) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR12) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR1) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairequniteq) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR) =>
% 99.42/16.62 ((
% 99.42/16.62 (ksndsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (ksndpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairsurjEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodsndin) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairmemEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairmemER) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempaircEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodfstpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodsndpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairsurjEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrI) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrSub) =>
% 99.42/16.62 ((
% 99.42/16.62 (setOfPairsIsBReln) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrERa) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrEL1) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrEL2) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrER) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcImageSingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (apProp) =>
% 99.42/16.62 ((
% 99.42/16.62 (app) =>
% 99.42/16.62 ((
% 99.42/16.62 (infuncsetfunc) =>
% 99.42/16.62 ((
% 99.42/16.62 (ap2p) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcinfuncset) =>
% 99.42/16.62 ((
% 99.42/16.62 (lamProp) =>
% 99.42/16.62 ((
% 99.42/16.62 (lamp) =>
% 99.42/16.62 ((
% 99.42/16.62 (lam2p) =>
% 99.42/16.62 ((
% 99.42/16.62 (brelnall1) =>
% 99.42/16.62 ((
% 99.42/16.62 (brelnall2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1E2) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp1) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp3) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp2) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcextLem) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp4) =>
% 99.42/16.62 ((
% 99.42/16.62 (subbreln) =>
% 99.42/16.62 ((
% 99.42/16.62 (eqbreln) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcext) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcext2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ap2apEq1) =>
% 99.42/16.62 ((
% 99.42/16.62 (ap2apEq2) =>
% 99.42/16.62 ((
% 99.42/16.62 (beta1) =>
% 99.42/16.62 ((
% 99.42/16.62 (eta1) =>
% 99.42/16.62 ((
% 99.42/16.62 (lam2lamEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (beta2) =>
% 99.42/16.62 ((
% 99.42/16.62 (eta2) =>
% 99.42/16.62 ((
% 99.42/16.62 (iffalseProp1) =>
% 99.42/16.62 ((
% 99.42/16.62 (iffalseProp2) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrueProp1) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrueProp2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ifSingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (ifp) =>
% 99.42/16.62 ((
% 99.42/16.62 (theeq) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrue) =>
% 99.42/16.62 ((
% 99.42/16.62 (iffalse) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrueorfalse) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (powersetT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (setextT) =>
% 99.42/16.62 ((
% 99.42/16.62 (subsetTI) =>
% 99.42/16.62 ((
% 99.42/16.62 (powersetTI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (powersetTE1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTE1) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectTELcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectTERcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT1) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT2) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT3) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementE1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementSub1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementSub2) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTnotintersectT) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementImpComplementIntersect) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementSubsetComplementIntersect) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementInPowersetComplementIntersect) =>
% 99.42/16.62 ((
% 99.42/16.62 (contraSubsetComplement) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTcontraSubset) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTILcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTIRcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInUnion) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInUnion2) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInIntersectUnions) =>
% 99.42/16.62 ((
% 99.42/16.62 (intersectInPowersetIntersectUnions) =>
% 99.42/16.62 ((
% 99.42/16.62 (inComplementUnionImpNotIn1) =>
% 99.42/16.62 ((
% 99.42/16.62 (inComplementUnionImpInComplement1) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTE) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTEcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2a1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementUnionInPowersetComplement) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2a2) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1a) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1b) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2a) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2b2) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2b) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule0) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule1) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule2) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule3) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule4) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_1) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_2) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_3) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_4) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz1_5) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1all2) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1SetBreln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (choice2fnsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (setOfPairsIsBReln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1all1) =>
% 99.42/16.62 ((
% 99.42/16.62 (subbreln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (eqbreln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1invprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1invI) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1invE) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compI) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compE) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1compEex) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionIL) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionI) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionE) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionEcases) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionCommutes) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2Ex) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2W) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2A) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2B) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1Ex) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1Ex1) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1Equiv) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1E) =>
% 99.42/16.62 ((
% 99.42/16.62 (image1I) =>
% 99.42/16.62 ((
% 99.42/16.62 (injFuncInInjFuncSet) =>
% 99.42/16.62 ((
% 99.42/16.62 (injFuncSetFuncIn) =>
% 99.42/16.62 ((
% 99.42/16.62 (injFuncSetFuncInj) =>
% 99.42/16.62 ((
% 99.42/16.62 (!!) @ (
% 99.42/16.62 (('#B') @ (
% 99.42/16.62 !!) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 !!))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#S') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 '#S') @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 '#S'))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 =>))))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#C') @ in)))) @
% 99.42/16.62 surjFuncSet)))))))) @
% 99.42/16.62 (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#B') @ (
% 99.42/16.62 (
% 99.42/16.62 ('#C') @ in)))) @
% 99.42/16.62 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl672])).
% 99.42/16.62 thf(zip_derived_cl699, plain,
% 99.42/16.62 (~ (((powerset__Cong) =>
% 99.42/16.62 (((setunion__Cong) =>
% 99.42/16.62 (((exuEu) =>
% 99.42/16.62 (((descr__Cong) =>
% 99.42/16.62 (((dsetconstr__Cong) =>
% 99.42/16.62 (((subsetI1) =>
% 99.42/16.62 (((eqimpsubset2) =>
% 99.42/16.62 (((eqimpsubset1) =>
% 99.42/16.62 (((subsetI2) =>
% 99.42/16.62 (((emptysetsubset) =>
% 99.42/16.62 (((subsetE) =>
% 99.42/16.62 (((subsetE2) =>
% 99.42/16.62 (((notsubsetI) =>
% 99.42/16.62 (((notequalI1) =>
% 99.42/16.62 (((notequalI2) =>
% 99.42/16.62 (((subsetRefl) =>
% 99.42/16.62 (((subsetTrans) =>
% 99.42/16.62 (((setadjoinSub) =>
% 99.42/16.62 (((setadjoinSub2) =>
% 99.42/16.62 (((subset2powerset) =>
% 99.42/16.62 (((setextsub) =>
% 99.42/16.62 (((subsetemptysetimpeq) =>
% 99.42/16.62 (((powersetI1) =>
% 99.42/16.62 (((powersetE1) =>
% 99.42/16.62 (((inPowerset) =>
% 99.42/16.62 (((powersetsubset) =>
% 99.42/16.62 (((sepInPowerset) =>
% 99.42/16.62 (((sepSubset) =>
% 99.42/16.62 (((binunionIL) =>
% 99.42/16.62 (((upairset2IR) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionEcases) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionE) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionRsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectI) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset5) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset2) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset3) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectER) =>
% 99.42/16.62 ((
% 99.42/16.62 (disjointsetsI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectRsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset4) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectSubset1) =>
% 99.42/16.62 ((
% 99.42/16.62 (bs114d) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusI) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusER) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusSubset2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusERneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusELneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusILneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusIRneg) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusLsub) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusSubset1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffE) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffI2) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffIneg1) =>
% 99.42/16.62 ((
% 99.42/16.62 (symdiffIneg2) =>
% 99.42/16.62 ((
% 99.42/16.62 (secondinupair) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairIL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairiskpair) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairp) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletonsubset) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletoninpowerset) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletoninpowunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairset2E) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairsubunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairinpowunion) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem1) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ubforcartprodlem3) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairin) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempair1) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempair) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionE2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton1) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setunionsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletonprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1E1) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1I) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1I2) =>
% 99.42/16.62 ((
% 99.42/16.62 (singletonsuniq) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjL1) =>
% 99.42/16.62 ((
% 99.42/16.62 (kfstsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (theprop) =>
% 99.42/16.62 ((
% 99.42/16.62 (kfstpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodfstin) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjL2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjL) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR11) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR12) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR1) =>
% 99.42/16.62 ((
% 99.42/16.62 (upairequniteq) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR2) =>
% 99.42/16.62 ((
% 99.42/16.62 (setukpairinjR) =>
% 99.42/16.62 ((
% 99.42/16.62 (ksndsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (ksndpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (kpairsurjEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodsndin) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairmemEL) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairmemER) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodmempaircEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodfstpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodsndpairEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (cartprodpairsurjEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrI) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrSub) =>
% 99.42/16.62 ((
% 99.42/16.62 (setOfPairsIsBReln) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrERa) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrEL1) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrEL2) =>
% 99.42/16.62 ((
% 99.42/16.62 (dpsetconstrER) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcImageSingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (apProp) =>
% 99.42/16.62 ((
% 99.42/16.62 (app) =>
% 99.42/16.62 ((
% 99.42/16.62 (infuncsetfunc) =>
% 99.42/16.62 ((
% 99.42/16.62 (ap2p) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcinfuncset) =>
% 99.42/16.62 ((
% 99.42/16.62 (lamProp) =>
% 99.42/16.62 ((
% 99.42/16.62 (lamp) =>
% 99.42/16.62 ((
% 99.42/16.62 (lam2p) =>
% 99.42/16.62 ((
% 99.42/16.62 (brelnall1) =>
% 99.42/16.62 ((
% 99.42/16.62 (brelnall2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ex1E2) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp1) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp3) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp2) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcextLem) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcGraphProp4) =>
% 99.42/16.62 ((
% 99.42/16.62 (subbreln) =>
% 99.42/16.62 ((
% 99.42/16.62 (eqbreln) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcext) =>
% 99.42/16.62 ((
% 99.42/16.62 (funcext2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ap2apEq1) =>
% 99.42/16.62 ((
% 99.42/16.62 (ap2apEq2) =>
% 99.42/16.62 ((
% 99.42/16.62 (beta1) =>
% 99.42/16.62 ((
% 99.42/16.62 (eta1) =>
% 99.42/16.62 ((
% 99.42/16.62 (lam2lamEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (beta2) =>
% 99.42/16.62 ((
% 99.42/16.62 (eta2) =>
% 99.42/16.62 ((
% 99.42/16.62 (iffalseProp1) =>
% 99.42/16.62 ((
% 99.42/16.62 (iffalseProp2) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrueProp1) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrueProp2) =>
% 99.42/16.62 ((
% 99.42/16.62 (ifSingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (ifp) =>
% 99.42/16.62 ((
% 99.42/16.62 (theeq) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrue) =>
% 99.42/16.62 ((
% 99.42/16.62 (iffalse) =>
% 99.42/16.62 ((
% 99.42/16.62 (iftrueorfalse) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (powersetT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (setminusT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementT_lem) =>
% 99.42/16.62 ((
% 99.42/16.62 (setextT) =>
% 99.42/16.62 ((
% 99.42/16.62 (subsetTI) =>
% 99.42/16.62 ((
% 99.42/16.62 (powersetTI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (powersetTE1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTE1) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectTELcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (binintersectTERcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT1) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT2) =>
% 99.42/16.62 ((
% 99.42/16.62 (contrasubsetT3) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementI1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementE1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementSub1) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementSub2) =>
% 99.42/16.62 ((
% 99.42/16.62 (doubleComplementEq) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTnotintersectT) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementImpComplementIntersect) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementSubsetComplementIntersect) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementInPowersetComplementIntersect) =>
% 99.42/16.62 ((
% 99.42/16.62 (contraSubsetComplement) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementTcontraSubset) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTILcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTIRcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInUnion) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInUnion2) =>
% 99.42/16.62 ((
% 99.42/16.62 (inIntersectImpInIntersectUnions) =>
% 99.42/16.62 ((
% 99.42/16.62 (intersectInPowersetIntersectUnions) =>
% 99.42/16.62 ((
% 99.42/16.62 (inComplementUnionImpNotIn1) =>
% 99.42/16.62 ((
% 99.42/16.62 (inComplementUnionImpInComplement1) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTE) =>
% 99.42/16.62 ((
% 99.42/16.62 (binunionTEcontra) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2a1) =>
% 99.42/16.62 ((
% 99.42/16.62 (complementUnionInPowersetComplement) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2a2) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1a) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1b) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan1) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2a) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2b2) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2b) =>
% 99.42/16.62 ((
% 99.42/16.62 (demorgan2) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule0) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule1) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz13rule2) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (woz1_2) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (woz1_5) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1all2) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1SetBreln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (choice2fnsingleton) =>
% 99.42/16.62 ((
% 99.42/16.62 (setOfPairsIsBReln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1all1) =>
% 99.42/16.62 ((
% 99.42/16.62 (subbreln1) =>
% 99.42/16.62 ((
% 99.42/16.62 (eqbreln1) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (breln1invI) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1invE) =>
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% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (breln1compEex) =>
% 99.42/16.62 ((
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% 99.42/16.62 ((
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% 99.42/16.62 ((
% 99.42/16.62 (breln1unionIR) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionI) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionE) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionEcases) =>
% 99.42/16.62 ((
% 99.42/16.62 (breln1unionCommutes) =>
% 99.42/16.62 ((
% 99.42/16.62 (woz2Ex) =>
% 99.42/16.62 ((
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% 99.42/16.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl699])).
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (ubforcartprodlem3) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (kpairsurjEq) =>
% 99.42/16.63 ((
% 99.42/16.63 (cartprodsndin) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (cartprodpairmemER) =>
% 99.42/16.63 ((
% 99.42/16.63 (cartprodmempaircEq) =>
% 99.42/16.63 ((
% 99.42/16.63 (cartprodfstpairEq) =>
% 99.42/16.63 ((
% 99.42/16.63 (cartprodsndpairEq) =>
% 99.42/16.63 ((
% 99.42/16.63 (cartprodpairsurjEq) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 (dpsetconstrEL2) =>
% 99.42/16.63 ((
% 99.42/16.63 (dpsetconstrER) =>
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% 99.42/16.63 (funcImageSingleton) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (ap2p) =>
% 99.42/16.63 ((
% 99.42/16.63 (funcinfuncset) =>
% 99.42/16.63 ((
% 99.42/16.63 (lamProp) =>
% 99.42/16.63 ((
% 99.42/16.63 (lamp) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (brelnall2) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (funcGraphProp3) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 (eta1) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (beta2) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (iffalseProp2) =>
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% 99.42/16.63 ((
% 99.42/16.63 (doubleComplementE1) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (doubleComplementSub2) =>
% 99.42/16.63 ((
% 99.42/16.63 (doubleComplementEq) =>
% 99.42/16.63 ((
% 99.42/16.63 (complementTnotintersectT) =>
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% 99.42/16.63 (complementImpComplementIntersect) =>
% 99.42/16.63 ((
% 99.42/16.63 (complementSubsetComplementIntersect) =>
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% 99.42/16.63 (complementInPowersetComplementIntersect) =>
% 99.42/16.63 ((
% 99.42/16.63 (contraSubsetComplement) =>
% 99.42/16.63 ((
% 99.42/16.63 (complementTcontraSubset) =>
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% 99.42/16.63 ((
% 99.42/16.63 (binunionTIRcontra) =>
% 99.42/16.63 ((
% 99.42/16.63 (inIntersectImpInUnion) =>
% 99.42/16.63 ((
% 99.42/16.63 (inIntersectImpInUnion2) =>
% 99.42/16.63 ((
% 99.42/16.63 (inIntersectImpInIntersectUnions) =>
% 99.42/16.63 ((
% 99.42/16.63 (intersectInPowersetIntersectUnions) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (inComplementUnionImpInComplement1) =>
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (demorgan2a) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (demorgan2b) =>
% 99.42/16.63 ((
% 99.42/16.63 (demorgan2) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (woz1_4) =>
% 99.42/16.63 ((
% 99.42/16.63 (woz1_5) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (breln1SetBreln1) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (setOfPairsIsBReln1) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (eqbreln1) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1invprop) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1invI) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1invE) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (breln1compI) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1compE) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1compEex) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1unionprop) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1unionIL) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (breln1unionI) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1unionE) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (injFuncSetFuncIn) =>
% 99.42/16.63 ((
% 99.42/16.63 (injFuncSetFuncInj) =>
% 99.42/16.63 ((
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% 99.42/16.63 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl714])).
% 99.42/16.63 thf(zip_derived_cl749, plain,
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% 99.42/16.63 (setminusI) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusEL) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusER) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusSubset2) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusERneg) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusELneg) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusILneg) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusIRneg) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusLsub) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusSubset1) =>
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (symdiffI2) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (symdiffIneg2) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (kpairiskpair) =>
% 99.42/16.63 ((
% 99.42/16.63 (kpairp) =>
% 99.42/16.63 ((
% 99.42/16.63 (singletonsubset) =>
% 99.42/16.63 ((
% 99.42/16.63 (singletoninpowerset) =>
% 99.42/16.63 ((
% 99.42/16.63 (singletoninpowunion) =>
% 99.42/16.63 ((
% 99.42/16.63 (upairset2E) =>
% 99.42/16.63 ((
% 99.42/16.63 (upairsubunion) =>
% 99.42/16.63 ((
% 99.42/16.63 (upairinpowunion) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (ubforcartprodlem2) =>
% 99.42/16.63 ((
% 99.42/16.63 (ubforcartprodlem3) =>
% 99.42/16.63 ((
% 99.42/16.63 (cartprodpairin) =>
% 99.42/16.63 ((
% 99.42/16.63 (cartprodmempair1) =>
% 99.42/16.63 ((
% 99.42/16.63 (cartprodmempair) =>
% 99.42/16.63 ((
% 99.42/16.63 (setunionE2) =>
% 99.42/16.63 ((
% 99.42/16.63 (setunionsingleton1) =>
% 99.42/16.63 ((
% 99.42/16.63 (setunionsingleton2) =>
% 99.42/16.63 ((
% 99.42/16.63 (setunionsingleton) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (ex1I) =>
% 99.42/16.63 ((
% 99.42/16.63 (ex1I2) =>
% 99.42/16.63 ((
% 99.42/16.63 (singletonsuniq) =>
% 99.42/16.63 ((
% 99.42/16.63 (setukpairinjL1) =>
% 99.42/16.63 ((
% 99.42/16.63 (kfstsingleton) =>
% 99.42/16.63 ((
% 99.42/16.63 (theprop) =>
% 99.42/16.63 ((
% 99.42/16.63 (kfstpairEq) =>
% 99.42/16.63 ((
% 99.42/16.63 (cartprodfstin) =>
% 99.42/16.63 ((
% 99.42/16.63 (setukpairinjL2) =>
% 99.42/16.63 ((
% 99.42/16.63 (setukpairinjL) =>
% 99.42/16.63 ((
% 99.42/16.63 (setukpairinjR11) =>
% 99.42/16.63 ((
% 99.42/16.63 (setukpairinjR12) =>
% 99.42/16.63 ((
% 99.42/16.63 (setukpairinjR1) =>
% 99.42/16.63 ((
% 99.42/16.63 (upairequniteq) =>
% 99.42/16.63 ((
% 99.42/16.63 (setukpairinjR2) =>
% 99.42/16.63 ((
% 99.42/16.63 (setukpairinjR) =>
% 99.42/16.63 ((
% 99.42/16.63 (ksndsingleton) =>
% 99.42/16.63 ((
% 99.42/16.63 (ksndpairEq) =>
% 99.42/16.63 ((
% 99.42/16.63 (kpairsurjEq) =>
% 99.42/16.63 ((
% 99.42/16.63 (cartprodsndin) =>
% 99.42/16.63 ((
% 99.42/16.63 (cartprodpairmemEL) =>
% 99.42/16.63 ((
% 99.42/16.63 (cartprodpairmemER) =>
% 99.42/16.63 ((
% 99.42/16.63 (cartprodmempaircEq) =>
% 99.42/16.63 ((
% 99.42/16.63 (cartprodfstpairEq) =>
% 99.42/16.63 ((
% 99.42/16.63 (cartprodsndpairEq) =>
% 99.42/16.63 ((
% 99.42/16.63 (cartprodpairsurjEq) =>
% 99.42/16.63 ((
% 99.42/16.63 (dpsetconstrI) =>
% 99.42/16.63 ((
% 99.42/16.63 (dpsetconstrSub) =>
% 99.42/16.63 ((
% 99.42/16.63 (setOfPairsIsBReln) =>
% 99.42/16.63 ((
% 99.42/16.63 (dpsetconstrERa) =>
% 99.42/16.63 ((
% 99.42/16.63 (dpsetconstrEL1) =>
% 99.42/16.63 ((
% 99.42/16.63 (dpsetconstrEL2) =>
% 99.42/16.63 ((
% 99.42/16.63 (dpsetconstrER) =>
% 99.42/16.63 ((
% 99.42/16.63 (funcImageSingleton) =>
% 99.42/16.63 ((
% 99.42/16.63 (apProp) =>
% 99.42/16.63 ((
% 99.42/16.63 (app) =>
% 99.42/16.63 ((
% 99.42/16.63 (infuncsetfunc) =>
% 99.42/16.63 ((
% 99.42/16.63 (ap2p) =>
% 99.42/16.63 ((
% 99.42/16.63 (funcinfuncset) =>
% 99.42/16.63 ((
% 99.42/16.63 (lamProp) =>
% 99.42/16.63 ((
% 99.42/16.63 (lamp) =>
% 99.42/16.63 ((
% 99.42/16.63 (lam2p) =>
% 99.42/16.63 ((
% 99.42/16.63 (brelnall1) =>
% 99.42/16.63 ((
% 99.42/16.63 (brelnall2) =>
% 99.42/16.63 ((
% 99.42/16.63 (ex1E2) =>
% 99.42/16.63 ((
% 99.42/16.63 (funcGraphProp1) =>
% 99.42/16.63 ((
% 99.42/16.63 (funcGraphProp3) =>
% 99.42/16.63 ((
% 99.42/16.63 (funcGraphProp2) =>
% 99.42/16.63 ((
% 99.42/16.63 (funcextLem) =>
% 99.42/16.63 ((
% 99.42/16.63 (funcGraphProp4) =>
% 99.42/16.63 ((
% 99.42/16.63 (subbreln) =>
% 99.42/16.63 ((
% 99.42/16.63 (eqbreln) =>
% 99.42/16.63 ((
% 99.42/16.63 (funcext) =>
% 99.42/16.63 ((
% 99.42/16.63 (funcext2) =>
% 99.42/16.63 ((
% 99.42/16.63 (ap2apEq1) =>
% 99.42/16.63 ((
% 99.42/16.63 (ap2apEq2) =>
% 99.42/16.63 ((
% 99.42/16.63 (beta1) =>
% 99.42/16.63 ((
% 99.42/16.63 (eta1) =>
% 99.42/16.63 ((
% 99.42/16.63 (lam2lamEq) =>
% 99.42/16.63 ((
% 99.42/16.63 (beta2) =>
% 99.42/16.63 ((
% 99.42/16.63 (eta2) =>
% 99.42/16.63 ((
% 99.42/16.63 (iffalseProp1) =>
% 99.42/16.63 ((
% 99.42/16.63 (iffalseProp2) =>
% 99.42/16.63 ((
% 99.42/16.63 (iftrueProp1) =>
% 99.42/16.63 ((
% 99.42/16.63 (iftrueProp2) =>
% 99.42/16.63 ((
% 99.42/16.63 (ifSingleton) =>
% 99.42/16.63 ((
% 99.42/16.63 (ifp) =>
% 99.42/16.63 ((
% 99.42/16.63 (theeq) =>
% 99.42/16.63 ((
% 99.42/16.63 (iftrue) =>
% 99.42/16.63 ((
% 99.42/16.63 (iffalse) =>
% 99.42/16.63 ((
% 99.42/16.63 (iftrueorfalse) =>
% 99.42/16.63 ((
% 99.42/16.63 (binintersectT_lem) =>
% 99.42/16.63 ((
% 99.42/16.63 (binunionT_lem) =>
% 99.42/16.63 ((
% 99.42/16.63 (powersetT_lem) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusT_lem) =>
% 99.42/16.63 ((
% 99.42/16.63 (complementT_lem) =>
% 99.42/16.63 ((
% 99.42/16.63 (setextT) =>
% 99.42/16.63 ((
% 99.42/16.63 (subsetTI) =>
% 99.42/16.63 ((
% 99.42/16.63 (powersetTI1) =>
% 99.42/16.63 ((
% 99.42/16.63 (powersetTE1) =>
% 99.42/16.63 ((
% 99.42/16.63 (complementTI1) =>
% 99.42/16.63 ((
% 99.42/16.63 (complementTE1) =>
% 99.42/16.63 ((
% 99.42/16.63 (binintersectTELcontra) =>
% 99.42/16.63 ((
% 99.42/16.63 (binintersectTERcontra) =>
% 99.42/16.63 ((
% 99.42/16.63 (contrasubsetT) =>
% 99.42/16.63 ((
% 99.42/16.63 (contrasubsetT1) =>
% 99.42/16.63 ((
% 99.42/16.63 (contrasubsetT2) =>
% 99.42/16.63 ((
% 99.42/16.63 (contrasubsetT3) =>
% 99.42/16.63 ((
% 99.42/16.63 (doubleComplementI1) =>
% 99.42/16.63 ((
% 99.42/16.63 (doubleComplementE1) =>
% 99.42/16.63 ((
% 99.42/16.63 (doubleComplementSub1) =>
% 99.42/16.63 ((
% 99.42/16.63 (doubleComplementSub2) =>
% 99.42/16.63 ((
% 99.42/16.63 (doubleComplementEq) =>
% 99.42/16.63 ((
% 99.42/16.63 (complementTnotintersectT) =>
% 99.42/16.63 ((
% 99.42/16.63 (complementImpComplementIntersect) =>
% 99.42/16.63 ((
% 99.42/16.63 (complementSubsetComplementIntersect) =>
% 99.42/16.63 ((
% 99.42/16.63 (complementInPowersetComplementIntersect) =>
% 99.42/16.63 ((
% 99.42/16.63 (contraSubsetComplement) =>
% 99.42/16.63 ((
% 99.42/16.63 (complementTcontraSubset) =>
% 99.42/16.63 ((
% 99.42/16.63 (binunionTILcontra) =>
% 99.42/16.63 ((
% 99.42/16.63 (binunionTIRcontra) =>
% 99.42/16.63 ((
% 99.42/16.63 (inIntersectImpInUnion) =>
% 99.42/16.63 ((
% 99.42/16.63 (inIntersectImpInUnion2) =>
% 99.42/16.63 ((
% 99.42/16.63 (inIntersectImpInIntersectUnions) =>
% 99.42/16.63 ((
% 99.42/16.63 (intersectInPowersetIntersectUnions) =>
% 99.42/16.63 ((
% 99.42/16.63 (inComplementUnionImpNotIn1) =>
% 99.42/16.63 ((
% 99.42/16.63 (inComplementUnionImpInComplement1) =>
% 99.42/16.63 ((
% 99.42/16.63 (binunionTE) =>
% 99.42/16.63 ((
% 99.42/16.63 (binunionTEcontra) =>
% 99.42/16.63 ((
% 99.42/16.63 (demorgan2a1) =>
% 99.42/16.63 ((
% 99.42/16.63 (complementUnionInPowersetComplement) =>
% 99.42/16.63 ((
% 99.42/16.63 (demorgan2a2) =>
% 99.42/16.63 ((
% 99.42/16.63 (demorgan1a) =>
% 99.42/16.63 ((
% 99.42/16.63 (demorgan1b) =>
% 99.42/16.63 ((
% 99.42/16.63 (demorgan1) =>
% 99.42/16.63 ((
% 99.42/16.63 (demorgan2a) =>
% 99.42/16.63 ((
% 99.42/16.63 (demorgan2b2) =>
% 99.42/16.63 ((
% 99.42/16.63 (demorgan2b) =>
% 99.42/16.63 ((
% 99.42/16.63 (demorgan2) =>
% 99.42/16.63 ((
% 99.42/16.63 (woz13rule0) =>
% 99.42/16.63 ((
% 99.42/16.63 (woz13rule1) =>
% 99.42/16.63 ((
% 99.42/16.63 (woz13rule2) =>
% 99.42/16.63 ((
% 99.42/16.63 (woz13rule3) =>
% 99.42/16.63 ((
% 99.42/16.63 (woz13rule4) =>
% 99.42/16.63 ((
% 99.42/16.63 (woz1_1) =>
% 99.42/16.63 ((
% 99.42/16.63 (woz1_2) =>
% 99.42/16.63 ((
% 99.42/16.63 (woz1_3) =>
% 99.42/16.63 ((
% 99.42/16.63 (woz1_4) =>
% 99.42/16.63 ((
% 99.42/16.63 (woz1_5) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1all2) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1SetBreln1) =>
% 99.42/16.63 ((
% 99.42/16.63 (choice2fnsingleton) =>
% 99.42/16.63 ((
% 99.42/16.63 (setOfPairsIsBReln1) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1all1) =>
% 99.42/16.63 ((
% 99.42/16.63 (subbreln1) =>
% 99.42/16.63 ((
% 99.42/16.63 (eqbreln1) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1invprop) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1invI) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1invE) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1compprop) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1compI) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1compE) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1compEex) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1unionprop) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1unionIL) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1unionIR) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1unionI) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1unionE) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1unionEcases) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1unionCommutes) =>
% 99.42/16.63 ((
% 99.42/16.63 (woz2Ex) =>
% 99.42/16.63 ((
% 99.42/16.63 (woz2W) =>
% 99.42/16.63 ((
% 99.42/16.63 (woz2A) =>
% 99.42/16.63 ((
% 99.42/16.63 (woz2B) =>
% 99.42/16.63 ((
% 99.42/16.63 (image1Ex) =>
% 99.42/16.63 ((
% 99.42/16.63 (image1Ex1) =>
% 99.42/16.63 ((
% 99.42/16.63 (image1Equiv) =>
% 99.42/16.63 ((
% 99.42/16.63 (image1E) =>
% 99.42/16.63 ((
% 99.42/16.63 (image1I) =>
% 99.42/16.63 ((
% 99.42/16.63 (injFuncInInjFuncSet) =>
% 99.42/16.63 ((
% 99.42/16.63 (injFuncSetFuncIn) =>
% 99.42/16.63 ((
% 99.42/16.63 (injFuncSetFuncInj) =>
% 99.42/16.63 ((
% 99.42/16.63 (!!) @ (
% 99.42/16.63 (('#B') @ (
% 99.42/16.63 !!) @
% 99.42/16.63 (
% 99.42/16.63 (
% 99.42/16.63 ('#B') @ (
% 99.42/16.63 (
% 99.42/16.63 ('#B') @ (
% 99.42/16.63 !!))) @
% 99.42/16.63 (
% 99.42/16.63 (
% 99.42/16.63 ('#S') @ (
% 99.42/16.63 (
% 99.42/16.63 ('#B') @ (
% 99.42/16.63 '#S') @
% 99.42/16.63 (
% 99.42/16.63 (
% 99.42/16.63 ('#B') @ (
% 99.42/16.63 (
% 99.42/16.63 ('#B') @ (
% 99.42/16.63 '#S'))) @
% 99.42/16.63 (
% 99.42/16.63 (
% 99.42/16.63 ('#B') @ (
% 99.42/16.63 (
% 99.42/16.63 ('#B') @ (
% 99.42/16.63 (
% 99.42/16.63 ('#B') @ (
% 99.42/16.63 =>))))) @
% 99.42/16.63 (
% 99.42/16.63 (
% 99.42/16.63 ('#B') @ (
% 99.42/16.63 (
% 99.42/16.63 ('#B') @ (
% 99.42/16.63 (
% 99.42/16.63 ('#C') @ in)))) @
% 99.42/16.63 surjFuncSet)))))))) @
% 99.42/16.63 (
% 99.42/16.63 (
% 99.42/16.63 ('#B') @ (
% 99.42/16.63 (
% 99.42/16.63 ('#B') @ (
% 99.42/16.63 (
% 99.42/16.63 ('#C') @ in)))) @
% 99.42/16.63 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.42/16.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl749])).
% 99.42/16.63 thf(zip_derived_cl789, plain,
% 99.42/16.63 (~ (((subsetI1) =>
% 99.42/16.63 (((eqimpsubset2) =>
% 99.42/16.63 (((eqimpsubset1) =>
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% 99.42/16.63 (((subsetE) =>
% 99.42/16.63 (((subsetE2) =>
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% 99.42/16.63 (((notequalI1) =>
% 99.42/16.63 (((notequalI2) =>
% 99.42/16.63 (((subsetRefl) =>
% 99.42/16.63 (((subsetTrans) =>
% 99.42/16.63 (((setadjoinSub) =>
% 99.42/16.63 (((setadjoinSub2) =>
% 99.42/16.63 (((subset2powerset) =>
% 99.42/16.63 (((setextsub) =>
% 99.42/16.63 (((subsetemptysetimpeq) =>
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% 99.42/16.63 (((powersetE1) =>
% 99.42/16.63 (((inPowerset) =>
% 99.42/16.63 (((powersetsubset) =>
% 99.42/16.63 (((sepInPowerset) =>
% 99.42/16.63 (((sepSubset) =>
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% 99.42/16.63 (((upairset2IR) =>
% 99.42/16.63 (((binunionIR) =>
% 99.42/16.63 (((binunionEcases) =>
% 99.42/16.63 (((binunionE) =>
% 99.42/16.63 (((binunionLsub) =>
% 99.42/16.63 (((binunionRsub) =>
% 99.42/16.63 ((
% 99.42/16.63 (binintersectI) =>
% 99.42/16.63 ((
% 99.42/16.63 (binintersectSubset5) =>
% 99.42/16.63 ((
% 99.42/16.63 (binintersectEL) =>
% 99.42/16.63 ((
% 99.42/16.63 (binintersectLsub) =>
% 99.42/16.63 ((
% 99.42/16.63 (binintersectSubset2) =>
% 99.42/16.63 ((
% 99.42/16.63 (binintersectSubset3) =>
% 99.42/16.63 ((
% 99.42/16.63 (binintersectER) =>
% 99.42/16.63 ((
% 99.42/16.63 (disjointsetsI1) =>
% 99.42/16.63 ((
% 99.42/16.63 (binintersectRsub) =>
% 99.42/16.63 ((
% 99.42/16.63 (binintersectSubset4) =>
% 99.42/16.63 ((
% 99.42/16.63 (binintersectSubset1) =>
% 99.42/16.63 ((
% 99.42/16.63 (bs114d) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusI) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusEL) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusER) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusSubset2) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusERneg) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusELneg) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusILneg) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusIRneg) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusLsub) =>
% 99.42/16.63 ((
% 99.42/16.63 (setminusSubset1) =>
% 99.42/16.63 ((
% 99.42/16.63 (symdiffE) =>
% 99.42/16.63 ((
% 99.42/16.63 (symdiffI1) =>
% 99.42/16.63 ((
% 99.42/16.63 (symdiffI2) =>
% 99.42/16.63 ((
% 99.42/16.63 (symdiffIneg1) =>
% 99.42/16.63 ((
% 99.42/16.63 (symdiffIneg2) =>
% 99.42/16.63 ((
% 99.42/16.63 (secondinupair) =>
% 99.42/16.63 ((
% 99.42/16.63 (setukpairIL) =>
% 99.42/16.63 ((
% 99.42/16.63 (setukpairIR) =>
% 99.42/16.63 ((
% 99.42/16.63 (kpairiskpair) =>
% 99.42/16.63 ((
% 99.42/16.63 (kpairp) =>
% 99.42/16.63 ((
% 99.42/16.63 (singletonsubset) =>
% 99.42/16.63 ((
% 99.42/16.63 (singletoninpowerset) =>
% 99.42/16.63 ((
% 99.42/16.63 (singletoninpowunion) =>
% 99.42/16.63 ((
% 99.42/16.63 (upairset2E) =>
% 99.42/16.63 ((
% 99.42/16.63 (upairsubunion) =>
% 99.42/16.63 ((
% 99.42/16.63 (upairinpowunion) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (demorgan2b) =>
% 99.42/16.63 ((
% 99.42/16.63 (demorgan2) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 (woz1_5) =>
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% 99.42/16.63 (breln1all2) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1SetBreln1) =>
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (breln1compprop) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (breln1compE) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1compEex) =>
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% 99.42/16.63 (breln1unionI) =>
% 99.42/16.63 ((
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% 99.42/16.63 (image1I) =>
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% 99.42/16.63 ((
% 99.42/16.63 (injFuncSetFuncIn) =>
% 99.42/16.63 ((
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% 99.42/16.63 (
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 (woz1_5) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (breln1SetBreln1) =>
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (breln1invI) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1invE) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1compprop) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1compI) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1compE) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1compEex) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1unionprop) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1unionIL) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (breln1unionI) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1unionE) =>
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% 99.42/16.63 (breln1unionEcases) =>
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% 99.42/16.63 (breln1unionCommutes) =>
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (image1I) =>
% 99.42/16.63 ((
% 99.42/16.63 (injFuncInInjFuncSet) =>
% 99.42/16.63 ((
% 99.42/16.63 (injFuncSetFuncIn) =>
% 99.42/16.63 ((
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% 99.42/16.63 (
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
% 99.42/16.63 (cartprodsndpairEq) =>
% 99.42/16.63 ((
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% 99.42/16.63 (dpsetconstrER) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 (brelnall2) =>
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% 99.42/16.63 (woz1_5) =>
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% 99.42/16.63 ((
% 99.42/16.63 (breln1invE) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1compprop) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1compI) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1compE) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1compEex) =>
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% 99.42/16.63 ((
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% 99.42/16.63 (breln1unionI) =>
% 99.42/16.63 ((
% 99.42/16.63 (breln1unionE) =>
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% 99.42/16.63 ((
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% 99.42/16.63 (image1I) =>
% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.63 ((
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% 99.42/16.64 ((
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% 99.42/16.64 ((
% 99.42/16.64 (breln1compE) =>
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% 99.42/16.64 (breln1compEex) =>
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% 99.42/16.64 ((
% 99.42/16.64 (image1Ex1) =>
% 99.42/16.64 ((
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% 99.42/16.65 ((
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% 99.42/16.65 ((
% 99.42/16.65 (image1I) =>
% 99.42/16.65 ((
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% 99.42/16.65 ((
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% 99.42/16.65 (
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% 99.42/16.65 ((
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% 99.42/16.65 ((
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% 99.42/16.65 ((
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% 99.42/16.65 ((
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% 99.42/16.65 ((
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% 99.42/16.65 ((
% 99.42/16.65 (funcGraphProp3) =>
% 99.42/16.65 ((
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% 99.42/16.65 ((
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% 99.42/16.65 ((
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% 99.77/16.65 (cartprodpairmemER) =>
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% 99.77/16.65 (cartprodmempaircEq) =>
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% 99.77/16.65 (cartprodsndpairEq) =>
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% 99.77/16.65 ((
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% 99.77/16.65 (ap2p) =>
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% 99.77/16.65 (funcinfuncset) =>
% 99.77/16.65 ((
% 99.77/16.65 (lamProp) =>
% 99.77/16.65 ((
% 99.77/16.65 (lamp) =>
% 99.77/16.65 ((
% 99.77/16.65 (lam2p) =>
% 99.77/16.65 ((
% 99.77/16.65 (brelnall1) =>
% 99.77/16.65 ((
% 99.77/16.65 (brelnall2) =>
% 99.77/16.65 ((
% 99.77/16.65 (ex1E2) =>
% 99.77/16.65 ((
% 99.77/16.65 (funcGraphProp1) =>
% 99.77/16.65 ((
% 99.77/16.65 (funcGraphProp3) =>
% 99.77/16.65 ((
% 99.77/16.65 (funcGraphProp2) =>
% 99.77/16.65 ((
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% 99.77/16.65 (funcGraphProp4) =>
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% 99.77/16.65 ((
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% 99.77/16.65 (contrasubsetT2) =>
% 99.77/16.65 ((
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% 99.77/16.65 ((
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% 99.77/16.65 (doubleComplementEq) =>
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% 99.77/16.65 (complementImpComplementIntersect) =>
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% 99.77/16.65 (complementSubsetComplementIntersect) =>
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% 99.77/16.65 ((
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% 99.77/16.65 (binunionTIRcontra) =>
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% 99.77/16.65 (inIntersectImpInUnion2) =>
% 99.77/16.65 ((
% 99.77/16.65 (inIntersectImpInIntersectUnions) =>
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% 99.77/16.65 (demorgan2a) =>
% 99.77/16.65 ((
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% 99.77/16.65 ((
% 99.77/16.65 (demorgan2b) =>
% 99.77/16.65 ((
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% 99.77/16.65 ((
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% 99.77/16.65 ((
% 99.77/16.65 (woz13rule2) =>
% 99.77/16.65 ((
% 99.77/16.65 (woz13rule3) =>
% 99.77/16.65 ((
% 99.77/16.65 (woz13rule4) =>
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% 99.77/16.65 (woz1_4) =>
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% 99.77/16.65 (woz1_5) =>
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% 99.77/16.65 (breln1all2) =>
% 99.77/16.65 ((
% 99.77/16.65 (breln1SetBreln1) =>
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% 99.77/16.65 ((
% 99.77/16.65 (breln1invE) =>
% 99.77/16.65 ((
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% 99.77/16.65 (breln1compI) =>
% 99.77/16.65 ((
% 99.77/16.65 (breln1compE) =>
% 99.77/16.65 ((
% 99.77/16.65 (breln1compEex) =>
% 99.77/16.65 ((
% 99.77/16.65 (breln1unionprop) =>
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% 99.77/16.65 ((
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% 99.77/16.65 ((
% 99.77/16.65 (breln1unionI) =>
% 99.77/16.65 ((
% 99.77/16.65 (breln1unionE) =>
% 99.77/16.65 ((
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% 99.77/16.65 (breln1unionCommutes) =>
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% 99.77/16.65 ((
% 99.77/16.65 (image1Ex1) =>
% 99.77/16.65 ((
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% 99.77/16.65 ((
% 99.77/16.65 (image1E) =>
% 99.77/16.65 ((
% 99.77/16.65 (image1I) =>
% 99.77/16.65 ((
% 99.77/16.65 (injFuncInInjFuncSet) =>
% 99.77/16.65 ((
% 99.77/16.65 (injFuncSetFuncIn) =>
% 99.77/16.65 ((
% 99.77/16.65 (injFuncSetFuncInj) =>
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% 99.77/16.65 (
% 99.77/16.65 (
% 99.77/16.65 ('#B') @ (
% 99.77/16.65 (
% 99.77/16.65 ('#B') @ (
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% 99.77/16.65 (
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% 99.77/16.65 (
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% 99.77/16.65 (
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% 99.77/16.65 (
% 99.77/16.65 (
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% 99.77/16.65 surjFuncSet)))))))) @
% 99.77/16.65 (
% 99.77/16.65 (
% 99.77/16.65 ('#B') @ (
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% 99.77/16.65 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.77/16.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1015])).
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% 99.77/16.65 (setminusIRneg) =>
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% 99.77/16.65 ((
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% 99.77/16.65 ((
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% 99.77/16.65 (kpairp) =>
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% 99.77/16.65 ((
% 99.77/16.65 (ubforcartprodlem3) =>
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% 99.77/16.65 ((
% 99.77/16.65 (cartprodmempair) =>
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% 99.77/16.65 ((
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% 99.77/16.65 ((
% 99.77/16.65 (setunionsingleton) =>
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% 99.77/16.66 ((
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% 99.77/16.66 ((
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% 99.77/16.66 (
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% 99.77/16.66 ((
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% 99.77/16.66 ((
% 99.77/16.66 (cartprodfstpairEq) =>
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% 99.77/16.66 (cartprodsndpairEq) =>
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% 99.77/16.66 ((
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% 99.77/16.66 ((
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% 99.77/16.66 ((
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% 99.77/16.66 ((
% 99.77/16.66 (eta1) =>
% 99.77/16.66 ((
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% 99.77/16.66 (ap2p) =>
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% 99.77/16.66 (lamProp) =>
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% 99.77/16.66 (lamp) =>
% 99.77/16.66 ((
% 99.77/16.66 (lam2p) =>
% 99.77/16.66 ((
% 99.77/16.66 (brelnall1) =>
% 99.77/16.66 ((
% 99.77/16.66 (brelnall2) =>
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% 99.77/16.66 (ex1E2) =>
% 99.77/16.66 ((
% 99.77/16.66 (funcGraphProp1) =>
% 99.77/16.66 ((
% 99.77/16.66 (funcGraphProp3) =>
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% 99.77/16.66 (funcGraphProp2) =>
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% 99.77/16.66 ((
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% 99.77/16.66 (doubleComplementSub2) =>
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% 99.77/16.66 (inIntersectImpInIntersectUnions) =>
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% 99.77/16.66 ((
% 99.77/16.66 (demorgan2a) =>
% 99.77/16.66 ((
% 99.77/16.66 (demorgan2b2) =>
% 99.77/16.66 ((
% 99.77/16.66 (demorgan2b) =>
% 99.77/16.66 ((
% 99.77/16.66 (demorgan2) =>
% 99.77/16.66 ((
% 99.77/16.66 (woz13rule0) =>
% 99.77/16.66 ((
% 99.77/16.66 (woz13rule1) =>
% 99.77/16.66 ((
% 99.77/16.66 (woz13rule2) =>
% 99.77/16.66 ((
% 99.77/16.66 (woz13rule3) =>
% 99.77/16.66 ((
% 99.77/16.66 (woz13rule4) =>
% 99.77/16.66 ((
% 99.77/16.66 (woz1_1) =>
% 99.77/16.66 ((
% 99.77/16.66 (woz1_2) =>
% 99.77/16.66 ((
% 99.77/16.66 (woz1_3) =>
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% 99.77/16.66 (woz1_4) =>
% 99.77/16.66 ((
% 99.77/16.66 (woz1_5) =>
% 99.77/16.66 ((
% 99.77/16.66 (breln1all2) =>
% 99.77/16.66 ((
% 99.77/16.66 (breln1SetBreln1) =>
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% 99.77/16.66 ((
% 99.77/16.66 (breln1invI) =>
% 99.77/16.66 ((
% 99.77/16.66 (breln1invE) =>
% 99.77/16.66 ((
% 99.77/16.66 (breln1compprop) =>
% 99.77/16.66 ((
% 99.77/16.66 (breln1compI) =>
% 99.77/16.66 ((
% 99.77/16.66 (breln1compE) =>
% 99.77/16.66 ((
% 99.77/16.66 (breln1compEex) =>
% 99.77/16.66 ((
% 99.77/16.66 (breln1unionprop) =>
% 99.77/16.66 ((
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% 99.77/16.66 ((
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% 99.77/16.66 ((
% 99.77/16.66 (breln1unionI) =>
% 99.77/16.66 ((
% 99.77/16.66 (breln1unionE) =>
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% 99.77/16.66 (breln1unionCommutes) =>
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% 99.77/16.66 (image1Ex1) =>
% 99.77/16.66 ((
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% 99.77/16.66 ((
% 99.77/16.66 (image1E) =>
% 99.77/16.66 ((
% 99.77/16.66 (image1I) =>
% 99.77/16.66 ((
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% 99.77/16.66 ((
% 99.77/16.66 (injFuncSetFuncIn) =>
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% 99.77/16.66 (
% 99.77/16.66 (
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% 99.77/16.66 (
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% 99.77/16.66 (
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% 99.77/16.66 surjFuncSet)))))))) @
% 99.77/16.66 (
% 99.77/16.66 (
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% 99.77/16.66 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.77/16.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1090])).
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% 99.77/16.66 (ubforcartprodlem1) =>
% 99.77/16.66 ((
% 99.77/16.66 (ubforcartprodlem2) =>
% 99.77/16.66 ((
% 99.77/16.66 (ubforcartprodlem3) =>
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% 99.77/16.66 ((
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% 99.77/16.66 ((
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% 99.77/16.66 ((
% 99.77/16.66 (cartprodmempaircEq) =>
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% 99.77/16.66 (cartprodfstpairEq) =>
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% 99.77/16.66 ((
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% 99.77/16.66 ((
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% 99.77/16.66 ((
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% 99.77/16.66 ((
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% 99.77/16.66 ((
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% 99.77/16.66 ((
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% 99.77/16.66 ((
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% 99.77/16.66 ((
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% 99.77/16.66 (kpairsurjEq) =>
% 99.77/16.66 ((
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% 99.77/16.66 ((
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% 99.77/16.66 ((
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% 99.77/16.66 ((
% 99.77/16.66 (cartprodsndpairEq) =>
% 99.77/16.66 ((
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% 99.77/16.66 ((
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% 99.77/16.66 ((
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% 99.77/16.67 ((
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% 99.77/16.67 ((
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% 99.77/16.67 (
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% 99.77/16.68 ((
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% 99.77/16.68 (
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% 99.77/16.68 ((
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% 99.77/16.68 ((
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% 99.77/16.68 (kpairsurjEq) =>
% 99.77/16.68 ((
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% 99.77/16.68 ((
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% 99.77/16.68 ((
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% 99.77/16.68 ((
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% 99.77/16.68 ((
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% 99.77/16.68 ((
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% 99.77/16.68 ((
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% 99.77/16.68 ((
% 99.77/16.68 (brelnall2) =>
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% 99.77/16.68 (ex1E2) =>
% 99.77/16.68 ((
% 99.77/16.68 (funcGraphProp1) =>
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% 99.77/16.68 (funcGraphProp3) =>
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% 99.77/16.68 ((
% 99.77/16.68 (demorgan2a) =>
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% 99.77/16.68 (demorgan2b2) =>
% 99.77/16.68 ((
% 99.77/16.68 (demorgan2b) =>
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% 99.77/16.68 (demorgan2) =>
% 99.77/16.68 ((
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% 99.77/16.68 ((
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% 99.77/16.68 ((
% 99.77/16.68 (woz13rule2) =>
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% 99.77/16.68 (woz13rule3) =>
% 99.77/16.68 ((
% 99.77/16.68 (woz13rule4) =>
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% 99.77/16.68 (woz1_5) =>
% 99.77/16.68 ((
% 99.77/16.68 (breln1all2) =>
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% 99.77/16.68 ((
% 99.77/16.68 (breln1invI) =>
% 99.77/16.68 ((
% 99.77/16.68 (breln1invE) =>
% 99.77/16.68 ((
% 99.77/16.68 (breln1compprop) =>
% 99.77/16.68 ((
% 99.77/16.68 (breln1compI) =>
% 99.77/16.68 ((
% 99.77/16.68 (breln1compE) =>
% 99.77/16.68 ((
% 99.77/16.68 (breln1compEex) =>
% 99.77/16.68 ((
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% 99.92/16.68 (breln1unionI) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 (
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% 99.92/16.68 (
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% 99.92/16.68 (
% 99.92/16.68 (
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% 99.92/16.68 ((
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% 99.92/16.68 (cartprodpairmemER) =>
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% 99.92/16.68 ((
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% 99.92/16.68 (ap2apEq2) =>
% 99.92/16.68 ((
% 99.92/16.68 (beta1) =>
% 99.92/16.68 ((
% 99.92/16.68 (eta1) =>
% 99.92/16.68 ((
% 99.92/16.68 (lam2lamEq) =>
% 99.92/16.68 ((
% 99.92/16.68 (beta2) =>
% 99.92/16.68 ((
% 99.92/16.68 (eta2) =>
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% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 (powersetTE1) =>
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% 99.92/16.68 (complementTE1) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (binintersectTERcontra) =>
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% 99.92/16.68 ((
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% 99.92/16.68 (contrasubsetT3) =>
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% 99.92/16.68 (doubleComplementSub2) =>
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% 99.92/16.68 (inIntersectImpInIntersectUnions) =>
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% 99.92/16.68 ((
% 99.92/16.68 (demorgan2a) =>
% 99.92/16.68 ((
% 99.92/16.68 (demorgan2b2) =>
% 99.92/16.68 ((
% 99.92/16.68 (demorgan2b) =>
% 99.92/16.68 ((
% 99.92/16.68 (demorgan2) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (woz13rule1) =>
% 99.92/16.68 ((
% 99.92/16.68 (woz13rule2) =>
% 99.92/16.68 ((
% 99.92/16.68 (woz13rule3) =>
% 99.92/16.68 ((
% 99.92/16.68 (woz13rule4) =>
% 99.92/16.68 ((
% 99.92/16.68 (woz1_1) =>
% 99.92/16.68 ((
% 99.92/16.68 (woz1_2) =>
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% 99.92/16.68 (woz1_3) =>
% 99.92/16.68 ((
% 99.92/16.68 (woz1_4) =>
% 99.92/16.68 ((
% 99.92/16.68 (woz1_5) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1all2) =>
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% 99.92/16.68 ((
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% 99.92/16.68 (breln1all1) =>
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% 99.92/16.68 ((
% 99.92/16.68 (eqbreln1) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (breln1invI) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1invE) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1compprop) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1compI) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1compE) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1compEex) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1unionprop) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1unionIL) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1unionIR) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1unionI) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1unionE) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1unionEcases) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1unionCommutes) =>
% 99.92/16.68 ((
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% 99.92/16.68 (woz2W) =>
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% 99.92/16.68 ((
% 99.92/16.68 (woz2B) =>
% 99.92/16.68 ((
% 99.92/16.68 (image1Ex) =>
% 99.92/16.68 ((
% 99.92/16.68 (image1Ex1) =>
% 99.92/16.68 ((
% 99.92/16.68 (image1Equiv) =>
% 99.92/16.68 ((
% 99.92/16.68 (image1E) =>
% 99.92/16.68 ((
% 99.92/16.68 (image1I) =>
% 99.92/16.68 ((
% 99.92/16.68 (injFuncInInjFuncSet) =>
% 99.92/16.68 ((
% 99.92/16.68 (injFuncSetFuncIn) =>
% 99.92/16.68 ((
% 99.92/16.68 (injFuncSetFuncInj) =>
% 99.92/16.68 ((
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% 99.92/16.68 (('#B') @ (
% 99.92/16.68 !!) @
% 99.92/16.68 (
% 99.92/16.68 (
% 99.92/16.68 ('#B') @ (
% 99.92/16.68 (
% 99.92/16.68 ('#B') @ (
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% 99.92/16.68 (
% 99.92/16.68 (
% 99.92/16.68 ('#S') @ (
% 99.92/16.68 (
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% 99.92/16.68 (
% 99.92/16.68 (
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% 99.92/16.68 (
% 99.92/16.68 ('#B') @ (
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% 99.92/16.68 (
% 99.92/16.68 (
% 99.92/16.68 ('#B') @ (
% 99.92/16.68 (
% 99.92/16.68 ('#B') @ (
% 99.92/16.68 (
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% 99.92/16.68 surjFuncSet)))))))) @
% 99.92/16.68 (
% 99.92/16.68 (
% 99.92/16.68 ('#B') @ (
% 99.92/16.68 (
% 99.92/16.68 ('#B') @ (
% 99.92/16.68 (
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% 99.92/16.68 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
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% 99.92/16.68 (((setminusIRneg) =>
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% 99.92/16.68 (((symdiffI2) =>
% 99.92/16.68 (((symdiffIneg1) =>
% 99.92/16.68 (((symdiffIneg2) =>
% 99.92/16.68 (((secondinupair) =>
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% 99.92/16.68 (((setukpairIR) =>
% 99.92/16.68 (((kpairiskpair) =>
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% 99.92/16.68 (((upairinpowunion) =>
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% 99.92/16.68 ((
% 99.92/16.68 (ubforcartprodlem3) =>
% 99.92/16.68 ((
% 99.92/16.68 (cartprodpairin) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (cartprodmempair) =>
% 99.92/16.68 ((
% 99.92/16.68 (setunionE2) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (kfstpairEq) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (kpairsurjEq) =>
% 99.92/16.68 ((
% 99.92/16.68 (cartprodsndin) =>
% 99.92/16.68 ((
% 99.92/16.68 (cartprodpairmemEL) =>
% 99.92/16.68 ((
% 99.92/16.68 (cartprodpairmemER) =>
% 99.92/16.68 ((
% 99.92/16.68 (cartprodmempaircEq) =>
% 99.92/16.68 ((
% 99.92/16.68 (cartprodfstpairEq) =>
% 99.92/16.68 ((
% 99.92/16.68 (cartprodsndpairEq) =>
% 99.92/16.68 ((
% 99.92/16.68 (cartprodpairsurjEq) =>
% 99.92/16.68 ((
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% 99.92/16.68 (dpsetconstrER) =>
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% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (ap2p) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 (lam2lamEq) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 (powersetT_lem) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 (subsetTI) =>
% 99.92/16.68 ((
% 99.92/16.68 (powersetTI1) =>
% 99.92/16.68 ((
% 99.92/16.68 (powersetTE1) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (complementTE1) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (binintersectTERcontra) =>
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% 99.92/16.68 (complementSubsetComplementIntersect) =>
% 99.92/16.68 ((
% 99.92/16.68 (complementInPowersetComplementIntersect) =>
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% 99.92/16.68 (contraSubsetComplement) =>
% 99.92/16.68 ((
% 99.92/16.68 (complementTcontraSubset) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (demorgan2a) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (woz13rule1) =>
% 99.92/16.68 ((
% 99.92/16.68 (woz13rule2) =>
% 99.92/16.68 ((
% 99.92/16.68 (woz13rule3) =>
% 99.92/16.68 ((
% 99.92/16.68 (woz13rule4) =>
% 99.92/16.68 ((
% 99.92/16.68 (woz1_1) =>
% 99.92/16.68 ((
% 99.92/16.68 (woz1_2) =>
% 99.92/16.68 ((
% 99.92/16.68 (woz1_3) =>
% 99.92/16.68 ((
% 99.92/16.68 (woz1_4) =>
% 99.92/16.68 ((
% 99.92/16.68 (woz1_5) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1all2) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (choice2fnsingleton) =>
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% 99.92/16.68 ((
% 99.92/16.68 (breln1all1) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (eqbreln1) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (breln1invI) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1invE) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1compprop) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1compI) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1compE) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1compEex) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (breln1unionIL) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1unionIR) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1unionI) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1unionE) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1unionEcases) =>
% 99.92/16.68 ((
% 99.92/16.68 (breln1unionCommutes) =>
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% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (woz2B) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (image1Ex1) =>
% 99.92/16.68 ((
% 99.92/16.68 (image1Equiv) =>
% 99.92/16.68 ((
% 99.92/16.68 (image1E) =>
% 99.92/16.68 ((
% 99.92/16.68 (image1I) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 (
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% 99.92/16.68 (
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% 99.92/16.68 (
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% 99.92/16.68 (
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% 99.92/16.68 (((setminusER) =>
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% 99.92/16.68 (((setminusIRneg) =>
% 99.92/16.68 (((setminusLsub) =>
% 99.92/16.68 (((setminusSubset1) =>
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% 99.92/16.68 (((symdiffIneg2) =>
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% 99.92/16.68 (((setukpairIL) =>
% 99.92/16.68 (((setukpairIR) =>
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% 99.92/16.68 (((kpairp) =>
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% 99.92/16.68 (((singletoninpowerset) =>
% 99.92/16.68 (((singletoninpowunion) =>
% 99.92/16.68 (((upairset2E) =>
% 99.92/16.68 (((upairsubunion) =>
% 99.92/16.68 (((upairinpowunion) =>
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% 99.92/16.68 (((ubforcartprodlem3) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (cartprodmempair) =>
% 99.92/16.68 ((
% 99.92/16.68 (setunionE2) =>
% 99.92/16.68 ((
% 99.92/16.68 (setunionsingleton1) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (kfstsingleton) =>
% 99.92/16.68 ((
% 99.92/16.68 (theprop) =>
% 99.92/16.68 ((
% 99.92/16.68 (kfstpairEq) =>
% 99.92/16.68 ((
% 99.92/16.68 (cartprodfstin) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (kpairsurjEq) =>
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% 99.92/16.68 (cartprodsndin) =>
% 99.92/16.68 ((
% 99.92/16.68 (cartprodpairmemEL) =>
% 99.92/16.68 ((
% 99.92/16.68 (cartprodpairmemER) =>
% 99.92/16.68 ((
% 99.92/16.68 (cartprodmempaircEq) =>
% 99.92/16.68 ((
% 99.92/16.68 (cartprodfstpairEq) =>
% 99.92/16.68 ((
% 99.92/16.68 (cartprodsndpairEq) =>
% 99.92/16.68 ((
% 99.92/16.68 (cartprodpairsurjEq) =>
% 99.92/16.68 ((
% 99.92/16.68 (dpsetconstrI) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (dpsetconstrEL2) =>
% 99.92/16.68 ((
% 99.92/16.68 (dpsetconstrER) =>
% 99.92/16.68 ((
% 99.92/16.68 (funcImageSingleton) =>
% 99.92/16.68 ((
% 99.92/16.68 (apProp) =>
% 99.92/16.68 ((
% 99.92/16.68 (app) =>
% 99.92/16.68 ((
% 99.92/16.68 (infuncsetfunc) =>
% 99.92/16.68 ((
% 99.92/16.68 (ap2p) =>
% 99.92/16.68 ((
% 99.92/16.68 (funcinfuncset) =>
% 99.92/16.68 ((
% 99.92/16.68 (lamProp) =>
% 99.92/16.68 ((
% 99.92/16.68 (lamp) =>
% 99.92/16.68 ((
% 99.92/16.68 (lam2p) =>
% 99.92/16.68 ((
% 99.92/16.68 (brelnall1) =>
% 99.92/16.68 ((
% 99.92/16.68 (brelnall2) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (eta1) =>
% 99.92/16.68 ((
% 99.92/16.68 (lam2lamEq) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (eta2) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (iffalseProp2) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 (iftrueorfalse) =>
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% 99.92/16.68 ((
% 99.92/16.68 (binunionT_lem) =>
% 99.92/16.68 ((
% 99.92/16.68 (powersetT_lem) =>
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% 99.92/16.68 ((
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% 99.92/16.68 (setextT) =>
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% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (powersetTE1) =>
% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
% 99.92/16.68 (binintersectTERcontra) =>
% 99.92/16.68 ((
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% 99.92/16.68 (complementInPowersetComplementIntersect) =>
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% 99.92/16.68 (contraSubsetComplement) =>
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% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.68 ((
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% 99.92/16.69 (
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% 99.92/16.69 (eqbreln) =>
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% 99.92/16.69 ((
% 99.92/16.69 (funcext2) =>
% 99.92/16.69 ((
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% 99.92/16.69 ((
% 99.92/16.69 (ap2apEq2) =>
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% 99.92/16.69 (beta1) =>
% 99.92/16.69 ((
% 99.92/16.69 (eta1) =>
% 99.92/16.69 ((
% 99.92/16.69 (lam2lamEq) =>
% 99.92/16.69 ((
% 99.92/16.69 (beta2) =>
% 99.92/16.69 ((
% 99.92/16.69 (eta2) =>
% 99.92/16.69 ((
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% 99.92/16.69 (iftrueProp2) =>
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% 99.92/16.69 (ifp) =>
% 99.92/16.69 ((
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% 99.92/16.69 ((
% 99.92/16.69 (iftrue) =>
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% 99.92/16.69 ((
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% 99.92/16.69 ((
% 99.92/16.69 (powersetT_lem) =>
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% 99.92/16.69 ((
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% 99.92/16.69 ((
% 99.92/16.69 (setextT) =>
% 99.92/16.69 ((
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% 99.92/16.69 (powersetTI1) =>
% 99.92/16.69 ((
% 99.92/16.69 (powersetTE1) =>
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% 99.92/16.69 ((
% 99.92/16.69 (complementTE1) =>
% 99.92/16.69 ((
% 99.92/16.69 (binintersectTELcontra) =>
% 99.92/16.69 ((
% 99.92/16.69 (binintersectTERcontra) =>
% 99.92/16.69 ((
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% 99.92/16.69 ((
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% 99.92/16.69 ((
% 99.92/16.69 (contrasubsetT2) =>
% 99.92/16.69 ((
% 99.92/16.69 (contrasubsetT3) =>
% 99.92/16.69 ((
% 99.92/16.69 (doubleComplementI1) =>
% 99.92/16.69 ((
% 99.92/16.69 (doubleComplementE1) =>
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% 99.92/16.69 (doubleComplementSub1) =>
% 99.92/16.69 ((
% 99.92/16.69 (doubleComplementSub2) =>
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% 99.92/16.69 (doubleComplementEq) =>
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% 99.92/16.69 ((
% 99.92/16.69 (complementSubsetComplementIntersect) =>
% 99.92/16.69 ((
% 99.92/16.69 (complementInPowersetComplementIntersect) =>
% 99.92/16.69 ((
% 99.92/16.69 (contraSubsetComplement) =>
% 99.92/16.69 ((
% 99.92/16.69 (complementTcontraSubset) =>
% 99.92/16.69 ((
% 99.92/16.69 (binunionTILcontra) =>
% 99.92/16.69 ((
% 99.92/16.69 (binunionTIRcontra) =>
% 99.92/16.69 ((
% 99.92/16.69 (inIntersectImpInUnion) =>
% 99.92/16.69 ((
% 99.92/16.69 (inIntersectImpInUnion2) =>
% 99.92/16.69 ((
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% 99.92/16.69 ((
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% 99.92/16.69 (demorgan1b) =>
% 99.92/16.69 ((
% 99.92/16.69 (demorgan1) =>
% 99.92/16.69 ((
% 99.92/16.69 (demorgan2a) =>
% 99.92/16.69 ((
% 99.92/16.69 (demorgan2b2) =>
% 99.92/16.69 ((
% 99.92/16.69 (demorgan2b) =>
% 99.92/16.69 ((
% 99.92/16.69 (demorgan2) =>
% 99.92/16.69 ((
% 99.92/16.69 (woz13rule0) =>
% 99.92/16.69 ((
% 99.92/16.69 (woz13rule1) =>
% 99.92/16.69 ((
% 99.92/16.69 (woz13rule2) =>
% 99.92/16.69 ((
% 99.92/16.69 (woz13rule3) =>
% 99.92/16.69 ((
% 99.92/16.69 (woz13rule4) =>
% 99.92/16.69 ((
% 99.92/16.69 (woz1_1) =>
% 99.92/16.69 ((
% 99.92/16.69 (woz1_2) =>
% 99.92/16.69 ((
% 99.92/16.69 (woz1_3) =>
% 99.92/16.69 ((
% 99.92/16.69 (woz1_4) =>
% 99.92/16.69 ((
% 99.92/16.69 (woz1_5) =>
% 99.92/16.69 ((
% 99.92/16.69 (breln1all2) =>
% 99.92/16.69 ((
% 99.92/16.69 (breln1SetBreln1) =>
% 99.92/16.69 ((
% 99.92/16.69 (choice2fnsingleton) =>
% 99.92/16.69 ((
% 99.92/16.69 (setOfPairsIsBReln1) =>
% 99.92/16.69 ((
% 99.92/16.69 (breln1all1) =>
% 99.92/16.69 ((
% 99.92/16.69 (subbreln1) =>
% 99.92/16.69 ((
% 99.92/16.69 (eqbreln1) =>
% 99.92/16.69 ((
% 99.92/16.69 (breln1invprop) =>
% 99.92/16.69 ((
% 99.92/16.69 (breln1invI) =>
% 99.92/16.69 ((
% 99.92/16.69 (breln1invE) =>
% 99.92/16.69 ((
% 99.92/16.69 (breln1compprop) =>
% 99.92/16.69 ((
% 99.92/16.69 (breln1compI) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1compE) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1compEex) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionprop) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionIL) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionIR) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionI) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionE) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionEcases) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionCommutes) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz2Ex) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz2W) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz2A) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz2B) =>
% 99.92/16.70 ((
% 99.92/16.70 (image1Ex) =>
% 99.92/16.70 ((
% 99.92/16.70 (image1Ex1) =>
% 99.92/16.70 ((
% 99.92/16.70 (image1Equiv) =>
% 99.92/16.70 ((
% 99.92/16.70 (image1E) =>
% 99.92/16.70 ((
% 99.92/16.70 (image1I) =>
% 99.92/16.70 ((
% 99.92/16.70 (injFuncInInjFuncSet) =>
% 99.92/16.70 ((
% 99.92/16.70 (injFuncSetFuncIn) =>
% 99.92/16.70 ((
% 99.92/16.70 (injFuncSetFuncInj) =>
% 99.92/16.70 ((
% 99.92/16.70 (!!) @ (
% 99.92/16.70 (('#B') @ (
% 99.92/16.70 !!) @
% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
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% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#S') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
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% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
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% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 =>))))) @
% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#C') @ in)))) @
% 99.92/16.70 surjFuncSet)))))))) @
% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#C') @ in)))) @
% 99.92/16.70 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.92/16.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1313])).
% 99.92/16.70 thf(zip_derived_cl1329, plain,
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% 99.92/16.70 (((symdiffI2) =>
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% 99.92/16.70 (((symdiffIneg2) =>
% 99.92/16.70 (((secondinupair) =>
% 99.92/16.70 (((setukpairIL) =>
% 99.92/16.70 (((setukpairIR) =>
% 99.92/16.70 (((kpairiskpair) =>
% 99.92/16.70 (((kpairp) =>
% 99.92/16.70 (((singletonsubset) =>
% 99.92/16.70 (((singletoninpowerset) =>
% 99.92/16.70 (((singletoninpowunion) =>
% 99.92/16.70 (((upairset2E) =>
% 99.92/16.70 (((upairsubunion) =>
% 99.92/16.70 (((upairinpowunion) =>
% 99.92/16.70 (((ubforcartprodlem1) =>
% 99.92/16.70 (((ubforcartprodlem2) =>
% 99.92/16.70 (((ubforcartprodlem3) =>
% 99.92/16.70 (((cartprodpairin) =>
% 99.92/16.70 (((cartprodmempair1) =>
% 99.92/16.70 (((cartprodmempair) =>
% 99.92/16.70 (((setunionE2) =>
% 99.92/16.70 (((setunionsingleton1) =>
% 99.92/16.70 (((setunionsingleton2) =>
% 99.92/16.70 (((setunionsingleton) =>
% 99.92/16.70 (((singletonprop) =>
% 99.92/16.70 (((ex1E1) =>
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% 99.92/16.70 (singletonsuniq) =>
% 99.92/16.70 ((
% 99.92/16.70 (setukpairinjL1) =>
% 99.92/16.70 ((
% 99.92/16.70 (kfstsingleton) =>
% 99.92/16.70 ((
% 99.92/16.70 (theprop) =>
% 99.92/16.70 ((
% 99.92/16.70 (kfstpairEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodfstin) =>
% 99.92/16.70 ((
% 99.92/16.70 (setukpairinjL2) =>
% 99.92/16.70 ((
% 99.92/16.70 (setukpairinjL) =>
% 99.92/16.70 ((
% 99.92/16.70 (setukpairinjR11) =>
% 99.92/16.70 ((
% 99.92/16.70 (setukpairinjR12) =>
% 99.92/16.70 ((
% 99.92/16.70 (setukpairinjR1) =>
% 99.92/16.70 ((
% 99.92/16.70 (upairequniteq) =>
% 99.92/16.70 ((
% 99.92/16.70 (setukpairinjR2) =>
% 99.92/16.70 ((
% 99.92/16.70 (setukpairinjR) =>
% 99.92/16.70 ((
% 99.92/16.70 (ksndsingleton) =>
% 99.92/16.70 ((
% 99.92/16.70 (ksndpairEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (kpairsurjEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodsndin) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodpairmemEL) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodpairmemER) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodmempaircEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodfstpairEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodsndpairEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodpairsurjEq) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (dpsetconstrSub) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (dpsetconstrERa) =>
% 99.92/16.70 ((
% 99.92/16.70 (dpsetconstrEL1) =>
% 99.92/16.70 ((
% 99.92/16.70 (dpsetconstrEL2) =>
% 99.92/16.70 ((
% 99.92/16.70 (dpsetconstrER) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcImageSingleton) =>
% 99.92/16.70 ((
% 99.92/16.70 (apProp) =>
% 99.92/16.70 ((
% 99.92/16.70 (app) =>
% 99.92/16.70 ((
% 99.92/16.70 (infuncsetfunc) =>
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% 99.92/16.70 (ap2p) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (lamp) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 (funcGraphProp3) =>
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% 99.92/16.70 (funcextLem) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcGraphProp4) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 (funcext2) =>
% 99.92/16.70 ((
% 99.92/16.70 (ap2apEq1) =>
% 99.92/16.70 ((
% 99.92/16.70 (ap2apEq2) =>
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% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 (iftrueorfalse) =>
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% 99.92/16.70 ((
% 99.92/16.70 (binunionT_lem) =>
% 99.92/16.70 ((
% 99.92/16.70 (powersetT_lem) =>
% 99.92/16.70 ((
% 99.92/16.70 (setminusT_lem) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (binintersectTERcontra) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (contrasubsetT2) =>
% 99.92/16.70 ((
% 99.92/16.70 (contrasubsetT3) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementI1) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementE1) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementSub1) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementSub2) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementTnotintersectT) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementImpComplementIntersect) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementSubsetComplementIntersect) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementInPowersetComplementIntersect) =>
% 99.92/16.70 ((
% 99.92/16.70 (contraSubsetComplement) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementTcontraSubset) =>
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% 99.92/16.70 ((
% 99.92/16.70 (inComplementUnionImpInComplement1) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (binunionTEcontra) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (complementUnionInPowersetComplement) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 (woz1_3) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (dpsetconstrER) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcImageSingleton) =>
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% 99.92/16.70 (app) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (ap2p) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcinfuncset) =>
% 99.92/16.70 ((
% 99.92/16.70 (lamProp) =>
% 99.92/16.70 ((
% 99.92/16.70 (lamp) =>
% 99.92/16.70 ((
% 99.92/16.70 (lam2p) =>
% 99.92/16.70 ((
% 99.92/16.70 (brelnall1) =>
% 99.92/16.70 ((
% 99.92/16.70 (brelnall2) =>
% 99.92/16.70 ((
% 99.92/16.70 (ex1E2) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcGraphProp1) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcGraphProp3) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcGraphProp2) =>
% 99.92/16.70 ((
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% 99.92/16.70 (funcGraphProp4) =>
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% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (ap2apEq2) =>
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% 99.92/16.70 ((
% 99.92/16.70 (eta1) =>
% 99.92/16.70 ((
% 99.92/16.70 (lam2lamEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (beta2) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 (iftrueProp1) =>
% 99.92/16.70 ((
% 99.92/16.70 (iftrueProp2) =>
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% 99.92/16.70 (ifp) =>
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% 99.92/16.70 (powersetTI1) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (binintersectTELcontra) =>
% 99.92/16.70 ((
% 99.92/16.70 (binintersectTERcontra) =>
% 99.92/16.70 ((
% 99.92/16.70 (contrasubsetT) =>
% 99.92/16.70 ((
% 99.92/16.70 (contrasubsetT1) =>
% 99.92/16.70 ((
% 99.92/16.70 (contrasubsetT2) =>
% 99.92/16.70 ((
% 99.92/16.70 (contrasubsetT3) =>
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% 99.92/16.70 (doubleComplementI1) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementE1) =>
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% 99.92/16.70 (doubleComplementSub1) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementSub2) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementEq) =>
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% 99.92/16.70 (complementTnotintersectT) =>
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% 99.92/16.70 (complementImpComplementIntersect) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementSubsetComplementIntersect) =>
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% 99.92/16.70 (complementInPowersetComplementIntersect) =>
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% 99.92/16.70 (contraSubsetComplement) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementTcontraSubset) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (binunionTIRcontra) =>
% 99.92/16.70 ((
% 99.92/16.70 (inIntersectImpInUnion) =>
% 99.92/16.70 ((
% 99.92/16.70 (inIntersectImpInUnion2) =>
% 99.92/16.70 ((
% 99.92/16.70 (inIntersectImpInIntersectUnions) =>
% 99.92/16.70 ((
% 99.92/16.70 (intersectInPowersetIntersectUnions) =>
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% 99.92/16.70 (inComplementUnionImpNotIn1) =>
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% 99.92/16.70 ((
% 99.92/16.70 (demorgan2a2) =>
% 99.92/16.70 ((
% 99.92/16.70 (demorgan1a) =>
% 99.92/16.70 ((
% 99.92/16.70 (demorgan1b) =>
% 99.92/16.70 ((
% 99.92/16.70 (demorgan1) =>
% 99.92/16.70 ((
% 99.92/16.70 (demorgan2a) =>
% 99.92/16.70 ((
% 99.92/16.70 (demorgan2b2) =>
% 99.92/16.70 ((
% 99.92/16.70 (demorgan2b) =>
% 99.92/16.70 ((
% 99.92/16.70 (demorgan2) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz13rule0) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz13rule1) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz13rule2) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz13rule3) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz13rule4) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz1_1) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz1_2) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz1_3) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz1_4) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz1_5) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1all2) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1SetBreln1) =>
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% 99.92/16.70 (choice2fnsingleton) =>
% 99.92/16.70 ((
% 99.92/16.70 (setOfPairsIsBReln1) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1all1) =>
% 99.92/16.70 ((
% 99.92/16.70 (subbreln1) =>
% 99.92/16.70 ((
% 99.92/16.70 (eqbreln1) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1invprop) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1invI) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1invE) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1compprop) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1compI) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1compE) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1compEex) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionprop) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionIL) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionIR) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionI) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionE) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionEcases) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionCommutes) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz2Ex) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (woz2B) =>
% 99.92/16.70 ((
% 99.92/16.70 (image1Ex) =>
% 99.92/16.70 ((
% 99.92/16.70 (image1Ex1) =>
% 99.92/16.70 ((
% 99.92/16.70 (image1Equiv) =>
% 99.92/16.70 ((
% 99.92/16.70 (image1E) =>
% 99.92/16.70 ((
% 99.92/16.70 (image1I) =>
% 99.92/16.70 ((
% 99.92/16.70 (injFuncInInjFuncSet) =>
% 99.92/16.70 ((
% 99.92/16.70 (injFuncSetFuncIn) =>
% 99.92/16.70 ((
% 99.92/16.70 (injFuncSetFuncInj) =>
% 99.92/16.70 ((
% 99.92/16.70 (!!) @ (
% 99.92/16.70 (('#B') @ (
% 99.92/16.70 !!) @
% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
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% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#S') @ (
% 99.92/16.70 (
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% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
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% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 =>))))) @
% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#C') @ in)))) @
% 99.92/16.70 surjFuncSet)))))))) @
% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#C') @ in)))) @
% 99.92/16.70 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.92/16.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1338])).
% 99.92/16.70 thf(zip_derived_cl1354, plain,
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% 99.92/16.70 (((singletoninpowerset) =>
% 99.92/16.70 (((singletoninpowunion) =>
% 99.92/16.70 (((upairset2E) =>
% 99.92/16.70 (((upairsubunion) =>
% 99.92/16.70 (((upairinpowunion) =>
% 99.92/16.70 (((ubforcartprodlem1) =>
% 99.92/16.70 (((ubforcartprodlem2) =>
% 99.92/16.70 (((ubforcartprodlem3) =>
% 99.92/16.70 (((cartprodpairin) =>
% 99.92/16.70 (((cartprodmempair1) =>
% 99.92/16.70 (((cartprodmempair) =>
% 99.92/16.70 (((setunionE2) =>
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% 99.92/16.70 (((setunionsingleton2) =>
% 99.92/16.70 (((setunionsingleton) =>
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% 99.92/16.70 (kfstpairEq) =>
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% 99.92/16.70 (cartprodfstin) =>
% 99.92/16.70 ((
% 99.92/16.70 (setukpairinjL2) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 (setukpairinjR) =>
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% 99.92/16.70 (ksndsingleton) =>
% 99.92/16.70 ((
% 99.92/16.70 (ksndpairEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (kpairsurjEq) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (cartprodpairmemEL) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodpairmemER) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodmempaircEq) =>
% 99.92/16.70 ((
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% 99.92/16.70 (cartprodsndpairEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodpairsurjEq) =>
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% 99.92/16.70 (dpsetconstrEL2) =>
% 99.92/16.70 ((
% 99.92/16.70 (dpsetconstrER) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcImageSingleton) =>
% 99.92/16.70 ((
% 99.92/16.70 (apProp) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (brelnall2) =>
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% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (funcext2) =>
% 99.92/16.70 ((
% 99.92/16.70 (ap2apEq1) =>
% 99.92/16.70 ((
% 99.92/16.70 (ap2apEq2) =>
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% 99.92/16.70 ((
% 99.92/16.70 (eta1) =>
% 99.92/16.70 ((
% 99.92/16.70 (lam2lamEq) =>
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% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (powersetT_lem) =>
% 99.92/16.70 ((
% 99.92/16.70 (setminusT_lem) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementT_lem) =>
% 99.92/16.70 ((
% 99.92/16.70 (setextT) =>
% 99.92/16.70 ((
% 99.92/16.70 (subsetTI) =>
% 99.92/16.70 ((
% 99.92/16.70 (powersetTI1) =>
% 99.92/16.70 ((
% 99.92/16.70 (powersetTE1) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (binintersectTELcontra) =>
% 99.92/16.70 ((
% 99.92/16.70 (binintersectTERcontra) =>
% 99.92/16.70 ((
% 99.92/16.70 (contrasubsetT) =>
% 99.92/16.70 ((
% 99.92/16.70 (contrasubsetT1) =>
% 99.92/16.70 ((
% 99.92/16.70 (contrasubsetT2) =>
% 99.92/16.70 ((
% 99.92/16.70 (contrasubsetT3) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementI1) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementE1) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementSub1) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementSub2) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementTnotintersectT) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementImpComplementIntersect) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementSubsetComplementIntersect) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementInPowersetComplementIntersect) =>
% 99.92/16.70 ((
% 99.92/16.70 (contraSubsetComplement) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementTcontraSubset) =>
% 99.92/16.70 ((
% 99.92/16.70 (binunionTILcontra) =>
% 99.92/16.70 ((
% 99.92/16.70 (binunionTIRcontra) =>
% 99.92/16.70 ((
% 99.92/16.70 (inIntersectImpInUnion) =>
% 99.92/16.70 ((
% 99.92/16.70 (inIntersectImpInUnion2) =>
% 99.92/16.70 ((
% 99.92/16.70 (inIntersectImpInIntersectUnions) =>
% 99.92/16.70 ((
% 99.92/16.70 (intersectInPowersetIntersectUnions) =>
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% 99.92/16.70 (complementUnionInPowersetComplement) =>
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% 99.92/16.70 (demorgan1a) =>
% 99.92/16.70 ((
% 99.92/16.70 (demorgan1b) =>
% 99.92/16.70 ((
% 99.92/16.70 (demorgan1) =>
% 99.92/16.70 ((
% 99.92/16.70 (demorgan2a) =>
% 99.92/16.70 ((
% 99.92/16.70 (demorgan2b2) =>
% 99.92/16.70 ((
% 99.92/16.70 (demorgan2b) =>
% 99.92/16.70 ((
% 99.92/16.70 (demorgan2) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz13rule0) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz13rule1) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz13rule2) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz13rule3) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz13rule4) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz1_1) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz1_2) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz1_3) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz1_4) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz1_5) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1all2) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1SetBreln1) =>
% 99.92/16.70 ((
% 99.92/16.70 (choice2fnsingleton) =>
% 99.92/16.70 ((
% 99.92/16.70 (setOfPairsIsBReln1) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1all1) =>
% 99.92/16.70 ((
% 99.92/16.70 (subbreln1) =>
% 99.92/16.70 ((
% 99.92/16.70 (eqbreln1) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1invprop) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1invI) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1invE) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1compprop) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1compI) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1compE) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1compEex) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionprop) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionIL) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionIR) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionI) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionE) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionEcases) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1unionCommutes) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz2Ex) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz2W) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz2A) =>
% 99.92/16.70 ((
% 99.92/16.70 (woz2B) =>
% 99.92/16.70 ((
% 99.92/16.70 (image1Ex) =>
% 99.92/16.70 ((
% 99.92/16.70 (image1Ex1) =>
% 99.92/16.70 ((
% 99.92/16.70 (image1Equiv) =>
% 99.92/16.70 ((
% 99.92/16.70 (image1E) =>
% 99.92/16.70 ((
% 99.92/16.70 (image1I) =>
% 99.92/16.70 ((
% 99.92/16.70 (injFuncInInjFuncSet) =>
% 99.92/16.70 ((
% 99.92/16.70 (injFuncSetFuncIn) =>
% 99.92/16.70 ((
% 99.92/16.70 (injFuncSetFuncInj) =>
% 99.92/16.70 ((
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% 99.92/16.70 (('#B') @ (
% 99.92/16.70 !!) @
% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
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% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#S') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 '#S') @
% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 '#S'))) @
% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 =>))))) @
% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#C') @ in)))) @
% 99.92/16.70 surjFuncSet)))))))) @
% 99.92/16.70 (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#B') @ (
% 99.92/16.70 (
% 99.92/16.70 ('#C') @ in)))) @
% 99.92/16.70 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.92/16.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1347])).
% 99.92/16.70 thf(zip_derived_cl1361, plain,
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% 99.92/16.70 (((secondinupair) =>
% 99.92/16.70 (((setukpairIL) =>
% 99.92/16.70 (((setukpairIR) =>
% 99.92/16.70 (((kpairiskpair) =>
% 99.92/16.70 (((kpairp) =>
% 99.92/16.70 (((singletonsubset) =>
% 99.92/16.70 (((singletoninpowerset) =>
% 99.92/16.70 (((singletoninpowunion) =>
% 99.92/16.70 (((upairset2E) =>
% 99.92/16.70 (((upairsubunion) =>
% 99.92/16.70 (((upairinpowunion) =>
% 99.92/16.70 (((ubforcartprodlem1) =>
% 99.92/16.70 (((ubforcartprodlem2) =>
% 99.92/16.70 (((ubforcartprodlem3) =>
% 99.92/16.70 (((cartprodpairin) =>
% 99.92/16.70 (((cartprodmempair1) =>
% 99.92/16.70 (((cartprodmempair) =>
% 99.92/16.70 (((setunionE2) =>
% 99.92/16.70 (((setunionsingleton1) =>
% 99.92/16.70 (((setunionsingleton2) =>
% 99.92/16.70 (((setunionsingleton) =>
% 99.92/16.70 (((singletonprop) =>
% 99.92/16.70 (((ex1E1) =>
% 99.92/16.70 (((ex1I) =>
% 99.92/16.70 (((ex1I2) =>
% 99.92/16.70 (((singletonsuniq) =>
% 99.92/16.70 (((setukpairinjL1) =>
% 99.92/16.70 (((kfstsingleton) =>
% 99.92/16.70 (((theprop) =>
% 99.92/16.70 ((
% 99.92/16.70 (kfstpairEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodfstin) =>
% 99.92/16.70 ((
% 99.92/16.70 (setukpairinjL2) =>
% 99.92/16.70 ((
% 99.92/16.70 (setukpairinjL) =>
% 99.92/16.70 ((
% 99.92/16.70 (setukpairinjR11) =>
% 99.92/16.70 ((
% 99.92/16.70 (setukpairinjR12) =>
% 99.92/16.70 ((
% 99.92/16.70 (setukpairinjR1) =>
% 99.92/16.70 ((
% 99.92/16.70 (upairequniteq) =>
% 99.92/16.70 ((
% 99.92/16.70 (setukpairinjR2) =>
% 99.92/16.70 ((
% 99.92/16.70 (setukpairinjR) =>
% 99.92/16.70 ((
% 99.92/16.70 (ksndsingleton) =>
% 99.92/16.70 ((
% 99.92/16.70 (ksndpairEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (kpairsurjEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodsndin) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodpairmemEL) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodpairmemER) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodmempaircEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodfstpairEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodsndpairEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (cartprodpairsurjEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (dpsetconstrI) =>
% 99.92/16.70 ((
% 99.92/16.70 (dpsetconstrSub) =>
% 99.92/16.70 ((
% 99.92/16.70 (setOfPairsIsBReln) =>
% 99.92/16.70 ((
% 99.92/16.70 (dpsetconstrERa) =>
% 99.92/16.70 ((
% 99.92/16.70 (dpsetconstrEL1) =>
% 99.92/16.70 ((
% 99.92/16.70 (dpsetconstrEL2) =>
% 99.92/16.70 ((
% 99.92/16.70 (dpsetconstrER) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcImageSingleton) =>
% 99.92/16.70 ((
% 99.92/16.70 (apProp) =>
% 99.92/16.70 ((
% 99.92/16.70 (app) =>
% 99.92/16.70 ((
% 99.92/16.70 (infuncsetfunc) =>
% 99.92/16.70 ((
% 99.92/16.70 (ap2p) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcinfuncset) =>
% 99.92/16.70 ((
% 99.92/16.70 (lamProp) =>
% 99.92/16.70 ((
% 99.92/16.70 (lamp) =>
% 99.92/16.70 ((
% 99.92/16.70 (lam2p) =>
% 99.92/16.70 ((
% 99.92/16.70 (brelnall1) =>
% 99.92/16.70 ((
% 99.92/16.70 (brelnall2) =>
% 99.92/16.70 ((
% 99.92/16.70 (ex1E2) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcGraphProp1) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcGraphProp3) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcGraphProp2) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcextLem) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcGraphProp4) =>
% 99.92/16.70 ((
% 99.92/16.70 (subbreln) =>
% 99.92/16.70 ((
% 99.92/16.70 (eqbreln) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcext) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcext2) =>
% 99.92/16.70 ((
% 99.92/16.70 (ap2apEq1) =>
% 99.92/16.70 ((
% 99.92/16.70 (ap2apEq2) =>
% 99.92/16.70 ((
% 99.92/16.70 (beta1) =>
% 99.92/16.70 ((
% 99.92/16.70 (eta1) =>
% 99.92/16.70 ((
% 99.92/16.70 (lam2lamEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (beta2) =>
% 99.92/16.70 ((
% 99.92/16.70 (eta2) =>
% 99.92/16.70 ((
% 99.92/16.70 (iffalseProp1) =>
% 99.92/16.70 ((
% 99.92/16.70 (iffalseProp2) =>
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% 99.92/16.70 (iftrueProp1) =>
% 99.92/16.70 ((
% 99.92/16.70 (iftrueProp2) =>
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% 99.92/16.70 (ifSingleton) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (binunionT_lem) =>
% 99.92/16.70 ((
% 99.92/16.70 (powersetT_lem) =>
% 99.92/16.70 ((
% 99.92/16.70 (setminusT_lem) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementT_lem) =>
% 99.92/16.70 ((
% 99.92/16.70 (setextT) =>
% 99.92/16.70 ((
% 99.92/16.70 (subsetTI) =>
% 99.92/16.70 ((
% 99.92/16.70 (powersetTI1) =>
% 99.92/16.70 ((
% 99.92/16.70 (powersetTE1) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementTI1) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementTE1) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (binintersectTERcontra) =>
% 99.92/16.70 ((
% 99.92/16.70 (contrasubsetT) =>
% 99.92/16.70 ((
% 99.92/16.70 (contrasubsetT1) =>
% 99.92/16.70 ((
% 99.92/16.70 (contrasubsetT2) =>
% 99.92/16.70 ((
% 99.92/16.70 (contrasubsetT3) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementI1) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementE1) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementSub1) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementSub2) =>
% 99.92/16.70 ((
% 99.92/16.70 (doubleComplementEq) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementTnotintersectT) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementImpComplementIntersect) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementSubsetComplementIntersect) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementInPowersetComplementIntersect) =>
% 99.92/16.70 ((
% 99.92/16.70 (contraSubsetComplement) =>
% 99.92/16.70 ((
% 99.92/16.70 (complementTcontraSubset) =>
% 99.92/16.70 ((
% 99.92/16.70 (binunionTILcontra) =>
% 99.92/16.70 ((
% 99.92/16.70 (binunionTIRcontra) =>
% 99.92/16.70 ((
% 99.92/16.70 (inIntersectImpInUnion) =>
% 99.92/16.70 ((
% 99.92/16.70 (inIntersectImpInUnion2) =>
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% 99.92/16.70 (inIntersectImpInIntersectUnions) =>
% 99.92/16.70 ((
% 99.92/16.70 (intersectInPowersetIntersectUnions) =>
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% 99.92/16.70 (inComplementUnionImpInComplement1) =>
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% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (complementUnionInPowersetComplement) =>
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% 99.92/16.70 (demorgan2a2) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (demorgan1b) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (demorgan2a) =>
% 99.92/16.70 ((
% 99.92/16.70 (demorgan2b2) =>
% 99.92/16.70 ((
% 99.92/16.70 (demorgan2b) =>
% 99.92/16.70 ((
% 99.92/16.70 (demorgan2) =>
% 99.92/16.70 ((
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% 99.92/16.70 (woz1_5) =>
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% 99.92/16.70 (breln1SetBreln1) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (ex1E2) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcGraphProp1) =>
% 99.92/16.70 ((
% 99.92/16.70 (funcGraphProp3) =>
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% 99.92/16.70 (funcGraphProp2) =>
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% 99.92/16.70 (woz13rule4) =>
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% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (breln1compI) =>
% 99.92/16.70 ((
% 99.92/16.70 (breln1compE) =>
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% 99.92/16.70 (breln1unionE) =>
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% 99.92/16.70 (image1E) =>
% 99.92/16.70 ((
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% 99.92/16.70 ((
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% 99.92/16.70 ((
% 99.92/16.70 (injFuncSetFuncIn) =>
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% 99.92/16.70 (
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% 99.92/16.70 surjFuncSet)))))))) @
% 99.92/16.70 (
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% 99.92/16.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1420])).
% 99.92/16.71 thf(zip_derived_cl1444, plain,
% 99.92/16.71 (~ (((singletoninpowunion) =>
% 99.92/16.71 (((upairset2E) =>
% 99.92/16.71 (((upairsubunion) =>
% 99.92/16.71 (((upairinpowunion) =>
% 99.92/16.71 (((ubforcartprodlem1) =>
% 99.92/16.71 (((ubforcartprodlem2) =>
% 99.92/16.71 (((ubforcartprodlem3) =>
% 99.92/16.71 (((cartprodpairin) =>
% 99.92/16.71 (((cartprodmempair1) =>
% 99.92/16.71 (((cartprodmempair) =>
% 99.92/16.71 (((setunionE2) =>
% 99.92/16.71 (((setunionsingleton1) =>
% 99.92/16.71 (((setunionsingleton2) =>
% 99.92/16.71 (((setunionsingleton) =>
% 99.92/16.71 (((singletonprop) =>
% 99.92/16.71 (((ex1E1) =>
% 99.92/16.71 (((ex1I) =>
% 99.92/16.71 (((ex1I2) =>
% 99.92/16.71 (((singletonsuniq) =>
% 99.92/16.71 (((setukpairinjL1) =>
% 99.92/16.71 (((kfstsingleton) =>
% 99.92/16.71 (((theprop) =>
% 99.92/16.71 (((kfstpairEq) =>
% 99.92/16.71 (((cartprodfstin) =>
% 99.92/16.71 (((setukpairinjL2) =>
% 99.92/16.71 (((setukpairinjL) =>
% 99.92/16.71 (((setukpairinjR11) =>
% 99.92/16.71 (((setukpairinjR12) =>
% 99.92/16.71 (((setukpairinjR1) =>
% 99.92/16.71 (((upairequniteq) =>
% 99.92/16.71 ((
% 99.92/16.71 (setukpairinjR2) =>
% 99.92/16.71 ((
% 99.92/16.71 (setukpairinjR) =>
% 99.92/16.71 ((
% 99.92/16.71 (ksndsingleton) =>
% 99.92/16.71 ((
% 99.92/16.71 (ksndpairEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (kpairsurjEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodsndin) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodpairmemEL) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodpairmemER) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodmempaircEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodfstpairEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodsndpairEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodpairsurjEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (dpsetconstrI) =>
% 99.92/16.71 ((
% 99.92/16.71 (dpsetconstrSub) =>
% 99.92/16.71 ((
% 99.92/16.71 (setOfPairsIsBReln) =>
% 99.92/16.71 ((
% 99.92/16.71 (dpsetconstrERa) =>
% 99.92/16.71 ((
% 99.92/16.71 (dpsetconstrEL1) =>
% 99.92/16.71 ((
% 99.92/16.71 (dpsetconstrEL2) =>
% 99.92/16.71 ((
% 99.92/16.71 (dpsetconstrER) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcImageSingleton) =>
% 99.92/16.71 ((
% 99.92/16.71 (apProp) =>
% 99.92/16.71 ((
% 99.92/16.71 (app) =>
% 99.92/16.71 ((
% 99.92/16.71 (infuncsetfunc) =>
% 99.92/16.71 ((
% 99.92/16.71 (ap2p) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcinfuncset) =>
% 99.92/16.71 ((
% 99.92/16.71 (lamProp) =>
% 99.92/16.71 ((
% 99.92/16.71 (lamp) =>
% 99.92/16.71 ((
% 99.92/16.71 (lam2p) =>
% 99.92/16.71 ((
% 99.92/16.71 (brelnall1) =>
% 99.92/16.71 ((
% 99.92/16.71 (brelnall2) =>
% 99.92/16.71 ((
% 99.92/16.71 (ex1E2) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcGraphProp1) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcGraphProp3) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcGraphProp2) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcextLem) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcGraphProp4) =>
% 99.92/16.71 ((
% 99.92/16.71 (subbreln) =>
% 99.92/16.71 ((
% 99.92/16.71 (eqbreln) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcext) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcext2) =>
% 99.92/16.71 ((
% 99.92/16.71 (ap2apEq1) =>
% 99.92/16.71 ((
% 99.92/16.71 (ap2apEq2) =>
% 99.92/16.71 ((
% 99.92/16.71 (beta1) =>
% 99.92/16.71 ((
% 99.92/16.71 (eta1) =>
% 99.92/16.71 ((
% 99.92/16.71 (lam2lamEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (beta2) =>
% 99.92/16.71 ((
% 99.92/16.71 (eta2) =>
% 99.92/16.71 ((
% 99.92/16.71 (iffalseProp1) =>
% 99.92/16.71 ((
% 99.92/16.71 (iffalseProp2) =>
% 99.92/16.71 ((
% 99.92/16.71 (iftrueProp1) =>
% 99.92/16.71 ((
% 99.92/16.71 (iftrueProp2) =>
% 99.92/16.71 ((
% 99.92/16.71 (ifSingleton) =>
% 99.92/16.71 ((
% 99.92/16.71 (ifp) =>
% 99.92/16.71 ((
% 99.92/16.71 (theeq) =>
% 99.92/16.71 ((
% 99.92/16.71 (iftrue) =>
% 99.92/16.71 ((
% 99.92/16.71 (iffalse) =>
% 99.92/16.71 ((
% 99.92/16.71 (iftrueorfalse) =>
% 99.92/16.71 ((
% 99.92/16.71 (binintersectT_lem) =>
% 99.92/16.71 ((
% 99.92/16.71 (binunionT_lem) =>
% 99.92/16.71 ((
% 99.92/16.71 (powersetT_lem) =>
% 99.92/16.71 ((
% 99.92/16.71 (setminusT_lem) =>
% 99.92/16.71 ((
% 99.92/16.71 (complementT_lem) =>
% 99.92/16.71 ((
% 99.92/16.71 (setextT) =>
% 99.92/16.71 ((
% 99.92/16.71 (subsetTI) =>
% 99.92/16.71 ((
% 99.92/16.71 (powersetTI1) =>
% 99.92/16.71 ((
% 99.92/16.71 (powersetTE1) =>
% 99.92/16.71 ((
% 99.92/16.71 (complementTI1) =>
% 99.92/16.71 ((
% 99.92/16.71 (complementTE1) =>
% 99.92/16.71 ((
% 99.92/16.71 (binintersectTELcontra) =>
% 99.92/16.71 ((
% 99.92/16.71 (binintersectTERcontra) =>
% 99.92/16.71 ((
% 99.92/16.71 (contrasubsetT) =>
% 99.92/16.71 ((
% 99.92/16.71 (contrasubsetT1) =>
% 99.92/16.71 ((
% 99.92/16.71 (contrasubsetT2) =>
% 99.92/16.71 ((
% 99.92/16.71 (contrasubsetT3) =>
% 99.92/16.71 ((
% 99.92/16.71 (doubleComplementI1) =>
% 99.92/16.71 ((
% 99.92/16.71 (doubleComplementE1) =>
% 99.92/16.71 ((
% 99.92/16.71 (doubleComplementSub1) =>
% 99.92/16.71 ((
% 99.92/16.71 (doubleComplementSub2) =>
% 99.92/16.71 ((
% 99.92/16.71 (doubleComplementEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (complementTnotintersectT) =>
% 99.92/16.71 ((
% 99.92/16.71 (complementImpComplementIntersect) =>
% 99.92/16.71 ((
% 99.92/16.71 (complementSubsetComplementIntersect) =>
% 99.92/16.71 ((
% 99.92/16.71 (complementInPowersetComplementIntersect) =>
% 99.92/16.71 ((
% 99.92/16.71 (contraSubsetComplement) =>
% 99.92/16.71 ((
% 99.92/16.71 (complementTcontraSubset) =>
% 99.92/16.71 ((
% 99.92/16.71 (binunionTILcontra) =>
% 99.92/16.71 ((
% 99.92/16.71 (binunionTIRcontra) =>
% 99.92/16.71 ((
% 99.92/16.71 (inIntersectImpInUnion) =>
% 99.92/16.71 ((
% 99.92/16.71 (inIntersectImpInUnion2) =>
% 99.92/16.71 ((
% 99.92/16.71 (inIntersectImpInIntersectUnions) =>
% 99.92/16.71 ((
% 99.92/16.71 (intersectInPowersetIntersectUnions) =>
% 99.92/16.71 ((
% 99.92/16.71 (inComplementUnionImpNotIn1) =>
% 99.92/16.71 ((
% 99.92/16.71 (inComplementUnionImpInComplement1) =>
% 99.92/16.71 ((
% 99.92/16.71 (binunionTE) =>
% 99.92/16.71 ((
% 99.92/16.71 (binunionTEcontra) =>
% 99.92/16.71 ((
% 99.92/16.71 (demorgan2a1) =>
% 99.92/16.71 ((
% 99.92/16.71 (complementUnionInPowersetComplement) =>
% 99.92/16.71 ((
% 99.92/16.71 (demorgan2a2) =>
% 99.92/16.71 ((
% 99.92/16.71 (demorgan1a) =>
% 99.92/16.71 ((
% 99.92/16.71 (demorgan1b) =>
% 99.92/16.71 ((
% 99.92/16.71 (demorgan1) =>
% 99.92/16.71 ((
% 99.92/16.71 (demorgan2a) =>
% 99.92/16.71 ((
% 99.92/16.71 (demorgan2b2) =>
% 99.92/16.71 ((
% 99.92/16.71 (demorgan2b) =>
% 99.92/16.71 ((
% 99.92/16.71 (demorgan2) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz13rule0) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz13rule1) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz13rule2) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz13rule3) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz13rule4) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz1_1) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz1_2) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz1_3) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz1_4) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz1_5) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1all2) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1SetBreln1) =>
% 99.92/16.71 ((
% 99.92/16.71 (choice2fnsingleton) =>
% 99.92/16.71 ((
% 99.92/16.71 (setOfPairsIsBReln1) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1all1) =>
% 99.92/16.71 ((
% 99.92/16.71 (subbreln1) =>
% 99.92/16.71 ((
% 99.92/16.71 (eqbreln1) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1invprop) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1invI) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1invE) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1compprop) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1compI) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1compE) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1compEex) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1unionprop) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1unionIL) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1unionIR) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1unionI) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1unionE) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1unionEcases) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1unionCommutes) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz2Ex) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz2W) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz2A) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz2B) =>
% 99.92/16.71 ((
% 99.92/16.71 (image1Ex) =>
% 99.92/16.71 ((
% 99.92/16.71 (image1Ex1) =>
% 99.92/16.71 ((
% 99.92/16.71 (image1Equiv) =>
% 99.92/16.71 ((
% 99.92/16.71 (image1E) =>
% 99.92/16.71 ((
% 99.92/16.71 (image1I) =>
% 99.92/16.71 ((
% 99.92/16.71 (injFuncInInjFuncSet) =>
% 99.92/16.71 ((
% 99.92/16.71 (injFuncSetFuncIn) =>
% 99.92/16.71 ((
% 99.92/16.71 (injFuncSetFuncInj) =>
% 99.92/16.71 ((
% 99.92/16.71 (!!) @ (
% 99.92/16.71 (('#B') @ (
% 99.92/16.71 !!) @
% 99.92/16.71 (
% 99.92/16.71 (
% 99.92/16.71 ('#B') @ (
% 99.92/16.71 (
% 99.92/16.71 ('#B') @ (
% 99.92/16.71 !!))) @
% 99.92/16.71 (
% 99.92/16.71 (
% 99.92/16.71 ('#S') @ (
% 99.92/16.71 (
% 99.92/16.71 ('#B') @ (
% 99.92/16.71 '#S') @
% 99.92/16.71 (
% 99.92/16.71 (
% 99.92/16.71 ('#B') @ (
% 99.92/16.71 (
% 99.92/16.71 ('#B') @ (
% 99.92/16.71 '#S'))) @
% 99.92/16.71 (
% 99.92/16.71 (
% 99.92/16.71 ('#B') @ (
% 99.92/16.71 (
% 99.92/16.71 ('#B') @ (
% 99.92/16.71 (
% 99.92/16.71 ('#B') @ (
% 99.92/16.71 =>))))) @
% 99.92/16.71 (
% 99.92/16.71 (
% 99.92/16.71 ('#B') @ (
% 99.92/16.71 (
% 99.92/16.71 ('#B') @ (
% 99.92/16.71 (
% 99.92/16.71 ('#C') @ in)))) @
% 99.92/16.71 surjFuncSet)))))))) @
% 99.92/16.71 (
% 99.92/16.71 (
% 99.92/16.71 ('#B') @ (
% 99.92/16.71 (
% 99.92/16.71 ('#B') @ (
% 99.92/16.71 (
% 99.92/16.71 ('#C') @ in)))) @
% 99.92/16.71 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.92/16.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1433])).
% 99.92/16.71 thf(zip_derived_cl1452, plain,
% 99.92/16.71 (~ (((upairset2E) =>
% 99.92/16.71 (((upairsubunion) =>
% 99.92/16.71 (((upairinpowunion) =>
% 99.92/16.71 (((ubforcartprodlem1) =>
% 99.92/16.71 (((ubforcartprodlem2) =>
% 99.92/16.71 (((ubforcartprodlem3) =>
% 99.92/16.71 (((cartprodpairin) =>
% 99.92/16.71 (((cartprodmempair1) =>
% 99.92/16.71 (((cartprodmempair) =>
% 99.92/16.71 (((setunionE2) =>
% 99.92/16.71 (((setunionsingleton1) =>
% 99.92/16.71 (((setunionsingleton2) =>
% 99.92/16.71 (((setunionsingleton) =>
% 99.92/16.71 (((singletonprop) =>
% 99.92/16.71 (((ex1E1) =>
% 99.92/16.71 (((ex1I) =>
% 99.92/16.71 (((ex1I2) =>
% 99.92/16.71 (((singletonsuniq) =>
% 99.92/16.71 (((setukpairinjL1) =>
% 99.92/16.71 (((kfstsingleton) =>
% 99.92/16.71 (((theprop) =>
% 99.92/16.71 (((kfstpairEq) =>
% 99.92/16.71 (((cartprodfstin) =>
% 99.92/16.71 (((setukpairinjL2) =>
% 99.92/16.71 (((setukpairinjL) =>
% 99.92/16.71 (((setukpairinjR11) =>
% 99.92/16.71 (((setukpairinjR12) =>
% 99.92/16.71 (((setukpairinjR1) =>
% 99.92/16.71 (((upairequniteq) =>
% 99.92/16.71 (((setukpairinjR2) =>
% 99.92/16.71 ((
% 99.92/16.71 (setukpairinjR) =>
% 99.92/16.71 ((
% 99.92/16.71 (ksndsingleton) =>
% 99.92/16.71 ((
% 99.92/16.71 (ksndpairEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (kpairsurjEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodsndin) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodpairmemEL) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodpairmemER) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodmempaircEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodfstpairEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodsndpairEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodpairsurjEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (dpsetconstrI) =>
% 99.92/16.71 ((
% 99.92/16.71 (dpsetconstrSub) =>
% 99.92/16.71 ((
% 99.92/16.71 (setOfPairsIsBReln) =>
% 99.92/16.71 ((
% 99.92/16.71 (dpsetconstrERa) =>
% 99.92/16.71 ((
% 99.92/16.71 (dpsetconstrEL1) =>
% 99.92/16.71 ((
% 99.92/16.71 (dpsetconstrEL2) =>
% 99.92/16.71 ((
% 99.92/16.71 (dpsetconstrER) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcImageSingleton) =>
% 99.92/16.71 ((
% 99.92/16.71 (apProp) =>
% 99.92/16.71 ((
% 99.92/16.71 (app) =>
% 99.92/16.71 ((
% 99.92/16.71 (infuncsetfunc) =>
% 99.92/16.71 ((
% 99.92/16.71 (ap2p) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcinfuncset) =>
% 99.92/16.71 ((
% 99.92/16.71 (lamProp) =>
% 99.92/16.71 ((
% 99.92/16.71 (lamp) =>
% 99.92/16.71 ((
% 99.92/16.71 (lam2p) =>
% 99.92/16.71 ((
% 99.92/16.71 (brelnall1) =>
% 99.92/16.71 ((
% 99.92/16.71 (brelnall2) =>
% 99.92/16.71 ((
% 99.92/16.71 (ex1E2) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcGraphProp1) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcGraphProp3) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcGraphProp2) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcextLem) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcGraphProp4) =>
% 99.92/16.71 ((
% 99.92/16.71 (subbreln) =>
% 99.92/16.71 ((
% 99.92/16.71 (eqbreln) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcext) =>
% 99.92/16.71 ((
% 99.92/16.71 (funcext2) =>
% 99.92/16.71 ((
% 99.92/16.71 (ap2apEq1) =>
% 99.92/16.71 ((
% 99.92/16.71 (ap2apEq2) =>
% 99.92/16.71 ((
% 99.92/16.71 (beta1) =>
% 99.92/16.71 ((
% 99.92/16.71 (eta1) =>
% 99.92/16.71 ((
% 99.92/16.71 (lam2lamEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (beta2) =>
% 99.92/16.71 ((
% 99.92/16.71 (eta2) =>
% 99.92/16.71 ((
% 99.92/16.71 (iffalseProp1) =>
% 99.92/16.71 ((
% 99.92/16.71 (iffalseProp2) =>
% 99.92/16.71 ((
% 99.92/16.71 (iftrueProp1) =>
% 99.92/16.71 ((
% 99.92/16.71 (iftrueProp2) =>
% 99.92/16.71 ((
% 99.92/16.71 (ifSingleton) =>
% 99.92/16.71 ((
% 99.92/16.71 (ifp) =>
% 99.92/16.71 ((
% 99.92/16.71 (theeq) =>
% 99.92/16.71 ((
% 99.92/16.71 (iftrue) =>
% 99.92/16.71 ((
% 99.92/16.71 (iffalse) =>
% 99.92/16.71 ((
% 99.92/16.71 (iftrueorfalse) =>
% 99.92/16.71 ((
% 99.92/16.71 (binintersectT_lem) =>
% 99.92/16.71 ((
% 99.92/16.71 (binunionT_lem) =>
% 99.92/16.71 ((
% 99.92/16.71 (powersetT_lem) =>
% 99.92/16.71 ((
% 99.92/16.71 (setminusT_lem) =>
% 99.92/16.71 ((
% 99.92/16.71 (complementT_lem) =>
% 99.92/16.71 ((
% 99.92/16.71 (setextT) =>
% 99.92/16.71 ((
% 99.92/16.71 (subsetTI) =>
% 99.92/16.71 ((
% 99.92/16.71 (powersetTI1) =>
% 99.92/16.71 ((
% 99.92/16.71 (powersetTE1) =>
% 99.92/16.71 ((
% 99.92/16.71 (complementTI1) =>
% 99.92/16.71 ((
% 99.92/16.71 (complementTE1) =>
% 99.92/16.71 ((
% 99.92/16.71 (binintersectTELcontra) =>
% 99.92/16.71 ((
% 99.92/16.71 (binintersectTERcontra) =>
% 99.92/16.71 ((
% 99.92/16.71 (contrasubsetT) =>
% 99.92/16.71 ((
% 99.92/16.71 (contrasubsetT1) =>
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% 99.92/16.71 (contrasubsetT2) =>
% 99.92/16.71 ((
% 99.92/16.71 (contrasubsetT3) =>
% 99.92/16.71 ((
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% 99.92/16.71 (doubleComplementE1) =>
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% 99.92/16.71 (doubleComplementSub2) =>
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% 99.92/16.71 (demorgan1) =>
% 99.92/16.71 ((
% 99.92/16.71 (demorgan2a) =>
% 99.92/16.71 ((
% 99.92/16.71 (demorgan2b2) =>
% 99.92/16.71 ((
% 99.92/16.71 (demorgan2b) =>
% 99.92/16.71 ((
% 99.92/16.71 (demorgan2) =>
% 99.92/16.71 ((
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% 99.92/16.71 ((
% 99.92/16.71 (woz13rule1) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz13rule2) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz13rule3) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz13rule4) =>
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% 99.92/16.71 (woz1_1) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz1_2) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz1_3) =>
% 99.92/16.71 ((
% 99.92/16.71 (woz1_4) =>
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% 99.92/16.71 (woz1_5) =>
% 99.92/16.71 ((
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% 99.92/16.71 ((
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% 99.92/16.71 ((
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% 99.92/16.71 ((
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% 99.92/16.71 ((
% 99.92/16.71 (breln1compprop) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1compI) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1compE) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1compEex) =>
% 99.92/16.71 ((
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% 99.92/16.71 ((
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% 99.92/16.71 ((
% 99.92/16.71 (breln1unionIR) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1unionI) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1unionE) =>
% 99.92/16.71 ((
% 99.92/16.71 (breln1unionEcases) =>
% 99.92/16.71 ((
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% 99.92/16.71 ((
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% 99.92/16.71 ((
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% 99.92/16.71 ((
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% 99.92/16.71 ((
% 99.92/16.71 (image1E) =>
% 99.92/16.71 ((
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% 99.92/16.71 ((
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% 99.92/16.71 (((cartprodmempair) =>
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% 99.92/16.71 (ksndpairEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (kpairsurjEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodsndin) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodpairmemEL) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodpairmemER) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodmempaircEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodfstpairEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodsndpairEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (cartprodpairsurjEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (dpsetconstrI) =>
% 99.92/16.71 ((
% 99.92/16.71 (dpsetconstrSub) =>
% 99.92/16.71 ((
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% 99.92/16.71 ((
% 99.92/16.71 (dpsetconstrEL2) =>
% 99.92/16.71 ((
% 99.92/16.71 (dpsetconstrER) =>
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% 99.92/16.71 (ap2p) =>
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% 99.92/16.71 (funcinfuncset) =>
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% 99.92/16.71 ((
% 99.92/16.71 (lamp) =>
% 99.92/16.71 ((
% 99.92/16.71 (lam2p) =>
% 99.92/16.71 ((
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% 99.92/16.71 (brelnall2) =>
% 99.92/16.71 ((
% 99.92/16.71 (ex1E2) =>
% 99.92/16.71 ((
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% 99.92/16.71 ((
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% 99.92/16.71 (funcGraphProp2) =>
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% 99.92/16.71 (funcGraphProp4) =>
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% 99.92/16.71 ((
% 99.92/16.71 (eta1) =>
% 99.92/16.71 ((
% 99.92/16.71 (lam2lamEq) =>
% 99.92/16.71 ((
% 99.92/16.71 (beta2) =>
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% 99.92/16.71 ((
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% 99.92/16.71 ((
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% 99.92/16.71 ((
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% 99.92/16.71 ((
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% 99.92/16.71 (inIntersectImpInUnion2) =>
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% 99.92/16.72 ((
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% 99.92/16.72 ((
% 99.92/16.72 (demorgan2b2) =>
% 99.92/16.72 ((
% 99.92/16.72 (demorgan2b) =>
% 99.92/16.72 ((
% 99.92/16.72 (demorgan2) =>
% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
% 99.92/16.72 (woz13rule2) =>
% 99.92/16.72 ((
% 99.92/16.72 (woz13rule3) =>
% 99.92/16.72 ((
% 99.92/16.72 (woz13rule4) =>
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% 99.92/16.72 ((
% 99.92/16.72 (woz1_2) =>
% 99.92/16.72 ((
% 99.92/16.72 (woz1_3) =>
% 99.92/16.72 ((
% 99.92/16.72 (woz1_4) =>
% 99.92/16.72 ((
% 99.92/16.72 (woz1_5) =>
% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
% 99.92/16.72 (breln1compE) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1compEex) =>
% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
% 99.92/16.72 (breln1unionIR) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1unionI) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1unionE) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1unionEcases) =>
% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
% 99.92/16.72 (image1Ex1) =>
% 99.92/16.72 ((
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% 99.92/16.72 ((
% 99.92/16.72 (image1E) =>
% 99.92/16.72 ((
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% 99.92/16.72 (cartprodmempaircEq) =>
% 99.92/16.72 ((
% 99.92/16.72 (cartprodfstpairEq) =>
% 99.92/16.72 ((
% 99.92/16.72 (cartprodsndpairEq) =>
% 99.92/16.72 ((
% 99.92/16.72 (cartprodpairsurjEq) =>
% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
% 99.92/16.72 (dpsetconstrER) =>
% 99.92/16.72 ((
% 99.92/16.72 (funcImageSingleton) =>
% 99.92/16.72 ((
% 99.92/16.72 (apProp) =>
% 99.92/16.72 ((
% 99.92/16.72 (app) =>
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% 99.92/16.72 (ap2p) =>
% 99.92/16.72 ((
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% 99.92/16.72 ((
% 99.92/16.72 (lam2p) =>
% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
% 99.92/16.72 (funcImageSingleton) =>
% 99.92/16.72 ((
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% 99.92/16.72 ((
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% 99.92/16.72 ((
% 99.92/16.72 (infuncsetfunc) =>
% 99.92/16.72 ((
% 99.92/16.72 (ap2p) =>
% 99.92/16.72 ((
% 99.92/16.72 (funcinfuncset) =>
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% 99.92/16.72 ((
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% 99.92/16.72 ((
% 99.92/16.72 (lam2p) =>
% 99.92/16.72 ((
% 99.92/16.72 (brelnall1) =>
% 99.92/16.72 ((
% 99.92/16.72 (brelnall2) =>
% 99.92/16.72 ((
% 99.92/16.72 (ex1E2) =>
% 99.92/16.72 ((
% 99.92/16.72 (funcGraphProp1) =>
% 99.92/16.72 ((
% 99.92/16.72 (funcGraphProp3) =>
% 99.92/16.72 ((
% 99.92/16.72 (funcGraphProp2) =>
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% 99.92/16.72 ((
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% 99.92/16.72 (contrasubsetT3) =>
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% 99.92/16.72 ((
% 99.92/16.72 (inIntersectImpInUnion2) =>
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% 99.92/16.72 (demorgan1b) =>
% 99.92/16.72 ((
% 99.92/16.72 (demorgan1) =>
% 99.92/16.72 ((
% 99.92/16.72 (demorgan2a) =>
% 99.92/16.72 ((
% 99.92/16.72 (demorgan2b2) =>
% 99.92/16.72 ((
% 99.92/16.72 (demorgan2b) =>
% 99.92/16.72 ((
% 99.92/16.72 (demorgan2) =>
% 99.92/16.72 ((
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% 99.92/16.72 ((
% 99.92/16.72 (woz13rule1) =>
% 99.92/16.72 ((
% 99.92/16.72 (woz13rule2) =>
% 99.92/16.72 ((
% 99.92/16.72 (woz13rule3) =>
% 99.92/16.72 ((
% 99.92/16.72 (woz13rule4) =>
% 99.92/16.72 ((
% 99.92/16.72 (woz1_1) =>
% 99.92/16.72 ((
% 99.92/16.72 (woz1_2) =>
% 99.92/16.72 ((
% 99.92/16.72 (woz1_3) =>
% 99.92/16.72 ((
% 99.92/16.72 (woz1_4) =>
% 99.92/16.72 ((
% 99.92/16.72 (woz1_5) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1all2) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1SetBreln1) =>
% 99.92/16.72 ((
% 99.92/16.72 (choice2fnsingleton) =>
% 99.92/16.72 ((
% 99.92/16.72 (setOfPairsIsBReln1) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1all1) =>
% 99.92/16.72 ((
% 99.92/16.72 (subbreln1) =>
% 99.92/16.72 ((
% 99.92/16.72 (eqbreln1) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1invprop) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1invI) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1invE) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1compprop) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1compI) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1compE) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1compEex) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1unionprop) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1unionIL) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1unionIR) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1unionI) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1unionE) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1unionEcases) =>
% 99.92/16.72 ((
% 99.92/16.72 (breln1unionCommutes) =>
% 99.92/16.72 ((
% 99.92/16.72 (woz2Ex) =>
% 99.92/16.72 ((
% 99.92/16.72 (woz2W) =>
% 99.92/16.72 ((
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% 99.92/16.72 ((
% 99.92/16.72 (woz2B) =>
% 99.92/16.72 ((
% 99.92/16.72 (image1Ex) =>
% 99.92/16.72 ((
% 99.92/16.72 (image1Ex1) =>
% 99.92/16.72 ((
% 99.92/16.72 (image1Equiv) =>
% 99.92/16.72 ((
% 99.92/16.72 (image1E) =>
% 99.92/16.72 ((
% 99.92/16.72 (image1I) =>
% 99.92/16.72 ((
% 99.92/16.72 (injFuncInInjFuncSet) =>
% 99.92/16.72 ((
% 99.92/16.72 (injFuncSetFuncIn) =>
% 99.92/16.72 ((
% 99.92/16.72 (injFuncSetFuncInj) =>
% 99.92/16.72 ((
% 99.92/16.72 (!!) @ (
% 99.92/16.72 (('#B') @ (
% 99.92/16.72 !!) @
% 99.92/16.72 (
% 99.92/16.72 (
% 99.92/16.72 ('#B') @ (
% 99.92/16.72 (
% 99.92/16.72 ('#B') @ (
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% 99.92/16.72 (
% 99.92/16.72 (
% 99.92/16.72 ('#S') @ (
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% 99.92/16.72 (
% 99.92/16.72 (
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% 99.92/16.72 (
% 99.92/16.72 ('#B') @ (
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% 99.92/16.72 (
% 99.92/16.72 (
% 99.92/16.72 ('#B') @ (
% 99.92/16.72 (
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% 99.92/16.72 (
% 99.92/16.72 (
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% 99.92/16.72 (
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% 99.92/16.72 surjFuncSet)))))))) @
% 99.92/16.72 (
% 99.92/16.72 (
% 99.92/16.72 ('#B') @ (
% 99.92/16.72 (
% 99.92/16.72 ('#B') @ (
% 99.92/16.72 (
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% 99.92/16.72 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.92/16.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1565])).
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% 99.92/16.72 (((kpairsurjEq) =>
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% 99.92/16.72 (((cartprodpairmemER) =>
% 99.92/16.72 (((cartprodmempaircEq) =>
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% 99.92/16.73 ((
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% 99.92/16.73 ((
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% 99.92/16.73 ((
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% 99.92/16.73 ((
% 99.92/16.73 (brelnall2) =>
% 99.92/16.73 ((
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% 99.92/16.73 ((
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% 99.92/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (complementTcontraSubset) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (binunionTIRcontra) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 (inComplementUnionImpInComplement1) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (complementUnionInPowersetComplement) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2a2) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (demorgan2a) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2b2) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2b) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 (woz13rule2) =>
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 (
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% 100.16/16.73 (
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% 100.16/16.73 surjFuncSet)))))))) @
% 100.16/16.73 (
% 100.16/16.73 (
% 100.16/16.73 ('#B') @ (
% 100.16/16.73 (
% 100.16/16.73 ('#B') @ (
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% 100.16/16.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1599])).
% 100.16/16.73 thf(zip_derived_cl1615, plain,
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% 100.16/16.73 (((ksndpairEq) =>
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% 100.16/16.73 (((cartprodpairmemER) =>
% 100.16/16.73 (((cartprodmempaircEq) =>
% 100.16/16.73 (((cartprodfstpairEq) =>
% 100.16/16.73 (((cartprodsndpairEq) =>
% 100.16/16.73 (((cartprodpairsurjEq) =>
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (infuncsetfunc) =>
% 100.16/16.73 ((
% 100.16/16.73 (ap2p) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (ex1E2) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 (contrasubsetT3) =>
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (inIntersectImpInUnion2) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (intersectInPowersetIntersectUnions) =>
% 100.16/16.73 ((
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% 100.16/16.73 (inComplementUnionImpInComplement1) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (complementUnionInPowersetComplement) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2a2) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan1a) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan1b) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan1) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2a) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2b2) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2b) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2) =>
% 100.16/16.73 ((
% 100.16/16.73 (woz13rule0) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (woz1_4) =>
% 100.16/16.73 ((
% 100.16/16.73 (woz1_5) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1all2) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1SetBreln1) =>
% 100.16/16.73 ((
% 100.16/16.73 (choice2fnsingleton) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (breln1invI) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1invE) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1compprop) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1compI) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1compE) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1compEex) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1unionprop) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1unionIL) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (breln1unionI) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (injFuncSetFuncIn) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 (
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% 100.16/16.73 (
% 100.16/16.73 (
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% 100.16/16.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1607])).
% 100.16/16.73 thf(zip_derived_cl1625, plain,
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 !!))) @
% 100.16/16.73 (
% 100.16/16.73 (
% 100.16/16.73 ('#S') @ (
% 100.16/16.73 (
% 100.16/16.73 ('#B') @ (
% 100.16/16.73 '#S') @
% 100.16/16.73 (
% 100.16/16.73 (
% 100.16/16.73 ('#B') @ (
% 100.16/16.73 (
% 100.16/16.73 ('#B') @ (
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% 100.16/16.73 (
% 100.16/16.73 (
% 100.16/16.73 ('#B') @ (
% 100.16/16.73 (
% 100.16/16.73 ('#B') @ (
% 100.16/16.73 (
% 100.16/16.73 ('#B') @ (
% 100.16/16.73 =>))))) @
% 100.16/16.73 (
% 100.16/16.73 (
% 100.16/16.73 ('#B') @ (
% 100.16/16.73 (
% 100.16/16.73 ('#B') @ (
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% 100.16/16.73 surjFuncSet)))))))) @
% 100.16/16.73 (
% 100.16/16.73 (
% 100.16/16.73 ('#B') @ (
% 100.16/16.73 (
% 100.16/16.73 ('#B') @ (
% 100.16/16.73 (
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% 100.16/16.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1649])).
% 100.16/16.73 thf(zip_derived_cl1678, plain,
% 100.16/16.73 (~ (((setukpairinjL) =>
% 100.16/16.73 (((setukpairinjR11) =>
% 100.16/16.73 (((setukpairinjR12) =>
% 100.16/16.73 (((setukpairinjR1) =>
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% 100.16/16.73 (((setukpairinjR2) =>
% 100.16/16.73 (((setukpairinjR) =>
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% 100.16/16.73 (((ksndpairEq) =>
% 100.16/16.73 (((kpairsurjEq) =>
% 100.16/16.73 (((cartprodsndin) =>
% 100.16/16.73 (((cartprodpairmemEL) =>
% 100.16/16.73 (((cartprodpairmemER) =>
% 100.16/16.73 (((cartprodmempaircEq) =>
% 100.16/16.73 (((cartprodfstpairEq) =>
% 100.16/16.73 (((cartprodsndpairEq) =>
% 100.16/16.73 (((cartprodpairsurjEq) =>
% 100.16/16.73 (((dpsetconstrI) =>
% 100.16/16.73 (((dpsetconstrSub) =>
% 100.16/16.73 (((setOfPairsIsBReln) =>
% 100.16/16.73 (((dpsetconstrERa) =>
% 100.16/16.73 (((dpsetconstrEL1) =>
% 100.16/16.73 (((dpsetconstrEL2) =>
% 100.16/16.73 (((dpsetconstrER) =>
% 100.16/16.73 (((funcImageSingleton) =>
% 100.16/16.73 (((apProp) =>
% 100.16/16.73 (((app) =>
% 100.16/16.73 (((infuncsetfunc) =>
% 100.16/16.73 (((ap2p) =>
% 100.16/16.73 (((funcinfuncset) =>
% 100.16/16.73 ((
% 100.16/16.73 (lamProp) =>
% 100.16/16.73 ((
% 100.16/16.73 (lamp) =>
% 100.16/16.73 ((
% 100.16/16.73 (lam2p) =>
% 100.16/16.73 ((
% 100.16/16.73 (brelnall1) =>
% 100.16/16.73 ((
% 100.16/16.73 (brelnall2) =>
% 100.16/16.73 ((
% 100.16/16.73 (ex1E2) =>
% 100.16/16.73 ((
% 100.16/16.73 (funcGraphProp1) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (inComplementUnionImpInComplement1) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (binunionTEcontra) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2a1) =>
% 100.16/16.73 ((
% 100.16/16.73 (complementUnionInPowersetComplement) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (demorgan1a) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan1b) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan1) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2a) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2b2) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2b) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2) =>
% 100.16/16.73 ((
% 100.16/16.73 (woz13rule0) =>
% 100.16/16.73 ((
% 100.16/16.73 (woz13rule1) =>
% 100.16/16.73 ((
% 100.16/16.73 (woz13rule2) =>
% 100.16/16.73 ((
% 100.16/16.73 (woz13rule3) =>
% 100.16/16.73 ((
% 100.16/16.73 (woz13rule4) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (woz1_5) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1all2) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1SetBreln1) =>
% 100.16/16.73 ((
% 100.16/16.73 (choice2fnsingleton) =>
% 100.16/16.73 ((
% 100.16/16.73 (setOfPairsIsBReln1) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1all1) =>
% 100.16/16.73 ((
% 100.16/16.73 (subbreln1) =>
% 100.16/16.73 ((
% 100.16/16.73 (eqbreln1) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1invprop) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1invI) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1invE) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (breln1compEex) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (breln1unionI) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1unionE) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1unionEcases) =>
% 100.16/16.73 ((
% 100.16/16.73 (breln1unionCommutes) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (injFuncSetFuncInj) =>
% 100.16/16.73 ((
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% 100.16/16.73 (
% 100.16/16.73 (
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% 100.16/16.73 (
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% 100.16/16.73 (
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% 100.16/16.73 (
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% 100.16/16.73 (
% 100.16/16.73 (
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% 100.16/16.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1664])).
% 100.16/16.73 thf(zip_derived_cl1695, plain,
% 100.16/16.73 (~ (((setukpairinjR11) =>
% 100.16/16.73 (((setukpairinjR12) =>
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (complementUnionInPowersetComplement) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (demorgan1b) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan1) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2a) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2b2) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2b) =>
% 100.16/16.73 ((
% 100.16/16.73 (demorgan2) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (woz1_3) =>
% 100.16/16.73 ((
% 100.16/16.73 (woz1_4) =>
% 100.16/16.73 ((
% 100.16/16.73 (woz1_5) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.73 ((
% 100.16/16.73 (eqbreln1) =>
% 100.16/16.73 ((
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% 100.16/16.73 ((
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% 100.16/16.74 ((
% 100.16/16.74 (breln1invE) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (breln1compEex) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (breln1unionI) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionE) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionEcases) =>
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 (
% 100.16/16.74 (
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% 100.16/16.74 (
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% 100.16/16.74 (
% 100.16/16.74 (
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% 100.16/16.74 (
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% 100.16/16.74 (
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% 100.16/16.74 (
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% 100.16/16.74 (
% 100.16/16.74 (
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% 100.16/16.74 (
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% 100.16/16.74 (
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% 100.16/16.74 (
% 100.16/16.74 (
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% 100.16/16.74 (
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% 100.16/16.74 (
% 100.16/16.74 (
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% 100.16/16.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1678])).
% 100.16/16.74 thf(zip_derived_cl1711, plain,
% 100.16/16.74 (~ (((setukpairinjR12) =>
% 100.16/16.74 (((setukpairinjR1) =>
% 100.16/16.74 (((upairequniteq) =>
% 100.16/16.74 (((setukpairinjR2) =>
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% 100.16/16.74 (((ksndsingleton) =>
% 100.16/16.74 (((ksndpairEq) =>
% 100.16/16.74 (((kpairsurjEq) =>
% 100.16/16.74 (((cartprodsndin) =>
% 100.16/16.74 (((cartprodpairmemEL) =>
% 100.16/16.74 (((cartprodpairmemER) =>
% 100.16/16.74 (((cartprodmempaircEq) =>
% 100.16/16.74 (((cartprodfstpairEq) =>
% 100.16/16.74 (((cartprodsndpairEq) =>
% 100.16/16.74 (((cartprodpairsurjEq) =>
% 100.16/16.74 (((dpsetconstrI) =>
% 100.16/16.74 (((dpsetconstrSub) =>
% 100.16/16.74 (((setOfPairsIsBReln) =>
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% 100.16/16.74 (((dpsetconstrEL1) =>
% 100.16/16.74 (((dpsetconstrEL2) =>
% 100.16/16.74 (((dpsetconstrER) =>
% 100.16/16.74 (((funcImageSingleton) =>
% 100.16/16.74 (((apProp) =>
% 100.16/16.74 (((app) =>
% 100.16/16.74 (((infuncsetfunc) =>
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% 100.16/16.74 (((lamp) =>
% 100.16/16.74 ((
% 100.16/16.74 (lam2p) =>
% 100.16/16.74 ((
% 100.16/16.74 (brelnall1) =>
% 100.16/16.74 ((
% 100.16/16.74 (brelnall2) =>
% 100.16/16.74 ((
% 100.16/16.74 (ex1E2) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (setminusT_lem) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (setextT) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (powersetTI1) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (complementTE1) =>
% 100.16/16.74 ((
% 100.16/16.74 (binintersectTELcontra) =>
% 100.16/16.74 ((
% 100.16/16.74 (binintersectTERcontra) =>
% 100.16/16.74 ((
% 100.16/16.74 (contrasubsetT) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (contrasubsetT2) =>
% 100.16/16.74 ((
% 100.16/16.74 (contrasubsetT3) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (doubleComplementSub2) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (complementTnotintersectT) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (complementSubsetComplementIntersect) =>
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% 100.16/16.74 (complementInPowersetComplementIntersect) =>
% 100.16/16.74 ((
% 100.16/16.74 (contraSubsetComplement) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementTcontraSubset) =>
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% 100.16/16.74 ((
% 100.16/16.74 (binunionTIRcontra) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (inIntersectImpInUnion2) =>
% 100.16/16.74 ((
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% 100.16/16.74 (intersectInPowersetIntersectUnions) =>
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% 100.16/16.74 ((
% 100.16/16.74 (inComplementUnionImpInComplement1) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (binunionTEcontra) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2a1) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementUnionInPowersetComplement) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2a2) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (demorgan1b) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan1) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2a) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2b2) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2b) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule0) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule1) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (woz13rule3) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (woz1_3) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_4) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_5) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (setOfPairsIsBReln1) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (breln1invE) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (breln1compEex) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 (
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% 100.16/16.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1695])).
% 100.16/16.74 thf(zip_derived_cl1725, plain,
% 100.16/16.74 (~ (((setukpairinjR1) =>
% 100.16/16.74 (((upairequniteq) =>
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% 100.16/16.74 (((cartprodpairmemER) =>
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% 100.16/16.74 ((
% 100.16/16.74 (brelnall2) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (ap2apEq2) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 (contrasubsetT2) =>
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% 100.16/16.74 (inIntersectImpInUnion2) =>
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% 100.16/16.74 ((
% 100.16/16.74 (demorgan2b2) =>
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% 100.16/16.74 (demorgan2b) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (woz13rule2) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule3) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule4) =>
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% 100.16/16.74 ((
% 100.16/16.74 (woz1_2) =>
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% 100.16/16.74 (woz1_3) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_4) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_5) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (breln1invE) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (breln1compI) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (breln1compEex) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (breln1unionI) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionE) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (injFuncSetFuncIn) =>
% 100.16/16.74 ((
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% 100.16/16.74 (
% 100.16/16.74 (
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% 100.16/16.74 (
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% 100.16/16.74 (
% 100.16/16.74 (
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% 100.16/16.74 thf(zip_derived_cl1738, plain,
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% 100.16/16.74 ((
% 100.16/16.74 (eta1) =>
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (demorgan2b2) =>
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (woz1_5) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 (
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% 100.16/16.74 (
% 100.16/16.74 ('#C') @ in)))) @
% 100.16/16.74 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.16/16.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1725])).
% 100.16/16.74 thf(zip_derived_cl1749, plain,
% 100.16/16.74 (~ (((setukpairinjR2) =>
% 100.16/16.74 (((setukpairinjR) =>
% 100.16/16.74 (((ksndsingleton) =>
% 100.16/16.74 (((ksndpairEq) =>
% 100.16/16.74 (((kpairsurjEq) =>
% 100.16/16.74 (((cartprodsndin) =>
% 100.16/16.74 (((cartprodpairmemEL) =>
% 100.16/16.74 (((cartprodpairmemER) =>
% 100.16/16.74 (((cartprodmempaircEq) =>
% 100.16/16.74 (((cartprodfstpairEq) =>
% 100.16/16.74 (((cartprodsndpairEq) =>
% 100.16/16.74 (((cartprodpairsurjEq) =>
% 100.16/16.74 (((dpsetconstrI) =>
% 100.16/16.74 (((dpsetconstrSub) =>
% 100.16/16.74 (((setOfPairsIsBReln) =>
% 100.16/16.74 (((dpsetconstrERa) =>
% 100.16/16.74 (((dpsetconstrEL1) =>
% 100.16/16.74 (((dpsetconstrEL2) =>
% 100.16/16.74 (((dpsetconstrER) =>
% 100.16/16.74 (((funcImageSingleton) =>
% 100.16/16.74 (((apProp) =>
% 100.16/16.74 (((app) =>
% 100.16/16.74 (((infuncsetfunc) =>
% 100.16/16.74 (((ap2p) =>
% 100.16/16.74 (((funcinfuncset) =>
% 100.16/16.74 (((lamProp) =>
% 100.16/16.74 (((lamp) =>
% 100.16/16.74 (((lam2p) =>
% 100.16/16.74 (((brelnall1) =>
% 100.16/16.74 (((brelnall2) =>
% 100.16/16.74 ((
% 100.16/16.74 (ex1E2) =>
% 100.16/16.74 ((
% 100.16/16.74 (funcGraphProp1) =>
% 100.16/16.74 ((
% 100.16/16.74 (funcGraphProp3) =>
% 100.16/16.74 ((
% 100.16/16.74 (funcGraphProp2) =>
% 100.16/16.74 ((
% 100.16/16.74 (funcextLem) =>
% 100.16/16.74 ((
% 100.16/16.74 (funcGraphProp4) =>
% 100.16/16.74 ((
% 100.16/16.74 (subbreln) =>
% 100.16/16.74 ((
% 100.16/16.74 (eqbreln) =>
% 100.16/16.74 ((
% 100.16/16.74 (funcext) =>
% 100.16/16.74 ((
% 100.16/16.74 (funcext2) =>
% 100.16/16.74 ((
% 100.16/16.74 (ap2apEq1) =>
% 100.16/16.74 ((
% 100.16/16.74 (ap2apEq2) =>
% 100.16/16.74 ((
% 100.16/16.74 (beta1) =>
% 100.16/16.74 ((
% 100.16/16.74 (eta1) =>
% 100.16/16.74 ((
% 100.16/16.74 (lam2lamEq) =>
% 100.16/16.74 ((
% 100.16/16.74 (beta2) =>
% 100.16/16.74 ((
% 100.16/16.74 (eta2) =>
% 100.16/16.74 ((
% 100.16/16.74 (iffalseProp1) =>
% 100.16/16.74 ((
% 100.16/16.74 (iffalseProp2) =>
% 100.16/16.74 ((
% 100.16/16.74 (iftrueProp1) =>
% 100.16/16.74 ((
% 100.16/16.74 (iftrueProp2) =>
% 100.16/16.74 ((
% 100.16/16.74 (ifSingleton) =>
% 100.16/16.74 ((
% 100.16/16.74 (ifp) =>
% 100.16/16.74 ((
% 100.16/16.74 (theeq) =>
% 100.16/16.74 ((
% 100.16/16.74 (iftrue) =>
% 100.16/16.74 ((
% 100.16/16.74 (iffalse) =>
% 100.16/16.74 ((
% 100.16/16.74 (iftrueorfalse) =>
% 100.16/16.74 ((
% 100.16/16.74 (binintersectT_lem) =>
% 100.16/16.74 ((
% 100.16/16.74 (binunionT_lem) =>
% 100.16/16.74 ((
% 100.16/16.74 (powersetT_lem) =>
% 100.16/16.74 ((
% 100.16/16.74 (setminusT_lem) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementT_lem) =>
% 100.16/16.74 ((
% 100.16/16.74 (setextT) =>
% 100.16/16.74 ((
% 100.16/16.74 (subsetTI) =>
% 100.16/16.74 ((
% 100.16/16.74 (powersetTI1) =>
% 100.16/16.74 ((
% 100.16/16.74 (powersetTE1) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementTI1) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementTE1) =>
% 100.16/16.74 ((
% 100.16/16.74 (binintersectTELcontra) =>
% 100.16/16.74 ((
% 100.16/16.74 (binintersectTERcontra) =>
% 100.16/16.74 ((
% 100.16/16.74 (contrasubsetT) =>
% 100.16/16.74 ((
% 100.16/16.74 (contrasubsetT1) =>
% 100.16/16.74 ((
% 100.16/16.74 (contrasubsetT2) =>
% 100.16/16.74 ((
% 100.16/16.74 (contrasubsetT3) =>
% 100.16/16.74 ((
% 100.16/16.74 (doubleComplementI1) =>
% 100.16/16.74 ((
% 100.16/16.74 (doubleComplementE1) =>
% 100.16/16.74 ((
% 100.16/16.74 (doubleComplementSub1) =>
% 100.16/16.74 ((
% 100.16/16.74 (doubleComplementSub2) =>
% 100.16/16.74 ((
% 100.16/16.74 (doubleComplementEq) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementTnotintersectT) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementImpComplementIntersect) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementSubsetComplementIntersect) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementInPowersetComplementIntersect) =>
% 100.16/16.74 ((
% 100.16/16.74 (contraSubsetComplement) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementTcontraSubset) =>
% 100.16/16.74 ((
% 100.16/16.74 (binunionTILcontra) =>
% 100.16/16.74 ((
% 100.16/16.74 (binunionTIRcontra) =>
% 100.16/16.74 ((
% 100.16/16.74 (inIntersectImpInUnion) =>
% 100.16/16.74 ((
% 100.16/16.74 (inIntersectImpInUnion2) =>
% 100.16/16.74 ((
% 100.16/16.74 (inIntersectImpInIntersectUnions) =>
% 100.16/16.74 ((
% 100.16/16.74 (intersectInPowersetIntersectUnions) =>
% 100.16/16.74 ((
% 100.16/16.74 (inComplementUnionImpNotIn1) =>
% 100.16/16.74 ((
% 100.16/16.74 (inComplementUnionImpInComplement1) =>
% 100.16/16.74 ((
% 100.16/16.74 (binunionTE) =>
% 100.16/16.74 ((
% 100.16/16.74 (binunionTEcontra) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2a1) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementUnionInPowersetComplement) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2a2) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan1a) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan1b) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan1) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2a) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2b2) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2b) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule0) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule1) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule2) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule3) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule4) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_1) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_2) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_3) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_4) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_5) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1all2) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1SetBreln1) =>
% 100.16/16.74 ((
% 100.16/16.74 (choice2fnsingleton) =>
% 100.16/16.74 ((
% 100.16/16.74 (setOfPairsIsBReln1) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1all1) =>
% 100.16/16.74 ((
% 100.16/16.74 (subbreln1) =>
% 100.16/16.74 ((
% 100.16/16.74 (eqbreln1) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1invprop) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1invI) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1invE) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1compprop) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1compI) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1compE) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1compEex) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionprop) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionIL) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionIR) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionI) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionE) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionEcases) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionCommutes) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz2Ex) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz2W) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz2A) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz2B) =>
% 100.16/16.74 ((
% 100.16/16.74 (image1Ex) =>
% 100.16/16.74 ((
% 100.16/16.74 (image1Ex1) =>
% 100.16/16.74 ((
% 100.16/16.74 (image1Equiv) =>
% 100.16/16.74 ((
% 100.16/16.74 (image1E) =>
% 100.16/16.74 ((
% 100.16/16.74 (image1I) =>
% 100.16/16.74 ((
% 100.16/16.74 (injFuncInInjFuncSet) =>
% 100.16/16.74 ((
% 100.16/16.74 (injFuncSetFuncIn) =>
% 100.16/16.74 ((
% 100.16/16.74 (injFuncSetFuncInj) =>
% 100.16/16.74 ((
% 100.16/16.74 (!!) @ (
% 100.16/16.74 (('#B') @ (
% 100.16/16.74 !!) @
% 100.16/16.74 (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 !!))) @
% 100.16/16.74 (
% 100.16/16.74 (
% 100.16/16.74 ('#S') @ (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 '#S') @
% 100.16/16.74 (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 '#S'))) @
% 100.16/16.74 (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 =>))))) @
% 100.16/16.74 (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 (
% 100.16/16.74 ('#C') @ in)))) @
% 100.16/16.74 surjFuncSet)))))))) @
% 100.16/16.74 (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 (
% 100.16/16.74 ('#C') @ in)))) @
% 100.16/16.74 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.16/16.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1738])).
% 100.16/16.74 thf(zip_derived_cl1760, plain,
% 100.16/16.74 (~ (((setukpairinjR) =>
% 100.16/16.74 (((ksndsingleton) =>
% 100.16/16.74 (((ksndpairEq) =>
% 100.16/16.74 (((kpairsurjEq) =>
% 100.16/16.74 (((cartprodsndin) =>
% 100.16/16.74 (((cartprodpairmemEL) =>
% 100.16/16.74 (((cartprodpairmemER) =>
% 100.16/16.74 (((cartprodmempaircEq) =>
% 100.16/16.74 (((cartprodfstpairEq) =>
% 100.16/16.74 (((cartprodsndpairEq) =>
% 100.16/16.74 (((cartprodpairsurjEq) =>
% 100.16/16.74 (((dpsetconstrI) =>
% 100.16/16.74 (((dpsetconstrSub) =>
% 100.16/16.74 (((setOfPairsIsBReln) =>
% 100.16/16.74 (((dpsetconstrERa) =>
% 100.16/16.74 (((dpsetconstrEL1) =>
% 100.16/16.74 (((dpsetconstrEL2) =>
% 100.16/16.74 (((dpsetconstrER) =>
% 100.16/16.74 (((funcImageSingleton) =>
% 100.16/16.74 (((apProp) =>
% 100.16/16.74 (((app) =>
% 100.16/16.74 (((infuncsetfunc) =>
% 100.16/16.74 (((ap2p) =>
% 100.16/16.74 (((funcinfuncset) =>
% 100.16/16.74 (((lamProp) =>
% 100.16/16.74 (((lamp) =>
% 100.16/16.74 (((lam2p) =>
% 100.16/16.74 (((brelnall1) =>
% 100.16/16.74 (((brelnall2) =>
% 100.16/16.74 (((ex1E2) =>
% 100.16/16.74 ((
% 100.16/16.74 (funcGraphProp1) =>
% 100.16/16.74 ((
% 100.16/16.74 (funcGraphProp3) =>
% 100.16/16.74 ((
% 100.16/16.74 (funcGraphProp2) =>
% 100.16/16.74 ((
% 100.16/16.74 (funcextLem) =>
% 100.16/16.74 ((
% 100.16/16.74 (funcGraphProp4) =>
% 100.16/16.74 ((
% 100.16/16.74 (subbreln) =>
% 100.16/16.74 ((
% 100.16/16.74 (eqbreln) =>
% 100.16/16.74 ((
% 100.16/16.74 (funcext) =>
% 100.16/16.74 ((
% 100.16/16.74 (funcext2) =>
% 100.16/16.74 ((
% 100.16/16.74 (ap2apEq1) =>
% 100.16/16.74 ((
% 100.16/16.74 (ap2apEq2) =>
% 100.16/16.74 ((
% 100.16/16.74 (beta1) =>
% 100.16/16.74 ((
% 100.16/16.74 (eta1) =>
% 100.16/16.74 ((
% 100.16/16.74 (lam2lamEq) =>
% 100.16/16.74 ((
% 100.16/16.74 (beta2) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (iffalseProp2) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (theeq) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (iftrueorfalse) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (binunionT_lem) =>
% 100.16/16.74 ((
% 100.16/16.74 (powersetT_lem) =>
% 100.16/16.74 ((
% 100.16/16.74 (setminusT_lem) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementT_lem) =>
% 100.16/16.74 ((
% 100.16/16.74 (setextT) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (powersetTE1) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (complementTE1) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (binintersectTERcontra) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (contrasubsetT1) =>
% 100.16/16.74 ((
% 100.16/16.74 (contrasubsetT2) =>
% 100.16/16.74 ((
% 100.16/16.74 (contrasubsetT3) =>
% 100.16/16.74 ((
% 100.16/16.74 (doubleComplementI1) =>
% 100.16/16.74 ((
% 100.16/16.74 (doubleComplementE1) =>
% 100.16/16.74 ((
% 100.16/16.74 (doubleComplementSub1) =>
% 100.16/16.74 ((
% 100.16/16.74 (doubleComplementSub2) =>
% 100.16/16.74 ((
% 100.16/16.74 (doubleComplementEq) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementTnotintersectT) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementImpComplementIntersect) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementSubsetComplementIntersect) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementInPowersetComplementIntersect) =>
% 100.16/16.74 ((
% 100.16/16.74 (contraSubsetComplement) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementTcontraSubset) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (binunionTIRcontra) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (intersectInPowersetIntersectUnions) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (inComplementUnionImpInComplement1) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (complementUnionInPowersetComplement) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2a2) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan1a) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan1b) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan1) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2a) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2b2) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2b) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule0) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (woz13rule2) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule3) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule4) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_1) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_2) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_3) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_4) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_5) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1all2) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1SetBreln1) =>
% 100.16/16.74 ((
% 100.16/16.74 (choice2fnsingleton) =>
% 100.16/16.74 ((
% 100.16/16.74 (setOfPairsIsBReln1) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1all1) =>
% 100.16/16.74 ((
% 100.16/16.74 (subbreln1) =>
% 100.16/16.74 ((
% 100.16/16.74 (eqbreln1) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1invprop) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (breln1invE) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1compprop) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1compI) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1compE) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1compEex) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionprop) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionIL) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionIR) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionI) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionE) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionEcases) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionCommutes) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz2Ex) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (woz2B) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (image1Equiv) =>
% 100.16/16.74 ((
% 100.16/16.74 (image1E) =>
% 100.16/16.74 ((
% 100.16/16.74 (image1I) =>
% 100.16/16.74 ((
% 100.16/16.74 (injFuncInInjFuncSet) =>
% 100.16/16.74 ((
% 100.16/16.74 (injFuncSetFuncIn) =>
% 100.16/16.74 ((
% 100.16/16.74 (injFuncSetFuncInj) =>
% 100.16/16.74 ((
% 100.16/16.74 (!!) @ (
% 100.16/16.74 (('#B') @ (
% 100.16/16.74 !!) @
% 100.16/16.74 (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 !!))) @
% 100.16/16.74 (
% 100.16/16.74 (
% 100.16/16.74 ('#S') @ (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
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% 100.16/16.74 (
% 100.16/16.74 (
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% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
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% 100.16/16.74 (
% 100.16/16.74 (
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% 100.16/16.74 (
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% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
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% 100.16/16.74 (
% 100.16/16.74 (
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% 100.16/16.74 (
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% 100.16/16.74 surjFuncSet)))))))) @
% 100.16/16.74 (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 (
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% 100.16/16.74 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.16/16.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1749])).
% 100.16/16.74 thf(zip_derived_cl1770, plain,
% 100.16/16.74 (~ (((ksndsingleton) =>
% 100.16/16.74 (((ksndpairEq) =>
% 100.16/16.74 (((kpairsurjEq) =>
% 100.16/16.74 (((cartprodsndin) =>
% 100.16/16.74 (((cartprodpairmemEL) =>
% 100.16/16.74 (((cartprodpairmemER) =>
% 100.16/16.74 (((cartprodmempaircEq) =>
% 100.16/16.74 (((cartprodfstpairEq) =>
% 100.16/16.74 (((cartprodsndpairEq) =>
% 100.16/16.74 (((cartprodpairsurjEq) =>
% 100.16/16.74 (((dpsetconstrI) =>
% 100.16/16.74 (((dpsetconstrSub) =>
% 100.16/16.74 (((setOfPairsIsBReln) =>
% 100.16/16.74 (((dpsetconstrERa) =>
% 100.16/16.74 (((dpsetconstrEL1) =>
% 100.16/16.74 (((dpsetconstrEL2) =>
% 100.16/16.74 (((dpsetconstrER) =>
% 100.16/16.74 (((funcImageSingleton) =>
% 100.16/16.74 (((apProp) =>
% 100.16/16.74 (((app) =>
% 100.16/16.74 (((infuncsetfunc) =>
% 100.16/16.74 (((ap2p) =>
% 100.16/16.74 (((funcinfuncset) =>
% 100.16/16.74 (((lamProp) =>
% 100.16/16.74 (((lamp) =>
% 100.16/16.74 (((lam2p) =>
% 100.16/16.74 (((brelnall1) =>
% 100.16/16.74 (((brelnall2) =>
% 100.16/16.74 (((ex1E2) =>
% 100.16/16.74 (((funcGraphProp1) =>
% 100.16/16.74 ((
% 100.16/16.74 (funcGraphProp3) =>
% 100.16/16.74 ((
% 100.16/16.74 (funcGraphProp2) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (funcGraphProp4) =>
% 100.16/16.74 ((
% 100.16/16.74 (subbreln) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (funcext2) =>
% 100.16/16.74 ((
% 100.16/16.74 (ap2apEq1) =>
% 100.16/16.74 ((
% 100.16/16.74 (ap2apEq2) =>
% 100.16/16.74 ((
% 100.16/16.74 (beta1) =>
% 100.16/16.74 ((
% 100.16/16.74 (eta1) =>
% 100.16/16.74 ((
% 100.16/16.74 (lam2lamEq) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (powersetT_lem) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (complementTE1) =>
% 100.16/16.74 ((
% 100.16/16.74 (binintersectTELcontra) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (contrasubsetT2) =>
% 100.16/16.74 ((
% 100.16/16.74 (contrasubsetT3) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 (complementInPowersetComplementIntersect) =>
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% 100.16/16.74 ((
% 100.16/16.74 (complementTcontraSubset) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (binunionTIRcontra) =>
% 100.16/16.74 ((
% 100.16/16.74 (inIntersectImpInUnion) =>
% 100.16/16.74 ((
% 100.16/16.74 (inIntersectImpInUnion2) =>
% 100.16/16.74 ((
% 100.16/16.74 (inIntersectImpInIntersectUnions) =>
% 100.16/16.74 ((
% 100.16/16.74 (intersectInPowersetIntersectUnions) =>
% 100.16/16.74 ((
% 100.16/16.74 (inComplementUnionImpNotIn1) =>
% 100.16/16.74 ((
% 100.16/16.74 (inComplementUnionImpInComplement1) =>
% 100.16/16.74 ((
% 100.16/16.74 (binunionTE) =>
% 100.16/16.74 ((
% 100.16/16.74 (binunionTEcontra) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2a1) =>
% 100.16/16.74 ((
% 100.16/16.74 (complementUnionInPowersetComplement) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2a2) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan1a) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan1b) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan1) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2a) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2b2) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2b) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule0) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule1) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule2) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule3) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule4) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_1) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_2) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_3) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_4) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_5) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1all2) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1SetBreln1) =>
% 100.16/16.74 ((
% 100.16/16.74 (choice2fnsingleton) =>
% 100.16/16.74 ((
% 100.16/16.74 (setOfPairsIsBReln1) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1all1) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (eqbreln1) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1invprop) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1invI) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1invE) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1compprop) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1compI) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1compE) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1compEex) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionprop) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionIL) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionIR) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionI) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionE) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionEcases) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (image1Ex1) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (image1E) =>
% 100.16/16.74 ((
% 100.16/16.74 (image1I) =>
% 100.16/16.74 ((
% 100.16/16.74 (injFuncInInjFuncSet) =>
% 100.16/16.74 ((
% 100.16/16.74 (injFuncSetFuncIn) =>
% 100.16/16.74 ((
% 100.16/16.74 (injFuncSetFuncInj) =>
% 100.16/16.74 ((
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% 100.16/16.74 (('#B') @ (
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% 100.16/16.74 (
% 100.16/16.74 (
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% 100.16/16.74 (
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% 100.16/16.74 (
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% 100.16/16.74 (
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% 100.16/16.74 (
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% 100.16/16.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1760])).
% 100.16/16.74 thf(zip_derived_cl1779, plain,
% 100.16/16.74 (~ (((ksndpairEq) =>
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% 100.16/16.74 (((cartprodsndin) =>
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% 100.16/16.74 (((cartprodpairmemER) =>
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% 100.16/16.74 (((cartprodsndpairEq) =>
% 100.16/16.74 (((cartprodpairsurjEq) =>
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% 100.16/16.74 (((dpsetconstrERa) =>
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 (((cartprodsndpairEq) =>
% 100.16/16.74 (((cartprodpairsurjEq) =>
% 100.16/16.74 (((dpsetconstrI) =>
% 100.16/16.74 (((dpsetconstrSub) =>
% 100.16/16.74 (((setOfPairsIsBReln) =>
% 100.16/16.74 (((dpsetconstrERa) =>
% 100.16/16.74 (((dpsetconstrEL1) =>
% 100.16/16.74 (((dpsetconstrEL2) =>
% 100.16/16.74 (((dpsetconstrER) =>
% 100.16/16.74 (((funcImageSingleton) =>
% 100.16/16.74 (((apProp) =>
% 100.16/16.74 (((app) =>
% 100.16/16.74 (((infuncsetfunc) =>
% 100.16/16.74 (((ap2p) =>
% 100.16/16.74 (((funcinfuncset) =>
% 100.16/16.74 (((lamProp) =>
% 100.16/16.74 (((lamp) =>
% 100.16/16.74 (((lam2p) =>
% 100.16/16.74 (((brelnall1) =>
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% 100.16/16.74 (((ex1E2) =>
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (demorgan2a) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2b2) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2b) =>
% 100.16/16.74 ((
% 100.16/16.74 (demorgan2) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule0) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule1) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule2) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule3) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz13rule4) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (woz1_2) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_3) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_4) =>
% 100.16/16.74 ((
% 100.16/16.74 (woz1_5) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (breln1invI) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1invE) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (breln1compE) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1compEex) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionprop) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (breln1unionIR) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionI) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionE) =>
% 100.16/16.74 ((
% 100.16/16.74 (breln1unionEcases) =>
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% 100.16/16.74 ((
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% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (woz2B) =>
% 100.16/16.74 ((
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% 100.16/16.74 ((
% 100.16/16.74 (image1Ex1) =>
% 100.16/16.74 ((
% 100.16/16.74 (image1Equiv) =>
% 100.16/16.74 ((
% 100.16/16.74 (image1E) =>
% 100.16/16.74 ((
% 100.16/16.74 (image1I) =>
% 100.16/16.74 ((
% 100.16/16.74 (injFuncInInjFuncSet) =>
% 100.16/16.74 ((
% 100.16/16.74 (injFuncSetFuncIn) =>
% 100.16/16.74 ((
% 100.16/16.74 (injFuncSetFuncInj) =>
% 100.16/16.74 ((
% 100.16/16.74 (!!) @ (
% 100.16/16.74 (('#B') @ (
% 100.16/16.74 !!) @
% 100.16/16.74 (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 !!))) @
% 100.16/16.74 (
% 100.16/16.74 (
% 100.16/16.74 ('#S') @ (
% 100.16/16.74 (
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% 100.16/16.74 (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 (
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% 100.16/16.74 (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 =>))))) @
% 100.16/16.74 (
% 100.16/16.74 (
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% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 (
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% 100.16/16.74 surjFuncSet)))))))) @
% 100.16/16.74 (
% 100.16/16.74 (
% 100.16/16.74 ('#B') @ (
% 100.16/16.74 (
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% 100.16/16.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1807])).
% 100.16/16.74 thf(zip_derived_cl1825, plain,
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% 100.16/16.74 (((cartprodsndpairEq) =>
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% 100.16/16.74 (((lam2p) =>
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% 100.16/16.74 (((ex1E2) =>
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% 100.16/16.75 (funcext2) =>
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% 100.16/16.75 ((
% 100.16/16.75 (ap2apEq2) =>
% 100.16/16.75 ((
% 100.16/16.75 (beta1) =>
% 100.16/16.75 ((
% 100.16/16.75 (eta1) =>
% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
% 100.16/16.75 (contrasubsetT3) =>
% 100.16/16.75 ((
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% 100.16/16.75 ((
% 100.16/16.75 (complementInPowersetComplementIntersect) =>
% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
% 100.16/16.75 (intersectInPowersetIntersectUnions) =>
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% 100.16/16.75 (inComplementUnionImpNotIn1) =>
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% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
% 100.16/16.75 (breln1all2) =>
% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
% 100.16/16.75 (breln1all1) =>
% 100.16/16.75 ((
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% 100.16/16.75 ((
% 100.16/16.75 (eqbreln1) =>
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% 100.16/16.75 ((
% 100.16/16.75 (breln1invI) =>
% 100.16/16.75 ((
% 100.16/16.75 (breln1invE) =>
% 100.16/16.75 ((
% 100.16/16.75 (breln1compprop) =>
% 100.16/16.75 ((
% 100.16/16.75 (breln1compI) =>
% 100.16/16.75 ((
% 100.16/16.75 (breln1compE) =>
% 100.16/16.75 ((
% 100.16/16.75 (breln1compEex) =>
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% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
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% 100.16/16.75 ((
% 100.16/16.75 (image1E) =>
% 100.16/16.75 ((
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% 100.16/16.75 ((
% 100.16/16.75 (injFuncInInjFuncSet) =>
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% 100.16/16.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1816])).
% 100.16/16.75 thf(zip_derived_cl1833, plain,
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% 100.16/16.75 (((cartprodsndpairEq) =>
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% 100.16/16.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1825])).
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% 100.16/16.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1833])).
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% 100.16/16.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1848])).
% 100.16/16.75 thf(zip_derived_cl1865, plain,
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% 100.33/16.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1982])).
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% 100.33/16.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1992])).
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% 100.33/16.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2002])).
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% 100.33/16.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2012])).
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% 100.33/16.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2059])).
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% 100.33/16.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2070])).
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% 100.33/16.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2081])).
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% 100.33/16.77 (((eta1) =>
% 100.33/16.77 (((lam2lamEq) =>
% 100.33/16.77 (((beta2) =>
% 100.33/16.77 (((eta2) =>
% 100.33/16.77 (((iffalseProp1) =>
% 100.33/16.77 (((iffalseProp2) =>
% 100.33/16.77 (((iftrueProp1) =>
% 100.33/16.77 (((iftrueProp2) =>
% 100.33/16.77 (((ifSingleton) =>
% 100.33/16.77 (((ifp) =>
% 100.33/16.77 (((theeq) =>
% 100.33/16.77 (((iftrue) =>
% 100.33/16.77 (((iffalse) =>
% 100.33/16.77 (((iftrueorfalse) =>
% 100.33/16.77 (((binintersectT_lem) =>
% 100.33/16.77 (((binunionT_lem) =>
% 100.33/16.77 (((powersetT_lem) =>
% 100.33/16.77 (((setminusT_lem) =>
% 100.33/16.77 (((complementT_lem) =>
% 100.33/16.77 (((setextT) =>
% 100.33/16.77 (((subsetTI) =>
% 100.33/16.77 (((powersetTI1) =>
% 100.33/16.77 (((powersetTE1) =>
% 100.33/16.77 (((complementTI1) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTE1) =>
% 100.33/16.77 ((
% 100.33/16.77 (binintersectTELcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (binintersectTERcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT1) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT2) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT3) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementI1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementE1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementSub1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementSub2) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementEq) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTnotintersectT) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementImpComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementSubsetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementInPowersetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (contraSubsetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTcontraSubset) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTILcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTIRcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion2) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (intersectInPowersetIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpNotIn1) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpInComplement1) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTE) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTEcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a1) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementUnionInPowersetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule0) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_5) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all2) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1SetBreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (choice2fnsingleton) =>
% 100.33/16.77 ((
% 100.33/16.77 (setOfPairsIsBReln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all1) =>
% 100.33/16.77 ((
% 100.33/16.77 (subbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (eqbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compEex) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIL) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIR) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionEcases) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionCommutes) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2W) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2A) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2B) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Ex1) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Equiv) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1E) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1I) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncInInjFuncSet) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncIn) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncInj) =>
% 100.33/16.77 ((
% 100.33/16.77 (!!) @ (
% 100.33/16.77 (('#B') @ (
% 100.33/16.77 !!) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 !!))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#S') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 '#S') @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 '#S'))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 =>))))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#C') @ in)))) @
% 100.33/16.77 surjFuncSet)))))))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#C') @ in)))) @
% 100.33/16.77 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2091])).
% 100.33/16.77 thf(zip_derived_cl2115, plain,
% 100.33/16.77 (~ (((funcext) =>
% 100.33/16.77 (((funcext2) =>
% 100.33/16.77 (((ap2apEq1) =>
% 100.33/16.77 (((ap2apEq2) =>
% 100.33/16.77 (((beta1) =>
% 100.33/16.77 (((eta1) =>
% 100.33/16.77 (((lam2lamEq) =>
% 100.33/16.77 (((beta2) =>
% 100.33/16.77 (((eta2) =>
% 100.33/16.77 (((iffalseProp1) =>
% 100.33/16.77 (((iffalseProp2) =>
% 100.33/16.77 (((iftrueProp1) =>
% 100.33/16.77 (((iftrueProp2) =>
% 100.33/16.77 (((ifSingleton) =>
% 100.33/16.77 (((ifp) =>
% 100.33/16.77 (((theeq) =>
% 100.33/16.77 (((iftrue) =>
% 100.33/16.77 (((iffalse) =>
% 100.33/16.77 (((iftrueorfalse) =>
% 100.33/16.77 (((binintersectT_lem) =>
% 100.33/16.77 (((binunionT_lem) =>
% 100.33/16.77 (((powersetT_lem) =>
% 100.33/16.77 (((setminusT_lem) =>
% 100.33/16.77 (((complementT_lem) =>
% 100.33/16.77 (((setextT) =>
% 100.33/16.77 (((subsetTI) =>
% 100.33/16.77 (((powersetTI1) =>
% 100.33/16.77 (((powersetTE1) =>
% 100.33/16.77 (((complementTI1) =>
% 100.33/16.77 (((complementTE1) =>
% 100.33/16.77 ((
% 100.33/16.77 (binintersectTELcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (binintersectTERcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT1) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT2) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT3) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementI1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementE1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementSub1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementSub2) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementEq) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTnotintersectT) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementImpComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementSubsetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementInPowersetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (contraSubsetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTcontraSubset) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTILcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTIRcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion2) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (intersectInPowersetIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpNotIn1) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpInComplement1) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTE) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTEcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a1) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementUnionInPowersetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule0) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_5) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all2) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1SetBreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (choice2fnsingleton) =>
% 100.33/16.77 ((
% 100.33/16.77 (setOfPairsIsBReln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all1) =>
% 100.33/16.77 ((
% 100.33/16.77 (subbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (eqbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compEex) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIL) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIR) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionEcases) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionCommutes) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2W) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2A) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2B) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Ex1) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Equiv) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1E) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1I) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncInInjFuncSet) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncIn) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncInj) =>
% 100.33/16.77 ((
% 100.33/16.77 (!!) @ (
% 100.33/16.77 (('#B') @ (
% 100.33/16.77 !!) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 !!))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#S') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 '#S') @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 '#S'))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 =>))))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#C') @ in)))) @
% 100.33/16.77 surjFuncSet)))))))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#C') @ in)))) @
% 100.33/16.77 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2102])).
% 100.33/16.77 thf(zip_derived_cl2130, plain,
% 100.33/16.77 (~ (((funcext2) =>
% 100.33/16.77 (((ap2apEq1) =>
% 100.33/16.77 (((ap2apEq2) =>
% 100.33/16.77 (((beta1) =>
% 100.33/16.77 (((eta1) =>
% 100.33/16.77 (((lam2lamEq) =>
% 100.33/16.77 (((beta2) =>
% 100.33/16.77 (((eta2) =>
% 100.33/16.77 (((iffalseProp1) =>
% 100.33/16.77 (((iffalseProp2) =>
% 100.33/16.77 (((iftrueProp1) =>
% 100.33/16.77 (((iftrueProp2) =>
% 100.33/16.77 (((ifSingleton) =>
% 100.33/16.77 (((ifp) =>
% 100.33/16.77 (((theeq) =>
% 100.33/16.77 (((iftrue) =>
% 100.33/16.77 (((iffalse) =>
% 100.33/16.77 (((iftrueorfalse) =>
% 100.33/16.77 (((binintersectT_lem) =>
% 100.33/16.77 (((binunionT_lem) =>
% 100.33/16.77 (((powersetT_lem) =>
% 100.33/16.77 (((setminusT_lem) =>
% 100.33/16.77 (((complementT_lem) =>
% 100.33/16.77 (((setextT) =>
% 100.33/16.77 (((subsetTI) =>
% 100.33/16.77 (((powersetTI1) =>
% 100.33/16.77 (((powersetTE1) =>
% 100.33/16.77 (((complementTI1) =>
% 100.33/16.77 (((complementTE1) =>
% 100.33/16.77 (((binintersectTELcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (binintersectTERcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT1) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT2) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT3) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementI1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementE1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementSub1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementSub2) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementEq) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTnotintersectT) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementImpComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementSubsetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementInPowersetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (contraSubsetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTcontraSubset) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTILcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTIRcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion2) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (intersectInPowersetIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpNotIn1) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpInComplement1) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTE) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTEcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a1) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementUnionInPowersetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule0) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_5) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all2) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1SetBreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (choice2fnsingleton) =>
% 100.33/16.77 ((
% 100.33/16.77 (setOfPairsIsBReln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all1) =>
% 100.33/16.77 ((
% 100.33/16.77 (subbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (eqbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compEex) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIL) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIR) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionEcases) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionCommutes) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2W) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2A) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2B) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Ex1) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Equiv) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1E) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1I) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncInInjFuncSet) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncIn) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncInj) =>
% 100.33/16.77 ((
% 100.33/16.77 (!!) @ (
% 100.33/16.77 (('#B') @ (
% 100.33/16.77 !!) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 !!))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#S') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 '#S') @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 '#S'))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 =>))))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#C') @ in)))) @
% 100.33/16.77 surjFuncSet)))))))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#C') @ in)))) @
% 100.33/16.77 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2115])).
% 100.33/16.77 thf(zip_derived_cl2146, plain,
% 100.33/16.77 (~ (((ap2apEq1) =>
% 100.33/16.77 (((ap2apEq2) =>
% 100.33/16.77 (((beta1) =>
% 100.33/16.77 (((eta1) =>
% 100.33/16.77 (((lam2lamEq) =>
% 100.33/16.77 (((beta2) =>
% 100.33/16.77 (((eta2) =>
% 100.33/16.77 (((iffalseProp1) =>
% 100.33/16.77 (((iffalseProp2) =>
% 100.33/16.77 (((iftrueProp1) =>
% 100.33/16.77 (((iftrueProp2) =>
% 100.33/16.77 (((ifSingleton) =>
% 100.33/16.77 (((ifp) =>
% 100.33/16.77 (((theeq) =>
% 100.33/16.77 (((iftrue) =>
% 100.33/16.77 (((iffalse) =>
% 100.33/16.77 (((iftrueorfalse) =>
% 100.33/16.77 (((binintersectT_lem) =>
% 100.33/16.77 (((binunionT_lem) =>
% 100.33/16.77 (((powersetT_lem) =>
% 100.33/16.77 (((setminusT_lem) =>
% 100.33/16.77 (((complementT_lem) =>
% 100.33/16.77 (((setextT) =>
% 100.33/16.77 (((subsetTI) =>
% 100.33/16.77 (((powersetTI1) =>
% 100.33/16.77 (((powersetTE1) =>
% 100.33/16.77 (((complementTI1) =>
% 100.33/16.77 (((complementTE1) =>
% 100.33/16.77 (((binintersectTELcontra) =>
% 100.33/16.77 (((binintersectTERcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT1) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT2) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT3) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementI1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementE1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementSub1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementSub2) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementEq) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTnotintersectT) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementImpComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementSubsetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementInPowersetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (contraSubsetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTcontraSubset) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTILcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTIRcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion2) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (intersectInPowersetIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpNotIn1) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpInComplement1) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTE) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTEcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a1) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementUnionInPowersetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule0) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_5) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all2) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1SetBreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (choice2fnsingleton) =>
% 100.33/16.77 ((
% 100.33/16.77 (setOfPairsIsBReln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all1) =>
% 100.33/16.77 ((
% 100.33/16.77 (subbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (eqbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compEex) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIL) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIR) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionEcases) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionCommutes) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2W) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2A) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2B) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Ex1) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Equiv) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1E) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1I) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncInInjFuncSet) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncIn) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncInj) =>
% 100.33/16.77 ((
% 100.33/16.77 (!!) @ (
% 100.33/16.77 (('#B') @ (
% 100.33/16.77 !!) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 !!))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#S') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 '#S') @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 '#S'))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 =>))))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#C') @ in)))) @
% 100.33/16.77 surjFuncSet)))))))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#C') @ in)))) @
% 100.33/16.77 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2130])).
% 100.33/16.77 thf(zip_derived_cl2163, plain,
% 100.33/16.77 (~ (((ap2apEq2) =>
% 100.33/16.77 (((beta1) =>
% 100.33/16.77 (((eta1) =>
% 100.33/16.77 (((lam2lamEq) =>
% 100.33/16.77 (((beta2) =>
% 100.33/16.77 (((eta2) =>
% 100.33/16.77 (((iffalseProp1) =>
% 100.33/16.77 (((iffalseProp2) =>
% 100.33/16.77 (((iftrueProp1) =>
% 100.33/16.77 (((iftrueProp2) =>
% 100.33/16.77 (((ifSingleton) =>
% 100.33/16.77 (((ifp) =>
% 100.33/16.77 (((theeq) =>
% 100.33/16.77 (((iftrue) =>
% 100.33/16.77 (((iffalse) =>
% 100.33/16.77 (((iftrueorfalse) =>
% 100.33/16.77 (((binintersectT_lem) =>
% 100.33/16.77 (((binunionT_lem) =>
% 100.33/16.77 (((powersetT_lem) =>
% 100.33/16.77 (((setminusT_lem) =>
% 100.33/16.77 (((complementT_lem) =>
% 100.33/16.77 (((setextT) =>
% 100.33/16.77 (((subsetTI) =>
% 100.33/16.77 (((powersetTI1) =>
% 100.33/16.77 (((powersetTE1) =>
% 100.33/16.77 (((complementTI1) =>
% 100.33/16.77 (((complementTE1) =>
% 100.33/16.77 (((binintersectTELcontra) =>
% 100.33/16.77 (((binintersectTERcontra) =>
% 100.33/16.77 (((contrasubsetT) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT1) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT2) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT3) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementI1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementE1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementSub1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementSub2) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementEq) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTnotintersectT) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementImpComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementSubsetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementInPowersetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (contraSubsetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTcontraSubset) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTILcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTIRcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion2) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (intersectInPowersetIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpNotIn1) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpInComplement1) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTE) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTEcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a1) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementUnionInPowersetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule0) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_5) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all2) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1SetBreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (choice2fnsingleton) =>
% 100.33/16.77 ((
% 100.33/16.77 (setOfPairsIsBReln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all1) =>
% 100.33/16.77 ((
% 100.33/16.77 (subbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (eqbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compEex) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIL) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIR) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionEcases) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionCommutes) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2W) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2A) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2B) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Ex1) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Equiv) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1E) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1I) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncInInjFuncSet) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncIn) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncInj) =>
% 100.33/16.77 ((
% 100.33/16.77 (!!) @ (
% 100.33/16.77 (('#B') @ (
% 100.33/16.77 !!) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 !!))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#S') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 '#S') @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 '#S'))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 =>))))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#C') @ in)))) @
% 100.33/16.77 surjFuncSet)))))))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#C') @ in)))) @
% 100.33/16.77 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2146])).
% 100.33/16.77 thf(zip_derived_cl2181, plain,
% 100.33/16.77 (~ (((beta1) =>
% 100.33/16.77 (((eta1) =>
% 100.33/16.77 (((lam2lamEq) =>
% 100.33/16.77 (((beta2) =>
% 100.33/16.77 (((eta2) =>
% 100.33/16.77 (((iffalseProp1) =>
% 100.33/16.77 (((iffalseProp2) =>
% 100.33/16.77 (((iftrueProp1) =>
% 100.33/16.77 (((iftrueProp2) =>
% 100.33/16.77 (((ifSingleton) =>
% 100.33/16.77 (((ifp) =>
% 100.33/16.77 (((theeq) =>
% 100.33/16.77 (((iftrue) =>
% 100.33/16.77 (((iffalse) =>
% 100.33/16.77 (((iftrueorfalse) =>
% 100.33/16.77 (((binintersectT_lem) =>
% 100.33/16.77 (((binunionT_lem) =>
% 100.33/16.77 (((powersetT_lem) =>
% 100.33/16.77 (((setminusT_lem) =>
% 100.33/16.77 (((complementT_lem) =>
% 100.33/16.77 (((setextT) =>
% 100.33/16.77 (((subsetTI) =>
% 100.33/16.77 (((powersetTI1) =>
% 100.33/16.77 (((powersetTE1) =>
% 100.33/16.77 (((complementTI1) =>
% 100.33/16.77 (((complementTE1) =>
% 100.33/16.77 (((binintersectTELcontra) =>
% 100.33/16.77 (((binintersectTERcontra) =>
% 100.33/16.77 (((contrasubsetT) =>
% 100.33/16.77 (((contrasubsetT1) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT2) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT3) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementI1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementE1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementSub1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementSub2) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementEq) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTnotintersectT) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementImpComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementSubsetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementInPowersetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (contraSubsetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTcontraSubset) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTILcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTIRcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion2) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (intersectInPowersetIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpNotIn1) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpInComplement1) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTE) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTEcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a1) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementUnionInPowersetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule0) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_5) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all2) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1SetBreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (choice2fnsingleton) =>
% 100.33/16.77 ((
% 100.33/16.77 (setOfPairsIsBReln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all1) =>
% 100.33/16.77 ((
% 100.33/16.77 (subbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (eqbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compEex) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIL) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIR) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionEcases) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionCommutes) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2W) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2A) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2B) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Ex1) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Equiv) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1E) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1I) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncInInjFuncSet) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncIn) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncInj) =>
% 100.33/16.77 ((
% 100.33/16.77 (!!) @ (
% 100.33/16.77 (('#B') @ (
% 100.33/16.77 !!) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 !!))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#S') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 '#S') @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 '#S'))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 =>))))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#C') @ in)))) @
% 100.33/16.77 surjFuncSet)))))))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#C') @ in)))) @
% 100.33/16.77 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2163])).
% 100.33/16.77 thf(zip_derived_cl2198, plain,
% 100.33/16.77 (~ (((eta1) =>
% 100.33/16.77 (((lam2lamEq) =>
% 100.33/16.77 (((beta2) =>
% 100.33/16.77 (((eta2) =>
% 100.33/16.77 (((iffalseProp1) =>
% 100.33/16.77 (((iffalseProp2) =>
% 100.33/16.77 (((iftrueProp1) =>
% 100.33/16.77 (((iftrueProp2) =>
% 100.33/16.77 (((ifSingleton) =>
% 100.33/16.77 (((ifp) =>
% 100.33/16.77 (((theeq) =>
% 100.33/16.77 (((iftrue) =>
% 100.33/16.77 (((iffalse) =>
% 100.33/16.77 (((iftrueorfalse) =>
% 100.33/16.77 (((binintersectT_lem) =>
% 100.33/16.77 (((binunionT_lem) =>
% 100.33/16.77 (((powersetT_lem) =>
% 100.33/16.77 (((setminusT_lem) =>
% 100.33/16.77 (((complementT_lem) =>
% 100.33/16.77 (((setextT) =>
% 100.33/16.77 (((subsetTI) =>
% 100.33/16.77 (((powersetTI1) =>
% 100.33/16.77 (((powersetTE1) =>
% 100.33/16.77 (((complementTI1) =>
% 100.33/16.77 (((complementTE1) =>
% 100.33/16.77 (((binintersectTELcontra) =>
% 100.33/16.77 (((binintersectTERcontra) =>
% 100.33/16.77 (((contrasubsetT) =>
% 100.33/16.77 (((contrasubsetT1) =>
% 100.33/16.77 (((contrasubsetT2) =>
% 100.33/16.77 ((
% 100.33/16.77 (contrasubsetT3) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementI1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementE1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementSub1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementSub2) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementEq) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTnotintersectT) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementImpComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementSubsetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementInPowersetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (contraSubsetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTcontraSubset) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTILcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTIRcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion2) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (intersectInPowersetIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpNotIn1) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpInComplement1) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTE) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTEcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a1) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementUnionInPowersetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule0) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule2) =>
% 100.33/16.77 ((
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% 100.33/16.77 ((
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% 100.33/16.77 ((
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% 100.33/16.77 ((
% 100.33/16.77 (woz1_2) =>
% 100.33/16.77 ((
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% 100.33/16.77 ((
% 100.33/16.77 (woz1_4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_5) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all2) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1SetBreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (choice2fnsingleton) =>
% 100.33/16.77 ((
% 100.33/16.77 (setOfPairsIsBReln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all1) =>
% 100.33/16.77 ((
% 100.33/16.77 (subbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (eqbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compEex) =>
% 100.33/16.77 ((
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% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIL) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIR) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionEcases) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionCommutes) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2W) =>
% 100.33/16.77 ((
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% 100.33/16.77 ((
% 100.33/16.77 (woz2B) =>
% 100.33/16.77 ((
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% 100.33/16.77 ((
% 100.33/16.77 (image1Ex1) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Equiv) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1E) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1I) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncInInjFuncSet) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncIn) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncInj) =>
% 100.33/16.77 ((
% 100.33/16.77 (!!) @ (
% 100.33/16.77 (('#B') @ (
% 100.33/16.77 !!) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 !!))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#S') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 '#S') @
% 100.33/16.77 (
% 100.33/16.77 (
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% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
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% 100.33/16.77 (
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% 100.33/16.77 (
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% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
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% 100.33/16.77 (
% 100.33/16.77 (
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% 100.33/16.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2198])).
% 100.33/16.77 thf(zip_derived_cl2228, plain,
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% 100.33/16.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2213])).
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% 100.33/16.77 (inComplementUnionImpNotIn1) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpInComplement1) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTE) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTEcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a1) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementUnionInPowersetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule0) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_5) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all2) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1SetBreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (choice2fnsingleton) =>
% 100.33/16.77 ((
% 100.33/16.77 (setOfPairsIsBReln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all1) =>
% 100.33/16.77 ((
% 100.33/16.77 (subbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (eqbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compEex) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIL) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIR) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionEcases) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionCommutes) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2W) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2A) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2B) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Ex1) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Equiv) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1E) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1I) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncInInjFuncSet) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncIn) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncInj) =>
% 100.33/16.77 ((
% 100.33/16.77 (!!) @ (
% 100.33/16.77 (('#B') @ (
% 100.33/16.77 !!) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 !!))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#S') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 '#S') @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 '#S'))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 =>))))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#C') @ in)))) @
% 100.33/16.77 surjFuncSet)))))))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#C') @ in)))) @
% 100.33/16.77 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2228])).
% 100.33/16.77 thf(zip_derived_cl2261, plain,
% 100.33/16.77 (~ (((iffalseProp1) =>
% 100.33/16.77 (((iffalseProp2) =>
% 100.33/16.77 (((iftrueProp1) =>
% 100.33/16.77 (((iftrueProp2) =>
% 100.33/16.77 (((ifSingleton) =>
% 100.33/16.77 (((ifp) =>
% 100.33/16.77 (((theeq) =>
% 100.33/16.77 (((iftrue) =>
% 100.33/16.77 (((iffalse) =>
% 100.33/16.77 (((iftrueorfalse) =>
% 100.33/16.77 (((binintersectT_lem) =>
% 100.33/16.77 (((binunionT_lem) =>
% 100.33/16.77 (((powersetT_lem) =>
% 100.33/16.77 (((setminusT_lem) =>
% 100.33/16.77 (((complementT_lem) =>
% 100.33/16.77 (((setextT) =>
% 100.33/16.77 (((subsetTI) =>
% 100.33/16.77 (((powersetTI1) =>
% 100.33/16.77 (((powersetTE1) =>
% 100.33/16.77 (((complementTI1) =>
% 100.33/16.77 (((complementTE1) =>
% 100.33/16.77 (((binintersectTELcontra) =>
% 100.33/16.77 (((binintersectTERcontra) =>
% 100.33/16.77 (((contrasubsetT) =>
% 100.33/16.77 (((contrasubsetT1) =>
% 100.33/16.77 (((contrasubsetT2) =>
% 100.33/16.77 (((contrasubsetT3) =>
% 100.33/16.77 (((doubleComplementI1) =>
% 100.33/16.77 (((doubleComplementE1) =>
% 100.33/16.77 (((doubleComplementSub1) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementSub2) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementEq) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTnotintersectT) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementImpComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementSubsetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementInPowersetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (contraSubsetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTcontraSubset) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTILcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTIRcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion2) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (intersectInPowersetIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpNotIn1) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpInComplement1) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTE) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTEcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a1) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementUnionInPowersetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule0) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_5) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all2) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1SetBreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (choice2fnsingleton) =>
% 100.33/16.77 ((
% 100.33/16.77 (setOfPairsIsBReln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all1) =>
% 100.33/16.77 ((
% 100.33/16.77 (subbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (eqbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compEex) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIL) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIR) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionEcases) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionCommutes) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2W) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2A) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2B) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Ex1) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Equiv) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1E) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1I) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncInInjFuncSet) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncIn) =>
% 100.33/16.77 ((
% 100.33/16.77 (injFuncSetFuncInj) =>
% 100.33/16.77 ((
% 100.33/16.77 (!!) @ (
% 100.33/16.77 (('#B') @ (
% 100.33/16.77 !!) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 !!))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#S') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 '#S') @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 '#S'))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 =>))))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#C') @ in)))) @
% 100.33/16.77 surjFuncSet)))))))) @
% 100.33/16.77 (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#B') @ (
% 100.33/16.77 (
% 100.33/16.77 ('#C') @ in)))) @
% 100.33/16.77 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2244])).
% 100.33/16.77 thf(zip_derived_cl2279, plain,
% 100.33/16.77 (~ (((iffalseProp2) =>
% 100.33/16.77 (((iftrueProp1) =>
% 100.33/16.77 (((iftrueProp2) =>
% 100.33/16.77 (((ifSingleton) =>
% 100.33/16.77 (((ifp) =>
% 100.33/16.77 (((theeq) =>
% 100.33/16.77 (((iftrue) =>
% 100.33/16.77 (((iffalse) =>
% 100.33/16.77 (((iftrueorfalse) =>
% 100.33/16.77 (((binintersectT_lem) =>
% 100.33/16.77 (((binunionT_lem) =>
% 100.33/16.77 (((powersetT_lem) =>
% 100.33/16.77 (((setminusT_lem) =>
% 100.33/16.77 (((complementT_lem) =>
% 100.33/16.77 (((setextT) =>
% 100.33/16.77 (((subsetTI) =>
% 100.33/16.77 (((powersetTI1) =>
% 100.33/16.77 (((powersetTE1) =>
% 100.33/16.77 (((complementTI1) =>
% 100.33/16.77 (((complementTE1) =>
% 100.33/16.77 (((binintersectTELcontra) =>
% 100.33/16.77 (((binintersectTERcontra) =>
% 100.33/16.77 (((contrasubsetT) =>
% 100.33/16.77 (((contrasubsetT1) =>
% 100.33/16.77 (((contrasubsetT2) =>
% 100.33/16.77 (((contrasubsetT3) =>
% 100.33/16.77 (((doubleComplementI1) =>
% 100.33/16.77 (((doubleComplementE1) =>
% 100.33/16.77 (((doubleComplementSub1) =>
% 100.33/16.77 (((doubleComplementSub2) =>
% 100.33/16.77 ((
% 100.33/16.77 (doubleComplementEq) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTnotintersectT) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementImpComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementSubsetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementInPowersetComplementIntersect) =>
% 100.33/16.77 ((
% 100.33/16.77 (contraSubsetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementTcontraSubset) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTILcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTIRcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInUnion2) =>
% 100.33/16.77 ((
% 100.33/16.77 (inIntersectImpInIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (intersectInPowersetIntersectUnions) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpNotIn1) =>
% 100.33/16.77 ((
% 100.33/16.77 (inComplementUnionImpInComplement1) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTE) =>
% 100.33/16.77 ((
% 100.33/16.77 (binunionTEcontra) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a1) =>
% 100.33/16.77 ((
% 100.33/16.77 (complementUnionInPowersetComplement) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan1) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2a) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b2) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2b) =>
% 100.33/16.77 ((
% 100.33/16.77 (demorgan2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule0) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz13rule4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_1) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_2) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_3) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_4) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz1_5) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all2) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1SetBreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (choice2fnsingleton) =>
% 100.33/16.77 ((
% 100.33/16.77 (setOfPairsIsBReln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1all1) =>
% 100.33/16.77 ((
% 100.33/16.77 (subbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (eqbreln1) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1invE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1compEex) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionprop) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIL) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionIR) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionI) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionE) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionEcases) =>
% 100.33/16.77 ((
% 100.33/16.77 (breln1unionCommutes) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2Ex) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2W) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2A) =>
% 100.33/16.77 ((
% 100.33/16.77 (woz2B) =>
% 100.33/16.77 ((
% 100.33/16.77 (image1Ex) =>
% 100.33/16.77 ((
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% 100.33/16.78 ((
% 100.33/16.78 (binunionTIRcontra) =>
% 100.33/16.78 ((
% 100.33/16.78 (inIntersectImpInUnion) =>
% 100.33/16.78 ((
% 100.33/16.78 (inIntersectImpInUnion2) =>
% 100.33/16.78 ((
% 100.33/16.78 (inIntersectImpInIntersectUnions) =>
% 100.33/16.78 ((
% 100.33/16.78 (intersectInPowersetIntersectUnions) =>
% 100.33/16.78 ((
% 100.33/16.78 (inComplementUnionImpNotIn1) =>
% 100.33/16.78 ((
% 100.33/16.78 (inComplementUnionImpInComplement1) =>
% 100.33/16.78 ((
% 100.33/16.78 (binunionTE) =>
% 100.33/16.78 ((
% 100.33/16.78 (binunionTEcontra) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2a1) =>
% 100.33/16.78 ((
% 100.33/16.78 (complementUnionInPowersetComplement) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2a2) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan1a) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan1b) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan1) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2a) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2b2) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2b) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule0) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule1) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule2) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule3) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule4) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_1) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_2) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_3) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_4) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_5) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1all2) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1SetBreln1) =>
% 100.33/16.78 ((
% 100.33/16.78 (choice2fnsingleton) =>
% 100.33/16.78 ((
% 100.33/16.78 (setOfPairsIsBReln1) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1all1) =>
% 100.33/16.78 ((
% 100.33/16.78 (subbreln1) =>
% 100.33/16.78 ((
% 100.33/16.78 (eqbreln1) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1invprop) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1invI) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1invE) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1compprop) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1compI) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1compE) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1compEex) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionprop) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionIL) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionIR) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionI) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionE) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionEcases) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionCommutes) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz2Ex) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz2W) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz2A) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz2B) =>
% 100.33/16.78 ((
% 100.33/16.78 (image1Ex) =>
% 100.33/16.78 ((
% 100.33/16.78 (image1Ex1) =>
% 100.33/16.78 ((
% 100.33/16.78 (image1Equiv) =>
% 100.33/16.78 ((
% 100.33/16.78 (image1E) =>
% 100.33/16.78 ((
% 100.33/16.78 (image1I) =>
% 100.33/16.78 ((
% 100.33/16.78 (injFuncInInjFuncSet) =>
% 100.33/16.78 ((
% 100.33/16.78 (injFuncSetFuncIn) =>
% 100.33/16.78 ((
% 100.33/16.78 (injFuncSetFuncInj) =>
% 100.33/16.78 ((
% 100.33/16.78 (!!) @ (
% 100.33/16.78 (('#B') @ (
% 100.33/16.78 !!) @
% 100.33/16.78 (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 !!))) @
% 100.33/16.78 (
% 100.33/16.78 (
% 100.33/16.78 ('#S') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 '#S') @
% 100.33/16.78 (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 '#S'))) @
% 100.33/16.78 (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 =>))))) @
% 100.33/16.78 (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#C') @ in)))) @
% 100.33/16.78 surjFuncSet)))))))) @
% 100.33/16.78 (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#C') @ in)))) @
% 100.33/16.78 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2321])).
% 100.33/16.78 thf(zip_derived_cl2353, plain,
% 100.33/16.78 (~ (((ifp) =>
% 100.33/16.78 (((theeq) =>
% 100.33/16.78 (((iftrue) =>
% 100.33/16.78 (((iffalse) =>
% 100.33/16.78 (((iftrueorfalse) =>
% 100.33/16.78 (((binintersectT_lem) =>
% 100.33/16.78 (((binunionT_lem) =>
% 100.33/16.78 (((powersetT_lem) =>
% 100.33/16.78 (((setminusT_lem) =>
% 100.33/16.78 (((complementT_lem) =>
% 100.33/16.78 (((setextT) =>
% 100.33/16.78 (((subsetTI) =>
% 100.33/16.78 (((powersetTI1) =>
% 100.33/16.78 (((powersetTE1) =>
% 100.33/16.78 (((complementTI1) =>
% 100.33/16.78 (((complementTE1) =>
% 100.33/16.78 (((binintersectTELcontra) =>
% 100.33/16.78 (((binintersectTERcontra) =>
% 100.33/16.78 (((contrasubsetT) =>
% 100.33/16.78 (((contrasubsetT1) =>
% 100.33/16.78 (((contrasubsetT2) =>
% 100.33/16.78 (((contrasubsetT3) =>
% 100.33/16.78 (((doubleComplementI1) =>
% 100.33/16.78 (((doubleComplementE1) =>
% 100.33/16.78 (((doubleComplementSub1) =>
% 100.33/16.78 (((doubleComplementSub2) =>
% 100.33/16.78 (((doubleComplementEq) =>
% 100.33/16.78 (((complementTnotintersectT) =>
% 100.33/16.78 (((complementImpComplementIntersect) =>
% 100.33/16.78 (((complementSubsetComplementIntersect) =>
% 100.33/16.78 ((
% 100.33/16.78 (complementInPowersetComplementIntersect) =>
% 100.33/16.78 ((
% 100.33/16.78 (contraSubsetComplement) =>
% 100.33/16.78 ((
% 100.33/16.78 (complementTcontraSubset) =>
% 100.33/16.78 ((
% 100.33/16.78 (binunionTILcontra) =>
% 100.33/16.78 ((
% 100.33/16.78 (binunionTIRcontra) =>
% 100.33/16.78 ((
% 100.33/16.78 (inIntersectImpInUnion) =>
% 100.33/16.78 ((
% 100.33/16.78 (inIntersectImpInUnion2) =>
% 100.33/16.78 ((
% 100.33/16.78 (inIntersectImpInIntersectUnions) =>
% 100.33/16.78 ((
% 100.33/16.78 (intersectInPowersetIntersectUnions) =>
% 100.33/16.78 ((
% 100.33/16.78 (inComplementUnionImpNotIn1) =>
% 100.33/16.78 ((
% 100.33/16.78 (inComplementUnionImpInComplement1) =>
% 100.33/16.78 ((
% 100.33/16.78 (binunionTE) =>
% 100.33/16.78 ((
% 100.33/16.78 (binunionTEcontra) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2a1) =>
% 100.33/16.78 ((
% 100.33/16.78 (complementUnionInPowersetComplement) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2a2) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan1a) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan1b) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan1) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2a) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2b2) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2b) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule0) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule1) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule2) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule3) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule4) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_1) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_2) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_3) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_4) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_5) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1all2) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1SetBreln1) =>
% 100.33/16.78 ((
% 100.33/16.78 (choice2fnsingleton) =>
% 100.33/16.78 ((
% 100.33/16.78 (setOfPairsIsBReln1) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1all1) =>
% 100.33/16.78 ((
% 100.33/16.78 (subbreln1) =>
% 100.33/16.78 ((
% 100.33/16.78 (eqbreln1) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1invprop) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1invI) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1invE) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1compprop) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1compI) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1compE) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1compEex) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionprop) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionIL) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionIR) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionI) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionE) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionEcases) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionCommutes) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz2Ex) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz2W) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz2A) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz2B) =>
% 100.33/16.78 ((
% 100.33/16.78 (image1Ex) =>
% 100.33/16.78 ((
% 100.33/16.78 (image1Ex1) =>
% 100.33/16.78 ((
% 100.33/16.78 (image1Equiv) =>
% 100.33/16.78 ((
% 100.33/16.78 (image1E) =>
% 100.33/16.78 ((
% 100.33/16.78 (image1I) =>
% 100.33/16.78 ((
% 100.33/16.78 (injFuncInInjFuncSet) =>
% 100.33/16.78 ((
% 100.33/16.78 (injFuncSetFuncIn) =>
% 100.33/16.78 ((
% 100.33/16.78 (injFuncSetFuncInj) =>
% 100.33/16.78 ((
% 100.33/16.78 (!!) @ (
% 100.33/16.78 (('#B') @ (
% 100.33/16.78 !!) @
% 100.33/16.78 (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 !!))) @
% 100.33/16.78 (
% 100.33/16.78 (
% 100.33/16.78 ('#S') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 '#S') @
% 100.33/16.78 (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 '#S'))) @
% 100.33/16.78 (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 =>))))) @
% 100.33/16.78 (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#C') @ in)))) @
% 100.33/16.78 surjFuncSet)))))))) @
% 100.33/16.78 (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#B') @ (
% 100.33/16.78 (
% 100.33/16.78 ('#C') @ in)))) @
% 100.33/16.78 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2337])).
% 100.33/16.78 thf(zip_derived_cl2374, plain,
% 100.33/16.78 (~ (((theeq) =>
% 100.33/16.78 (((iftrue) =>
% 100.33/16.78 (((iffalse) =>
% 100.33/16.78 (((iftrueorfalse) =>
% 100.33/16.78 (((binintersectT_lem) =>
% 100.33/16.78 (((binunionT_lem) =>
% 100.33/16.78 (((powersetT_lem) =>
% 100.33/16.78 (((setminusT_lem) =>
% 100.33/16.78 (((complementT_lem) =>
% 100.33/16.78 (((setextT) =>
% 100.33/16.78 (((subsetTI) =>
% 100.33/16.78 (((powersetTI1) =>
% 100.33/16.78 (((powersetTE1) =>
% 100.33/16.78 (((complementTI1) =>
% 100.33/16.78 (((complementTE1) =>
% 100.33/16.78 (((binintersectTELcontra) =>
% 100.33/16.78 (((binintersectTERcontra) =>
% 100.33/16.78 (((contrasubsetT) =>
% 100.33/16.78 (((contrasubsetT1) =>
% 100.33/16.78 (((contrasubsetT2) =>
% 100.33/16.78 (((contrasubsetT3) =>
% 100.33/16.78 (((doubleComplementI1) =>
% 100.33/16.78 (((doubleComplementE1) =>
% 100.33/16.78 (((doubleComplementSub1) =>
% 100.33/16.78 (((doubleComplementSub2) =>
% 100.33/16.78 (((doubleComplementEq) =>
% 100.33/16.78 (((complementTnotintersectT) =>
% 100.33/16.78 (((complementImpComplementIntersect) =>
% 100.33/16.78 (((complementSubsetComplementIntersect) =>
% 100.33/16.78 (((complementInPowersetComplementIntersect) =>
% 100.33/16.78 ((
% 100.33/16.78 (contraSubsetComplement) =>
% 100.33/16.78 ((
% 100.33/16.78 (complementTcontraSubset) =>
% 100.33/16.78 ((
% 100.33/16.78 (binunionTILcontra) =>
% 100.33/16.78 ((
% 100.33/16.78 (binunionTIRcontra) =>
% 100.33/16.78 ((
% 100.33/16.78 (inIntersectImpInUnion) =>
% 100.33/16.78 ((
% 100.33/16.78 (inIntersectImpInUnion2) =>
% 100.33/16.78 ((
% 100.33/16.78 (inIntersectImpInIntersectUnions) =>
% 100.33/16.78 ((
% 100.33/16.78 (intersectInPowersetIntersectUnions) =>
% 100.33/16.78 ((
% 100.33/16.78 (inComplementUnionImpNotIn1) =>
% 100.33/16.78 ((
% 100.33/16.78 (inComplementUnionImpInComplement1) =>
% 100.33/16.78 ((
% 100.33/16.78 (binunionTE) =>
% 100.33/16.78 ((
% 100.33/16.78 (binunionTEcontra) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2a1) =>
% 100.33/16.78 ((
% 100.33/16.78 (complementUnionInPowersetComplement) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2a2) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan1a) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan1b) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan1) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2a) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2b2) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2b) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule0) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule1) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule2) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule3) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule4) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_1) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_2) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_3) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_4) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_5) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1all2) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1SetBreln1) =>
% 100.33/16.78 ((
% 100.33/16.78 (choice2fnsingleton) =>
% 100.33/16.78 ((
% 100.33/16.78 (setOfPairsIsBReln1) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1all1) =>
% 100.33/16.78 ((
% 100.33/16.78 (subbreln1) =>
% 100.33/16.78 ((
% 100.33/16.78 (eqbreln1) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1invprop) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1invI) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1invE) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1compprop) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1compI) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1compE) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1compEex) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionprop) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionIL) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionIR) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionI) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionE) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionEcases) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionCommutes) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz2Ex) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz2W) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz2A) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz2B) =>
% 100.33/16.78 ((
% 100.33/16.78 (image1Ex) =>
% 100.33/16.78 ((
% 100.33/16.78 (image1Ex1) =>
% 100.33/16.78 ((
% 100.33/16.78 (image1Equiv) =>
% 100.33/16.78 ((
% 100.33/16.78 (image1E) =>
% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
% 100.33/16.78 (demorgan2b) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule0) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule1) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule2) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz13rule3) =>
% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
% 100.33/16.78 (woz1_4) =>
% 100.33/16.78 ((
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% 100.33/16.78 (breln1all2) =>
% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
% 100.33/16.78 (breln1all1) =>
% 100.33/16.78 ((
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% 100.33/16.78 ((
% 100.33/16.78 (eqbreln1) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1invprop) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1invI) =>
% 100.33/16.78 ((
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% 100.33/16.78 ((
% 100.33/16.78 (breln1compprop) =>
% 100.33/16.78 ((
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% 100.33/16.78 ((
% 100.33/16.78 (breln1compE) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1compEex) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionprop) =>
% 100.33/16.78 ((
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% 100.33/16.78 ((
% 100.33/16.78 (breln1unionIR) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionI) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionE) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionEcases) =>
% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
% 100.33/16.78 (injFuncSetFuncInj) =>
% 100.33/16.78 ((
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% 100.33/16.78 (
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% 100.33/16.78 (
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% 100.33/16.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2408])).
% 100.33/16.78 thf(zip_derived_cl2442, plain,
% 100.33/16.78 (~ (((binintersectT_lem) =>
% 100.33/16.78 (((binunionT_lem) =>
% 100.33/16.78 (((powersetT_lem) =>
% 100.33/16.78 (((setminusT_lem) =>
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% 100.33/16.78 (((binunionTIRcontra) =>
% 100.33/16.78 ((
% 100.33/16.78 (inIntersectImpInUnion) =>
% 100.33/16.78 ((
% 100.33/16.78 (inIntersectImpInUnion2) =>
% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
% 100.33/16.78 (demorgan2a1) =>
% 100.33/16.78 ((
% 100.33/16.78 (complementUnionInPowersetComplement) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2a2) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan1a) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan1b) =>
% 100.33/16.78 ((
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% 100.33/16.78 ((
% 100.33/16.78 (demorgan2a) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2b2) =>
% 100.33/16.78 ((
% 100.33/16.78 (demorgan2b) =>
% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
% 100.33/16.78 (woz13rule2) =>
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% 100.33/16.78 ((
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% 100.33/16.78 ((
% 100.33/16.78 (woz1_2) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_3) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_4) =>
% 100.33/16.78 ((
% 100.33/16.78 (woz1_5) =>
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% 100.33/16.78 (breln1all2) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1SetBreln1) =>
% 100.33/16.78 ((
% 100.33/16.78 (choice2fnsingleton) =>
% 100.33/16.78 ((
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% 100.33/16.78 ((
% 100.33/16.78 (breln1all1) =>
% 100.33/16.78 ((
% 100.33/16.78 (subbreln1) =>
% 100.33/16.78 ((
% 100.33/16.78 (eqbreln1) =>
% 100.33/16.78 ((
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% 100.33/16.78 ((
% 100.33/16.78 (breln1invI) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1invE) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1compprop) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1compI) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1compE) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1compEex) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionprop) =>
% 100.33/16.78 ((
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% 100.33/16.78 ((
% 100.33/16.78 (breln1unionIR) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionI) =>
% 100.33/16.78 ((
% 100.33/16.78 (breln1unionE) =>
% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 (
% 100.33/16.78 (
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% 100.33/16.78 (
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% 100.33/16.78 (
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% 100.33/16.78 (
% 100.33/16.78 (
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% 100.33/16.78 (
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% 100.33/16.78 (
% 100.33/16.78 (
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% 100.33/16.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2427])).
% 100.33/16.78 thf(zip_derived_cl2454, plain,
% 100.33/16.78 (~ (((binunionT_lem) =>
% 100.33/16.78 (((powersetT_lem) =>
% 100.33/16.78 (((setminusT_lem) =>
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
% 100.33/16.78 (complementUnionInPowersetComplement) =>
% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 ((
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% 100.33/16.78 (
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% 100.33/16.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2442])).
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% 100.33/16.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2454])).
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% 100.33/16.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2465])).
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% 100.33/16.78 (breln1compE) =>
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% 100.33/16.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2506])).
% 100.33/16.78 thf(zip_derived_cl2527, plain,
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% 100.33/16.78 ((
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% 100.33/16.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2518])).
% 100.33/16.78 thf(zip_derived_cl2535, plain,
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% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2527])).
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% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2543])).
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% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2551])).
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% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (woz1_4) =>
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% 100.33/16.79 (woz1_5) =>
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (breln1compE) =>
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% 100.33/16.79 (breln1compEex) =>
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% 100.33/16.79 (breln1unionIL) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (breln1unionI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionE) =>
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% 100.33/16.79 ((
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% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2560])).
% 100.33/16.79 thf(zip_derived_cl2581, plain,
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% 100.33/16.79 (((contrasubsetT2) =>
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% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (demorgan2b) =>
% 100.33/16.79 ((
% 100.33/16.79 (demorgan2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule0) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (woz13rule2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule4) =>
% 100.33/16.79 ((
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% 100.33/16.79 (woz1_3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_5) =>
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% 100.33/16.79 (breln1unionI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionE) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2570])).
% 100.33/16.79 thf(zip_derived_cl2594, plain,
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% 100.33/16.79 (((contrasubsetT3) =>
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% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2581])).
% 100.33/16.79 thf(zip_derived_cl2610, plain,
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% 100.33/16.79 ((
% 100.33/16.79 (choice2fnsingleton) =>
% 100.33/16.79 ((
% 100.33/16.79 (setOfPairsIsBReln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all1) =>
% 100.33/16.79 ((
% 100.33/16.79 (subbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (eqbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compEex) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIL) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIR) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionEcases) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionCommutes) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2Ex) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2W) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2A) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2B) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Ex) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Ex1) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Equiv) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1E) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1I) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncInInjFuncSet) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncIn) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncInj) =>
% 100.33/16.79 ((
% 100.33/16.79 (!!) @ (
% 100.33/16.79 (('#B') @ (
% 100.33/16.79 !!) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 !!))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#S') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 '#S') @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 '#S'))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 =>))))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#C') @ in)))) @
% 100.33/16.79 surjFuncSet)))))))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#C') @ in)))) @
% 100.33/16.79 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2594])).
% 100.33/16.79 thf(zip_derived_cl2629, plain,
% 100.33/16.79 (~ (((doubleComplementI1) =>
% 100.33/16.79 (((doubleComplementE1) =>
% 100.33/16.79 (((doubleComplementSub1) =>
% 100.33/16.79 (((doubleComplementSub2) =>
% 100.33/16.79 (((doubleComplementEq) =>
% 100.33/16.79 (((complementTnotintersectT) =>
% 100.33/16.79 (((complementImpComplementIntersect) =>
% 100.33/16.79 (((complementSubsetComplementIntersect) =>
% 100.33/16.79 (((complementInPowersetComplementIntersect) =>
% 100.33/16.79 (((contraSubsetComplement) =>
% 100.33/16.79 (((complementTcontraSubset) =>
% 100.33/16.79 (((binunionTILcontra) =>
% 100.33/16.79 (((binunionTIRcontra) =>
% 100.33/16.79 (((inIntersectImpInUnion) =>
% 100.33/16.79 (((inIntersectImpInUnion2) =>
% 100.33/16.79 (((inIntersectImpInIntersectUnions) =>
% 100.33/16.79 (((intersectInPowersetIntersectUnions) =>
% 100.33/16.79 (((inComplementUnionImpNotIn1) =>
% 100.33/16.79 (((inComplementUnionImpInComplement1) =>
% 100.33/16.79 (((binunionTE) =>
% 100.33/16.79 (((binunionTEcontra) =>
% 100.33/16.79 (((demorgan2a1) =>
% 100.33/16.79 (((complementUnionInPowersetComplement) =>
% 100.33/16.79 (((demorgan2a2) =>
% 100.33/16.79 (((demorgan1a) =>
% 100.33/16.79 (((demorgan1b) =>
% 100.33/16.79 (((demorgan1) =>
% 100.33/16.79 (((demorgan2a) =>
% 100.33/16.79 (((demorgan2b2) =>
% 100.33/16.79 (((demorgan2b) =>
% 100.33/16.79 ((
% 100.33/16.79 (demorgan2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule0) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule1) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_1) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_5) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all2) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1SetBreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (choice2fnsingleton) =>
% 100.33/16.79 ((
% 100.33/16.79 (setOfPairsIsBReln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all1) =>
% 100.33/16.79 ((
% 100.33/16.79 (subbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (eqbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compEex) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIL) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIR) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionEcases) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionCommutes) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2Ex) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2W) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2A) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2B) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Ex) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Ex1) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Equiv) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1E) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1I) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncInInjFuncSet) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncIn) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncInj) =>
% 100.33/16.79 ((
% 100.33/16.79 (!!) @ (
% 100.33/16.79 (('#B') @ (
% 100.33/16.79 !!) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 !!))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#S') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 '#S') @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 '#S'))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 =>))))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#C') @ in)))) @
% 100.33/16.79 surjFuncSet)))))))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#C') @ in)))) @
% 100.33/16.79 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2610])).
% 100.33/16.79 thf(zip_derived_cl2648, plain,
% 100.33/16.79 (~ (((doubleComplementE1) =>
% 100.33/16.79 (((doubleComplementSub1) =>
% 100.33/16.79 (((doubleComplementSub2) =>
% 100.33/16.79 (((doubleComplementEq) =>
% 100.33/16.79 (((complementTnotintersectT) =>
% 100.33/16.79 (((complementImpComplementIntersect) =>
% 100.33/16.79 (((complementSubsetComplementIntersect) =>
% 100.33/16.79 (((complementInPowersetComplementIntersect) =>
% 100.33/16.79 (((contraSubsetComplement) =>
% 100.33/16.79 (((complementTcontraSubset) =>
% 100.33/16.79 (((binunionTILcontra) =>
% 100.33/16.79 (((binunionTIRcontra) =>
% 100.33/16.79 (((inIntersectImpInUnion) =>
% 100.33/16.79 (((inIntersectImpInUnion2) =>
% 100.33/16.79 (((inIntersectImpInIntersectUnions) =>
% 100.33/16.79 (((intersectInPowersetIntersectUnions) =>
% 100.33/16.79 (((inComplementUnionImpNotIn1) =>
% 100.33/16.79 (((inComplementUnionImpInComplement1) =>
% 100.33/16.79 (((binunionTE) =>
% 100.33/16.79 (((binunionTEcontra) =>
% 100.33/16.79 (((demorgan2a1) =>
% 100.33/16.79 (((complementUnionInPowersetComplement) =>
% 100.33/16.79 (((demorgan2a2) =>
% 100.33/16.79 (((demorgan1a) =>
% 100.33/16.79 (((demorgan1b) =>
% 100.33/16.79 (((demorgan1) =>
% 100.33/16.79 (((demorgan2a) =>
% 100.33/16.79 (((demorgan2b2) =>
% 100.33/16.79 (((demorgan2b) =>
% 100.33/16.79 (((demorgan2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule0) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule1) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_1) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_5) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all2) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1SetBreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (choice2fnsingleton) =>
% 100.33/16.79 ((
% 100.33/16.79 (setOfPairsIsBReln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all1) =>
% 100.33/16.79 ((
% 100.33/16.79 (subbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (eqbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compEex) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIL) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIR) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionEcases) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionCommutes) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2Ex) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2W) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2A) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2B) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Ex) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Ex1) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Equiv) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1E) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1I) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncInInjFuncSet) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncIn) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncInj) =>
% 100.33/16.79 ((
% 100.33/16.79 (!!) @ (
% 100.33/16.79 (('#B') @ (
% 100.33/16.79 !!) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 !!))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#S') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 '#S') @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 '#S'))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 =>))))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#C') @ in)))) @
% 100.33/16.79 surjFuncSet)))))))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#C') @ in)))) @
% 100.33/16.79 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2629])).
% 100.33/16.79 thf(zip_derived_cl2665, plain,
% 100.33/16.79 (~ (((doubleComplementSub1) =>
% 100.33/16.79 (((doubleComplementSub2) =>
% 100.33/16.79 (((doubleComplementEq) =>
% 100.33/16.79 (((complementTnotintersectT) =>
% 100.33/16.79 (((complementImpComplementIntersect) =>
% 100.33/16.79 (((complementSubsetComplementIntersect) =>
% 100.33/16.79 (((complementInPowersetComplementIntersect) =>
% 100.33/16.79 (((contraSubsetComplement) =>
% 100.33/16.79 (((complementTcontraSubset) =>
% 100.33/16.79 (((binunionTILcontra) =>
% 100.33/16.79 (((binunionTIRcontra) =>
% 100.33/16.79 (((inIntersectImpInUnion) =>
% 100.33/16.79 (((inIntersectImpInUnion2) =>
% 100.33/16.79 (((inIntersectImpInIntersectUnions) =>
% 100.33/16.79 (((intersectInPowersetIntersectUnions) =>
% 100.33/16.79 (((inComplementUnionImpNotIn1) =>
% 100.33/16.79 (((inComplementUnionImpInComplement1) =>
% 100.33/16.79 (((binunionTE) =>
% 100.33/16.79 (((binunionTEcontra) =>
% 100.33/16.79 (((demorgan2a1) =>
% 100.33/16.79 (((complementUnionInPowersetComplement) =>
% 100.33/16.79 (((demorgan2a2) =>
% 100.33/16.79 (((demorgan1a) =>
% 100.33/16.79 (((demorgan1b) =>
% 100.33/16.79 (((demorgan1) =>
% 100.33/16.79 (((demorgan2a) =>
% 100.33/16.79 (((demorgan2b2) =>
% 100.33/16.79 (((demorgan2b) =>
% 100.33/16.79 (((demorgan2) =>
% 100.33/16.79 (((woz13rule0) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule1) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_1) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_5) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all2) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1SetBreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (choice2fnsingleton) =>
% 100.33/16.79 ((
% 100.33/16.79 (setOfPairsIsBReln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all1) =>
% 100.33/16.79 ((
% 100.33/16.79 (subbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (eqbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compEex) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIL) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIR) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionEcases) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionCommutes) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2Ex) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2W) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2A) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2B) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Ex) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Ex1) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Equiv) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1E) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1I) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncInInjFuncSet) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncIn) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncInj) =>
% 100.33/16.79 ((
% 100.33/16.79 (!!) @ (
% 100.33/16.79 (('#B') @ (
% 100.33/16.79 !!) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 !!))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#S') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 '#S') @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 '#S'))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 =>))))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#C') @ in)))) @
% 100.33/16.79 surjFuncSet)))))))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#C') @ in)))) @
% 100.33/16.79 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2648])).
% 100.33/16.79 thf(zip_derived_cl2680, plain,
% 100.33/16.79 (~ (((doubleComplementSub2) =>
% 100.33/16.79 (((doubleComplementEq) =>
% 100.33/16.79 (((complementTnotintersectT) =>
% 100.33/16.79 (((complementImpComplementIntersect) =>
% 100.33/16.79 (((complementSubsetComplementIntersect) =>
% 100.33/16.79 (((complementInPowersetComplementIntersect) =>
% 100.33/16.79 (((contraSubsetComplement) =>
% 100.33/16.79 (((complementTcontraSubset) =>
% 100.33/16.79 (((binunionTILcontra) =>
% 100.33/16.79 (((binunionTIRcontra) =>
% 100.33/16.79 (((inIntersectImpInUnion) =>
% 100.33/16.79 (((inIntersectImpInUnion2) =>
% 100.33/16.79 (((inIntersectImpInIntersectUnions) =>
% 100.33/16.79 (((intersectInPowersetIntersectUnions) =>
% 100.33/16.79 (((inComplementUnionImpNotIn1) =>
% 100.33/16.79 (((inComplementUnionImpInComplement1) =>
% 100.33/16.79 (((binunionTE) =>
% 100.33/16.79 (((binunionTEcontra) =>
% 100.33/16.79 (((demorgan2a1) =>
% 100.33/16.79 (((complementUnionInPowersetComplement) =>
% 100.33/16.79 (((demorgan2a2) =>
% 100.33/16.79 (((demorgan1a) =>
% 100.33/16.79 (((demorgan1b) =>
% 100.33/16.79 (((demorgan1) =>
% 100.33/16.79 (((demorgan2a) =>
% 100.33/16.79 (((demorgan2b2) =>
% 100.33/16.79 (((demorgan2b) =>
% 100.33/16.79 (((demorgan2) =>
% 100.33/16.79 (((woz13rule0) =>
% 100.33/16.79 (((woz13rule1) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_1) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_5) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all2) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1SetBreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (choice2fnsingleton) =>
% 100.33/16.79 ((
% 100.33/16.79 (setOfPairsIsBReln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all1) =>
% 100.33/16.79 ((
% 100.33/16.79 (subbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (eqbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compEex) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIL) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIR) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionEcases) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionCommutes) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2Ex) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2W) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2A) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2B) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Ex) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Ex1) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Equiv) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1E) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1I) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncInInjFuncSet) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncIn) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncInj) =>
% 100.33/16.79 ((
% 100.33/16.79 (!!) @ (
% 100.33/16.79 (('#B') @ (
% 100.33/16.79 !!) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 !!))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#S') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 '#S') @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 '#S'))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 =>))))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
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% 100.33/16.79 surjFuncSet)))))))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#C') @ in)))) @
% 100.33/16.79 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2665])).
% 100.33/16.79 thf(zip_derived_cl2692, plain,
% 100.33/16.79 (~ (((doubleComplementEq) =>
% 100.33/16.79 (((complementTnotintersectT) =>
% 100.33/16.79 (((complementImpComplementIntersect) =>
% 100.33/16.79 (((complementSubsetComplementIntersect) =>
% 100.33/16.79 (((complementInPowersetComplementIntersect) =>
% 100.33/16.79 (((contraSubsetComplement) =>
% 100.33/16.79 (((complementTcontraSubset) =>
% 100.33/16.79 (((binunionTILcontra) =>
% 100.33/16.79 (((binunionTIRcontra) =>
% 100.33/16.79 (((inIntersectImpInUnion) =>
% 100.33/16.79 (((inIntersectImpInUnion2) =>
% 100.33/16.79 (((inIntersectImpInIntersectUnions) =>
% 100.33/16.79 (((intersectInPowersetIntersectUnions) =>
% 100.33/16.79 (((inComplementUnionImpNotIn1) =>
% 100.33/16.79 (((inComplementUnionImpInComplement1) =>
% 100.33/16.79 (((binunionTE) =>
% 100.33/16.79 (((binunionTEcontra) =>
% 100.33/16.79 (((demorgan2a1) =>
% 100.33/16.79 (((complementUnionInPowersetComplement) =>
% 100.33/16.79 (((demorgan2a2) =>
% 100.33/16.79 (((demorgan1a) =>
% 100.33/16.79 (((demorgan1b) =>
% 100.33/16.79 (((demorgan1) =>
% 100.33/16.79 (((demorgan2a) =>
% 100.33/16.79 (((demorgan2b2) =>
% 100.33/16.79 (((demorgan2b) =>
% 100.33/16.79 (((demorgan2) =>
% 100.33/16.79 (((woz13rule0) =>
% 100.33/16.79 (((woz13rule1) =>
% 100.33/16.79 (((woz13rule2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_1) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_5) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all2) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1SetBreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (choice2fnsingleton) =>
% 100.33/16.79 ((
% 100.33/16.79 (setOfPairsIsBReln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all1) =>
% 100.33/16.79 ((
% 100.33/16.79 (subbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (eqbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compEex) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIL) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIR) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionEcases) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionCommutes) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2Ex) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2W) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2A) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2B) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Ex) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Ex1) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Equiv) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1E) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1I) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncInInjFuncSet) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncIn) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncInj) =>
% 100.33/16.79 ((
% 100.33/16.79 (!!) @ (
% 100.33/16.79 (('#B') @ (
% 100.33/16.79 !!) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 !!))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#S') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 '#S') @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 '#S'))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 =>))))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
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% 100.33/16.79 surjFuncSet)))))))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#C') @ in)))) @
% 100.33/16.79 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2680])).
% 100.33/16.79 thf(zip_derived_cl2704, plain,
% 100.33/16.79 (~ (((complementTnotintersectT) =>
% 100.33/16.79 (((complementImpComplementIntersect) =>
% 100.33/16.79 (((complementSubsetComplementIntersect) =>
% 100.33/16.79 (((complementInPowersetComplementIntersect) =>
% 100.33/16.79 (((contraSubsetComplement) =>
% 100.33/16.79 (((complementTcontraSubset) =>
% 100.33/16.79 (((binunionTILcontra) =>
% 100.33/16.79 (((binunionTIRcontra) =>
% 100.33/16.79 (((inIntersectImpInUnion) =>
% 100.33/16.79 (((inIntersectImpInUnion2) =>
% 100.33/16.79 (((inIntersectImpInIntersectUnions) =>
% 100.33/16.79 (((intersectInPowersetIntersectUnions) =>
% 100.33/16.79 (((inComplementUnionImpNotIn1) =>
% 100.33/16.79 (((inComplementUnionImpInComplement1) =>
% 100.33/16.79 (((binunionTE) =>
% 100.33/16.79 (((binunionTEcontra) =>
% 100.33/16.79 (((demorgan2a1) =>
% 100.33/16.79 (((complementUnionInPowersetComplement) =>
% 100.33/16.79 (((demorgan2a2) =>
% 100.33/16.79 (((demorgan1a) =>
% 100.33/16.79 (((demorgan1b) =>
% 100.33/16.79 (((demorgan1) =>
% 100.33/16.79 (((demorgan2a) =>
% 100.33/16.79 (((demorgan2b2) =>
% 100.33/16.79 (((demorgan2b) =>
% 100.33/16.79 (((demorgan2) =>
% 100.33/16.79 (((woz13rule0) =>
% 100.33/16.79 (((woz13rule1) =>
% 100.33/16.79 (((woz13rule2) =>
% 100.33/16.79 (((woz13rule3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz13rule4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_1) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_5) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all2) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1SetBreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (choice2fnsingleton) =>
% 100.33/16.79 ((
% 100.33/16.79 (setOfPairsIsBReln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all1) =>
% 100.33/16.79 ((
% 100.33/16.79 (subbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (eqbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compEex) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIL) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIR) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionEcases) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionCommutes) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2Ex) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2W) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (woz2B) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (image1Ex1) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Equiv) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1E) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1I) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncInInjFuncSet) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncIn) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncInj) =>
% 100.33/16.79 ((
% 100.33/16.79 (!!) @ (
% 100.33/16.79 (('#B') @ (
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% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
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% 100.33/16.79 (
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% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
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% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
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% 100.33/16.79 surjFuncSet)))))))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
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% 100.33/16.79 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2692])).
% 100.33/16.79 thf(zip_derived_cl2716, plain,
% 100.33/16.79 (~ (((complementImpComplementIntersect) =>
% 100.33/16.79 (((complementSubsetComplementIntersect) =>
% 100.33/16.79 (((complementInPowersetComplementIntersect) =>
% 100.33/16.79 (((contraSubsetComplement) =>
% 100.33/16.79 (((complementTcontraSubset) =>
% 100.33/16.79 (((binunionTILcontra) =>
% 100.33/16.79 (((binunionTIRcontra) =>
% 100.33/16.79 (((inIntersectImpInUnion) =>
% 100.33/16.79 (((inIntersectImpInUnion2) =>
% 100.33/16.79 (((inIntersectImpInIntersectUnions) =>
% 100.33/16.79 (((intersectInPowersetIntersectUnions) =>
% 100.33/16.79 (((inComplementUnionImpNotIn1) =>
% 100.33/16.79 (((inComplementUnionImpInComplement1) =>
% 100.33/16.79 (((binunionTE) =>
% 100.33/16.79 (((binunionTEcontra) =>
% 100.33/16.79 (((demorgan2a1) =>
% 100.33/16.79 (((complementUnionInPowersetComplement) =>
% 100.33/16.79 (((demorgan2a2) =>
% 100.33/16.79 (((demorgan1a) =>
% 100.33/16.79 (((demorgan1b) =>
% 100.33/16.79 (((demorgan1) =>
% 100.33/16.79 (((demorgan2a) =>
% 100.33/16.79 (((demorgan2b2) =>
% 100.33/16.79 (((demorgan2b) =>
% 100.33/16.79 (((demorgan2) =>
% 100.33/16.79 (((woz13rule0) =>
% 100.33/16.79 (((woz13rule1) =>
% 100.33/16.79 (((woz13rule2) =>
% 100.33/16.79 (((woz13rule3) =>
% 100.33/16.79 (((woz13rule4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_1) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_5) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all2) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1SetBreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (choice2fnsingleton) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (breln1all1) =>
% 100.33/16.79 ((
% 100.33/16.79 (subbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (eqbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compEex) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIL) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIR) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionEcases) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionCommutes) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (woz2B) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (image1Ex1) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Equiv) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1E) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1I) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncInInjFuncSet) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncIn) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncInj) =>
% 100.33/16.79 ((
% 100.33/16.79 (!!) @ (
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% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
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% 100.33/16.79 (
% 100.33/16.79 (
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% 100.33/16.79 (
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% 100.33/16.79 (
% 100.33/16.79 (
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% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
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% 100.33/16.79 (
% 100.33/16.79 (
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% 100.33/16.79 (
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% 100.33/16.79 (
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% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
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% 100.33/16.79 surjFuncSet)))))))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
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% 100.33/16.79 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2704])).
% 100.33/16.79 thf(zip_derived_cl2728, plain,
% 100.33/16.79 (~ (((complementSubsetComplementIntersect) =>
% 100.33/16.79 (((complementInPowersetComplementIntersect) =>
% 100.33/16.79 (((contraSubsetComplement) =>
% 100.33/16.79 (((complementTcontraSubset) =>
% 100.33/16.79 (((binunionTILcontra) =>
% 100.33/16.79 (((binunionTIRcontra) =>
% 100.33/16.79 (((inIntersectImpInUnion) =>
% 100.33/16.79 (((inIntersectImpInUnion2) =>
% 100.33/16.79 (((inIntersectImpInIntersectUnions) =>
% 100.33/16.79 (((intersectInPowersetIntersectUnions) =>
% 100.33/16.79 (((inComplementUnionImpNotIn1) =>
% 100.33/16.79 (((inComplementUnionImpInComplement1) =>
% 100.33/16.79 (((binunionTE) =>
% 100.33/16.79 (((binunionTEcontra) =>
% 100.33/16.79 (((demorgan2a1) =>
% 100.33/16.79 (((complementUnionInPowersetComplement) =>
% 100.33/16.79 (((demorgan2a2) =>
% 100.33/16.79 (((demorgan1a) =>
% 100.33/16.79 (((demorgan1b) =>
% 100.33/16.79 (((demorgan1) =>
% 100.33/16.79 (((demorgan2a) =>
% 100.33/16.79 (((demorgan2b2) =>
% 100.33/16.79 (((demorgan2b) =>
% 100.33/16.79 (((demorgan2) =>
% 100.33/16.79 (((woz13rule0) =>
% 100.33/16.79 (((woz13rule1) =>
% 100.33/16.79 (((woz13rule2) =>
% 100.33/16.79 (((woz13rule3) =>
% 100.33/16.79 (((woz13rule4) =>
% 100.33/16.79 (((woz1_1) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_5) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all2) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1SetBreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (choice2fnsingleton) =>
% 100.33/16.79 ((
% 100.33/16.79 (setOfPairsIsBReln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all1) =>
% 100.33/16.79 ((
% 100.33/16.79 (subbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (eqbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compEex) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIL) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIR) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionEcases) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionCommutes) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2Ex) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2W) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (woz2B) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Ex) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Ex1) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Equiv) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1E) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1I) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncInInjFuncSet) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncIn) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncInj) =>
% 100.33/16.79 ((
% 100.33/16.79 (!!) @ (
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% 100.33/16.79 !!) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
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% 100.33/16.79 ('#B') @ (
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% 100.33/16.79 (
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% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
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% 100.33/16.79 (
% 100.33/16.79 (
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% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
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% 100.33/16.79 surjFuncSet)))))))) @
% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
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% 100.33/16.79 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2716])).
% 100.33/16.79 thf(zip_derived_cl2738, plain,
% 100.33/16.79 (~ (((complementInPowersetComplementIntersect) =>
% 100.33/16.79 (((contraSubsetComplement) =>
% 100.33/16.79 (((complementTcontraSubset) =>
% 100.33/16.79 (((binunionTILcontra) =>
% 100.33/16.79 (((binunionTIRcontra) =>
% 100.33/16.79 (((inIntersectImpInUnion) =>
% 100.33/16.79 (((inIntersectImpInUnion2) =>
% 100.33/16.79 (((inIntersectImpInIntersectUnions) =>
% 100.33/16.79 (((intersectInPowersetIntersectUnions) =>
% 100.33/16.79 (((inComplementUnionImpNotIn1) =>
% 100.33/16.79 (((inComplementUnionImpInComplement1) =>
% 100.33/16.79 (((binunionTE) =>
% 100.33/16.79 (((binunionTEcontra) =>
% 100.33/16.79 (((demorgan2a1) =>
% 100.33/16.79 (((complementUnionInPowersetComplement) =>
% 100.33/16.79 (((demorgan2a2) =>
% 100.33/16.79 (((demorgan1a) =>
% 100.33/16.79 (((demorgan1b) =>
% 100.33/16.79 (((demorgan1) =>
% 100.33/16.79 (((demorgan2a) =>
% 100.33/16.79 (((demorgan2b2) =>
% 100.33/16.79 (((demorgan2b) =>
% 100.33/16.79 (((demorgan2) =>
% 100.33/16.79 (((woz13rule0) =>
% 100.33/16.79 (((woz13rule1) =>
% 100.33/16.79 (((woz13rule2) =>
% 100.33/16.79 (((woz13rule3) =>
% 100.33/16.79 (((woz13rule4) =>
% 100.33/16.79 (((woz1_1) =>
% 100.33/16.79 (((woz1_2) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_5) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all2) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1SetBreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (choice2fnsingleton) =>
% 100.33/16.79 ((
% 100.33/16.79 (setOfPairsIsBReln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all1) =>
% 100.33/16.79 ((
% 100.33/16.79 (subbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (eqbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compEex) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIL) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIR) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionEcases) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionCommutes) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2Ex) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz2W) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (woz2B) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Ex) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Ex1) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Equiv) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1E) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1I) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncInInjFuncSet) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncIn) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncInj) =>
% 100.33/16.79 ((
% 100.33/16.79 (!!) @ (
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% 100.33/16.79 (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
% 100.33/16.79 (
% 100.33/16.79 ('#B') @ (
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% 100.33/16.79 (
% 100.33/16.79 (
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% 100.33/16.79 (
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% 100.33/16.79 (
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% 100.33/16.79 (
% 100.33/16.79 (
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% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2728])).
% 100.33/16.79 thf(zip_derived_cl2746, plain,
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% 100.33/16.79 (((binunionTILcontra) =>
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% 100.33/16.79 (((inIntersectImpInUnion2) =>
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% 100.33/16.79 (((intersectInPowersetIntersectUnions) =>
% 100.33/16.79 (((inComplementUnionImpNotIn1) =>
% 100.33/16.79 (((inComplementUnionImpInComplement1) =>
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% 100.33/16.79 (((binunionTEcontra) =>
% 100.33/16.79 (((demorgan2a1) =>
% 100.33/16.79 (((complementUnionInPowersetComplement) =>
% 100.33/16.79 (((demorgan2a2) =>
% 100.33/16.79 (((demorgan1a) =>
% 100.33/16.79 (((demorgan1b) =>
% 100.33/16.79 (((demorgan1) =>
% 100.33/16.79 (((demorgan2a) =>
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% 100.33/16.79 (((demorgan2) =>
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% 100.33/16.79 (((woz13rule1) =>
% 100.33/16.79 (((woz13rule2) =>
% 100.33/16.79 (((woz13rule3) =>
% 100.33/16.79 (((woz13rule4) =>
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% 100.33/16.79 (((woz1_2) =>
% 100.33/16.79 (((woz1_3) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_4) =>
% 100.33/16.79 ((
% 100.33/16.79 (woz1_5) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all2) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1SetBreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (choice2fnsingleton) =>
% 100.33/16.79 ((
% 100.33/16.79 (setOfPairsIsBReln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all1) =>
% 100.33/16.79 ((
% 100.33/16.79 (subbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (eqbreln1) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compEex) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIL) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionIR) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionEcases) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionCommutes) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (woz2B) =>
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% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (image1Equiv) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1E) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1I) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncInInjFuncSet) =>
% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncIn) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 (
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% 100.33/16.79 (
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% 100.33/16.79 (
% 100.33/16.79 (
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% 100.33/16.79 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2738])).
% 100.33/16.79 thf(zip_derived_cl2754, plain,
% 100.33/16.79 (~ (((complementTcontraSubset) =>
% 100.33/16.79 (((binunionTILcontra) =>
% 100.33/16.79 (((binunionTIRcontra) =>
% 100.33/16.79 (((inIntersectImpInUnion) =>
% 100.33/16.79 (((inIntersectImpInUnion2) =>
% 100.33/16.79 (((inIntersectImpInIntersectUnions) =>
% 100.33/16.79 (((intersectInPowersetIntersectUnions) =>
% 100.33/16.79 (((inComplementUnionImpNotIn1) =>
% 100.33/16.79 (((inComplementUnionImpInComplement1) =>
% 100.33/16.79 (((binunionTE) =>
% 100.33/16.79 (((binunionTEcontra) =>
% 100.33/16.79 (((demorgan2a1) =>
% 100.33/16.79 (((complementUnionInPowersetComplement) =>
% 100.33/16.79 (((demorgan2a2) =>
% 100.33/16.79 (((demorgan1a) =>
% 100.33/16.79 (((demorgan1b) =>
% 100.33/16.79 (((demorgan1) =>
% 100.33/16.79 (((demorgan2a) =>
% 100.33/16.79 (((demorgan2b2) =>
% 100.33/16.79 (((demorgan2b) =>
% 100.33/16.79 (((demorgan2) =>
% 100.33/16.79 (((woz13rule0) =>
% 100.33/16.79 (((woz13rule1) =>
% 100.33/16.79 (((woz13rule2) =>
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% 100.33/16.79 (((woz1_2) =>
% 100.33/16.79 (((woz1_3) =>
% 100.33/16.79 (((woz1_4) =>
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (breln1invI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1invE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compprop) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compEex) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (breln1unionE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionEcases) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1unionCommutes) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (image1Ex1) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1Equiv) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1E) =>
% 100.33/16.79 ((
% 100.33/16.79 (image1I) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (injFuncSetFuncInj) =>
% 100.33/16.79 ((
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% 100.33/16.79 (
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% 100.33/16.79 (
% 100.33/16.79 (
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% 100.33/16.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2746])).
% 100.33/16.79 thf(zip_derived_cl2762, plain,
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% 100.33/16.79 (((binunionTIRcontra) =>
% 100.33/16.79 (((inIntersectImpInUnion) =>
% 100.33/16.79 (((inIntersectImpInUnion2) =>
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% 100.33/16.79 (((inComplementUnionImpNotIn1) =>
% 100.33/16.79 (((inComplementUnionImpInComplement1) =>
% 100.33/16.79 (((binunionTE) =>
% 100.33/16.79 (((binunionTEcontra) =>
% 100.33/16.79 (((demorgan2a1) =>
% 100.33/16.79 (((complementUnionInPowersetComplement) =>
% 100.33/16.79 (((demorgan2a2) =>
% 100.33/16.79 (((demorgan1a) =>
% 100.33/16.79 (((demorgan1b) =>
% 100.33/16.79 (((demorgan1) =>
% 100.33/16.79 (((demorgan2a) =>
% 100.33/16.79 (((demorgan2b2) =>
% 100.33/16.79 (((demorgan2b) =>
% 100.33/16.79 (((demorgan2) =>
% 100.33/16.79 (((woz13rule0) =>
% 100.33/16.79 (((woz13rule1) =>
% 100.33/16.79 (((woz13rule2) =>
% 100.33/16.79 (((woz13rule3) =>
% 100.33/16.79 (((woz13rule4) =>
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% 100.33/16.79 (((woz1_2) =>
% 100.33/16.79 (((woz1_3) =>
% 100.33/16.79 (((woz1_4) =>
% 100.33/16.79 (((woz1_5) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1all2) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1SetBreln1) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (eqbreln1) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (breln1invE) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (breln1compI) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compE) =>
% 100.33/16.79 ((
% 100.33/16.79 (breln1compEex) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (breln1unionE) =>
% 100.33/16.79 ((
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% 100.33/16.79 ((
% 100.33/16.79 (breln1unionCommutes) =>
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 ((
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% 100.33/16.79 thf(zip_derived_cl2771, plain,
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% 100.33/16.79 (((inComplementUnionImpInComplement1) =>
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% 100.33/16.79 (((demorgan1b) =>
% 100.33/16.79 (((demorgan1) =>
% 100.33/16.79 (((demorgan2a) =>
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#S') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 '#S') @
% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 '#S'))) @
% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 =>))))) @
% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 surjFuncSet)))))))) @
% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 ('#C') @ in)))) @
% 100.33/16.80 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2803])).
% 100.33/16.80 thf(zip_derived_cl2823, plain,
% 100.33/16.80 (~ (((inComplementUnionImpNotIn1) =>
% 100.33/16.80 (((inComplementUnionImpInComplement1) =>
% 100.33/16.80 (((binunionTE) =>
% 100.33/16.80 (((binunionTEcontra) =>
% 100.33/16.80 (((demorgan2a1) =>
% 100.33/16.80 (((complementUnionInPowersetComplement) =>
% 100.33/16.80 (((demorgan2a2) =>
% 100.33/16.80 (((demorgan1a) =>
% 100.33/16.80 (((demorgan1b) =>
% 100.33/16.80 (((demorgan1) =>
% 100.33/16.80 (((demorgan2a) =>
% 100.33/16.80 (((demorgan2b2) =>
% 100.33/16.80 (((demorgan2b) =>
% 100.33/16.80 (((demorgan2) =>
% 100.33/16.80 (((woz13rule0) =>
% 100.33/16.80 (((woz13rule1) =>
% 100.33/16.80 (((woz13rule2) =>
% 100.33/16.80 (((woz13rule3) =>
% 100.33/16.80 (((woz13rule4) =>
% 100.33/16.80 (((woz1_1) =>
% 100.33/16.80 (((woz1_2) =>
% 100.33/16.80 (((woz1_3) =>
% 100.33/16.80 (((woz1_4) =>
% 100.33/16.80 (((woz1_5) =>
% 100.33/16.80 (((breln1all2) =>
% 100.33/16.80 (((breln1SetBreln1) =>
% 100.33/16.80 (((choice2fnsingleton) =>
% 100.33/16.80 (((setOfPairsIsBReln1) =>
% 100.33/16.80 (((breln1all1) =>
% 100.33/16.80 (((subbreln1) =>
% 100.33/16.80 ((
% 100.33/16.80 (eqbreln1) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1invprop) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1invI) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1invE) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1compprop) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1compI) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1compE) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1compEex) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionprop) =>
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% 100.33/16.80 ((
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% 100.33/16.80 ((
% 100.33/16.80 (breln1unionI) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionE) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionEcases) =>
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
% 100.33/16.80 (image1Ex1) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1Equiv) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1E) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1I) =>
% 100.33/16.80 ((
% 100.33/16.80 (injFuncInInjFuncSet) =>
% 100.33/16.80 ((
% 100.33/16.80 (injFuncSetFuncIn) =>
% 100.33/16.80 ((
% 100.33/16.80 (injFuncSetFuncInj) =>
% 100.33/16.80 ((
% 100.33/16.80 (!!) @ (
% 100.33/16.80 (('#B') @ (
% 100.33/16.80 !!) @
% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 !!))) @
% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#S') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 '#S') @
% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 =>))))) @
% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 (
% 100.33/16.80 (
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% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2813])).
% 100.33/16.80 thf(zip_derived_cl2834, plain,
% 100.33/16.80 (~ (((inComplementUnionImpInComplement1) =>
% 100.33/16.80 (((binunionTE) =>
% 100.33/16.80 (((binunionTEcontra) =>
% 100.33/16.80 (((demorgan2a1) =>
% 100.33/16.80 (((complementUnionInPowersetComplement) =>
% 100.33/16.80 (((demorgan2a2) =>
% 100.33/16.80 (((demorgan1a) =>
% 100.33/16.80 (((demorgan1b) =>
% 100.33/16.80 (((demorgan1) =>
% 100.33/16.80 (((demorgan2a) =>
% 100.33/16.80 (((demorgan2b2) =>
% 100.33/16.80 (((demorgan2b) =>
% 100.33/16.80 (((demorgan2) =>
% 100.33/16.80 (((woz13rule0) =>
% 100.33/16.80 (((woz13rule1) =>
% 100.33/16.80 (((woz13rule2) =>
% 100.33/16.80 (((woz13rule3) =>
% 100.33/16.80 (((woz13rule4) =>
% 100.33/16.80 (((woz1_1) =>
% 100.33/16.80 (((woz1_2) =>
% 100.33/16.80 (((woz1_3) =>
% 100.33/16.80 (((woz1_4) =>
% 100.33/16.80 (((woz1_5) =>
% 100.33/16.80 (((breln1all2) =>
% 100.33/16.80 (((breln1SetBreln1) =>
% 100.33/16.80 (((choice2fnsingleton) =>
% 100.33/16.80 (((setOfPairsIsBReln1) =>
% 100.33/16.80 (((breln1all1) =>
% 100.33/16.80 (((subbreln1) =>
% 100.33/16.80 (((eqbreln1) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1invprop) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1invI) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1invE) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1compprop) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1compI) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1compE) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1compEex) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionprop) =>
% 100.33/16.80 ((
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% 100.33/16.80 ((
% 100.33/16.80 (breln1unionIR) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionI) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionE) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionEcases) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionCommutes) =>
% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
% 100.33/16.80 (woz2B) =>
% 100.33/16.80 ((
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% 100.33/16.80 ((
% 100.33/16.80 (image1Ex1) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1Equiv) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1E) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1I) =>
% 100.33/16.80 ((
% 100.33/16.80 (injFuncInInjFuncSet) =>
% 100.33/16.80 ((
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% 100.33/16.80 ((
% 100.33/16.80 (injFuncSetFuncInj) =>
% 100.33/16.80 ((
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% 100.33/16.80 !!) @
% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#S') @ (
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% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2823])).
% 100.33/16.80 thf(zip_derived_cl2845, plain,
% 100.33/16.80 (~ (((binunionTE) =>
% 100.33/16.80 (((binunionTEcontra) =>
% 100.33/16.80 (((demorgan2a1) =>
% 100.33/16.80 (((complementUnionInPowersetComplement) =>
% 100.33/16.80 (((demorgan2a2) =>
% 100.33/16.80 (((demorgan1a) =>
% 100.33/16.80 (((demorgan1b) =>
% 100.33/16.80 (((demorgan1) =>
% 100.33/16.80 (((demorgan2a) =>
% 100.33/16.80 (((demorgan2b2) =>
% 100.33/16.80 (((demorgan2b) =>
% 100.33/16.80 (((demorgan2) =>
% 100.33/16.80 (((woz13rule0) =>
% 100.33/16.80 (((woz13rule1) =>
% 100.33/16.80 (((woz13rule2) =>
% 100.33/16.80 (((woz13rule3) =>
% 100.33/16.80 (((woz13rule4) =>
% 100.33/16.80 (((woz1_1) =>
% 100.33/16.80 (((woz1_2) =>
% 100.33/16.80 (((woz1_3) =>
% 100.33/16.80 (((woz1_4) =>
% 100.33/16.80 (((woz1_5) =>
% 100.33/16.80 (((breln1all2) =>
% 100.33/16.80 (((breln1SetBreln1) =>
% 100.33/16.80 (((choice2fnsingleton) =>
% 100.33/16.80 (((setOfPairsIsBReln1) =>
% 100.33/16.80 (((breln1all1) =>
% 100.33/16.80 (((subbreln1) =>
% 100.33/16.80 (((eqbreln1) =>
% 100.33/16.80 (((breln1invprop) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1invI) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1invE) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1compprop) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1compI) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1compE) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1compEex) =>
% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
% 100.33/16.80 (breln1unionIR) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionI) =>
% 100.33/16.80 ((
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% 100.33/16.80 ((
% 100.33/16.80 (breln1unionEcases) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionCommutes) =>
% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
% 100.33/16.80 (injFuncSetFuncInj) =>
% 100.33/16.80 ((
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
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% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2834])).
% 100.33/16.80 thf(zip_derived_cl2857, plain,
% 100.33/16.80 (~ (((binunionTEcontra) =>
% 100.33/16.80 (((demorgan2a1) =>
% 100.33/16.80 (((complementUnionInPowersetComplement) =>
% 100.33/16.80 (((demorgan2a2) =>
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% 100.33/16.80 (((demorgan2a) =>
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% 100.33/16.80 (
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% 100.33/16.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2845])).
% 100.33/16.80 thf(zip_derived_cl2869, plain,
% 100.33/16.80 (~ (((demorgan2a1) =>
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% 100.33/16.80 (((demorgan2a2) =>
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% 100.33/16.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2857])).
% 100.33/16.80 thf(zip_derived_cl2881, plain,
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% 100.33/16.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2869])).
% 100.33/16.80 thf(zip_derived_cl2893, plain,
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% 100.33/16.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2881])).
% 100.33/16.80 thf(zip_derived_cl2906, plain,
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% 100.33/16.80 (((woz1_1) =>
% 100.33/16.80 (((woz1_2) =>
% 100.33/16.80 (((woz1_3) =>
% 100.33/16.80 (((woz1_4) =>
% 100.33/16.80 (((woz1_5) =>
% 100.33/16.80 (((breln1all2) =>
% 100.33/16.80 (((breln1SetBreln1) =>
% 100.33/16.80 (((choice2fnsingleton) =>
% 100.33/16.80 (((setOfPairsIsBReln1) =>
% 100.33/16.80 (((breln1all1) =>
% 100.33/16.80 (((subbreln1) =>
% 100.33/16.80 (((eqbreln1) =>
% 100.33/16.80 (((breln1invprop) =>
% 100.33/16.80 (((breln1invI) =>
% 100.33/16.80 (((breln1invE) =>
% 100.33/16.80 (((breln1compprop) =>
% 100.33/16.80 (((breln1compI) =>
% 100.33/16.80 (((breln1compE) =>
% 100.33/16.80 (((breln1compEex) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionprop) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionIL) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionIR) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionI) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionE) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionEcases) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionCommutes) =>
% 100.33/16.80 ((
% 100.33/16.80 (woz2Ex) =>
% 100.33/16.80 ((
% 100.33/16.80 (woz2W) =>
% 100.33/16.80 ((
% 100.33/16.80 (woz2A) =>
% 100.33/16.80 ((
% 100.33/16.80 (woz2B) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1Ex) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1Ex1) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1Equiv) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1E) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1I) =>
% 100.33/16.80 ((
% 100.33/16.80 (injFuncInInjFuncSet) =>
% 100.33/16.80 ((
% 100.33/16.80 (injFuncSetFuncIn) =>
% 100.33/16.80 ((
% 100.33/16.80 (injFuncSetFuncInj) =>
% 100.33/16.80 ((
% 100.33/16.80 (!!) @ (
% 100.33/16.80 (('#B') @ (
% 100.33/16.80 !!) @
% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#S') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 '#S') @
% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 =>))))) @
% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 surjFuncSet)))))))) @
% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#C') @ in)))) @
% 100.33/16.80 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2906])).
% 100.33/16.80 thf(zip_derived_cl2933, plain,
% 100.33/16.80 (~ (((demorgan1) =>
% 100.33/16.80 (((demorgan2a) =>
% 100.33/16.80 (((demorgan2b2) =>
% 100.33/16.80 (((demorgan2b) =>
% 100.33/16.80 (((demorgan2) =>
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% 100.33/16.80 (((woz13rule1) =>
% 100.33/16.80 (((woz13rule2) =>
% 100.33/16.80 (((woz13rule3) =>
% 100.33/16.80 (((woz13rule4) =>
% 100.33/16.80 (((woz1_1) =>
% 100.33/16.80 (((woz1_2) =>
% 100.33/16.80 (((woz1_3) =>
% 100.33/16.80 (((woz1_4) =>
% 100.33/16.80 (((woz1_5) =>
% 100.33/16.80 (((breln1all2) =>
% 100.33/16.80 (((breln1SetBreln1) =>
% 100.33/16.80 (((choice2fnsingleton) =>
% 100.33/16.80 (((setOfPairsIsBReln1) =>
% 100.33/16.80 (((breln1all1) =>
% 100.33/16.80 (((subbreln1) =>
% 100.33/16.80 (((eqbreln1) =>
% 100.33/16.80 (((breln1invprop) =>
% 100.33/16.80 (((breln1invI) =>
% 100.33/16.80 (((breln1invE) =>
% 100.33/16.80 (((breln1compprop) =>
% 100.33/16.80 (((breln1compI) =>
% 100.33/16.80 (((breln1compE) =>
% 100.33/16.80 (((breln1compEex) =>
% 100.33/16.80 (((breln1unionprop) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionIL) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionIR) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionI) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionE) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionEcases) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionCommutes) =>
% 100.33/16.80 ((
% 100.33/16.80 (woz2Ex) =>
% 100.33/16.80 ((
% 100.33/16.80 (woz2W) =>
% 100.33/16.80 ((
% 100.33/16.80 (woz2A) =>
% 100.33/16.80 ((
% 100.33/16.80 (woz2B) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1Ex) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1Ex1) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1Equiv) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1E) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1I) =>
% 100.33/16.80 ((
% 100.33/16.80 (injFuncInInjFuncSet) =>
% 100.33/16.80 ((
% 100.33/16.80 (injFuncSetFuncIn) =>
% 100.33/16.80 ((
% 100.33/16.80 (injFuncSetFuncInj) =>
% 100.33/16.80 ((
% 100.33/16.80 (!!) @ (
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#S') @ (
% 100.33/16.80 (
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 =>))))) @
% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 surjFuncSet)))))))) @
% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 ('#C') @ in)))) @
% 100.33/16.80 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2920])).
% 100.33/16.80 thf(zip_derived_cl2946, plain,
% 100.33/16.80 (~ (((demorgan2a) =>
% 100.33/16.80 (((demorgan2b2) =>
% 100.33/16.80 (((demorgan2b) =>
% 100.33/16.80 (((demorgan2) =>
% 100.33/16.80 (((woz13rule0) =>
% 100.33/16.80 (((woz13rule1) =>
% 100.33/16.80 (((woz13rule2) =>
% 100.33/16.80 (((woz13rule3) =>
% 100.33/16.80 (((woz13rule4) =>
% 100.33/16.80 (((woz1_1) =>
% 100.33/16.80 (((woz1_2) =>
% 100.33/16.80 (((woz1_3) =>
% 100.33/16.80 (((woz1_4) =>
% 100.33/16.80 (((woz1_5) =>
% 100.33/16.80 (((breln1all2) =>
% 100.33/16.80 (((breln1SetBreln1) =>
% 100.33/16.80 (((choice2fnsingleton) =>
% 100.33/16.80 (((setOfPairsIsBReln1) =>
% 100.33/16.80 (((breln1all1) =>
% 100.33/16.80 (((subbreln1) =>
% 100.33/16.80 (((eqbreln1) =>
% 100.33/16.80 (((breln1invprop) =>
% 100.33/16.80 (((breln1invI) =>
% 100.33/16.80 (((breln1invE) =>
% 100.33/16.80 (((breln1compprop) =>
% 100.33/16.80 (((breln1compI) =>
% 100.33/16.80 (((breln1compE) =>
% 100.33/16.80 (((breln1compEex) =>
% 100.33/16.80 (((breln1unionprop) =>
% 100.33/16.80 (((breln1unionIL) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionIR) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionI) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionE) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionEcases) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionCommutes) =>
% 100.33/16.80 ((
% 100.33/16.80 (woz2Ex) =>
% 100.33/16.80 ((
% 100.33/16.80 (woz2W) =>
% 100.33/16.80 ((
% 100.33/16.80 (woz2A) =>
% 100.33/16.80 ((
% 100.33/16.80 (woz2B) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1Ex) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1Ex1) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1Equiv) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1E) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1I) =>
% 100.33/16.80 ((
% 100.33/16.80 (injFuncInInjFuncSet) =>
% 100.33/16.80 ((
% 100.33/16.80 (injFuncSetFuncIn) =>
% 100.33/16.80 ((
% 100.33/16.80 (injFuncSetFuncInj) =>
% 100.33/16.80 ((
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#S') @ (
% 100.33/16.80 (
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 =>))))) @
% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 (
% 100.33/16.80 (
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% 100.33/16.80 ('#B') @ (
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% 100.33/16.80 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2933])).
% 100.33/16.80 thf(zip_derived_cl2958, plain,
% 100.33/16.80 (~ (((demorgan2b2) =>
% 100.33/16.80 (((demorgan2b) =>
% 100.33/16.80 (((demorgan2) =>
% 100.33/16.80 (((woz13rule0) =>
% 100.33/16.80 (((woz13rule1) =>
% 100.33/16.80 (((woz13rule2) =>
% 100.33/16.80 (((woz13rule3) =>
% 100.33/16.80 (((woz13rule4) =>
% 100.33/16.80 (((woz1_1) =>
% 100.33/16.80 (((woz1_2) =>
% 100.33/16.80 (((woz1_3) =>
% 100.33/16.80 (((woz1_4) =>
% 100.33/16.80 (((woz1_5) =>
% 100.33/16.80 (((breln1all2) =>
% 100.33/16.80 (((breln1SetBreln1) =>
% 100.33/16.80 (((choice2fnsingleton) =>
% 100.33/16.80 (((setOfPairsIsBReln1) =>
% 100.33/16.80 (((breln1all1) =>
% 100.33/16.80 (((subbreln1) =>
% 100.33/16.80 (((eqbreln1) =>
% 100.33/16.80 (((breln1invprop) =>
% 100.33/16.80 (((breln1invI) =>
% 100.33/16.80 (((breln1invE) =>
% 100.33/16.80 (((breln1compprop) =>
% 100.33/16.80 (((breln1compI) =>
% 100.33/16.80 (((breln1compE) =>
% 100.33/16.80 (((breln1compEex) =>
% 100.33/16.80 (((breln1unionprop) =>
% 100.33/16.80 (((breln1unionIL) =>
% 100.33/16.80 (((breln1unionIR) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionI) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionE) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionEcases) =>
% 100.33/16.80 ((
% 100.33/16.80 (breln1unionCommutes) =>
% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
% 100.33/16.80 (woz2B) =>
% 100.33/16.80 ((
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% 100.33/16.80 ((
% 100.33/16.80 (image1Ex1) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1Equiv) =>
% 100.33/16.80 ((
% 100.33/16.80 (image1E) =>
% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
% 100.33/16.80 (injFuncSetFuncInj) =>
% 100.33/16.80 ((
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% 100.33/16.80 (
% 100.33/16.80 (
% 100.33/16.80 ('#B') @ (
% 100.33/16.80 (
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% 100.33/16.80 (
% 100.33/16.80 (
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% 100.33/16.80 (
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% 100.33/16.80 (
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% 100.33/16.80 (
% 100.33/16.80 (
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% 100.33/16.80 funcSet))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 100.33/16.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2946])).
% 100.33/16.80 thf(zip_derived_cl2970, plain,
% 100.33/16.80 (~ (((demorgan2b) =>
% 100.33/16.80 (((demorgan2) =>
% 100.33/16.80 (((woz13rule0) =>
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% 100.33/16.80 (((woz1_2) =>
% 100.33/16.80 (((woz1_3) =>
% 100.33/16.80 (((woz1_4) =>
% 100.33/16.80 (((woz1_5) =>
% 100.33/16.80 (((breln1all2) =>
% 100.33/16.80 (((breln1SetBreln1) =>
% 100.33/16.80 (((choice2fnsingleton) =>
% 100.33/16.80 (((setOfPairsIsBReln1) =>
% 100.33/16.80 (((breln1all1) =>
% 100.33/16.80 (((subbreln1) =>
% 100.33/16.80 (((eqbreln1) =>
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% 100.33/16.80 (((breln1invI) =>
% 100.33/16.80 (((breln1invE) =>
% 100.33/16.80 (((breln1compprop) =>
% 100.33/16.80 (((breln1compI) =>
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.80 ((
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% 100.33/16.81 surjFuncSet)))))))) @
% 100.33/16.81 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @
% 100.33/16.81 funcSet))))))))))))))))))))))))),
% 100.33/16.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3493])).
% 100.33/16.81 thf(zip_derived_cl3526, plain,
% 100.33/16.81 (~ (((image1Equiv) =>
% 100.33/16.81 (((image1E) =>
% 100.33/16.81 (((image1I) =>
% 100.33/16.81 (((injFuncInInjFuncSet) =>
% 100.33/16.81 (((injFuncSetFuncIn) =>
% 100.33/16.81 (((injFuncSetFuncInj) =>